UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Product interactions and rivalry among multiproduct firms : an application of characteristics theory Burton, Peter Steven 1989

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-UBC_1989_A1 B87.pdf [ 14.29MB ]
Metadata
JSON: 831-1.0098243.json
JSON-LD: 831-1.0098243-ld.json
RDF/XML (Pretty): 831-1.0098243-rdf.xml
RDF/JSON: 831-1.0098243-rdf.json
Turtle: 831-1.0098243-turtle.txt
N-Triples: 831-1.0098243-rdf-ntriples.txt
Original Record: 831-1.0098243-source.json
Full Text
831-1.0098243-fulltext.txt
Citation
831-1.0098243.ris

Full Text

PRODUCT INTERACTIONS AND RIVALRY AMONG MULTIPRODUCT FIRMS: AN APPLICATION OF CHARACTERISTICS THEORY By Peter Steven Burton B. Sc., University of Saskatchewan, 1983 M. A., University of British Columbia, 1984 A T H E S I S S U B M I T T E D I N P A R T I A L F U L F I L L M E N T O F T H E R E Q U I R E M E N T S F O R T H E D E G R E E O F D O C T O R O F P H I L O S O P H Y in T H E F A C U L T Y O F G R A D U A T E S T U D I E S ( E C O N O M I C S ) We accept this thesis as conforming to the required standard T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A August 1989 © Peter Steven Burton, 1989 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. (Economics) The University of British Columbia 6224 Agricultural'Road Vancouver, Canada V6T 1W5 Date: Abstract A model based upon the differences in the profitability of producing various com-binations of goods is presented as a practical method of analysing product choice by multiproduct firms. Characteristics theory is used to construct the market opportunity frontiers that were formed by fifteen common insecticides during each year between 1944 and 1987. These frontiers, which utilize the three attributes that are used to compare the insecticides in the industry literature, illustrate the combinations of characteristics that the products yield for some budget. Construction of the frontiers provides the first opportunity to check the principal prediction of characteristics theory, that all products are priced to appear on the market opportunity frontiers. The prediction holds during fifteen years of the study. Deviations from the prediction during the other years are due to one product and can be accounted for by the measurement errors of the characteristics. The market opportunity frontiers are also utilized to calculate the implicit prices of characteristics on each facet of the frontier. These prices, and convexity of the frontier, are then used to determine bounds on the prices of eight additional products for which price data are unavailable. A proposition is presented which indicates that a product yields greater profits to a firm producing a product which neighbours it on the market opportunity frontier. Increased profits due to these relationships between certain combinations of products, such as whether they are neighbouring or chemically similar, are also shown to increase the probability that a firm will produce these combinations. Logit estimations are conducted to determine how the relationships between two 11 goods influence the probabilities of a firm introducing or producing both. The empirical results are able to predict (with a 50 to 60% success rate) the identity of the firms which introduced or produced particular products based upon the other products in each firm's portfolio. The principal contributions of this thesis are that it provides the first empirical sup-port for the predictions of characteristics theory and that it presents an approach which allows the empirical analysis of product choice by multiproduct firms. in Table of Contents Abstract ii Table of Contents iv List of Tables vii List of Figures ix Acknowledgement x 1 Introduction 1 2 Literature Review 5 2.1 Introduction 5 2.2 Multiproduct Firms 5 2.3 Characteristics Theory 8 2.4 Empirical Use of the Characteristics Approach 17 2.5 The Insecticide and Chemical Industries . . . . 21 2.6 Conclusion 23 3 Data Requirements and Sources 24 3.1 Introduction 24 3.2 Tests of Product Association 25 3.3 Data Requirements for the Application of Characteristics Theory . . . . 29 3.4 Data Sources 34 iv 3.5 Construction of a Market Opportunity Frontier 36 3.6 Conclusion ; 39 4 Predictions of Characteristics Theory 41 4.1 Introduction 41 4.2 Demand for Insecticides 41 4.3 Pricing of Products on the Market Opportunity Frontier 43 4.4 Prices of Characteristics 52 4.5 Bounds on Possible Prices of Products 60 4.6 Localized Competition 66 4.7 Conclusion . 69 5 Product Choice: A Model 71 5.1 Introduction 71 5.2 Product Interactions and Profitability 72 5.2.1 Local Monopoly Power 72 5.2.2 Cost Advantages . ."' 99 5.3 Profitability and the Probability of Introduction 106 5.4 Profitability and the Probability of Production 114 5.5 Conclusion 115 6 Product Choice: Empirical Results 117 6.1 Introduction 117 6.2 Estimation Procedure 117 6.2.1 The Introduction of New Products 118 6.2.2 The Production of Existing Products 125 6.3 Empirical Results 128 v 6.3.1 The Introduction of New Products 128 6.3.2 The Production of Existing Products 135 6.4 Conclusion 153 7 Conclusions 156 Appendices 159 A Insecticide Names 159 B Characteristics Data 163 B.l Data Selection 163 B.2 Characteristics Data . . . • 163 B.3 Characteristics Data Sources 190 C Prices of Insecticides (annual) 200 D Products Forming Facets and Implicit Prices of Characteristics 207 D.l Introduction . 207 D. 2 Units of Measurement and Product Codes 207 E Bounds on Prices 226 E. l Introduction 226 Bibliography 232 vi List of Tables 3.1 Contingency Table for Independence/Association 26 3.2 x2 Test of Independence/Association: Concentrates (1962) 27 4.1 Products Within the Frontier 47 4.2 Proportional Changes for Convexity 52 4.3 Prices of Characteristics (1957) 56 4.4 Association between Neighbouring/Chemically Similar Products 68 6.1 Products Introduced by the Same Firm 129 6.2 Variable Definitions: Introductions 131 6.3 Predicted Introductions of New Products (Logit) 134 6.4 Concentrates Produced by the Same Firm (Logit): I . . . .' 138 6.5 Variable Definitions: Production 141 6.6 Concentrates Produced by the Same Firm (Logit): II 142 6.7 Formulations Produced by the Same Firm (Logit): I 148 6.8 Formulations Produced by the Same Firm (Logit): II 151 B.l Aldicarb Characteristics 164 B.2 Aldrin Characteristics 165 B.3 Allethrin Characteristics 166 B.4 Azinphos-methyl (Guthion) Characteristics 167 B.5 Carbaryl (Sevin) Characteristics 168 B.6 Carbofuran Characteristics 169 vii B.7 Chlordane Characteristics 170 B.8 Chlorthion Characteristics . . . 171 B.9 DDT Characteristics 172 B.10 Demeton Characteristics 173 B. l l Diazinon Characteristics 174 B.12 Dieldrin Characteristics 175 B.13 Dimethoate (Cygon, Rogor) Characteristics 176 B.14 Endosulfan (Thiodan) Characteristics 177 B.15 Endrin Characteristics 178 B.16 Heptachlor Characteristics 179 B.17 Heptachlor Epoxide Characteristics 180 B.18 Isodrin Characteristics 181 B.19 Lindane Characteristics 182 B.20 Malathion Characteristics 183 B.21 Methoxychlor Characteristics 184 B.22 Methyl Parathion Characteristics 185 B.23 Parathion Characteristics 186 B.24 Pyrethrum Characteristics 187 B.25 Rotenone Characteristics 188 B. 26 Toxaphene Characteristics • • • 189 C. l Insecticide Prices ($U.S./lb.) 201 D. l Product Codes 208 E. l Predicted Bounds on Chemical Prices (US$/lb.) 1946-1975 227 E.2 Predicted Bounds on Chemical Prices (US$/lb.) 1976-87 230 vm List of Figures 2.1 A Characteristics Frontier (Gorman 1956/1980) 11 2.2 All Products Necessarily on Frontier (Lancaster, 1971) 19 3.1 Association of Insecticide Concentrates (1962) 28 3.2 The Market Opportunity Frontier (1957) 40 4.1 Testing the Predictions of Characteristics Theory 43 4.2 A Product Priced Within the Frontier 46 4.3 Price Reductions for Endrin to Reach the Frontier 48 4.4 Measurement Error in Zx 50 4.5 Implicit Price of Toxicity to Insects 58 4.6 Prices on Aldrin/Chlordane/DDT Facet 59 4.7 Bounds on Possible Prices 61 4.8 Regions with Lower Bounds on 63 4.9 Lower Bounds: C on the Edge of the Frontier 65 5.1 Market Opportunity Frontier of the Model 73 5.2 Demand for Product 3 76 ix Acknowledgement I would like to thank my thesis supervisor, Chris Archibald, for his excellent advice and technical support. His encouragement, patience and good company made this work much less daunting and more rewarding than would otherwise have been possible. I would also like to thank Mukesh Eswaran and Ken White for their valuable comments and their patience. Of course, I would like to give my warmest thanks to my parents and family for their unwavering support and for the encouragement that I have always received to pursue all areas I found of interest. The people of C Block also deserve my appreciation for putting up with me during these hectic years. Finally, I would like to give my special thanks to Shelley Phipps whose encouragement and smiles have brightened my life and made all of this a little easier. Chapter 1 Introduction The principal objective of this thesis is to analyse product choice by multiproduct firms. In particular, the purpose is to see if there is a consistent method of determining the probability that a firm will introduce a particular new product or produce a particular existing product. Traditional economic analysis requires detailed information on the research and de-velopment efforts that every firm devotes to a particular product in order to model a firm's probability of introducing that product. Similarly, determining whether a firm undertakes the production of an existing product requires information on the technology and costs of all firms. Unfortunately, such detailed information is rarely available. This thesis presents an alternative approach. It is based upon the idea that a product may yield greater profits if produced in combination with particular other goods. Certain combinations of goods are thought to capture some degree of local monopoly power or have the potential for cost advantages in the production of products requiring similar inputs and processes. These relationships between products are hypothesized to influence the probabilities that these combinations of products are introduced or produced by the same firm. One of the influences on the choice of certain combinations of products, the ability of these goods to exert a degree of local monopoly power, requires some indication of how competition is localized. Since traditional economic theory either treats groups of goods as having no a priori relationship or as trivial variations of the same product, there is no method of determining whether a product which has not yet been introduced will be able to have any degree of monopoly power in combination with other products. The localization of competition can, in theory, only be determined once the product is on the .1 Chapter 1. Introduction 2 market. Clearly, this is not an adequate framework for discussing strategic introduction of products by multiproduct firms. Commonly held perceptions, such as the ability of a firm to "corner a segment of the market" by producing certain products, would suggest that people believe that competition can be localized and that some combinations of goods are more likely than others to be in direct competition. Characteristics theory, in which products are believed to be valued for the characteristics they embody, avoids this shortcoming of traditional economic theory by specifying how competition among similar products may be localized as well as allowing for other phenomena such as the introduction of new goods and diversity of preferences. The market that is studied is the American insecticide industry during the period between 1944 and 1987. Characteristics theory is used to determine how competition is localized among twenty-three insecticides during each year of the period. The insecticides are described by the three attributes that are used to compare them in the insecticide literature; their toxicity to insects, their toxicity to mammals, and their persistence. To determine that a characteristics approach is appropriate for the analysis of this market, data from fifteen common insecticides are used to provide the first empirical support of the prediction that products are priced to appear on a convex market oppor-tunity frontier. This provides the first empirical support of characteristics theory since it has never been tested in a case in which the products are combinable and it is predicted that products should be on a convex frontier. A simple method of determining the implicit prices of characteristics is also utilized for the first time. This method requires the calculation of the implicit prices for each facet of the frontier based upon the prices of each product which forms the facet and the characteristics they embody. The procedure is able to determine the prices of char-acteristics in cases which violate the assumptions required for hedonic price analysis (ie. that there are an infinite number of indivisible, differentiated products). Implicit prices of characteristics allow predictions to be made about the possible bounds on the prices of up to ten additional products for which price data were not available. This allows the determination of the relative positions of a total of twenty-three products on the market Chapter 1. Introduction 3 opportunity frontiers. Locating products on a market opportunity frontier allows an objective indication of how competition is localized. Combinations of three products which form a facet on the frontier generate mixes of characteristics that are also on the frontier. These products are in direct competition with one another, allowing a firm which produces them to enjoy some degree of local monopoly power over these mixes of characteristics. In addition to the impact of any local monopoly power, the probability of producing certain combinations of goods may be influenced by any cost reductions associated with producing chemically similar products. If there is a poor correlation between the products that are chemically similar and those which are in direct competition, it is possible to distinguish the effects of each. These effects are assumed to be modified by other factors such as the period between introductions and the number of other products that are present. Empirical tests of the tendencies of firms to introduce or produce combinations of these goods based upon the the relationships between these products are used to de-termine the relative importance of the different incentives on product choice. Tests to determine whether firms maintain portfolios of similar products have been conducted in each of three areas; the introduction of new products, the production of concentrates, and the production of the final formulations. Judgement of the ability of the tests to fit the data is based upon the predictions they generate of which firm introduces or pro-duces each product. The ability of the empirical model to account for the identity of a firm which introduced or produced a product shows that it is not only possible but it can also be productive to analyse groups of similar products using the characteristics approach. It also shows that there is a consistent method of determining product choice of multiproduct firms. This thesis is organized in the following manner. In the next chapter I review the literature on multiproduct firms, on characteristics theory, on the empirical uses of the characteristics approach and on the insecticide and chemical industries. Chapter 3 de-scribes the data, their sources, and the transformations required for their use in the Chapter 1. Introduction 4 characteristics approach. The procedure and results of the check on the main prediction of characteristics theory are presented in Chapter 4. This involves determining whether any products are priced significantly within the frontier based upon the measurement errors of the characteristics. The chapter also presents the method used to calculate the implicit prices of characteristics and describes how the theory is used to determine which combinations of products have the potential for some degree of local monopoly power. In Chapter 5 a model is presented connecting the relationships between products to the probability that a firm will introduce or produce certain combinations of products. Chapter 6 discusses the estimation procedures and results from the introduction of new products and the production of existing products. Finally, conclusions are presented in Chapter 7. Chapter 2 Literature Review 2.1 Introduction This chapter presents an overview of the rather disjoint areas of literature that are used in this analysis. The first section outlines the existing literature on multiproduct firms. Although most articles are theoretical in nature there are some which undertake empirical analysis of product choice by multiproduct firms. The second section deals with the development and present standing of characteristics theory. Empirical applications of the characteristics approach, and variations of this idea, are presented in Section 3. Section 4 provides a brief overview of literature dealing with the chemical industry. Finally, concluding remarks are given in Section 5. 2.2 Multiproduct Firms Despite the fact that most firms produce a number of products, many of which have similar characteristics, economic theory has had little to say about the choice of such product portfolios. The principal hypotheses that have been proposed fall into three categories. First, the shared use of inputs may provide cost advantages in the joint production of products. Second, a degree of local monopoly power may be possible if a firm produces every product which has a similar mix of characteristics (ie. the firm "corners a segment of the market"). Finally, risk aversion may encourage the production of products with very different mixes of characteristics to offset local fluctuations in demand. Any empirical research into the choice of product portfolios, and in particular a test for tendencies to produce goods with similar mixes of characteristics, will therefore have to distinguish this influence from the effects of cost economies or risk aversion. 5 Chapter 2. Literature Review 6 The literature concerning cost advantages of providing more than one product was recently reviewed by Bailey and Friedlander (1982). Analysis has been dominated by the concept of "economies of scope" introduced by Panzar and Willig (1981). The idea is based upon the possibility that benefits may arise from sharing inputs in the production of a number of goods. A similar concept, the subadditivity of costs, was introduced by Faulhaber (1975) to describe the cases in which joint production of specific quantities of two goods could result in lower costs than by separate production. Since cost advantages may arise from sharing an input, any products which have similar components or undergo similar production processes may be subject to this effect. Distinguishing the pursuit of local monopoly power from cost advantages will thus require that there is an incomplete correlation between the products' chemical structures (or preparation procedures) and their inherent characteristics. Of course, strategic choice of product types may arise for other reasons than cost differentials. Hotelling's (1929) classic article on the choice of product types by competing firms relies upon the ability of these firms to establish some degree of monopoly power over a portion of the market. Although this approach has recently experienced a resurgence in popularity under such authors such as D'Aspremont, Gabszewicz and Thisse (1979), Caplin and Nalebuff (1986), and Economides (1984, 1986a, 1986b), most articles have restricted themselves to the case of single product firms. Some mention has been made of multiproduct firms in reference to their ability to deter entry by product proliferation. Archibald and Rosenbluth (1975) noted that com-petition in prices is not an effective barrier to entry but that pre-emptive diversification can fill this role. This possibility that product proliferation may be used to deter en-try was also brought up in articles by Hay (1976), Lane(1980), as well as Prescott and Vischer(1977). Schmalensee's (1978) discussion of the breakfast cereal industry revealed that at least a casual belief exists that firms do undertake pre-emptive product selections. Furthermore, he showed that there is a theoretical possibility that it would be profitable for firms to undertake such pre-emption. Eaton and Lipsey (1979) also provided a strong argument that pre-emption will take Chapter 2. Literature Review 7 place in growing spatial markets. In addition to being one of the few papers explicitly dealing with multiproduct(/location) firms, this article formed the basis for a number of works by West (1979, 1981a, 1981b). These, in turn, appear to be the only empirical tests that have been undertaken to determine whether or not firms make strategic product choices. Using contingency tables, West tested for tendencies to introduce new supermar-ket locations in circumstances in which their markets border those of existing locations of the same firm. By using the firm which introduced a new location as the dependent variable, a number of problems were created. By necessity, relatively few categories were used to provide a simplified description of each firm's relations with its neighbours (ie. a location with only one neighbouring store of the same type as itself is treated the same as a location with all but one neighbouring stores of that type). Furthermore, the use of expected relative frequencies derived from the total number of supermarkets which each firm owns in the province is not necessarily appropriate for testing a particular portion of the market (ie. monopoly control of other regions would bias the expected frequencies). Nonetheless, West's work did break new ground by attempting to analyse multilocation decisions and, in addition, he did reveal the existence of pre-emptive location selection by supermarkets. Apparently the only paper to have explicitly explored firms' selection of product portfolios is by Brander and Eaton (1984). Although the subject is inherently complex, the use of a simple four product model allowed the authors to determine that, if entry were prevented, existing firms would tend to choose clustered products to extract local monopoly rents. The possibility of entry presents the interesting result that it may be better for each firm to choose distant products (ie. subjected to greater competition) if this threat of potential negative profits would deter entry. Although the literature dealing with multiproduct firms is not yet well developed, there is already some indication of what considerations may influence product choice. It will therefore be necessary to take the effects of production costs, local monopoly, and the threat of entry, into account when undertaking empirical studies on the decisions of multiproduct firms. Chapter 2. Literature Review 8 2.3 Characteristics Theory The idea that commodities may be represented by their intrinsic characteristics has reoccurred many times in economic thought. Early writers, such as Menger (1871) and Jevons (1879), were aware that many commodities do not have independent demands since they contribute similar components towards the same objective. "...that one commodity can often replace another, and serve the same pur-poses more or less perfectly. The same, or nearly the same substance, is often obtained from two or three sources. The constituents of wheat, barley, oats, and rye are closely similar, if not identical." (S.W. Jevons 1879, p.145) Menger, in particular, had addressed the problem of qualitative differences between goods. His analysis clearly broke the problem into two parts. The first consists of sub-jective preferences across various attributes which provide satisfaction, while the second involves the objective determination of the attributes that are available from particular products. This distinction forms the very basis of present day characteristics theory. Al-though other contributions by Menger, such as his pioneering work in utility theory, were known to English-speaking economists, his approach to qualitatively different products appears to have received little recognition until his work was translated into English in 1950. Perhaps coincidentally, it was in the 1950s that a number of authors pointed out the validity of viewing goods as indirect means of pursuing a consumer's objectives. The terminology and structure of these ideas were subject to considerable variation but it is undeniable that many of the basic elements of present characteristics theory had already been formulated. Perhaps the earliest approach was taken by Theil (1952) and Houthakker (1952). Their papers centred on the idea that "commodities" could be described as aggregates of homogeneous "qualities". This idea was offered to provide some perspective on the intrinsic substitutability of various goods. These authors, and others such as May (1954), do not appear to have produced a wider acceptance or a greater clarification of the Chapter 2. Literature Review 9 approach. Their works, however, did express some of the basic ideas inherent in modern characteristics theory. One of the most direct statements made at this time supporting the validity of a characteristics approach was by J.R. Hicks (1956). "The commodities which he (the consumer) purchases are for the most part means to the attainment of objectives, not objectives themselves." (J.R. Hicks 1956, p.166) Hicks proposed that this approach added to the theory of demand if there were tech-nical changes or changes in objectives. He regarded these issues, however, as being overly complicated and believed that the definition of the objectives was virtually impossible. Despite this, Hicks maintained that if we retained an underlying belief that goods are of value for their inherent characteristics "...we should do something to protect ourselves from one of the superficialities that are the diseases of our occupation". By the mid-1950s there had still not been an explicit exploration of a characteristics model although many authors made some reference to the intrinsic attributes of goods. Gorman (1956/1980) undertook such a description (although he failed to publish it un-til 1980) with insight which was not to appear in the literature until the mid-sixties. The structure of the basic characteristics model has not changed substantially since this seminal article. The key contribution of this paper was that it clearly exposed the re-quirements of such a model: A good's characteristics should be measurable and additive, and product types should be defined by their characteristics mix. Goods can, thus, be related to characteristics by equation 2.1. (2.1) Z = BX Z is an (rxl) vector of characteristics z± X is an (nxl) vector of goods Xj B is an (rxn) matrix with elements 6;J which give the amount of characteristic Z{ per unit of the good Xj Chapter 2. Literature Review 10 If a consumer's utility is a function of the total amount of each characteristic he consumes, the consumer's optimization problem becomes equation 2.2. PX <k (2.2) max U = f(Z) s.t. X Z — BX P is an (nxl) vector of product prices pj A; is a budget constraint The prices of the characteristics (qj) will be dependent upon which constraints are binding for a particular consumer. Therefore, the characteristics prices will be identical for all consumers who purchase the same group of goods (although corner solutions will be bounded by these common values). One should not overlook the importance of Gorman's diagram (Figure 2.1) which de-picts products in a normalized characteristics space1. In the cases when the consumption of each type of product is viewed as an activity, this illustration allows an easy, objective representation of characteristics that are available under any given budget constraint. Gorman also observed that a product with a relatively high price (such as product C in Figure 2.1) may completely exclude itself from the market on efficiency grounds. This makes it possible to predict what is the highest possible price that a product can maintain in a market. The greater part of Gorman's paper is concerned with finding characteristics prices which are equivalent for all consumers. Gorman noted that consumers often pick products which have quite different mixes of characteristics, and cited this as a justification for the assumption that the frontier might be linear over many products. The observation is of little value, however, since it assumes that consumers' indifference curves are basically invariant over time and circumstances. As an example, the fact that a consumer purchases four types of coffee beans does not preclude definite preferences between the blend he may drink in the morning and the blend he might drink at night. In fact, the desire 1 Labelling has been altered for consistency. Chapter 2. Literature Review 11 Figure 2.1: A Characteristics Frontier (Gorman 1956/1980) to find common prices ignores a major distinction of the characteristics approach: The preferences of consumers do not need to be (and generally cannot be) approximated by one representative indifference curve. Despite difficulties in application of the theory, it cannot be denied that Gorman's work showed insight that was well ahead of its time. Since Gorman's article was not published until 1980, a number of authors (eg. Strotz 1957, Morishima 1959) continued to use models which had some similarity to a character-istics approach. These models did not explore the conditions for the use of characteristics theory, nor comment on the technical interrelations of selling prices. In a manner rem-iniscent of Gorman, Ironmonger (1961/1972) also developed a relatively sophisticated model based upon our present approach to characteristics theory but failed to publish it until 1972. The mid-1960s appear to have experienced a resurgence in the characteristics ap-proach. Becker (1965) postulated that household utility might be a function of "com-modities" which were created by combining time and market goods. Quandt and Baumol (1966) used the idea of "abstract modes of transport" to define the continuum of types Chapter 2. Literature Review 12 of transportation services available. Each of these papers show a greater insight into the use of characteristics theory but still fail to outline the approach in general form. Lancaster (1966) did the most to generalize the structure of characteristics theory and to popularize its use. In addition to revealing the points independently developed by Gorman, the author noted a number of important variations on the basic theory. One possibility which Lancaster acknowledges, but does not pursue, is that combinations of goods may possess different characteristics than they would separately. Similarly, Lancaster (1971) noted that people may sometimes see different properties in a good. Nevertheless, it is generally assumed that people see the same properties but merely have different preferences. Another generalization which was used allowed for the distinction between goods and activities. Consumption may be viewed as an activity with goods as inputs and characteristics as outputs (equation 2.3). (2.3) Z = BY, X = AY X is an ( n x l ) vector of goods Xj 7 is an ( m x l ) vector of activities y^ Z is an ( r x l ) vector of characteristics z; A is an (nxm) matrix of elements cijj. which give the amount of good Xj that is necessary for one unit of activity yk B is an (rxm) matrix of elements 6^  which give the amount of characteristic Zi per activity yk The use of activities allows an explanation of intrinsic complementarity, that a col-lection of goods is required for an activity, in a manner similar to Morishima (1959). Intrinsic substitutes, on the other hand, do not require activities in their explanation; they are goods which yield positive amounts of a characteristic which is in the production or utility function. This more general approach is made very difficult by the complexity of dealing with goods which may be used in a number of activities. Later works by Lancaster (1971, 1975), in fact, concentrated on cases in which there were one-to-one Chapter 2. Literature Review 13 relationships between goods and activities. One of the major contributions of Lancaster (1966) was the concept of the "efficiency substitution effect". Although the regular substitution effect involves the change of a preferred characteristics mix due to a relative price change, the efficiency substitution effect is only concerned with switching goods to achieve the chosen characteristics mix in the most efficient manner. This may be viewed as an effort to consume on the "efficiency frontier" once a characteristics mix has been chosen. Lancaster was aware that manageable problems would require a method of restricting an analysis to some group of goods. To allow for this, he defined such a collection of products as an "intrinsic commodity group" consisting of goods which are used only to produce a set of characteristics not available from any other products. This distinction implies that efficiency substitution effects only occur for relative price changes within the group and will not be affected by the price changes of other goods. It should be noted that the definition is distinct from Chamberlin's (1933) concept of "group" since each product is not necessarily subjected to a large number of competitors. Another distinction .was later drawn by Lancaster (1971) between the term "properties", used in reference to any attribute of a good, and the term "characteristics", used for the objective properties which are relevant to choices by people. Lancaster's articles, while not the first to use characteristics theory, certainly were the first to make the approach widely known. His contributions were also significant because they classified concepts associated with characteristics theory (eg. efficiency frontier, intrinsic commodity group) and set much of the terminology which is still in use today. A number of articles in the 1970s utilized the characteristics approach to reanal-yse traditionally accepted economic theory. This represents a departure from the usual use of characteristics theory, the investigation of generally ignored topics such as the introduction of new goods. Lipsey and Rosenbluth (1971) explored the conditions in characteristics theory which would result in inferior or Giffen goods. By defining prefer-ences over characteristics rather than goods, the authors showed how Giffen goods can Chapter 2. Literature Review 14 occur without abandoning commonly held ideas about the attributes of the utility func-tions. Characteristics theory was also utilized by Auld (1972) to outline the implications of imperfect information on product choice without resorting to the shifting of indiffer-ence curves. A similar analysis was used by Auld (1974) to show that advertising may have greater benefits to the firm if it is used to stress characteristics which a good has a comparative disadvantage in. Archibald and Rosenbluth (1975) applied the characteristics approach to find what conditions are required for Chamberlin's (1933) theory of monopolistic competition to hold. The assumptions, made by Chamberlin are not generally applicable since they require that goods be defined by a large number of characteristics. In the process of ex-ploring this issue, the authors clarified and generalized much of earlier analysis, including denning the necessary conditions for partial equilibrium analysis: There must be an objec-tive basis for defining a group, weak separability of the utility function and no significant cost repercussions. The final point had previously been ignored due to assumptions of constant returns to scale. Archibald and Rosenbluth also made the distinction between the "market opportunity frontier" and Lancaster's "representative efficiency frontier". Defined as the characteristics combinations that cannot be purchased for less than the entire budget, the market opportunity frontier differs by allowing negative marginal util-ity and thus upward sloping regions of the frontier. One of the most important concepts introduced by Archibald and Rosenbluth is the idea of "neighbour", also referred to as the "neighbour relation". If all convex combi-nations of two goods are on the market opportunity frontier, these goods are said to be neighbours. The concept is of particular importance because it can be objectively determined and because it does not require the assumptions on preferences that are nec-essary in the spatial models. Issues which spatial models generally need to assume away, such as differences in the curvature or symmetry of the utility functions, do not affect observations of which products neighbour one another in characteristics space. The re-lationship is important because it states which products are in direct competition with one another, and also because a large number of neighbours, which does not hold if Chapter 2. Literature Review 15 there are few relevant characteristics, is a necessary condition in the standard theory of monopolistic competition. Archibald and Rosenbluth also pointed out that economies of scale in a characteristics model offers an explanation for the relative scarcity of types of goods and for the coexis-tence of large and small firms. In addition, they noted the possibility of entry deterrence by brand proliferation. Following a reference (ie. Archibald and Rosenbluth, 1975) to the use of a charac-teristics approach in production theory, Archibald and Rosenbluth (1978) undertook a preliminary exploration of this topic. A key distinction was made between a technolog-ical change involving an alteration of the production function, and one which involves the introduction of new products. Although changes in the production function can be handled by traditional theory, the characteristics approach has a particular advantage in looking at new product introductions. The authors also specified the optimization problems faced by firms when the characteristics approach is used in producer theory. Each firm, k, minimizes the cost of achieving a given vector of characteristics, Z", by solving the optimization decision given in equation 2.4. (2.4) minP'X s.t. Z" < BX Z* is an (rxl) vector of characteristics zl* X is an (nxl) vector of inputs xJ > 0 B is an (rxn) matrix of elements blJ indicating the amount of characteristic z1 provided by input x^ P is an (nxl) vector of prices pi of inputs xJ The solution to the dual problem (equation 2.5) yields a vector of implicit prices ,Q", for each vector of characteristics, Z". Chapter 2. Literature Review 16 (2.5) maxQ'Z' -s.t. Q'B < P' Q is an (rxl) vector of implicit prices of the characteristics The cost function is found for each level of the firm's output, qk, by choosing a vector of characteristics, Zx, and therefore a vector of characteristics prices, Q", which solve the optimization problem in equation 2.6. (2.6) minQ'Z s.t. fk(Z) > qk Vgfc > 0 z fk(Z) is the production function of firm k The application of the characteristics approach to traditional economic theory was continued by Archibald, Eaton and Lipsey (1986) who looked at the importance of prod-uct and firm specific capital. They noted that the specificity of capital, with the resulting commitment, has both harmful and beneficial implications. The disadvantage of product specific capital arises because it may eliminate options in the face of uncertainty. At the same time, this commitment to a product has the effect of deterring entry. The relations between spatial and characteristics models was discussed by Archibald and Eaton (1989). They pointed out that spatial models are a special case of the char-acteristic approach. The differences between the two approaches is primarily due to the fact that products (locations) in the spatial models are seen as noncombinable. If com-binability were not costless within an intrinsic commodity group, the market opportunity frontier would not be convex and any interest in which products directly compete against each other would require more information about the indifference curves. Nonconvexity would also preclude any method to check whether the chosen characteristics adequately describe the products. Another difference is that spatial models generally assume a definite distance metric while the characteristics approach can only resort to subjective metrics or pseudometrics, such as those developed by Archibald and Eaton (1989), or use a discrete metric based on the neighbour relation. Although it is necessary for spatial models to make some assumption about diverse preferences, it is generally only assumed Chapter 2. Literature Review 17 that they differ by being uniformly distributed over locations. Despite an eclectic start, the characteristics approach has evolved into what is presently a reasonably mature concept. In addition to the general consensus that has developed on terminology and methodology, there have also been a number of attempts to reanal-yse traditional theory in light of this new approach. Nonetheless, the most important benefits of characteristics theory remain its abilities to allow for the introduction of new products, and to provide an objective means of determining which goods are in direct competition. 2.4 Empirical Use of the Characteristics Approach Empirical analyses based upon characteristics theory have not been as common as the theoretical works in that area. Although many papers have made some reference to the idea that goods can be viewed as bundles of characteristics, few have used models which are consistent with theoretical articles such as Lancaster's seminal paper (1966). Hedonic price analysis, at one time a very popular procedure, is occasionally referred to as a method which is based upon the characteristics approach. Although the technique was widely accepted following works by Adelman and Griliches (1961), Griliches (1961, 1971), and in particular by Rosen (1974), subsequent questions addressed by Brown and Rosen (1982) revealed that Rosen's procedure either requires restrictions on functional form or estimation across a number of markets. Nonetheless, a large number of empirical studies made use of hedonic price analysis2, and the procedure is still commonly used in studies of housing prices and of the impact of environmental externalities. Regardless of the popularity of hedonic price analysis, its supposed relation to the characteristics approach does not bear up to close scrutiny. Lucas (1975) clearly dis-tinguished the assumptions which result in fundamentally different bases for the two approaches. The predominant difference is that utility in the characteristics approach is only dependent upon the characteristics that are inherently available in the goods that are consumed. On the other hand, hedonic pricing associates an additional value with 2See, for example, Nelson (1978), Goodman (1978), and Hirsch (1981). Chapter 2. Literature Review 18 quantities of the goods consumed and, thus, with that aspect of a good which makes it more than the sum of its parts (ie. the gestalt of the good). The idea involves more than placing a value on a particular brand. It requires a common valuation of each member of a class of products, with each good's particular characteristics causing some deviation from the basic value. Hedonic price analysis also may not be appropriate because of its requirements for a great (ie. infinite) variety of indivisible differentiated products as well as the restriction that a consumer only picks one of the products. The specification of utility functions in the characteristics approach, in addition to its theoretical justification, has the effect of allowing the construction of a convex market opportunity frontier. Information can be gained about which products are in direct competition only by constructing such a frontier unless very restrictive assumptions are made about preferences. Since this thesis makes use of characteristics theory primarily for its ability to determine how competition is localized the large number of studies that have made use of hedonic pricing are not directly applicable. Numerous other papers have also made some reference to the characteristics of prod-ucts. These" involve subjects that are as diverse as the concept of "human capital" and the idea that coal, electricity and petroleum have value for the energy they embody (Berndt and Wood, 1975). Bailey (1956) described "burdening" of blast furnaces in which the inputs were distinguished by their intrinsic characteristics. Similarly, Cowing (1974) dis-cussed boiler-turbine generators by categorizing them according to their capacities and their efficiencies. Unfortunately, these papers do not make explicit use of Lancaster's style of analysis which would allow testing the prediction that all products are priced to appear on a convex market opportunity frontier. Even Lancaster did not make empirical use of a combinable characteristics model. Analysis of new cars by Lancaster (1971), although dealing with noncombinable purchases, did show some tendency to produce convex frontiers with relatively few characteristics. This analysis should not be regarded as lending much empirical support to the approach since the products that were chosen only require that the ratio of characteristics remains unchanged for them to remain on the frontier. This can be seen by Figure 2.2. Each product could expand or contract Chapter 2. Literature Review 19 Figure 2.2: All Products Necessarily on Frontier (Lancaster, 1971) along its ray from the origin (ie. retaining the same ratio of characteristics) and would always remain on the frontier. Furthermore, the relatively few products and the long list of characteristics which the industry literature attributes to them made it virtually impossible to not be able to construct a convex frontier. The importance of costless combinability is that it provides one of the sufficient condi-tions for the prediction that all products are priced to be on a convex market opportunity frontier. Existence on the frontier is, in turn, necessary to determine the characteristics' prices, and to establish which products are in direct competition. Without combinability, articles that have made an effort to measure the prices of characteristics have relied upon a priori assumptions about the nature and distribution of preferences. Morey's (1981) analysis of skiing destination shares can only be thought of as a combinable model if preferences are assumed to be invariant. Unfortunately, this was explicitly ruled out by the assumption that skiers have diminishing marginal utilities of skiing at any particu-lar site. Other spatial models, since they inherently face costly combinability, have also found it necessary to utilize rather restrictive assumptions. For instance, West (1979, Chapter 2. Literature Review 20 1981a, 1981b) utilized directional symmetry to calculate which locations were in direct competition with one another. Although Shaw (1982) made explicit use of some aspects of characteristics theory and studied combinable products he was also unable to construct market opportunity frontiers. His analysis of the chemical fertilizer industry in the United Kingdom did not include any information on prices. Because of this, his use of characteristics ratios provided by each product is, at best, an incomplete measure of how rival firms choose to position products in characteristics space. Another analysis which might be thought of as dealing with a case of combinable products is found in Kerr (1981). While it is possible to imagine that a cattle breeder would view his herd's production function as being dependent upon the genetic makeup of the founding livestock, each animal has a unique characteristic mix and, thus, any frontier would be in a constant state of flux depending upon the cattle that are available each period. Since it was necessary to statistically estimate his model's frontier, Kerr was also forced to assume that the desired characteristics ratio was stable over time and regions of the country. The market opportunity frontier, thus, was reduced to a single, probabilistic facet, allowing the model little possibility of showing any product to be within a convex market opportunity frontier that existed in any period. In addition to Kerr's thesis, perhaps the only empirical work that has made explicit use of market opportunity frontiers has been portfolio analysis3. By assuming that an investor's utility is a function of the variability of the return and the expected level of return, it can be shown that investors will prefer "Markowitz-efficient assets". These assets have characteristics which place them on an efficiency frontier which corresponds to a market opportunity frontier. Despite the prediction that investors will only choose assets that are on a convex frontier, this approach also does not appear to have ever been tested. There is definitely some opportunity for empirical work based upon the characteristics approach. Although there have been many references to the characteristics of products, 3Refer to Francis and Archer (1979) for a good outline of mathematical portfolio analysis. Chapter 2. Literature Review 21 few articles have explicitly based their analysis on objective functions which are only dependent upon products' inherent characteristics. Furthermore, despite the very strong prediction that costlessly combinable goods will all be priced on a convex market op-portunity frontier, no one appears to have tested whether all products appear on such a frontier. 2.5 The Insecticide and Chemical Industries This thesis uses the insecticide industry as the subject area in the discussion of characteristics theory and product choice by multiproduct firms. This area was chosen because of the relatively large number of insecticides that have been introduced since World War II. Furthermore, these products have been introduced by a relatively small number of firms allowing the opportunity to investigate the interactions of multiproduct firms. Finally, the insecticides satisfy the requirements for the use of characteristics theory including being distinguished by a few well-defined characteristics. Unfortunately, the economic literature that has dealt with insecticides has generally ignored the issue of product choice by the firms producing the chemicals. Articles that have dealt with insecticides, such as those by Carlson (1977), Sarhan et al. (1979), Regev et al. (1983) and Lichtenberg (1987), have concentrated on the productivity and externalities of insecticide use. A very brief description of the insecticide industry is presented in order to indicate the major influences on a firm in the industry. The widespread use of insecticides began with the development of cheap and effective compounds (eg. DDT) during the Second World War. Many new insecticides were introduced in the period following the War although the rate of introduction has declined since the 1960s. Widespread concern about the effects of pesticide use also developed in the mid-1960s largely in response to Rachel Carson's book Silent Spring (1962). By the early 1970s concern about the persistence of a number of products prompted legislation restricting their production and use. The 1970s also saw large increases in the price of petroleum which forms the basis of many of the feedstocks used in the chemical industry. The use of many insecticides has also been Chapter 2. Literature Review 22 reduced due to the recent development of "Integrated Pest Management"; an approach emphasizing alternative methods of pest control and more selective use of insecticides. The basic structure of the industry is such that new products have been introduced by a relatively small group of firms. The company responsible for an introduction generally undertakes production of the concentrate as well as licensing a few other firms. Production of insecticides takes place on a relatively small scale in comparison to other aspects of the chemical industry. Furthermore, most insecticides are produced using batch processes and require similar facilities (eg. reaction vessels, dehydrators). The concen-trates, generally produced in relatively few locations, are comparatively high-valued and are shipped in bulk to the many small formulators which are scattered throughout the country. Finally, the chemicals are diluted, mixed and packaged into the formulations which appear on the retail market4. Thus, the insecticide industry presents the opportunity to study the introduction of new products and the production of existing goods. It also provides information on the product portfolios of firms and the prices of goods throughout the development of the industry. Furthermore, the minimal degree of product-specific capital allows the assumptions of easy entry and exit in the production of the products, particularly the formulations. The analysis is also simplified by the well-specified structures of the in-secticides; this ensures that patent protection of new products is not easily infringed upon. Despite these advantages there does not appear to be much economic literature associated with the production side of this industry. Although few economic articles have discussed insecticides there is some literature dealing with the introduction of new products in other branches of the chemical industry. Davies (1962) paid particular attention to research and development in the pharmaceuti-cal industry while Gittins (1969) and Mansfield (1977) were concerned with the chemical industry as a whole. These articles will be of some value in this analysis since the in-secticide industry is similar to other branches of the chemical industry in being heavily dependent upon concerted research and development strategies for the large number of 4Refer to Heaton (1986) for abetter overview of the insecticide industry. Chapter 2. Literature Review 23 products that have been introduced since the Second World War. Not only are the research and development approaches similar in the different branches of the chemical industry but many of the same firms are involved as well. The articles that have just been mentioned will therefore provide the basic approach used in modelling research and development in the insecticide industry. One shortcoming of this literature is that it ap-pears to deal exclusively with firms' decisions to develop particular products. It ignores issues involved in the selection of product portfolios such as differential abilities of firms to corner a segment of the market. Nonetheless, the attributes of the insecticide indus-try and the existence of a recognized line of research on other branches of the chemical industry provide considerable justification for choosing insecticides as the subject area for this analysis. 2.6 Conclusion This chapter provided an overview of the diverse areas of literature that are pertinent to this thesis. Existing literature on product choice by multiproduct firms has presented cost advantages, local monopoly power, and entry preemptions as possible influences on product choice. Empirical work in this area is not extensive. Although characteristics theory has been developed for some time there are also few empirical applications of the approach. Despite this, the intuitive appeal of the idea that goods are valued for their inherent characteristics has resulted in a large number of works making some reference to the characteristics of goods. Unfortunately, these articles have not used a framework which would allow any checks of the predictions of characteristics theory. Finally, there is some literature dealing with the introduction of new products in the chemical industry but little attention has been paid to complications that result because these are multiproduct firms. Chapter 3 Data Requirements and Sources 3.1 Introduction This chapter consists of four distinct parts. The first part briefly analyses the data to determine the extent to which various combinations of products are in firms' portfolios. The next section outlines the data requirements for the use of characteristics theory to determine which combinations of goods provide some degree of local monopoly power. The third section lists the sources of data that were used and discusses how the charac-teristics data were constructed. Finally, the fourth section describes the procedure used for the construction of a market opportunity frontier. Characteristics theory uses such a frontier, as the basis of its predictions of which combinations of goods provide some degree of local monopoly power. The application of characteristics theory to the analysis of the choice of product portfolios is based upon the hypotheses that there are significant associations among some of the products. The first section of the chapter outlines the procedures used to test these hypotheses and the results of the tests. Significant association of the insecticides suggests that the choice of product portfolios is not random and may be one aspect of interfirm rivalry. It is hypothesized that certain relationships between products (eg. the potential for local monopoly) account for such associations. The use of characteristics theory to account for firms choosing particular combinations of products requires data that are not listed in common economic sources. In particular, this chapter discusses which characteristics are considered to be important by the indus-try, how these characteristics are measured, the amounts of the characteristics that are inherent in a unit of each product, and whether the products are costlessly combinable. The analysis also utilizes data of a more traditional nature such as the prices of each 24 Chapter 3. Data Requirements and Sources 25 product, the identity of the firm to introduce it (and the identities of firms that produce it), when the product was introduced and when it was withdrawn from the market. Finally, the chapter outlines the procedure for the construction of convex market op-portunity frontiers to describe the market for insecticides. These frontiers are particularly important since they provide the first opportunity to empirically check the prediction that all products are priced to appear on a convex market opportunity frontier. More importantly for this thesis, they also indicate how competition is localized and, therefore, indicate which combinations of products provide some degree of local monopoly power. This information is important since one of the central hypotheses of the empirical study of product choice is that firms have incentives to choose products which provide local monopoly power. 3.2 Tests of Product Association This section is presented in order to lend some support to the assertion that firms' selections of products are not fundamentally random. There are, in fact, significant associations between certain combinations of products. These can be illustrated by con-ducting a simple \ 2 test for the independence of two products. First, a contigency table is constructed illustrating the presence or absence of two products in each firm's portfolio of products as in Table 3.1. The term N indicates the total number of firms while a indicates the number of firms which produce both products 1 and 2. The terms in the other cells are similarly defined. Recall that if the two variables were completely independent then the value of any cell would equal the product of its marginal values divided by the total number of observations (eg. the expected value of a is (a 6)(a + c)/(a + b + c + d)). Let Oij be the number of observations in the cell in row i and column j and let be the number of observations that would be expected in that cell if the variables were independent. Recall that the statistic for a %2 test of independence with 1 degree of freedom is given by the following formula. Note that a "continuity correction factor" (ie. 1/2) is used since there is only one degree of freedom. Chapter 3. Data Requirements and Sources 26 Table 3.1: Contingency Table for Independence/Association Product 1 Product 2 Present A b s e n t Present a b a + b Absent C d c + d a + c b + d N = a + b + c + d 2 f f ( f a - ^ l - i ) ' i = ij= i The calculated value of the statistic is compared with the critical value of a \ 2 distri-bution (ie. P(x2 > 3.84) = 0.05) to determine if there is a significant reason to reject the null hypothesis that the products are independent. The results of using this procedure to analyse the production of concentrates in 1962, for example, are presented in Table 3.2. The data sources for this test are discussed in Section 3.4 along with the other data sources for the thesis. Only those values that are significant at the 10% level or less are included. The results that are significant at the 5% level are indicated with an asterisk, *, while those that are significant at 1% are indicated with a double asterisk, **. Although it is not indicated by the \ 2 values each of the combinations which have a significant association are positively associated. This suggests that firms do not choose one line of products to the exclusion of another but that they merely have different like-lihoods of producing certain combinations. Also note that DDT shows little association with most other products, reflecting the popularity of the product at that time. Most firms sold DDT concentrate in addition to the other products in their portfolios. Chapter 3. Data Requirements and Sources Table 3.2: %2 Test of Independence/Association: Concentrates (1962) TOX PAR MPA MAL HEP END DIE DDT CHL ALD 3.98" 3.54 5.93" 9.53" 9.53" 3.21 CHL 7.70"" 5.05" 5.11" DDT DIE 6.72*" 6.62* 13.4" END 6.72** 22.6*" 6.72*" HEP 7.69" MAL 5.44" 9.72*" 2.76 MPA 2.76 PAR 5.44" key: ALD Aldrin HEP Heptachlor CHL Chlordane MAL Malathion DDT DDT MPA Methyl-Parathion DIE Dieldrin PAR Parathion END Endrin TOX Toxaphene Chapter 3. Data Requirements and Sources 28 Figure 3.1: Association of Insecticide Concentrates (1962) The associations indicated by Table 3.2 can be roughly illustrated using the inverse of the x2 value as a Euclidean measure of distance between the products as in Figure 3.1. Some mention is made of this technique by Goldsmith et ol. (1986). A high degree of association between two products (ie. a high x2 value) is indicated by a small distance between the products. Increased distances reflect lower significance and are drawn less exactly. Note that Figure 3.1 does not represent a three-dimensional diagram but merely overlapping measures of interproduct "distances". Note that some products which are closely associated such as Methyl-Parathion (MPA) and Endrin (END) have very different chemical structures. Others, such as Aldrin (ALD) and Dieldrin (DIE) are almost identical chemicals. This suggests that the chemical relations between the insecticides are not the only factors that influence which goods are produced together. As mentioned earlier, the pursuit of local monopoly power is also hypothesized to influence product choice. Following sections of this chapter out-line the requirements for the use of characteristics theory to determine how competition is localized, the data sources, and the procedure for constructing a market opportunity Chapter 3. Data Requirements and Sources 29 frontier. 3.3 Data Requirements for the Application of Characteristics Theory This section discusses the conditions that are required for the application of the characteristics approach to the study of insecticides. The principal requirement is that the characteristics should represent a general consensus of opinion regarding which of the products' attributes are important. Examples in which the characteristics are completely agreed upon occur when the product is only specified in terms of these characteristics (eg. the only information that is relevant to the choice of chemical fertilizers is their content of nitrogen, phosphorus, and potash, eg. 10-15-10). To determine which characteristics are generally considered to be important by the users of insecticides it is necessary to refer to the literature of the chemical and agri-cultural industries. By far the most commonly mentioned attribute considered in the industry literature is, of course, the insecticide's ability to kill insects1. Another com-monly mentioned concern has been the toxicity of the insecticide to humans. Finally, persistence is also considered to be of some importance in the selection of insecticides. In addition to agreement about the characteristic, there must be some consensus about how it is measured or categorized. This consensus of opinion regarding the choice of characteristics and their measurement can be checked by studying industry beliefs and, in particular, the industry literature. Studies on the toxicity to insects have been carried out on a variety of species, the most frequently used being the common house fly (Musca domestica L.)(Kuhr and Dorough 1976, Metcalf 1972). Similar studies on the toxicity of insecticides to mammals use the laboratory rat as the most common test organism (Metcalf 1972). The method of testing which is most commonly used to determine toxicity of a chemi-cal to insects is by topical application2. The insecticide is dissolved in a constant amount 1 This may not be as much of a forgone conclusion as it first appears. Plapp (1981) puzzled why other measures (eg. the ratio of toxicities to insects and mammals) are never used, instead of just the toxicity to insects. 2 A good summary of the procedures used for testing toxicity to insects and mammals is given by Chapter 3. Data Requirements and Sources 30 of relatively nontoxic solvent and applied to the insect's body. The dosage of the in-secticide is measured in micrograms of chemical per gram of the insect's body weight. By assuming that the insect population possesses a normally distributed threshold of susceptibility to the insecticide, the percentage mortality which results from each dosage is treated as a value in the cumulative normal distribution. This percentage is then con-verted into the corresponding value of the standardized random variable, Z, and plotted against the log of dosage to yield a straight line. Matsumura (1985) pointed out that the log of the dosage is used because many biochemical and physiological reactions increase in relation to the proportional change in the stimulus not to the amount of the change. Of course, since the insects exhibit a susceptibility which is normally distributed across the log of the insecticide dosage, the dosage which is lethal to fifty-percent of the popula-tion, LD50, is the value which can be most accurately determined and is also the dosage at which most insects possess a susceptibility threshold. The testing procedure for rats is very similar except they are most commonly sub-jected to an oral dose of the insecticide. Studies are generally conducted using oral inges-tion of the chemical because it is expected to be the most common manner in which people are exposed to insecticides other than through occupational exposure (Matsumura,1985). The pesticides are generally mixed with the animal's food, administered in capsule form, or by stomach tube. Another procedure, acute dermal toxicity, is commonly used to de-termine hazards to industry workers. This involves application of the pesticide dissolved in a solvent to a shaved area of the animal's skin. Irrespective of the testing procedure used, the relationship between dosage (measured in grams of chemical per kilogram of the animal's body weight) and percentage mortality is determined in the same manner as for the insects. Again, the LD50 value is most commonly reported. It may be interesting to note that some efforts have been made in the pesticide liter-ature to interpret the ratios of insect and mammal LD50 values. The testing procedures used were the same as those outlined above (ie. topical doses for houseflies and oral Matsumura (1985). Chapter 3. Data Requirements and Sources 31 doses for the rats). Winteringham (1969) pointed out that minor variations in the struc-ture of compounds, within a chemical group may yield strikingly different insect/mammal selectivities. The lack of correlation between the chemical structures, and therefore pro-duction processes, and the characteristics provided is important in the empirical section of this thesis. It will provide the possibility of distinguishing whether the choice of prod-ucts reflects the pursuit of local monopoly power or the benefits of joint production of goods with similar production processes. Plapp(1981) reviewed the same "selectivity ratios" and commented on the lack of correlation between the ratios and the popularity of each insecticide. Although neither author may have realized it, Winteringham and Plapp made implicit use of ideas which are fundamental to characteristics theory. Plapp, in particular, implied that products are valued for agreed upon characteristics. Unfortu-nately, neither author took the additional step of including prices to reveal the amounts of characteristics that are available for a given expenditure. Although commonly mentioned in a somewhat vague context, the persistence of in-secticides has also been an important consideration in the selection of products. Greater persistence provides a larger total exposure, the actual characteristic of interest, to a kilo-gram of an insecticide. A more persistent chemical allows a single application to provide a greater duration of insect control but also subjects man and the environment to a greater chance of coming into contact with the chemical. While some users of insecticides may not willingly alter their demands due to environmental considerations, legislation may place restrictions on the conditions and timing of some pesticide applications thereby producing similar effects on demand. The most commonly used measure of persistence is the half-life, ti, of an insecticide. The use of this measure is based upon the observation that pesticides in the environment generally degrade by a constant proportion per unit time. Unfortunately, some chemicals may not have precisely constant rates of decay. In these cases, approximate "half-lives" are calculated by determining the time required for dissipation of half of the insecticide when it was applied at a normal rate. The principal environment that has been used in studies of persistence has been the Chapter 3. Data Requirements and Sources 32 soil (Kuhr and Dorough, 1976) since it is a major recipient of chemicals which have missed the foliage, been washed off, or have been used to combat soil insects. Since soil type may affect the degree to which a chemical is exposed to environmental influences, most studies are based on the loam and sandy loam soils used in temperate agriculture. The only other characteristic which the industry literature appears to make any ref-erence to is the phototoxicity of the insecticides. In almost every case, however, the only information provided is that the chemical is not harmful to plants at normal rates of application. Thus, insecticides are compared in the industry literature using only three charac-teristics, toxicity to insects, toxicity to mammals and persistence. Furthermore, there appears to be a general consensus that toxicity is measured by LD50 values and that per-sistence is measured by the insecticide's half-life in soil. The additional restrictions that are discussed in the following paragraphs must also be met in order that characteristics theory can be used to determine how competition is localized. These conditions allow for the construction of a convex market opportunity frontier which indicates which products are in direct competition. Recall that Archibald and Rosenbluth (1975) developed the term "market opportunity frontier" to describe the combinations of characteristics that cannot be purchased for less than the entire budget. To serve as an objective indicator of how competition is localized, the market opportunity frontier must not be affected by such things as the quantity demanded of a product by any one agent. For instance, if a farmer were to purchase a quantity of an insecticide that significantly influenced that product's price then that farmer would face a different market opportunity frontier than other individuals. The differences in the market opportunity frontiers may indicate differ-ences in how competition is localized and, therefore, the use of any one frontier would not completely describe the combinations of goods that would allow local monopoly power. There is an implicit assumption in this application of characteristics theory, as is the case in much of traditional economic analysis, that the quantity demanded by a firm purchasing an insecticide does not alter the price. In other words, the firms purchasing the insecticides are essentially price takers. This requires that that each expenditure Chapter 3. Data Requirements and Sources 33 on the products is sufficiently small that it does not influence their prices or, following Archibald and Rosenbluth (1975), that the total quantity demanded is greater than the minimum efficient scale of production (ie. there must be no significant cost repercussions due to choice of quantity). Since the production of an insecticide involves few fixed costs (ie. it is undertaken on a small scale and many of the production facilities have alternate uses) and since insecticides are primarily used by a large number of small firms (eg. farms) it suggests that it is reasonable to assume that prices are not affected by the quantity demanded by any one firm. Although it is not a requirement for the use of characteristics theory, the approach will generally only simplify the analysis if there are more goods than characteristics. Otherwise the dimensionality can be reduced by leaving the analysis in goods space. Since there are only three potentially relevant characteristics mentioned in the literature, and since these three are used to describe twenty-three products3, dimensionality is greatly reduced by doing the analysis in characteristics space. Many uses of the characteristics approach, such as this thesis, require that further conditions hold. These conditions are sufficient to ensure the convexity of the market opportunity frontier which is used to determine the "neighbour relations" outlined by Archibald and Rosenbluth (1975). These relations, in turn, are used to determine how competition is localized. The required restrictions are that the characteristics be additive and that the goods be divisible and subject to costless combinability. Although products may be represented by characteristics which are objectively mea-surable but nonadditive (eg. colour)4, the convexity of the frontier can not be determined across these dimensions. Similarly, if products are not divisible and their prices are large relative to the budget constraint, it won't be possible to generate convex combinations of the products. If there is a significant cost to combining the goods (eg. two products may be available only in stores that are distant from one another) there may be uncer-tainty about the neighbour relations and thus about the extent to which competition is 3lsodrin was never introduced and neighbour relations could not be determined for Carbaryl. 4Refer to Lipsey and Rosenbluth (1971) for a discussion on the use of qualitative variables. Chapter 3. Data Requirements and Sources 34 localized. Since the principal use that will be made of characteristics theory will be to determine how competition is localized, agreement on additive characteristics as well as divisibility and costless combinability of the products are all required for this analysis. The only restrictions on the objective functions of those purchasing the products are that the functions be defined over some or all of the characteristics of interest and that they are locally nonsatiable. Since the analysis is not concerned with knowing which products are purchased by any particular firm there are no concavity requirements on the objective functions. The following sections list the data sources and discuss the transformations that are required for their use in constructing a market opportunity frontier. 3.4 Data Sources This section discusses the data sources used in this thesis and refers the reader to the appropriate appendices for any sources which are too lengthy to be contained in this chapter. First, in order to make it perfectly clear which products are being discussed, refer to Appendix A for a list of the common and chemical5 names of the twenty-five insecticides that will be compared in a characteristics framework. Incomplete information on some of these products will result in only twenty-three of them being used in the analysis. This appendix also lists the chemical group to which each insecticide belongs. Since the principal purpose of this thesis is to determine the influences on a firm's choice of products, information is required on the identity of the firms that introduced or produced the insecticides. The identity of the firm which was granted the patent for a particular product, and the year in which it was granted, is available from Worthing (1987). Information on the production of insecticides is available in The Pesticide Hand-book (Entoma) (annual) which lists the concentrates and formulations produced by each firm in the American insecticide industry during each year. The production of concen-trates is analysed every five years between 1952 and 1982 inclusive (1956 is used instead 5 The nomenclature is based upon the rules of the International Union of Pure and Applied Chemistry (IUPAC) as cited by Worthing (1987). Chapter 3. Data Requirements and Sources 35 of 1957 due to unavailability of data). The production of formulations is analysed every ten years during the same period. Finally, the dates when pesticides were suspended or cancelled are also given in The Pesticide Handbook. Recall that the investigation of the pursuit of local monopoly power as a possible influence on product choice will be done by constructing a market opportunity frontier. Naturally, this requires information on the characteristics and prices of all products. Refer to Appendix B for a complete listing of all data on the characteristics of insecticides, with their sources listed at the end of the appendix. Original sources are used whenever possible and any data from summary articles are clearly indicated. Results listed as inequalities or ranges are not used. The data reported in three papers (out of 113) are not used since they differ by several orders of magnitude from all other sources. These articles are by Marsh and Eden (1955), Oliver and Eden (1955), and by Sun and Johnson (1960). The characteristics data that are used have some shortcomings as well. For instance, no information is available on the toxicity of rotenone to the house fly (Musca domestica L.) so data on its toxicity to the milkweed bug (Oncopeltus faciatus) are used instead. Another problem is that the rapid breakdown of allethrin, pyrethrum, and rotenone limit their use as soil insecticides and therefore their half-lives on exposure to sunlight and air are used as measures of their persistence. Finally, two insecticides, Aldrin and Heptachlor, have by-products, Dieldrin and Hep-tachlor Epoxide respectively, which are also highly toxic. The overall persistence (ie. expected life) of the insecticides is approximated by the sum of the expected lives of each separately. The combined toxicity to insects is determined by taking a weighted mean of the toxicities of each product. Each chemical's relative contribution to overall persistence is used as its weighting in combining the toxic effects. The same procedure is used to determine the overall toxicity of the insecticides, and their by-products, to mammals. The insecticide prices used in the construction of the market opportunity frontiers are based upon weekly price quotations recorded in the newspaper, The Chemical Marketing Reporter (weekly). Yearly averages of these price quotations were calculated and are also Chapter 3. Data Requirements and Sources 36 available in a summary publication of the newspaper, Chemical Pricing Patterns (1966), and in the U.S. Department of Agriculture publication, The Pesticide Review (annual). The quantities and values, and the calculated unit values, of annual sales of a few of the products can be found in a publication of the U.S. Tariff Commission, Synthetic Organic Chemicals (annual), and correspond well with the yearly averages of prices from The Chemical Marketing Reporter. Refer to Appendix C for a list of the prices used in the analysis. Recall that predictions about the neighbour relations, and hence the localization of competition, of products on the market opportunity frontier requires that they can be combined at little or no cost. Products are assumed to be costlessly combinable if they can be" used in a "tank mix" (ie. they merely have to be stirred together and do not produce chemical, physical, or biological incompatabilities). Information on the compatibility of such combinations of insecticides is gathered from the Farm Chemicals Handbook (annual) and from a publication of the Canadian Agricultural Chemicals Association, the Pesticide Safety Handbook (1965). Thus, the characteristics and prices of the insecticides can be used to construct a market opportunity frontier for each year of the study period (ie. 1944 to 1987). These illustrate the combinations of characteristics that cannot be purchased for less than the entire budget. Archibald and Rosenbluth (1975) pointed out that if all convex combinations of the characteristics offered by two products are on the market opportunity frontier (ie. the products are "neighbours" on the frontier) then these goods are in direct competition and have some degree of local monopoly power over particular combinations of characteristics. This information is of interest since it is the pursuit of local monopoly power which is hypothesized to be one of the influences determining which firms are likely to introduce or produce which products. 3.5 Construction of a Market Opportunity Frontier This section outlines the procedure used to construct market opportunity frontiers to describe the market for insecticides. Recall that the industry literature listed toxicity to insects, toxicity to mammals and Chapter 3. Data Requirements and Sources 37 persistence as the only relevant characteristics of insecticides. Also recall that persistence is measured by the half-life of the insecticide and that the toxicity is measured by an LD50 value indicating the dosage that is lethal to 50% of the subject population. To convert LD50 values into a form which may be used in characteristics space, it is necessary to transform the variable so that it can be measured in an additive manner. This is done in such a way that more of the good results in a greater quantity of the characteristic (ie. a larger population of insects or mammals is placed in danger). The amount of characteristic i which is available from one unit of good j (ie. b;j), is measured by taking the reciprocal of the LD50 value as in equation 3.1. 1 1 insects ( 3 1 ) B - = ID— 1 = L U ^ i [ 2 mammals LD 5oij Median lethal dosage of insecticide j to subject i This provides a measure of the mass of either insects or mammals which potentially may be subjected to a 50% chance of mortality by one kilogram of the chemical. The total amount of characteristic i that is available from a quantity, Xj, of a particular good is given in equation 3.2. (3.2) Z i j = bijXj Zij Mass of subject i that is endangered by insecticide j Since the possible purchases of insecticide j are subject to a budget constraint, k, the total amount of characteristic i which is available for a given expenditure is given by equation 3.3. (3.3) = Pj PjLD50ij Pj Price of insecticide j Chapter 3. Data Requirements and Sources 38 The frontier can be normalized to represent the amount of each characteristic which is available per dollar by dividing each term by the budget constraint (equation 3.4). (3.4) ^ = 1 k pjLD50ij Equation 3.4 measures the subject mass which potentially may face a 50% chance of mortality from a one dollar expenditure on the insecticide. Of course, this measure of toxicity is additive, making it possible to predict that all. goods are priced on the frontier in these dimensions. The total exposure to one kilogram of an insecticide, 63^ , is related to the half-life by equation 3.5. (3.5) 63J = ^ b3j Total exposure (measured in kilogram days) to one kilogram of insecticide j (ti)j Half-life of insecticide j The total exposure to an insecticide will also depend upon the quantity of the product that is available under a budget constraint, k. Again, the measure can be normalized to yield the total exposure that is available for one dollar's worth of the insecticide (equation 3.6). It can also be predicted that goods are priced on the frontier in this dimension since the total exposure is an additive measure. (3.6) f « = M . • z3j Total exposure generated from one unit of insecticide j Pj Price of insecticide j Costless combinability is the final condition which is used in determining if the mar-ket opportunity frontier is convex. The best indicator of whether two insecticides are Chapter 3. Data Requirements and Sources 39 costlessly combinable is that they are approved as a "tank mix". In other words, com-bining the insecticides only requires that the two chemicals be stirred together in the sprayer tank and will not result in any chemical, physical or biological incompatibility. Of the twenty-three insecticides used in the analysis, data was available from the Farm Chemicals Handbook (annual) on the combinability of eighteen of the products. All 153 combinations of these insecticides are approved as "tank mixes". On this evidence it is concluded that there are no significant costs to combining any of the products. At this point, enough information is available to draw a market opportunity frontier. As an example, Figure 3.2 shows the frontier in 1957. Similarly, frontiers are constructed for each year of the study period (ie. 1944 to 1987). Since the objective functions are assumed to be locally nonsatiable, the products are costlessly combinable, and the characteristics are additive, characteristics theory predicts that all of the products are be priced so that they appear on the market opportunity frontier. This prediction will be checked in the following chapter. 3.6 Conclusion This chapter presented results which indicate that firms do not choose products in-dependently of one another. It also listed the sources of data used in this thesis and mentioned how the measures of the characteristics were constructed and how the pub-lished data could be used to construct additive characteristics. This conclusion serves as the basis for the investigation of whether characteristics theory predicts any other influences on product choice. The chapter then discussed the requirements for any use of characteristics theory (ie. consensus about characteristics and their measurement) and for the construction of convex market opportunity frontiers (ie. additive characteristics and goods which are divisible and costlessly combinable). Information of the prices and characteristics of each product was then used to construct market opportunity frontiers for each year of the analysis. Chapter 3. Data Requirements and Sources 40 Persistence..kg.days of exposure/I Mammals...l000s kgs. at 50% risk/$ Insects...1000s k*s. at 50% risk/$ Figure 3.2: The Market Opportunity Frontier (1957) Chapter 4 Predictions of Characteristics Theory 4.1 Introduction The principal objective of this chapter is to investigate the predictions of character-istics theory. These include the prediction that divisible and combinable products with additive characteristics are priced to appear on a convex market opportunity frontier. Confirmation of this prediction provides greater justification for this application of the characteristics approach and is the first empirical support for the theory. The chapter also undertakes the first use of characteristics theory to determine the implicit prices of characteristics. The procedure is fundamentally different from hedonic price analysis since there is no requirement for a large number of differentiated products and empirical estimation is not required. Predictions are also made about bounds on the possible prices of goods for which price data are not available. These are based upon a good's charac-teristics mix and the prices and characteristics of other goods. Finally, it is determined which products are neighbours on the market opportunity frontiers. This knowledge of how competition is localized serves as the basis for empirical tests to determine the influence of the pursuit of local monopoly power on product choice. 4.2 Demand for Insecticides The characteristics approach suggests that the demand for insecticides is derived from the use of their inherent characteristics as inputs in agricultural or horticultural production functions. Diverse production technologies, fi(Z), are allowed for and are only subject to the restrictions that they depend upon one or more of the characteristics and that they are locally nonsatiable. Each firm i (eg. a farmer) demanding insecticides 41 Chapter 4. Predictions of Characteristics Theory 42 is assumed to solve the optimization problem given by equation 4.1. In other words, a farmer is assumed to choose a vector of insecticide quantities, X, in order to minimize the cost of achieving a given level of output, . This is somewhat more complex than a normal cost minimization problem since the production function, fi(Z),. is defined in terms of the insecticides'characteristics. The characteristics that are available from the chosen insecticides are indicated by the relation Z = BX. Z = BX (4.1) mmP'X s.t. X fi(Z) > q ; Z an (rxl) vector of characteristics X an (nxl) vector of inputs (ie. insecticides) B an (rxn) matrix of elements indicating the amount of each characteristic provided per unit of each input P an (nxl) vector of input prices ql the quantity of output of firm i The solution vector, X?, has at most r non-zero elements with their values dependent upon the prices of these goods. If the insecticides are divisible and costlessly combinable with additive and objectively measurable characteristics then these elements represent insecticides which are neighbours on a convex market opportunity frontier. Recall that Archibald and Rosenbluth (1975) defined the market opportunity frontier to be the com-binations of characteristics that are available for some budget and requiring the entire budget. A convex combination of the characteristics offered by nonneighbouring products would yield a point within the frontier. This is not optimal since points on the frontier provide greater amounts of the characteristics for the same budget. Similarly, a farmer will only purchase an insecticide if it offers a combination of characteristics that is on the frontier. Thus, zero sales are expected of any insecticide which does not appear on the frontier. This prediction that products are only purchased if they appear on a convex market opportunity frontier is one of the main implications of the use of characteristics Chapter 4. Predictions of Characteristics Theory 43 Z2 Figure 4.1: Testing the Predictions of Characteristics Theory theory. The following section of this chapter outlines a procedure to test the prediction and also presents the results of this analysis. 4.3 Pricing of Products on the Market Opportunity Frontier The principal prediction that arises when characteristics theory is applied to divisible and combinable products with additive characteristics is that all of the products are expected to be priced to appear on a convex market opportunity frontier. If it does not hold it would suggest that characteristics theory is invalid (or that the characteristics chosen are not appropriate for this analysis). The intuition of how the prediction is tested can be illustrated with an example in which a number of goods (eg. A,...E) offer varying amount of two characteristics, Zj and Z2, for some budget (Figure 4.1). A pair of products are used to construct a line illustrating all convex and non-convex combinations of the characteristics they offer (eg. line bd formed by B and D). If all other products (ie. A,C, and E) offer less of the characteristics per dollar than points on the line that preserve the same ratios of characteristics (ie. A',C, and E'), then the Chapter 4. Predictions of Characteristics Theory 44 products used to construct the line (ie. B and D) are on the convex market opportunity-frontier. What is more, these products are neighbours on the frontier. In other words, all combinations of characteristics between the ratios defined by B and D are most inexpensively supplied by using only these two products. This procedure is repeated by checking every product against the lines constructed by all possible pairs of products. If all products appear on the convex frontier then the prediction of characteristics theory is upheld. The procedure that was outlined is easily generalized to the three characteristics case used in this thesis1. The second step involved in checking the validity of the characteristics approach re-quires determining which of the products being considered could potentially be priced too high to be on the market opportunity frontier (ie. they offer combinations of char-acteristics that are within the frontier). At this point it may simplify the discussion by defining the "edge of a market opportunity frontier" to be the points on the frontier which offer the most extreme ratios of characteristics. For instance, the edge of the fron-tier in Figure 4.1 is composed of the two points on the frontier defined by products A and E. Products on the edges of the market opportunity frontier (ie. A and E) could not be within the frontier regardless of their price levels and must be distinguished from those goods which potentially are able to exclude themselves from the market by pricing themselves within the frontier. To see this, imagine that product A has a higher price than in Figure 4.1. This would be indicated by a contraction along its ray from the origin. Regardless of the extent of its price rise, product A would always appear on the frontier. The only difference would be that the slope of facet AB may change at higher prices of A. In contrast to the previous scenerio, imagine that product B has a higher price than in Figure 4.1. Again, this would be indicated by a contraction along its ray from the origin. In this case, however, a sufficiently high price of B would cause it to 1In general, if r characteristics are used to describe a number of products in a characteristics space, each group of r goods can be used to define an r-1 dimensional hyperplane which represents all convex and non-convex combinations of the characteristics provided by these r goods for some budget. If all other goods offer combinations of characteristics which lie within a half-space defined by this supporting hyperplane, the r products which lie on the hyperplane are neighbours on the market opportunity frontier. If each product that is checked appears on the market opportunity frontier at least once, it can be concluded that these products form a convex frontier. Chapter 4. Predictions of Characteristics Theory 45 be dominated by a convex combination of A and D. Thus, products that are not on the edge of the frontier (eg. B) could be priced so high that they appear within the frontier. Observations of the prices of products which can not be within the frontier do not lend support to the predictions of characteristics theory (ie. they could not contradict the theory) and therefore are excluded from the analysis. Therefore, an important point that is required for the test results to lend support to the characteristics approach is that some observations are not on the edge of the frontier when the products are defined by all their relevant characteristics. The failure of Lancaster (1971) to distinguish between products which could or could not contradict the theory when the products were denned by all the characteristics listed is one of the principal reason why his analysis does not lend empirical support to the characteristics approach. The completed check of the prediction that all products are priced on the frontier is conducted separately for each year of the study (ie. 44 years in total). The test involves a total of fifteen insecticides described by three inherent characteristics. Data exist on the characteristics of an additional ten insecticides but there is no information on their prices so they are not included in this portion of the analysis. The results from each year indicate the number of products which have the potential of not being on the market opportunity frontier, the number that actually are not on the frontier, and the relative price that the latter would require to reach the frontier. A test of the prediction may reveal that some products appear not to be on the frontier making it is necessary to know whether they lie significantly within it. Although there is no exact rule about what amount of deviation would be acceptable, a number of products which are substantially within the frontier would create some doubt about the validity of the chosen characteristics and about the applicability of the characteristics approach. Since there are no other commonly mentioned attributes in the literature, the only alternative would be to adopt different proxies for the characteristics or to abandon this use of characteristics theory. On the other hand, a minor deviation from the frontier may be possible if there were a slight cost to combining products or if there were errors in the measurement of the characteristics but would not necessarily invalidate the use of Chapter 4. Predictions of Characteristics Theory 46 Z2 0 Figure 4.2: A Product Priced Within the Frontier the characteristics approach. The measurement of the degree to which a product lies within the market opportunity frontier is based upon the percentage of the current price that would be required to achieve the frontier. The extent to which a product (eg. C in Figure 4.2) lies within a convex frontier can be measured by the comparing the characteristics provided by a dollar's expenditure on a product (ie. OC) with the amounts that would be necessary to reach the frontier (ie. OC). The ratio O C / O C indicates the relative price, in comparison to the existing price, that would be required for the product to appear on the frontier. Recall that products on the edges of the frontier (ie. A and E) could not he within the frontier even at very high prices. Refer to Appendix D for each year's list of the products which form the facets on the characteristics frontiers and the characteristics prices that are generated by each facet. It also lists any products which lie within the frontier and the relative price that they would require to reach the frontier. As an example, in 1955 Endrin (product 15) was within the convex frontier. If it had reduced its price to 68 percent of its current level (ie. OC/OC) it would have neighboured Aldrin (2), Dieldrin (12) and Parathion (22) on Chapter 4. Predictions of Characteristics Theory 47 Table 4.1: Products Within the Frontier Chemical Within the Frontier (Potential) (Observed) Mean Degree Within (1 - P C / P C ) Aldrin Chlordane Dieldrin Endrin Heptachlor Lindane Malathion Methyl-Parathion 29 0 38 0 28 0 29 28 29 0 33 0 30 0 31 0 0.248 Total 247 28 the frontier. Note that in fifteen years of the study all products are priced on the market opportunity frontier. Table 4.1 indicates that in the 44 year study period there were 247 incidents in which products could have been priced high enough to lie within the market opportunity frontier. Cf these, 28 incidents actually occurred, all of which were due to Endrin. The reductions in prices that are required for Endrin to reach the frontier are illustrated in Figure 4.3. The persistence of the cases involving Endrin might suggest that there has been an error in the measurement of the product's characteristics. Other explanations are possible (eg. advertising, errors in optimization or a fourth characteristic) but the persistence with which the product is within the frontier and the absence of any indication in the literature of a fourth characteristic would suggest that measurement error is the most plausible explanation. The next section of this thesis will calculate the measurement errors that would be required for a market opportunity frontier with all products actually priced on the frontier to show the observed irregularities. The possibility of measurement error of the characteristics is investigated by consider-ing the minimum deviation from the reported values of the characteristics that would be required for all products to be on the market opportunity frontier. These hypothesized Chapter 4. Predictions of Characteristics Theory 48 Price 50-Reduction (%) 40-30-20-10-0 55 60 65 70 75 80 Y e a r Figure 4.3: Price Reductions for Endrin to Reach the Frontier "measurement errors" are defined as a proportion of the recorded values to facilitate comparison of the different insecticides. This is because the amount of a characteristic that is inherent in various insecticides may differ by as much as six orders of magni-tude. As an example, the half-life of Pyrethrum is approximately 0.0025 days (ie. about four minutes) while Isodrin has a half-life of approximately 1900 days (ie. about five years). If the measurement errors of these two products are comparable they must be measured as proportions of the recorded values and not as quantities. Refer to Appendix B for further evidence about the heterogeneity of the insecticides. Additional justification for the assumption of a proportional measurement error is provided by the observation (Matsumura, 1985) that the susceptibility of insects and mammals to insecticides is ap-proximately normally distributed across proportional increases in dosage. Furthermore, the measure of the persistence of insecticides (ie. a half-life) is based on a geometric decay rate in which it is the rate of decay that is actually estimated (ie. the constant proportion of the products that dissipates per unit time). Thus, the possibility that measurement error can be compared if treated as proportions of the recorded reflects the initial approaches to measuring the characteristics. Chapter 4. Predictions of Characteristics Theory 49 For simplicity, proportionate measurement errors are hypothesized to occur in only one characteristic. Each characteristic is examined in turn to determine if it could account for Endrin appearing within the frontier. Note that the true minimum deviations that would be required for all products to be on the frontier will necessarily be less than or equal to the minimum deviations that would be required in any one characteristic. Therefore, the procedure that is used is very conservative and is more likely to reject the possibility that measurement error could account for a product appearing to be within the frontier. Determining the minimum deviations that would be required for all products to be on the frontier is undertaken by minimizing the sum of squared deviations between the products and a hypothetical frontier containing all of the products (ie. In Figure 4.4, the products B, C, and D are compared with the hypothetical frontier AbcdE). Note that only the product within the frontier and the products forming the facet which it would intersect (ie. B and D) need to be considered. A simple linear regression is run with these products to determine the deviations that would be required for all products to be on the frontier. The data are then adjusted by the residuals, ej, which minimized the sum of squared disturbances. This, in effect, creates a frontier which contains all products and lists measurement errors which could cause the observed placement of products. The test is run three times for each year of the study, each time assuming a measure-ment error in a different characteristic. The true minimum sum of squared disturbance must be less than or equal to the smallest of the sum of squared residuals from the tests, J2i ei- (ie- The test results place upper bounds on the possible minimum sum of squared disturbances needed for all products to be on the frontier.) Note that in the case of per-sistence the residuals are measured as the proportion of the recorded value. In the other two cases a residual is a proportion of the "true" (adjusted) value of the characteristic. This is done to allow the error terms to be compared with the proportionate variance of the untransformed toxicity variables (ie. the LD50 values). Varian (1985) proposed that the statistic S in Equation 4.2 has a chi-squared distri-bution. Chapter 4. Predictions of Characteristics Theory 50 Figure 4.4: Measurement Error in Z\ (4.2) S = Sum of Squared Residuals e\ Variance of the Data a2 Note that Varian expressed some concern that this form of the statistic might be of limited use in economic analysis since the appropriate data are rarely reported with their standard deviations. This thesis, however, is able to make use of the statistic since most insecticides have a number of measures of their characteristics reported. The tests that are conducted have the assumption that all products are on the frontier. In order to reduce the chance of falsely attributing any observations off the frontier to measurement error, the null hypotheses are that measurement errors of the characteristics could not account for the observed positions of the products in characteristics space. The alternative hypotheses are, of course, that the measurement errors could account for the observations. In order to reject the null hypotheses it is necessary to show that the required "errors" (ie. ej) are smaller than would be expected considering the variance , <r2, of the data. Note that the variance is estimated by defining each observation to be the difference between the reported value of a characteristic and the value of Chapter 4. Predictions of Characteristics Theory 51 that characteristic that is used (ie. the mean) measured as a proportion of the mean. The alternative of finding the estimated variance for each product and then using these "sample" values to determine some overall estimate of the variance results in even greater values and thus a greater probability of accepting the hypothesis of measurement error. The critical value of the chi-squared test with fifteen degrees of freedom which gives a probability of 95% that it is exceeded is 7.26. The critical value at the 99% level is 5.23. A calculated value of S which is less than these critical values would reject the null hypothesis. Table 4.2 lists the largest values of the "measurement errors" from any of the yearly repetitions of the tests. They indicate that it is possible to accept (ie. not reject) the hypothesis that error in the measurement of toxicity to mammals could not cause the observations. Note that the critical value of the chi-squared test which gives a probability of 5% that it is exceeded is 25.0. Thus, even a null hypothesis with a much greater probability of attributing the observations to measurement error (ie. HQ\ measurement error of the toxicity to mammals could account for the observations) would be rejected. Returning to the original hypotheses, note that it is possible to reject the hypotheses that errors in the measurement of toxicity to insects or of persistence could not account for the observed positions of Endrin. Thus, the null hypotheses are rejected and the alternative hypotheses (ie. Hi: Measurement errors could account for the observations) are accepted. Although the tests can not be used to determine if the observations are actually caused by measurement errors, they do indicate that measurement error is a possibility that would explain the results. Varian also proposed that equation 4.2 could be rearranged to yield the critical value of the standard deviation of the data, cra=5%, that would be required to reject the hypothesis. Refer to Table 4.2 again to note that the critical values of the standard deviations that could allow for all products to be actually on the frontier are well within the observed standard deviations of the data. Furthermore, measurement error of the toxicity to insects could account for the observations with the smallest standard deviation of the (4.3) Critical Value of Standard Deviation = <ra=5% = Chapter 4. Predictions of Characteristics Theory 52 Table 4.2: Proportional Changes for Convexity Chemical Mammals Insects Persistence Dieldrin -0.114 0.003 Endrin 1.110 -0.130 -0.307 Heptachlor -0.058 0.146 0.1580 Lindane -0.037 0.0263 0.0459 Methyl- P arathion 0.0294 -0.0004 s>? 1.250 0.040 0.121 o 0.167 0.163 0.276 s 44.814 1.497 1.593 0.415 0.074 0.129 data (ie. 0.074 rather than 0.129). All subsequent work is based upon the hypothesis that there are errors in measurement of the chemicals' toxicity to insects. It is felt that this is more probable than an error in the measurement of persistence since the toxicity of Endrin is only based upon one observation (persistence is based upon three) and smaller measurement errors could account for the products within the frontier. In addition to the prediction that all products are priced on the market opportunity frontier, characteristics theory can also be used to determine the implicit prices of char-acteristics. This procedure and its results are explored in the following section of this chapter. 4.4 Prices of Characteristics Recall that a market opportunity frontier is composed of a number of facets rep-resenting convex combinations of products which are neighbours on the frontier. This section of the thesis is concerned with calculating the implicit prices of characteristics on each of these facets. In addition to any direct value of knowing the prices of toxicity to insects or of persistence these prices also allow bounds to be placed on the possible prices of products for which the market prices are not known. In the case that is studied, there is information Chapter 4. Predictions of Characteristics Theory 53 available on the prices and characteristics of fifteen of the most common insecticides but only on characteristics of the ten next most common. If the insecticides which have known prices are on a convex frontier, convexity will be imposed on the remaining products in an effort to determine their neighbour relations. Although this is not the primary concern of this thesis, the calculation of implicit prices of characteristics may be considered to be of some value in providing an alter-native to hedonic price analysis. These calculations do not require the large number of differentiated products that are needed for hedonic price analysis, the procedure can be used with divisible and combinable products and there is no need for statistical estimation of the prices. The calculation of the implicit prices of characteristics for each facet of the market op-portunity frontier is undertaken in the following manner. The (rxn) matrix that Gorman (1956/1980) used to represent the relationships between products and the characteristics they embody (ie. matrix B in equation 4.4) is only square in a trivial case. If the matrix B were square it would allow a one-to-one correspondence between characteristics and goods. This would make it possible to relate the prices of characteristics and goods in a manner that is directly derived from the relations between goods and their characteris-tics. Note that equation 4.4 corresponds to the simplified model outlined by Lancaster (1966) in which there is a one-to-one correspondence between goods and activities. (4.4) Z = BX Z is an (rxl) vector of characteristics z; X is an (nxl) vector of goods Xj B is an (rxn) matrix with elements bij which give the amount of characteristic Zi per unit of the good Xj Following Archibald and Rosenbluth (1975) it is assumed that there are no occurrences of "oligopolistic instability" in which an infinitely small change in price would alter the neighbour relations of products on the frontier. The authors observed that under these conditions the number of neighbouring products which form each facet of the market Chapter 4. Predictions of Characteristics Theory 54 opportunity frontier will necessarily be the same as the number of relevant characteristics, r. This observation forms the basis for using a square (rxr) submatrix of B (ie. Bj) to specify the relationship between goods forming a facet, / , and the characteristics they supply, Zf, as written in equation 4.5. (4.5) Zf = BfXf Zf is an (rxl) vector of characteristics Zfi Xf is an (rxl) vector of neighbouring goods Xfj Bj is an (rxr) matrix of elements bfij which give the amount of characteristic Zfi per unit of the good Xfj The products forming a facet are subject to the same budget constraint, k, whether they are specified in characteristics space or in goods space (equation 4.6). (4.6) X'fPf = k = Z'fQf Pf is an (rx 1) vector of prices pj of the products which form facet / Qf is an (rxl) vector of imputed prices qfi which holds along the facet Rewriting this budget constraint using the relationship between the goods and char-acteristics yields X'fPf = k = X'fB'fQf . Cancelling X'f allows the vector of prices of the characteristics, Qf, to be related to the vector of product prices, Pf, by equation 4.7. (4.7) Qf=B'f'Pf Although Lipsey and Rosenbluth (1971) and Lucas (1975) did point out that it should be possible to determine the prices of characteristics on each facet, the actual calculations have never been carried out before. In addition to their benefit in determining the neighbour relations of products with unknown prices, any fluctuations in the implicit Chapter 4. Predictions of Characteristics Theory 55 prices over the study period can be used to give some indication of broad trends in the relative valuations of the three characteristics. These prices do not allow a more precise measure of changes in the overall valuations of the characteristics since quantity weighted price indices of the characteristics would require information that is not available for these products. Refer to Table 4.3 for a list of the implicit prices of toxicity to mammals, toxicity to insects and persistence for each facet of the frontier during one year of the study, 1957. Appendix D contains a complete listing of implicit prices of characteristics for each facet of each year's frontier The implicit prices show that, in almost all positive price is attached to toxicity to insects and a negative price is associated with toxicity to mammals. The prices for persistence of insecticides do not appear to be exclusively positive or negative. These observations confirm casual reasoning about the desirability of each characteristic. In particular, it could be imagined that persistent insecticides would be desired at the beginning of the agricultural year or in cases in which they do not come in contact with people. Less persistent chemicals may be desired just prior to produce being taken to market or in cases where the chemicals must be applied where they may come in contact with people. It may be interesting to note that one facet which has a price of toxicity to mam-mals which does not correspond to predictions (ie. Allethrin/Pyrethrum/Rotenone) may reflect the high value that was placed on the products being the most shortlived com-bination available rather than any desire to harm mammals. This makes the ratio of the characteristics very close to zero and allows a small error to change the signs of the prices of the characteristics. In particular, the relative price of toxicity to mammals in comparison to persistence (ie. -0.0041 ($/l0OOkg.)(kg.days/ $) ) is so close to zero that it is conceivable that the ratio is actually positive and therefore the price of toxicity to mammals is positive. Similarly, the Chlordane/DDT/Methoxychlor combination is the most persistent and the implicit prices may reveal more about the concern for persistence than for the chemicals' ability to kill the insects on a single exposure. The wide variation of the implicit prices of the characteristics reflect the differences Chapter 4. Predictions of Characteristics Theory 56 Table 4.3: Prices of Characteristics (1957) Toxicity Products Forming a (US$/biomass at 50% risk) Persistence Facet of the Frontier Mammals Insects (US$/kg.day) (1000's kg.) (lOOOOO's kg.) Aldrin/Chlordane/DDT -0.401 0.660 0.00955 Aldrin / C hlordane / Dieldrin -0.618 1.15 0.00662 Aldrin / D D T / Toxaphene -0.0416 0.218 0.00302 Aldrin/Dieldrin/Parathion -0.0227 0.690 -0.0122 Aldrin/Parathion/Toxaphene 0.019 0.158 0.00149 Allethrin/Lindane/Malathion -42.2 130. -6.39 Allethrin/Lindane/Methoxychlor -270. 451. -5.12 Allethrin / Malat hion / Methyl- Parathion -8.21 83.8 -108. Allethrin / Methyl- P arathion / Rotenone -6.31 83.2 -249. Allethrin / Pyrethrum / Rotenone 58.2 194. -14200 Chlor dane / D D T / Methoxy chlor -29.5 -5.17 0.652 Chlordane /Dieldrin / Methoxy chlor -13.2 19.9 -0.0199 Dieldrin/Lindane/Methoxy chlor -17.7 28.8 -0.135 Dieldrin/Lindane/Methyl-Parathion -0.271 2.86 -0.0983 Dieldrin/Methyl-Parathion/Parathion -0.0250 0.720 -0.0135 Lindane/Malathion/Methyl-Parathion -1.25 11.4 -0.779 Methyl- P arathion /Parathion / Rotenone 3.64 -28.6 -21.6 Chapter 4. Predictions of Characteristics Theory 57 in the amounts of characteristics that are offered by the various facets. Since each combination of goods is on the frontier at the given prices, it still offers more of a particular ratio of characteristics for every dollar than any other group. Perhaps the greatest significance of Table 4.3 is that it indicates that firms differ in their valuation of insecticide characteristics by at least three orders of magnitude. This suggests that any attempt at aggregation to create some form of "representative consumer" of these products is highly unrealistic. In other words, a price increase in one product would imply that a representative consumer would purchase greater quantities of all substitutes. The implicit prices paid for characteristics on each facet of the frontier suggest that the same price increase would be expected to affect only the purchases of products on the same facets of the frontier. As an example, an increase in the price of only the most short-lived insecticide is not expected to increase the sales of the most persistent chemicals since purchasing both products would imply considerably different valuations of the characteristics. Although a representative consumer would purchase some amount of every product, the purchase of certain combinations of goods suggest valuations of characteristics which are completely inconsistent with the purchase of certain other goods. In order to more easily see how the prices of a characteristics vary over time the maximum, minimum and mean implicit prices of the toxicity to insects are illustrated in Figure 4.5. Note that the two facets with negative prices for toxicity to insects have not been included. The diagram shows that the maximum price that was paid throughout the 1950s and 1960s to potentially kill half of a 100 000 kg. biomass of insects was approximately US$500. The price rose to $2000 by the mid-1980s. The minimum price underwent considerably more fluctuations during these periods. In particular, the sharp decline in prices in the mid 1960s may reflect increasing environmental concern about these products (ie. DDT, Toxaphene, and Aldrin) before the use of Aldrin and DDT was restricted in the early 1970s. It is difficult to distinguish the reasons for the price increases during the 1970s since restrictions were placed on the use of a number of the insecticides during this period and price of petroleum, an important source of feedstock for much of the chemical industry, also rose dramatically. Also note that the relative stability of Chapter 4. Predictions of Characteristics Theory 58 •••to 8 3 >' 2l YEAR LEGEND tUxirnupn Price 4e»p Prie« ; *iftwiv.»n.?rif«.. Figure 4.5: Implicit Price of Toxicity to Insects (current) prices prior to the 1970s indicate a decline in the real price of insecticides. Rather than looking at all facets of the frontier, Figure 4.6 gives the implicit prices that are paid for the characteristics by someone choosing a combination of Aldrin, Chlordane and DDT. The price of persistence (ie. the effects of exposure to one kilogram of the insecticide for a day) was multiplied by one hundred to allow it to be plotted on the same graph. It is therefore the price paid for the effects of one kilogram of the insecticide for one hundred days. Prices of toxicities to insects and mammals are the amounts paid to subject 100 000 kg. or 1000 kg. biomasses respectively to a 50% probability of mortality. The introduction of new products during the 1950s and 1960s resulted in the Aldrin/Chlordane/DDT combination being increasingly valued for its ability to kill insects rather than for its persistent effects. Again, note the relative decline in the prices paid for persistence of this combination during the mid 1960s. However, as the uses of these and other products were restricted during the early 1970s more was paid for their value as being some of the most persistent insecticides available. As can be seen, the use of the characteristics approach to calculate the prices of the characteristics is particularly valuable since no information is needed about the amount Chapter 4. Predictions of Characteristics Theory 59 LEGEND Persistence fx 100) TTpxjcity to Insects "5.9 jr© 1 1 1 1 i t ,9» I960 IMS 1970 1*79 IMO Year « • Figure 4.6: Prices on Aldrin/Chlordane/DDT Facet spent on the products, the quantities of goods involved, or the nature of the objective functions. The only requirement of the objective functions is that they be locally non-satiable. Surprisingly, however, this procedure appears to have never been used for the actual calculation of characteristics' prices. The use of characteristics theory is distinctly different from hedonic price analysis as popularized by authors such as Griliches (1961, 1971) and Rosen (1974), since no value is placed upon consuming quantities of goods other than the value that is derived from consuming their inherent characteristics. There is also no need for a very large number of indivisible differentiated products and no need for empirical estimation with its associated problems. In one sense this use of the characteristics approach complements hedonic price analysis since it requires divisible and combinable products while hedonic analysis assumes indivisible and noncombinable products. To this point, it has been shown that there is empirical support for the prediction that products are priced to appear on a convex market opportunity frontier. It has also been shown how to calculate the implicit prices of the characteristics on the frontier. These two pieces of information provide some indication of the bounds on the possible Chapter 4. Predictions of Characteristics Theory 60 prices of other products. This procedure will be explored in the following section. 4.5 Bounds on Possible Prices of Products The principal reason for determining the implicit prices of characteristics is to deter-mine the neighbour relations of products with unknown prices. This procedure is based upon finding bounds on the possible prices of goods for which the market prices are not known. Although neighbour relations are easily determined if there are two relevant char-acteristics, a simple two characteristics example is used to illustrate how predictions are made about the possible bounds of unknown prices. The results of equivalent predictions of possible prices in the three-characteristics case are also presented in this section. In a two-characteristics example, a product with an unknown price (eg. D in Figure 4.7) may offer a convex combination of the characteristics of two products forming a facet of the frontier (eg. B and C). If this is so, then there is an upper bound on the price of D, Pfj, that would allow it to remain on a convex frontier (ie. not excluded by a convex combination of B and C). Similarly, if all products are to be on the frontier, a convex combination of D and A cannot exclude B from the frontier. Therefore, Pp is a lower bound on the possible price of D. In three dimensions, an existing facet of the market opportunity frontier also places upper bounds on the prices of products which offer the appropriate ratio of characteristics (ie. the product can not lie within the frontier). The implicit prices on the facet are used to determine the price that is necessary for a product, D, to be on the existing frontier as in equation 4.8. (4.8) Pp = Q'FBD P2 is the price of product D required to bring it to the plane of facet / Q'f is the transposed (rxl) vector of implicit prices BD is the (rxl) vector of elements bn> representing the amount of characteristic i generated by one unit of product D Chapter 4. Predictions of Characteristics Theory 61 Figure 4.7: Bounds on Possible Prices The calculated value for the price of D can be thought of as the sum of the values of the characteristics it embodies. The unit values of the characteristics are determined by their implicit prices on the facet ABC (ie. Qj). The term P£, is an upper bound of the possible price of D (ie. Pp < Pp) if D offers the same ratio of characteristics as a convex combination of the products on the facet. Equation 4.9 merely states that product D offers an amount of each characteristic per dollar (ie. bio/Pf)) that is the same convex combination of the amounts offered by the other products (ie. sibiA/PA-\- s2biB/PB +(l — 3i ~ s2)bicIPc^i — l--r,s.t.O < Si,S2 < 1). This ensures that D is on the same plane as the facet ABC and is in the interior of the facet. This triangular region is analogous to the Une segment BC in the two characteristics case. Chapter 4. Predictions of Characteristics Theory 62 BT^BD 0 < S j < 1 (4.9) S = - ^ - s.t. ~ 3 ~ j = A,B,C S is an (rxl) vector of elements Sj j = A,B,C Bfp is an (rxr) matrix of elements bij/Pj j = A,B,C representing the amounts of characteristic i available for one dollar's worth of product j The facet also provides information on the lower bounds on prices for part of the area surrounding it. An existing element of the facet may offer the same characteristics as a convex combination of D and the other elements of the facet (ie. equation 4.10). This is analogous to equation 4.9 but D forms one of the corners of the facet while one of A, B or C is on the same plane but in the interior of the facet. In this case, the price of D that is calculated using the facet's implicit prices of characteristics provides a lower bound on the actual price (ie. Pp > Pf)). This, however, only provides information on products which are located in areas equivalent to the shaded regions in Figure 4.8 if the facet ABC were on the frontier. In general, an n-dimensional space will have lower bounds on the prices of products within n flat-sided (n-l)-dimensional cones2 originating from the corners of each facet. BnlBA 0 < Sj < 1 (4.10) 5 = - ^ s.t. ~ ° - j = B,C,D F a Hi Si = I Br>p is an (rxr) matrix of elements bij/Pj j = B,C, D BA is an (rxl) vector of elements The reason that the plane formed by the facet ABC forms a lower bound on the price of product D only if D is in the shaded regions can be seen with two examples. First, imagine that D is located in one of the shaded regions of Figure 4.8 (eg. in the one 2 T h e set 5 is a cone with a. vertex x, x £ S if Vj/ 6 5 and VA > 0 it holds that (1 — \)x + \y 6 S. Chapter 4. Predictions of Characteristics Theory 63 Figure 4.8: Regions with Lower Bounds on Pp nearest to C) and that the page represents the plane formed by the products A, B and C. A reduction in PD means that the product provides greater amounts of the characteristic for the same budget. Therefore, if the origin is beneath the page, the product D rises above the page. This means that a convex combination of the products most distant from D (ie. A and B) can be combined with D to dominate product C (ie. provide more characteristic for some budget). This, however, violates the prediction that all products are priced on the frontier. Therefore D can not rise above the page (ie: the region imposes a lower bound on Pp. The unshaded regions do not impose the same restrictions on the price of D. To see this, imagine that D is located next to the segment AB. A reduction in Pr> causes it to rise above the page. This time, a convex combination of C (or combinations of A, B and C) can only dominate points along the segment AB and points in the interior of the facet. However, there are no predictions concerning the convex combinations of the products. Therefore, there is no reason these combinations can not be dominated and no restriction on Po when D is outside of the shaded regions. Chapter 4. Predictions of Characteristics Theory 64 It may be interesting to note that equivalent facets in cases of three or more char-acteristics impose restrictions on prices in fifty percent of the surrounding region (if the facet is small relative to the region considered). This can be seen in three dimensions by noting that the lines which define one of the cones (ie. shaded regions) on the plane of the facet also define an equivalent region which includes the facet and the region extending beyond the side opposite the intersection of the lines. Recall that the region beyond the facet is unshaded to indicate that it does not impose any restriction on Pp. If the size of the facet is very small relative to the region considered, perhaps specified by a radial distance from the intersection of the lines, then the area imposing a restriction on PD is approximately equal to the area which does not. These observations can be repeated for every corner of the facet to indicate that a total of 50% of the area places a restriction on PD. A similar procedure can be used to demonstrate that this value holds in higher dimensions as well. Although each facet forms lower bounds on 50% of their surrounding region the total area with this restriction may be all of the region if there are any points (ie. products) which are not on the edge of the frontier. Recall that the term "points which are not on the edge of the frontier" is used in reference to products such as B in Figure 4.7 (ie. not A or C) and should not be confused with products that are priced within the frontier. Each product on the frontier is part of more than one facet. In turn, each facet generates a cone which imposes bounds on the prices of other products in a region (ie.cone) with an angle equivalent to the inside angle of the facet at that point. Note that these angles can be projected onto an arbitrary plane which supports the frontier at that point and that the sum of the inside angles of triangles covering the area around the point must be 360°. If the product is not on the edge of the frontier then the sum of the angles of the projections of the shaded regions (ie. imposing lower bounds on PD) derived from all the facets touching that point must equal 360°. Therefore, all of the region surrounding that point places restrictions on the lower bounds of prices. Unfortunately, two features prevent bounds being calculated for the price of every product. First, the shaded regions of a point that is not on the edge of the frontier may not intersect with the ray from the Chapter 4. Predictions of Characteristics Theory 65 / D/ Figure 4.9: Lower Bounds: C on the Edge of the Frontier origin representing the product with the unknown price. This may take place if one of the characteristics has a negative value. The second feature is that although products on the edge of the frontier may impose lower bounds on a part of the remaining region they do not impose bounds on all of it. This can be seen in Figure 4.9 where two facets ABC and BCD are positioned so that the line segments AC and CD are on the edge of the frontier. Note that the shaded regions again indicate the areas which impose a lower bound on the possible prices of another product and that they do not cover all of the surrounding region. When lower, or upper and lower, restrictions on prices are calculated, it is assumed that the product's actual price is just slightly greater than the highest lower bound. If only upper restrictions are calculated for the prices, it is assumed that the actual price is somewhat less than the smallest upper bound. All products, including those for which the prices have just been calculated, are then used to determine the neighbour relations. This procedure is identical to the method used to determine that all products are on the market opportunity frontier except that it is noted which combinations of products form facets on the frontier. Chapter 4. Predictions of Characteristics Theory 66 The predicted bounds on the prices are listed in Appendix E. Some of the bounds do not impose severe restrictions on the possible prices of goods. As an example, the 1957 price of Azinphos-Methyl must have been greater than 0.30 US$/lb. for all products to be on a convex frontier. However, other predictions are somewhat stronger as can be seen by the prediction that the 1957 price of Heptachlor must have been between 0.81 and 1.48 US$/lb. When the price was known the following year it was 0.90 US$/lb. Note that the bounds could not be calculated for the price of Carbaryl and that Isodrin was never introduced. The procedure that was just outlined gives an indication of the possible prices of a total of eight additional products. This means that twenty-three products can now be located relative to one another on the market opportunity frontier. These neighbour relations of products on the frontier are hypothesized to influence the probability of these products being introduced, or produced, by the same firm. 4.6 Localized Competition Recall that the empirical section of this thesis requires information about how com-petition was localized among different products in the market for insecticides. Archibald and Rosenbluth (1975) pointed out that competition is restricted to be between products which neighbour one another on facets of a convex market opportunity frontier (ie. all convex combinations of the products are also on the frontier). This greatly simplifies any analysis of similar products by allowing any study of the pursuit of local monopoly power to concentrate on the interactions of products which neighbour one another on the frontier. The procedure that is used to determine whether all products are priced to be on the market opportunity frontier is repeated to find out which products neighbour one another. Each combination of three products is again used to generate a plane in charac-teristics space. If no other good offers a combination of characteristics that is beyond that which is provided by the plane, then the original three products must be on the frontier. Chapter 4. Predictions of Characteristics Theory 67 What is more, they must neighbour one another on a facet of the frontier. This proce-dure is repeated for all possible combinations of three products, in a three-dimensionsal characteristics space, and for each year of the study. As an example of the findings, in 1957 Chlordane neighboured five products of the nineteen used to construct the frontier. It is hypothesized that firms producing the five products (ie. Aldrin, Chlorthion, DDT, Dieldrin, and Methoxychlor) have greater incentives to produce Chlordane than firms producing other products. Estimations are conducted of the extent to which this potential for local monopoly power as well as other product interactions (eg. cost advantages from producing chemically similar products) influence the probability of producing certain combinations of goods. Distinguishing the pursuit of local monopoly power from the effects of cost advantages of certain combinations of products requires that there is an incomplete correlation be-tween the products which are neighbours on the frontier and those which are chemically similar. As an example, the degree to which these variables are associated is determined for the data used to estimate the influences on the introduction of new products. The data consists of 221 observations of product pairs of which 114 pairs are neither neigh-bouring nor chemically similar while 59 pairs are neighbouring but not chemically similar. Of the chemically similar pairs, 22 are not neighbouring while 26 are neighbouring. These figures are summarized in the Table 4.4. Recall that if the two variables were completely independent then the value of any cell would equal the product of its marginal values divided by the total number of observa-tions. In other words, if the neighbour relations and chemical similarity of products were independent, the expected number of observations that would be neither neighbouring nor chemically similar is 106.5 (ie. 173 x 136/221). Let Oij be the number of observations in the cell in row i and column j and let e^ -be the number of observations that would be expected in that cell if the variables were independent. Recall that the statistic for a %2 test of independence with 1 degree of freedom is given by Chapter 4. Predictions of Characteristics Theory 68 Neighbouring Chemically Similar Yes No Yes 26 22 48 No 59 114 173 85 136 221 Table 4.4: Association between Neighbouring/Chemically Similar Products i = l j = l eij The calculated value of this statistic is 5.5. It is not possible to reject the hypothesis of independence of the variables at the 99% confidence level (ie. P{x\ > 6.63) = 0.01). However, it is possible to reject independence at the 95% confidence level (ie. P(xl > 3.84) = 0.05). Since the neighbour relations and chemical similarity of products are not independent and since there does not appear to be an actual test for association (ie. one that could reject th^ hypothesis that they are perfectly associated) some measure of their association is required. Yule's Coefficient of Colligation is used since it allows an intuitive interpretation of the measure in terms of the ability of one variable to predict or represent the other. The coefficient and it interpretation are outlined by Kendall and Stuart (1977). Yule's Coefficient of Colligation, Y, is calculated with the following formula: The measure indicates the relative reduction in the probability of prediction error produced by knowledge of the category of the other variable. Since the calculated value Chapter 4. Predictions of Characteristics Theory 69 of this measure is 0.204 it indicates that the knowledge of one of the variables only leads to a 20% reduction in the error of predicting the other. Note that this value is approximately the same as the value of the measure of association that was proposed by Kendall and Stuart (1977) (ie. 0.170). Thus, although the neighbour relations and the chemical similarity of the insecticides are not independent, it still should be possible to distinguish the effects of these two influences. 4.7 Conclusion This chapter outlined a procedure to check the validity of using the characteristics approach. This was done by checking its principle prediction, that all goods are priced to appear on a convex market opportunity frontier. It was shown that the prediction held during fifteen years of the study period. In other terms, of 247 instances in which products could be priced within the frontier (and therefore would contradict the prediction) only twenty-eight instances occurred, all of which were due to one product. Furthermore, using Varian's (1985) non-parametric estimation technique it was shown that the contradictions to the theory could be accounted for by measurement error of the characteristics. Next, it was shown how to calculate the implicit prices of the characteristics. This is the first time that characteristics theory has been used to calculate these prices and the results correspond well to intuition about the values of the characteristics. The implicit prices of characteristics were used to determine the approximate prices of other products in an effort to determine their neighbour relations on the market opportunity frontier. In addition to the fifteen products for which price data are available another eight products could be located on the market opportunity frontier because of the predicted bounds on their prices. Finally, the construction of the market opportunity frontier allowed the determination of neighbour relations of a total of twenty-three products. These neighbour relations were also shown to be not completely associated with another hypothesized influence on product choice (ie. the chemical similarity of products). A model is developed in the following chapter to more formally indicate the effects of these relations on the probability Chapter 4. Predictions of Characteristics Theory that a firm will produce certain combinations of products. Chapter 5 Product Choice: A Model 5.1 Introduction The purpose of this chapter is to provide some theoretical foundations for the hy-potheses that are checked in the empirical section of this thesis. It is not meant to provide a major contribution to the thesis but merely to indicate plausible reasons for observing certain patterns of product choice. A number of simple mathematical models are constructed to indicate which combina-tions of products are likely to be produced by the same firm. The models are based upon the idea that all existing products have some influence on which firm actually introduces a new product. These influences are studied by determining which relationships between certain combinations of products increase the probability that these goods are introduced by the same firm. As an example, imagine that a new product is introduced into a market in which firms generally produce goods which are neighbours on the market opportunity frontier. It seems natural to predict that the firm which made the introduction is one of the firms which introduced the product's neighbours. This chapter is composed of two parts. In the first, a model is constructed to de-termine the connection between various product relationships and the profitability of producing these combinations of goods. Propositions are presented which maintain that a product yields greater profits to a firm producing a neighbouring good than it would yield to another firm. This is due to the local monopoly power that the firm gains over particular combinations of characteristics. Other propositions are presented, which main-tain that a reduction in the marginal cost of a product increases its own profits and reduces the equilibrium profits of all other products. Such changes in production costs are hypothesized to be caused by the joint production of chemically similar products. 71 Chapter 5. Product Choice: A Model 72 The second part of the chapter presents a model which relates the profitability of producing a product to the equilibrium probability that a firm will introduce it. This is done by noting the profits that would accrue to various firms if the product were discovered by either themselves or other firms and relating these profits to the equilibrium research effort of each firm. It is found that firms which would receive greater profits from a good, or have more effective research effort, also have a higher probability of introducing the product. In total, the chapter attempts to relate how the connections or relationships between products affect the probability of a firm producing certain product combinations. The relative importance of the various influences (ie. the pursuit of local monopoly power or cost advantages from producing certain product combinations) will be empirically determined in the next chapter. 5.2 Product Interactions and Profitability The hypothesis that a product yields greater profits to a firm which produces a good which neighbours it on the market opportunity frontier or which provides a cost advantage is investigated in this section of the thesis. The model is based upon the approach used by Dixit (1986) to obtain comparative statics results for oligopolies. The application of this approach to a system of asymmetric interrelated demands of more than two products is greatly simplified by the localized competition predicted by characteristics theory. Admittedly, some of the concepts used by both Dixit and this analysis (eg. conjectures1, reaction functions, stability) have little basis in a model with no time dependence. How-ever, the lack of dynamic models, or more general static models, which could be effec-tively applied to oligopolies limits this model to the use of these somewhat inappropriate methods. 1Concerns about the use of conjectural variations do not detract from the analysis since most results hold under Bertrand assumptions. Chapter 5. Product Choice: A Model 73 Figure 5.1: Market Opportunity Frontier of the Model 5.2.1 Local Monopoly Power This section presents four cases. These cases are used to determine how the prof-itability of a product varies according to which other products are produced by the same firm. In particular, does a product yield greater profits when produced by the same firm as a neighbouring good or by the same firm as a nonneighbouring good. It is assumed that there are three products, 1, 2, and 3, which offer different ratios of two relevant characteristics as in Figure 5.1. Imagine that three firms are interested in producing product 1. The only difference between the firms is that one is not producing any other products in the market, one is producing a neighbouring product (ie. 2), and one is producing a nonneighbouring product (ie. 3). The objective of this analysis is to determine which of the three firms would receive the greatest profits from producing product 1. Recall that the derived demands for these products are generated by each firm, i, with a production function which depends upon these characteristics, fi(z1,z2), as it solves the optimization problem given by equation 5.1. This amounts to the selection of inputs such as insecticides in order to minimize the costs of achieving the chosen output level Chapter 5. Product Choice: A Model 74 such as agricultural production. Z' = BX-(5.1) minP'Xi s.t. "~ i = l,2...N X' U{Zi)>q: Z is a (2x1) vector of characteristics used by firm i X is a (3x1) vector of inputs (eg. insecticides) purchased by firm i B is a (2x3) matrix of elements indicating the amount of each characteristic provided by each input P is a (3x1) vector of input prices q± is the quantity of output of firm i In this case the solution vector, X?, has at most 2 non-zero elements with their values dependent upon the prices of these goods. In general, if there are r relevant characteristics each firm chooses, at most, r inputs in quantities greater than zero. Recall that if the inputs (eg. insecticides) are divisible and costlessly combinable and if the characteristics are additive and objectively measurable then the inputs that are chosen are neighbours on a convex market opportunity frontier. A firm will never combine nonneighbouring products2 (ie. 1 and 3) since their combination would be within the frontier and could be improved upon by a combination of products 1 and 2 or 2 and 3. In other words, each firm's solution vector can only take one of these five possible forms3. 0 0 x}(P\P2) 0 0 or a?(Pa) or 0 or z?(P\P2) or * a (P a ,P s ) 0 0 *f(P3) 0 xf (P a ,P» ) The market-wide demand of any one of the products is determined by aggregating over every firm's derived demand for that product (ie. Qi = J^iLi xl j = 1> 2, 3). Obviously, 2 This analysis refers to the joint use of nonneighbouring products and not to their purchase. It may be possible to observe a firm purchasing nonneighbouring products if the firm employs more than one production process. 3Clearly, a firm could also choose to consume none of the products in this market. Chapter 5. Product Choice: A Model 75 this implies that the quantity demanded of a product is a function of its price and the prices of its neighbouring products (ie. Q\Pl, P2),Q2(P1, P2, P3), and Q3{P2,P3)). General functional forms are used since linearity is unrealistic and does not simplify the analysis or change the results. This will be illustrated more clearly in later sections of this analysis. Downward sloping demand functions result in the following inequalities (using sub-scripts to denote partial derivatives). (5.2) Q\<0, Q22<0, Ql<0 Since the products offer different amounts of the same characteristics (ie. they are substitutes) the following inequalities hold. (5.3) Ql>0, Ql>0, Ql>0, Q32>0 However, note that localization of competition implies that the price of one product does not directly influence the quantity demanded of nonadjacent products (ie. Q\ = o, Ql = o). Let Ci(Qi) be the cost of production of product j and CQ((5j) be the correspond-ing marginal costs. It is initially assumed that there is no cost advantage from joint production of the insecticides (ie. C^(Q\ Qj) = C^Q1) + Cj(Qj) f j). The firms producing the products are assumed to undertake competition in prices. Furthermore, it is believed that these firms form expectations or conjectures about the effects of their pricing decisions on the prices of other products. In particular, the "conjec-tural variation" term, denotes an expectation formed by the firm producing product i: It is the expectation of the change in the choice of the price of product j if there was a change in the choice of the price of i as in equation 5.4. dPj (5.4) ^(P\P^) = J p r i,j = 1,2,3 i^j Objections to the use of conjectural variations do not detract from most of the results of this chapter. Such objections can be allowed for by assuming Nash conjectures (ie. vji = 0). Chapter 5. Product Choice: A Model 76 Q3 Figure 5.2: Demand for Product 3 Note that much of this analysis is similar to other analyses of competition among oligopolists with differentiated products. However, there are some important differences. First, the use of characteristics theory results in the prediction that demand is localized (ie. Q\ — 0, Q\ = 0). Another difference is that a drop in the price of a product may force other goods within the market opportunity frontier. If a product were excluded from the market it would cause a jump in the quantitity demanded of the neighbouring products that remain. Thus, the demand curves may have plateaus similar to the demand for product 3 represented by the dotted line in Figure 5.2. Note that this ignores the conjectured response of other firms to a change in the price of a product. If a firm expects the producers of neighbouring goods to choose lower prices whenever the firm lowers the price of its product (ie. v13 > 0) then the "demand curve" for product 3 that is perceived by the firm is represented by the thin solid line in Figure 5.2 when the current price is P3'. Depending upon the values of the conjectures the possibility of a jump in demand is either ehminated or takes place at lower prices. Finally, the actual choices of other prices under' alternative values of Pz results in Chapter 5. Product Choice: A Model 77 an equilibrium quantity of product 3 represented by the thick solid line in Figure 5.2 when Pz" is the current price. Any jump in the actual quantity demanded only takes place if product 2 is priced at its average variable cost (ie. its AVC curve and demand curve are tangent). At any higher price product 2 would reduce its price rather than face the outcome of being within the frontier and having its sales drop to zero. Again, the possibility of a jump in the demand for product 3 is either eliminated or occurs at a price that is low enough to force product 2 to price at its average variable cost. Note that this possibility of excluding others from a market by the choice of price is not necessarily in contradiction to Archibald and Rosenbluth's (1975) claim that it is not possible, since they were obviously considering products with similar lower bounds on their prices. However, there is no reason to believe that such bounds should be similar for different products especially since the consumers of the products base their decisions on the characteristics available for some budget and various insecticides offer amounts of characteristics that differ by several orders of magnitude. At this point, it is necessary to determine whether the jumps in demand, which characteristics theory allows for, cause significantly different results from other systems of interrelated demands. Obviously, the effects of these plateaus depend upon whether the current price is above or below their levels. If the current price is above the plateau a comparative statics result which would normally indicate a decline in price is even more likely to suggest such a decline. On the other hand, a result indicating an increase in price would be unaffected by these plateaus. If the current price were below the plateau a comparative statics result indicating a decrease in price would also be unaffected. However, a result indicating an increase in price would be less likely to actually be to the firm's advantage. Note that these effects may occur whether a firm is controlling one product or several. This explanation can be put in another way. The existence of any discrete jumps in the quantity demand for a product may alter the profitability of that product and therefore the effort that all firms would undertake to introduce it. In addition to this effect, a firm which, because of the other products in its portfolio, found it advantageous to decrease its price to just above the plateau, may now choose a Chapter 5. Product Choice: A Model 78 price slightly lower than the plateau to take advantage of the large increase in quantity demanded. Other firms which have higher optimal prices would not find such a price decrease advantageous. Thus, the following model, which does not allow for the discrete jumps in demand, is likely to overestimate a tendency to increase prices and underestimate a tendency to decrease prices. Results of the empirical section are therefore less likely to corroborate predictions that depend upon price increases (eg. incentives to produce neighbouring products). As was mentioned earlier, four cases are presented in this model. In the first case, each product is produced by a different firm. In the second, products 1 and 2 (ie. neighbouring products) are produced by one of the firms. In this case product 3 is produced by another firm. In the third case products 1 and 3 (ie. nonneighbouring products) are produced by one firm and product 2 is produced by another firm. Finally, the fourth case presents a general model which employs a parameter to capture the differences in the first two cases and, depending upon the conjectures, can encompass all three cases. The general case is used to show that each product yields higher profits in Case II (ie. one of the firms producing neighbouring products) than in Case I (ie. each good produced by a separate firm). Case II is related to Case III (ie. one firm producing nonneighbouring products) by noting that, if conjectural variations are equal to zero, Case III is equivalent to Case I. This is used to show that, at least under Nash conjectures, the production of a product yields greater profits to a firm which produces a neighbouring good than it would yield to a firm which produces a nonneighbouring good. Case I: Each product is produced by a different firm. Firms 1, 2 and 3, producing products 1, 2 and 3 respectively, solve the optimization problems given by equation 5.5. (5.5) max TT} = PiQi - C^Q1) 1 = 1,2,3 Chapter 5. Product Choice: A Model 79 If a firm were to take the partial derivative of 7r} with respect to Pl (ie. Trlu) it would not obtain what it perceives to be the entire effect of its price change on its profits. The discrepancy is due to the conjectures held by the firm about how the prices of neighbouring products are adjusted in response to a change in P%. Thus, firm i has a perceived "marginal profit" (with respect to prices) of fil(Pl, P-'...Pk) which depends upon the effect of its own price, 7r}-, as well as the conjectured price changes of all neighbouring products, ...vkl, and their effects upon product z's profits, 7r/j-.-7r}fc. fii(P\P^...Pk) = 7:iIl+Tiiyi + ...^Ikuki The firms attempt to maximize their expected profits by choosing prices which set their perceived marginal profits equal to zero as in equations 5.6, 5.7 and 5.8. f.o.c. (5.6) p\P\P2) = Q1 + (P1-C1Q)(Q{ + Qyi) = 0 (5.7) p\p\p>,p*) = Q 2 + ( P 2 - c2Q)(Q22 + qy2 + qy2) = 0 (5.8) p\P2, P3) = Q3 + (P3 - C3 )(Ql + Q\v2*) = 0 Note that these results encompass linear functional forms (ie. Q1 = b\ — b\Pi + b\P2i Q\ = b\), constant marginal costs (ie. CQ = c1) and Nash conjectures (ie. = 0) as special cases. Imposition of any or all of these special assumptions is not necessary since the first order conditions are already in a form which is most easily usable in later sections of the analysis. Second order conditions and stability conditions are explored in the general case (ie. Case IV). Assuming that an equilibrium exists the equilibrium prices are denoted as P J * , P J " , and Pj~. The corresponding equilibrium profits are represented as 7r}*,7r|Y, and 7 T 3 " . The general case refers to these equilibrium prices and profits and suggests how they relate to the corresponding equilibrium values from Case II and Case III. Chapter 5. Product Choice: A Model 80 Case II: In this case, products 1 and 2 are produced by the same firm. (3 is produced by another firm.) The firm producing 1 and 2 solves the following optimization problem: (5.9) maxir]'2 = P1Q1 + P2Q2-C1'2(Q\Q2) Recall that it is assumed there are no cost advantages from the joint production of two goods (ie. C1'2(Q1,Q2) = CL(QL) + C2(Q2)). The first order conditions are written as equations 5.10 and 5.11. f.o.c. (5.10) /x1 = Q' + (P1 - C^Ql + (P2 - C2)Ql = 0 (5.11) u2 = Q2 + (P2 - C2Q){Q22 + Q2^2) + (P 1 - Cl)Q\ = 0 The firm producing product 3 has the following optimization problem: (5.12) max K3H = P3Q3 - C3(Q3) The first order conditions are the same as those in Case I. f.o.c. (5.13) fx3 = Q3 + (P 3 - CQ)(QI + Q%v23) = 0 Again, the second order conditions and stability conditions are shown in the general case. As in Case I, linearity and the other restrictions are not required for subsequent analysis. Assuming that an equilbrium exists the equilibrium prices are represented as Ph, P?l and P//, and the corresponding profits as Tr}'2" and wfi. Case III: In this instance, products 1 and 3 are produced by the same firm. (Product 2 is produced by another firm.) Chapter 5. Product Choice: A Model 81 The firm producing 1 and 3 solves the optimization problem given by (5.14) generating the first order conditions in equations 5.15 and 5.16. (5.14) max = PlQl + P3Q3 - C\QX) - C 3(Q 3) f.o.c. (515) / i 1 = Q 1 4- {P1 - Cl){Q\ + Qy1) + (P 3 - C%)Qlvn = 0 (5.16) u 3 = Q3 + (P1 - C^qy3 + (P3 - Cl)(Ql + c-y*) = 0 The other firm, which produces product 2, has the following optimization problem: (5.17) max T T 2 I H = P2Q2 - C2(Q2) f.o.c. (5.18) u2 = Q2 + (P 2 - C2Q)(Q22 + Q2y2 + Qlu32) = 0 Once again, the second order conditions and stability conditions are reviewed in the general case. The equilibrium prices in this case are denoted as P}JJ,PJJJ and P 3//. The profits are designated as ir\ff and ir}^. Note that under Bertrand assumptions (ie. v13' = 0) the first order conditions and therefore the equilibrium prices and profits are the same in this case and in Case I. Case IV is utilized to compare the profits to corresponding profits in the previous two cases. This case contains Case I (ie. all products are produced by separate firms) and Case II (ie. one firm produces neighbouring products) as extremes depending upon the value of a parameter, 6. This parameter is merely used as a mathematical construct to provide continuity and encompass the previous three cases and intermediate possibil-ities. Continuity allows a general solution to the optimization problem. The parameter is used because comparison and interpretation of explicitly calculated levels of equilib-rium prices and profits is very difficult unless the outcomes are constructed as part of a more general model. For example, the explicit calculation of profit levels in even the Chapter 5. Product Choice: A Model 82 simplest of models (ie. three products with linear demands, constant marginal costs, and Bertrand assumptions) would result in the comparison of fractions containing sixth and seventh degree polynomials. The use of the parameter, 9, will allow comparative statics to indicate how the equilibrium prices and profits are related in Case I, II and III. Case IV: In this case each product is produced by a separate firm. A parameter, 6, is introduced to allow for differences in the optimizing behaviour in Case I and II. This case involves each product being produced by a separate firm as in Case I but with one difference. Expectations of how P1 and P2 are linked are constructed to be special cases of a more general model which includes the possibility of the firms responding to changes in each other's price in a way that mimics the effects of collusion between the firms (ie. first and second order conditions that are identical to those that would occur if one firm were producing both products). Suppose firm 1 believes that P2 is linked to P1 in a way that mimics the perceived marginal profit of product 1 under the joint profit maximization of products 1 and 2. Then firm 1 will believe that the total change in P2 must increase the profits of firm 1 as much as the change in P1 increased firm 2's profits (ie. nldP2 = Tr^dP1 or equivalently (P 1 - ClQ)Q\dP2 = (P2 - CDQldP1). In other words, firm 1 must believe that P2 is chosen so that firm 1 receives the entire benefit that an adjustment of its price yields either to itself or to firm 2. The responses, which mimic collusion, hold when the parameter, 6, equals one. Note that the anticipated responses of other firms are based upon the total derivatives of the prices. Therefore, the total amount that P2 must change in response to a change in P1 includes the conjectured responses of other prices. The conjectural variation term, v3%, will be used to describe conjectures about the changes in prices that mimic the collusive outcome. For values of 6 equal to zero the conjectural variation term (ie. v31) is intended to capture the noncollusive response of the other firm's price. Intermediate cases can be constructed by taking a convex combination of the previous Chapter 5. Product Choice: A Model 83 responses (ie. vn and v3%). As an example, the response of P2 to a change in P1 can be summarized in the following manner: dP2 _ dP~i ~ < ' (P2—C2)Q2 1 ) 2 1 = {pi-c\)Q\ w i t t l weighting 8 K »21 < {P^CJ]QQ\ w i t h weighting (1 - 8) Q ' Similarly, firm 2 assigns a weight 8 to the response of firm 1 that mimics collusion (ie. dP1 /dP2 — P12) and assigns a weight (1 — 8) to a smaller response by firm 1 (ie. dPi/dP2 = v12 < v12). The optimization problems of the three firms are the same as in Case I (ie. equation 5.5). Using the parameter, the first order conditions for maximizing the expected profits can be written as equations 5.19, 5.20 and 5.21. f.o.c. (5.19) p1 = Q1 + (Pl - ClQ) [Q\ + Q\ ((1 - &yi + 8v21)] = 0 (5.20) p2 =.Q2 + (P2 - C2) [Q\ + Q2y2 + Q\ ((1 - 8)u12 + 8ul2)\ =0 (5.21) p3 = Q3 + (P3 - C3) [Ql + Q\u23} = 0 Notice that the continuity provided by the parameter, 8, allows the calculation of general first (and second) order conditions which encompass the conditions of Cases I and II. If 8 is equal to zero the first order conditions are identical to the conditions in Case I (ie. goods produced by separate firms). If, however, 8 is equal to one then the first order conditions are the same, as in Case II (ie. a firm producing neighbouring products). It is difficult to directly compare the cases to Case III (ie. a firm producing nonneighbouring products) since the nonadjacency of products 1 and 3 complicates the relationships. Note that if the values of v21 and v12 are substituted into the first order conditions then they can be rewritten as equations 5.22, 5.23 and 5.24. Chapter 5. Product Choice: A Model 84 f.o.c. (5.22) u1 = Q1 + (P 1 - C7J) [Q\ + (1 - 0)Q^ 2 1 + 0 ( P 2 - C 2 ) Q 2 = O (5.23) / = Q2 + (P 2 - C3) [Ql + Q-y2 + (1 -6)Qy3] + 6(Pl - ClQ)Q\ = 0 (5.24) u3 = Q3 + (P 3 - C 3 ) [Ql + Q3y3} = 0 The second order conditions are rather lengthy so additional notation will be intro-duced. The terms refer to the partial derivative of fil with respect to the price of product j. Recall that \il is the perceived or expected "marginal profit" (with respect to Pl) of product i. The values of the terms /i*- for i,j = 1, 2, 3 are listed in equations 5.25 through 5.32. (5.25) p\ = 2Q\ + (P1 - C^Q], - ClQQQ\Q\ +(1 - 9) [Qlu21 + (P1 - ClQ){Q\2v21 + Q\vf) - C\qQy'Q\ +0 [(P2 - CQ)Q\\ - CQQQ\Q2\\ (5.26) nl = Ql + (P1 " ClQ)Q\2 - C\QQ\Q\ +(i - 9) [(P1 - c\ ){Q\yi + qy1) - c^Qy'Qi] +9 [Ql + (P2 - C2)Q2l2 - C2QQQlQl] (5.27) p\ = 9 [(P2 - C2Q)Q213 - C2QQlQl] Chapter 5. Product Choice: A Model 85 (5.28) nl = Ql + (P2 - c2Q)(q221 + Q>32) - c2QQ(Ql + Ql»32)Ql +(1 - 9) [(P2 - C2Q){QW2 + Q\u\2) - c2QQqy2q2\ +8 \Q\ + (P1 - CtfQl - C^QQIQ] (5.29) u\ = 2Q22 + qy2 + (P2 - c2)(q222 + q\y2 + qy2) - c2QQ(Q\ + qy2)q +(i - e) [qy2 + (P2 - c2Q){q\y2 + qy2) - c2QQqy2q +8 [(P1 - Cq)q\2 - cLQQq\q\\ (5.30) fil = Ql + (P2 - c2)(q223 + q\y2 + qy2) - c2QQ(q22 + qy2)q\ Hi-e){(p2-c2Q)qiy2-c2QQqy2q23} (5.3i) pi = Q\ + (P3 -c3)(ql2 + q\y3 + qy3) -c3QQ(ql + qy3)q32 (5.32)^ = 2q33 + qy3 + ( p 3 - c3)(<233 + q\y3 + qy3) -c3QQ(qi + qy3)q33 Note that p\ is equal to zero. The second order conditions for the maximization of profits by the firms depend upon the conjectures of how the other product's price is linked to their own. This is analogous to the first order conditions in which the perceived "marginal profit" included a term to indicate how its own price and the expected response of other prices would affect its profit. Again, it should be emphasized that the use of linear Chapter 5. Product Choice: A Model 86 functional forms and the elimination of conjectures may simplify some of the second order conditions but do not help with the comparison of profit levels in the different cases. In the second order conditions the effect of a price change of P1 on the marginal profits (with respect to price) of firm 1 (ie. fix) consists only of the direct effects, u\, if the firms choose prices in a manner that mimics collusion (ie. assigned a weight of 9). Alternatively, (ie. assigned a weight of (1 - 6)) the effects of the price change include the direct and expected indirect effects (ie. fi\ + u\v21). Bearing this in mind the second order conditions for firms 1 and 2 are given by equations 5.33 through 5.35. s.o.c. (5.33) Bfi\ + (1 - 8)(fi\ + u\u21) = u\ + (1 - 9)u\v21 < 0 (5.34) 9{u\ + u23u32) + (1 - 6){u22 + ^ v12 + u\v32) = u\ + (1 - 9)u.\v12 + /x^3 2 < 0 (5.35) 0(/*l// 2-/z 2/4)>O The second order conditions for firm 3 are listed in equation 5.36. s.o.c. (5.36) / i 3 + u32u23 < 0 Note that these second order conditions correspond to the conditions of Case I if 0 = 0. This involves each product being produced by a separate firm. If 6 = 1 the second order conditions correspond to the conditions for Case II (ie. neighbouring products produced by the same firm). Up to this point the first and second order conditions for profit maximization have been identified for each firm. These conditions are dependent upon the values of the parameter 6 and include the conditions for Case I and II as special cases. In addition to these conditions for optimization, the conditions for stability of the system will also be investigated. These conditions for stability are required in order to establish the existence of stable equilibria and to determine the effects of changes in 8. The use of 9 to describe Chapter 5. Product Choice: A Model 87 a general model allows the continuity that is necessary for the imposition of the stability conditions which will, in turn, be used to sign the comparative statics results. Recall that the demands and pricing decisions for products 1, 2 and 3 are interrelated. The stability of this system is explored under a myopic adjustment process in which a firm increases the price of a product if it perceives that such an action will increase its profits. In other words, if there are positive perceived marginal profits with respect to price (ie. //' > 0) then firm i will increase its price Pl at some positive adjustment speed sl (ie. P% = slfil). Taking linear approximations around the equilibrium prices P ^ P 2 * , and P 3* yields the relationship given in equation 5.37. As was mentioned earlier the idea of stability has little basis in a model with no time dependence and the approach is in no way attempting to construct a truly dynamic model. However, the exercise of determining these simple stability conditions is of great value in suggesting the signs of comparative statics results. Dixit (1986) also claims that the use of such a myopic adjustment process "is no worse than the tatonnement of competitive models". P 1 (5.37) P 2 -V? P 3 0 ,1 . .1 ,2,,2 ,2,,2 - V i - V i p i _ p i -p3 _ p3x Recall that the term u\ is equal to zero and therefore is not included in the coefficient matrix. Stability of this system requires that the coefficient matrix has eigenvalues with negative real parts. A necessary condition for this is that the sum of the eigenvalues is negative (ie. the trace of the coefficient matrix is negative). I l l 'J. '2. \ iJ U ^ A s u1 + s fi2 + s /x3 < 0 .2 2 3 . . 3 This condition holds for all adjustment speeds, s1 > 0, if each term is negative. Intuitively, u\ < 0 indicate that marginal profits are decreasing in the firm's price. In other words, the firm can not continue to increase profits by continueing to increase price. Another necessary condition for stability is that the coefficient matrix has a determinant Chapter 5. Product Choice: A Model 88 that is negative4. Intuitively, this implies that if reaction functions are upward sloping they cross from below. Further discussion of this condition will be made in the following paragraphs. Note that linearity of functional forms would not avoid the need for any of these stability conditions. In summary, for arbitrary adjustment speeds the stability of the system requires that the inequalities in equations 5.38 and 5.39 hold. (5.38) /*! < 0, pl<0, p33<0 /c o n \ 1 2 3 , 1 2 3 1 2 3 1 2 3 ^ n (5.39) ptp2p3 + p3pxp2 - PxPzPi - PIP-LH < 0 The assumptions on the signs of these terms are valuable for the analysis of the profitability of various product combinations. Also note that the idea that an increase in own price reduces marginal profits (ie. p\ < 0) corresponds to the second order condition under Bertrand assumptions. Up to this point the general model has been developed to indicate the necessary conditions for profit maximization and stability of the system. Before these conditions are used in the analysis of the comparative statics some mention will be made of the "reaction functions" of the firms. A more accurate description of the "reaction function of firm 1" in a game with no time dependence is the locus of prices chosen by firm 1 in response to particular prices of product 2. The slope of the reaction function, r12, indicates the adjustment of P 1 that would be made in response to a change in P2 (ie. r12 = dP1 /dP2). This is found by totally differentiating the first order conditions of firms 1 and 3. nldPt-r p\dP2 + p\dP3 = 0 p\dP2 + p\dP3 = 0 The terms are rearranged to solve for the changes in the equilibrium prices. dP1 -1 t4 ~ / * 3 dP3 0 »\ . . ^ 2 . dP2 In general, a coefficient matrix of rank n should have a determinant of the sign ( —1)™. Chapter 5. Product Choice: A Model 89 This allows the following result to describe the slope of a reaction function. 12 _ D£^_ = PIPI - T ~ dP* p\p\ The reaction functions have been introduced at this stage because much of the later analysis is done under the assumption that the reaction functions have positive slopes. This is commonly viewed as the "normal case" when firms producing substitutes are competing in prices. Assuming that marginal profits are increasing in the prices of other products (ie. pl- > 0), the positively sloped reaction functions imply that more complex combinations of terms (ie. p\p\—p\p\) are positive. Intuitively, in two dimensions pl- > 0 would imply that the prices which yield maximum profits increase for higher values of other product prices. Therefore, reaction functions are positively sloped. Note that linear models necessarily impose the restriction that pl- > 0 and, therefore, that reaction functions have,positive slopes. In three dimensions, the analysis is more complicated since the profits of any one firm depend upon the prices of all other firms. The restriction, plj > 0, must be supplemented by the assumption of positively sloped reaction functions. Recall that a reaction function only refers to the relationship between the prices of two products and therefore does not completely describe the function in three space. Recall that the parameter, 9, is included in the terms pl- (see Equations 5.25 to 5.32). Thus, 9 allows the imposition of these restrictions in a form that is general enough to encompass Cases I and II. This concludes the development of the model itself. The next step involves determin-ing the conditions that are required for profits to be monotonic in 9. This indicates the conditions under which either Case I or Case II yields higher profits. Profits are related to the parameter 9 in two steps. First, it is determined how the equilibrium prices are related to 9. Then it is determined how the profits are related to the equilibrium prices. Proposition I: If reaction functions have positive slopes then equilibrium prices are increasing in 9. Chapter 5. Product Choice: A Model 90 Proof: Totally differentiating the first order conditions (equations 5.19, 5.20 and 5.21) yields the following relationship: (5.40) A A A A A A 0 p\ dP1 As dP2 + A de = o dP3 0 Note that p\ is equal to zero and that 9 does not appear in p3 so the term p3e is also equal to zero. The equations are rearranged as (5.41) to solve for the effects of the parameter on the prices. Let A signify the determinant of the coefficient matrix (ie. A = A\AiA + AAA ~ AAA ~ AAA)- R - e c a l l that the stability conditions require that this term is negative. d9 The effects of a change in the parameter 9 on the price of the first product are given by equation 5.42. dP1 1 " dP1 ' - 1 "A" (AA - AsA) (AsA - A2A) (A2A3 - As A) A (5.41) dP2 -AA AA (AsA - A1A3) A dP3 AA -AA (AA - AA) 0 (5.42) {A2A3 - A3A)A + (^3^2 - A2A)A\ >0 d9 A This expression can be signed using the maximization and stability conditions that were mentioned earlier. First, recall that stability requires that A is negative. Also recall that the slope of the reaction function describing the response of P1 to a change in P2 is given by dP1 ,^12 — r = A3A AA dP2 AA Stability conditions (ie. p\ < 0,A < 0) imply that the term AA ~ AA m u s t be positive to ensure that the slope of the reaction function is positive. Note the equivalent reaction function for the other firm can be written as Chapter 5. Product Choice: A Model 91 21 _ U r ^1^3 r — dP1 plul - nlpl If the reaction function has a positive slope (ie. r21 > 0) and u\ is also positive, then the term — MIA*!) m u s ^ D e positive. The only terms in equation 5.42 that remain to be signed are u-1 and \i2e. These terms are written as equations 5.43 and 5.44 respectively. (5.43) u] = (P2 - C2Q)Ql - (P 1 - )Q\v21 (5.44) u2 = (P1 - C^Ql - (P 2 - C20)Q\v™ Recall that it was assumed that the conjectures v2X and v12 referred to cases mimicking less than complete collusion. The effects of complete collusion were captured by P21 and i>12. Thus the following inequalities hold: , . 2 i , r.2i _ ( P 2 ~ CQ)QI (P'-Cl)Ql v12 < v12 = (P2-C2)Q2 Note that Bertrand competition (ie. u12 = v21 = 0) is merely a special case of these inequalities. The inequalities just mentioned imply that (i\ and y?e are positive. These are the final terms needed to sign equation 5.42. Subject to the condition that reaction functions have positive slopes and that marginal profits are increasing in other prices, it can be concluded that an increase in the weighting assigned to the response that mimics collusion (ie. 6) increases the price of product 1. The other comparative statics results can also be signed. Equation 5.45 indicates the effects of a change in the parameter 9 on the price of the second good. (5.45) = \V\ILIIII - ulu33fil] > 0 Chapter 5, Product Choice: A Model 92 Again, the stability of the system requires that A, p\ and p% are negative. Since it was shown that pi is positive it holds that AAA is positive. Similarly, since pi and pi are positive and p3 is negative it must hold that p\p\p\ is negative. This allows the conclusion that (5.45) is positive and that an increase in 6 increases the price of the second product. Finally, the comparative statics results for the third product are given in equation 5.46. d6 ~ ~~ A (5.46) AAA AAA > 0 Note that this expression is very similar to equation 5.45. In fact, it can be rewritten as (5.47) dP3 -A r A - L / 1 3 9 9 3 l \ zAdp^ PI de .32 > Q de -Since the reaction functions are assumed to have positive slopes (ie. r32 > 0) equation 5.47 must be positive. Thus, each of the equilibrium prices has been shown to increase with the value of e on the conditions that- marginal profits are increasing in other prices and that reaction functions have positive slopes • The intuition behind this proposition is that if firms 1 and 2 assign a greater weight to price responses that mimic collusion (ie. for increased e), then each firm receives the benefits that its higher prices would normally yield to the other firm. If behaving in a manner that mimics collusion, the other firm would respond to a price rise by raising its price so that the original firm receives the same benefit as the original price change brought to the second firm. Both firms 1 and 2 now receive the full benefits that their actions yield to either firm. They would normally have lost some or all of the benefits of higher prices as consumers switch away from the more expensive product. Firm 2 still faces the situation in which a rise in its price will encourage some consumers to choose product 3 but it does receive the benefits from any consumers which switch to product Chapter 5. Product Choice: A Model 93 1. Increased benefits at every price level increases the price level at which the perceived marginal profits are zero. This shifts out the reaction function and under the assumption of upward sloping reaction functions it must hold that the equilibrium prices are greater. Proposition I can be used to determine whether the equilibrium prices are higher in Case I or II. It was shown that equilibrium prices are monotonically increasing in 8. The case in which a firm produces neighbouring products (ie. Case II) corresponds to a value of 9 of one while the case in which each product is produced separately (ie. Case I) corresponds to a value of 8 of zero. Therefore, it can be concluded that the equilibrium prices of each of the products are higher in Case II than they are in Case I. Note that it was concluded earlier that the equilibrium prices are the same in Case III and in Case I if the conjectures correspond to Bertrand assumptions (ie. v%3 = 0). Thus, under Bertrand assumptions the following relationships hold: Pxu > P}~ = Pm, Pn > Pi" = P?n, Pn > Pf = Pm Note that this result will not hold under all circumstances. For example, if reaction functions were downward sloping, behaviour which mimics collusion would result in at least one price being lower (ie. dP1 /d8 < 0). Similarly, under more general assumptions about firms' conjectures the equalities need not hold. Recall that the overall objective of this section was to determine whether the products yield higher profits in Case I, II or III. At this point the prices have been compared. In the next step it will be determined how the profit levels are affected by changes in the equilibrium prices. Proposition II: If the slopes of reaction functions are positive and firms' responses to a price change of the other firm are no greater than would occur if they were mimicking collusion, then the profits of all products increase with the value of the parameter 8. Proof: Chapter 5. Product Choice: A Model 94 Equation 5.48 indicates the profits from the production of product 1 with the corre-sponding first order conditions given by equation 5.49. (5.48) ir1 =P1Q1-C\Q1) (5.49) A = Q1 + (P1 - CQ)[Q\ + Q\((l - ey21) + 6P21)} = 0 Totally differentiating (5.48) yields (5.50) dir1 = [Q1 + (P 1 - C^QWdP1 + [(P1 - C^QWdP2 . The first order conditions, (5.49), are combined with this equation to determine the effects of 6 on the profits from product 1 as in Equation 5.51. (5-51) = - ch)Ql f(i - ey1 + ^ 2l1 dF>1 dd v n^iiy i j d 9 dP2 HP1 - Ch)Q\^ > 0 Since prices are greater than marginal cost (ie. (Pl — Cq) > 0, i = 1,2,3) and the goods are substitutes (ie. Q%- > 0, i ^ j) the sign of (5.51) is dependent upon the sign of the term dP2 dP1 Substitute in the values for dP1 /d9 and dP2/dO, and note that it can be concluded that (5.51) is positive for all values of 6 if (1 - i>21r12) and r 2 1 — ((1 — 8)v21 + 6v21) are positive. Since P21 is the reciprocal of P12, a sufficient condition is that the firm must respond to a price change of the other firm by an amount less than would be required to increase the profits of the other firm by as much as its profits were increased (ie. r 1 2 < P12). The firm must also not overestimate the response of the other firm to a price change. A similar procedure is used to determine the effects of 9 on the profits of products 2 and 3. Again the first order conditions and the total differentials of the profit functions are used to determine dir2/d6 and dirz/d6. Chapter 5. Product Choice: A Model 95 ( 5 . 5 2 ) ^ = ( P 2 - C J ) Q ? +(P2~C2Q)Ql dP1 le dP3 - [(i - ey2 + on12] dP2 ~dT de — V 32 dP2 ~dJ > o (5.53) <J7T3 le {P*-CZQ)Q\ dP2 lie .23 dP3 de = {P3-C3Q)Q\ »yz dP2 ~dJ > o Again, sufficient conditions for the sign of dir2'/'dO to be positive if r21 < v2X, r 1 2 > ((1 — ey2 + Ov12) and r 3 2 > v32. In other words, if firm 2 does not overestimate the responses of the other firms to increased values of B and responds less than it would if it were mimicking collusion then its profits will increase. Finally, the sign of dir3/dQ is positive since Proposition I showed that dP2/dO is positive, stability conditions require that /ig is negative and the second order conditions imply that u.\ + u^v23 should be negative. Thus, subject to the conditions that reaction functions are upward sloping and firms do not overestimate the responses of other firms, the profits of each of the products are monotonically increasing in 0, the weighting assigned to responses that mimic joint profit maximization • The intuition behind this result is based upon the observation that once a firm has chosen an optimal price for the demand curve that it faces it can still increase its profits if that demand schedule shifts out. The demand curve will shift out if the prices of neighbouring products (ie. substitutes) increase. An increased weight assigned to price responses that mimic collusion increases the proportion of the entire benefits (ie. that accrue to either firm) that a firm receives from increasing its price. This increase in marginal profits (with respect to price) results in higher equilibrium prices. Therefore, the demand curves of neighbouring products shift out and their profits increase as well. One of the implications of this result is that since Case II corresponds to B = 1 and Case I corresponds to B = 0 the inequalities in equation 5.54 must hold. In other words, the maximum profits from the joint production of neighbouring products is greater than Chapter 5. Product Choice: A Model 96 the profits from producing each separately. Product 3 has higher profits since the exercise of local monopoly power by goods 1 and 2 shifts out the demand function of good 3. (5.54) > T)" + ie]", TT£ > Trf If the firm with product 3 were also to produce product 1 it would receive irjff from the combination. Under the assumption of Bertrand conjectures this is the same as the profit that the products yield when produced by different firms (ie. T^ff = T}X + Tj"). The benefits that firm 3 realizes from the production of 1 are measured as TJff —T3' = T\* (ie. the increase in profits it would receive from producing the combination rather than just product 3). Throughout the analysis that follows, the benefits that a firm realizes from the production of good 1 are measured as the difference between the profits it would receive from producing its current product plus good 1 and the profits it would receive if it only produced its current good and some other firm produced good 1. Note that product 2 also yields the same profits to firm 2 regardless of whether firms 1 or 3 are producing product 1 (ie. irjjj = T2*). Under other assumptions about the conjectures the prices and profits of all firms can be higher in Case III but it is difficult to compare these profits to Case II. Next, recall the case in which a firm (eg. firm 2) produces both product 1 and product 2. This firm would receive T}'2' from the combination. Proposition II results in the conclusion that the additional benefit that producing product 1 would yield to firm 2 (ie. irj'f2" — -ITJ" = T]'2" — TJII) is greater than the additional benefit that firm 3 would receive from producing good 1. The benefit to firm 3 of producing good 1 depends upon whether the alternative is that firm 2 would produce good 1 (ie. Tjff — TJJ) or that firm 1 would produce good 1 (ie. TJfT* — Tj"). It is not intuitive that firm 3's profits depend upon the market structure in the remainder of the economy (ie. whether firm 2 has a local monopoly by producing goods 1 and 2). However, Proposition II suggests that firm 3 would receive greater profits from producing good 3 if firm 2 were to produce good 1 rather than firm 1 producing good 1 (ie. Tj] > Tj"). Therefore, the benefits that firm 3 receives from producing good 1 are higher if the alternative is that firm 1 were to Chapter 5. Product Choice: A Model 97 produce good 1 rather than firm 2 producing good 1 (ie. njff — TT3" > TT]'H — -K]J). Thus, a product yields greater profits to a firm which produces a neighbouring product than it would yield to other firms. The value of producing product 1 in the various cases can be summarized by the following relationships: 1,2- 2* 1,2* 2- \ 1* 1,3* 3* \ 1,3* 3* ^11 - 7 7 I I I - *II - ^ 1 ^KI - 1 7 III - 1 1 1 ^  17III - ^11 The result, T r n ' — iTjjj > Tr]ff — itjj, that a product yields greater profits to the producer of a neighbouring good may not be intuitively obvious. It might be argued that producing neighbouring goods causes the firm to compete against itself. However, this analysis shows that there is an incentive to form a local monopoly in order to obtain higher profits. The ordering of the profits is somewhat analogous to the results of Brander and Eaton (1984). They concluded that a "segmented" market structure, in which each firm pro-duces close substitutes, gives rise to higher prices and profits than an "interlaced" market structure in which firms produce distant substitutes. Brander and Eaton go on to pro-pose that either configuration can be a Nash equilibrium in a simultaneous selection of product portfolios. A later section of this chapter deals with the effects of the profitability of producing a product on the probability that the firm will introduce it. Since selec-tion of the product is dependent upon the returns to research effort and since different firms possess different marginal profitabilities this situation does not correspond to the simultaneous selection of product portfolios. It does, in fact, more closely correspond to Brander and Eaton's proposition that under sequential entry market segmentation is the Nash equilibrium. Before proceeding it should be noted that the results suggest that if a potential new product would not enable a particular firm to "corner a segment of the market" an alternative possibility exists. The firm which cannot control a segment of the market by producing a good may encourage the production of that good by a firm which could use it to control a segment of the market. The higher prices of the goods under local monopoly control will increase the demand for other products allowing higher equilibrium prices Chapter 5. Product Choice: A Model 98 and profits. This increase in profits may be larger than the profits that the product would have yielded if the first firm had introduced it. (ie. there is the possibility that 7rfj > fljj-j*). This situation may be easier to explain with a simple locational example. A particular store location may not be profitable to most firms since whenever prices are increased sufficiently to cover costs most customers switch to another store that is nearby. If the firm with the nearby location were to take over the store in question it would receive the benefits from any customers switching to the nearby location. It could raise the prices in both stores and increase its profits as long as most customers are not willing to go to more distant locations. Distant stores also benefit from this exercise of local monopoly power due to the increased demand caused by any customers that are willing to switch to the more distant locations. Although this scenario indicates some differences in the incentives of various firms the results can not be distinguished from a case in which all firms are trying, to a greater or lesser extent, to introduce the new product. Therefore, the empirical tests are not affected by this possibility. The empirical section of this thesis will check the hypothesis that there is a higher probability-that products are introduced by firms which introduced neighbouring prod-ucts rather than by other firms. It should also be noted that it will be determined if the time between introductions has an effect upon these relationships. The benefits of introducing neighbouring products are not expected to be constant over time. Limited patent fife and the threat of entry suggest that the period between two introductions affects the profitability of the second product. Intuitively, the benefits from introducing a product which neighbours an existing product of that firm are maximized if there is patent protection on both products for as much time as possible. Alternatively, the profits are minimized if the patent on the first product has already expired when the second product is introduced. The effects that the time since the introduction of neighbouring products has on the present value of the new introduction can be seen by some very simple calculations. Assume that there is a limited patent period, T, and that product 2 has been introduced tQ periods prior to product 1. The relations between the demands for products 1, 2 and Chapter 5. Product Choice: A Model 99 3 are the same as in the previous examples. Recall that the profits that are available during each period in which the firm controls the patents of products 1 and 2 is it^f". It is assumed that entry of new firms in the production of a product results in zero profits after the product's patent life has expired. The expiration of the patent on product 2 results in entry of other firms into the production of that good which, in turn, causes the equilibrium value of P2 to be reduced until profits are zero and entry ceases. Positively sloped reaction functions suggest that the reduction of one price results in the reduction of all equilibrium prices. The equilibrium profits of all products are also reduced due to the relationships between equilibrium prices and profits stated in Proposition II. The resulting equilibrium profit of product 1 is designated as ity". Equation 5 . 5 5 specifies the present value, at the time of the introduction of product 1, of the additional profits that would accrue to a firm which had previously introduced product 2 . There is a period, T — t0, in which the firm enjoys the additional profits that are provided by having patents on both products. The remaining interval between the expiry of the existing product's patent at T — t0 and the new product's patent at T only allows the firm to receive irv* per period. Subsequent periods provide no benefit since entry causes all profits to go to zero. ( 5 . 5 5 ) PV^TT 1' 2) = [T~t0 e-rt{irn~ - vj^)dt + f e~Tt^dt Jt=0 Jt=T-t„ Compare this to the present value of the benefits that would accrue to a firm that had introduced a nonneighbouring product. ( 5 . 5 6 ) PVfir1'3) = [T~t0 e- r t(7r}>3/ - KZu)dt + f e~Tt^ydt Jt=0 Jt=T-to The magnitude of the difference between these two cases is affected by the time between introductions. To.explore this effect the variable T 2 , 3 is defined as the difference between the present value of the benefits in each case (ie. T 2 ' 3 = PV(-K1,2) — PV(7r 1 , 3 ) ) . This difference between the benefits declines as the time between introductions increases. This can be seen more easily by taking the derivative of T 2 , 3 with respect to the time between introductions, t0, as in equation 5 . 57 . Chapter 5. Product Choice: A Model 100 (5.57) d r 2 - 3 .1,2* II .2-77/ dt0 — 7T Recall that Proposition II showed that 7r 1,2- Therefore, the difference in the profits received by a firm with a neighbouring product and a firm without such a product will decline as the time between the introductions increases. A later section of the model connects the profitability of a product and the probability that a particular firm will be responsible for the introduction. This suggests that the work to this point generates two hypotheses that can be checked in the empirical section. First, that there is an higher probability that products are introduced by firms which have introduced neighbouring products rather than by other firms. Second, that as the time between two introductions increases there is a decreasing probability that a new product will be introduced by a firm which introduced one of its neighbours. As was mentioned earlier, the indications that firms would raise their prices to increase profits may actually overstate the response that would take place if this analysis were applied in the characteristics approach. Therefore, any empirical results which support the conclusion that firms are pursueing local monopoly power are less likely to be falsely positive, (ie. the tests have more power). At this point another relationship between products is explored as a possible influence on the profitability of producing certain product combinations. This relationship is that certain combinations of products may yield cost advantages when produced jointly. 5.2.2 Cost Advantages The production of groups of insecticides which require similar production processes and similar inputs are assumed to cause production cost differentials. In other words, a product is assumed to have different production costs according to which other prod-ucts are being produced by that firm. This section relates these differences in costs to differences in the profitability of producing a good. The analysis uses the same system of demands as was used earlier. Recall that the Chapter 5. Product Choice: A Model 101 system consists of three products, 1, 2 and 3, which are differentiated by two characteris-tics. In this case it is assumed that the nonneighbouring products, 1 and 3, are produced with similar production processes and that this reduces either the fixed or marginal costs of producing the new product (ie. product 1). The additional profits that the production of product 1 yields to a firm which also produces good 3 (ie. Case III in the previous section) is compared with the profits that arise if product 1 is produced by another firm (ie. Case I). It is obvious that a reduction in the fixed cost of producing product 1 has no effect on marginal costs and therefore optimal pricing decisions will not be changed. The additional profits that product 1 yields in the two cases will only differ by the differences in the fixed costs. Everything pertaining to pricing decisions is the same as if the products were produced by separate firms. Therefore the equilibrium prices and profits of other goods are not altered (ie. 7r|f7 = 7r|"). The effects of producing 1 and 3 together can be seen by the following relationships: 1,3* 3* \ 1* 2* 2* Tm >ti , *m =lxi A reduction in the marginal costs of producing product 1 is somewhat more compli-cated than the discussion of fixed costs. The parameter A is introduced as a measure of the reduction in marginal cost that is available when product 1 is produced in con-junction with product 3. The reduction in marginal cost can also be viewed as a unit subsidy on product 1 which is only available to the producer of good 3. Unfortunately, the comparative statics results from a firm producing products 1 and 3 are complex and difficult to interpret. To avoid the complications an alternative scenario is investigated. Products 1, 2 and 3 are assumed to be produced in such a way as to maximize the profits accrueing to each individually (ie. as if they were produced by separate firms). The model determines the effects of a reduction in marginal cost of one product on the profits received by each of the goods. By employing consistent conjectures it is possible to hypothesize the actual response of a firm producing products 1 and 3 since one of its options is that the product facing the reduction in price is restricted from adjusting Chapter 5. Product Choice: A Model 102 its price. The use of Bertrand assumptions would suggest that the effects of a shift in marginal cost depends upon the specification of demands. Some mention will be made of the conditions that would be required for Bertrand assumptions to yield the same results as consistent conjectures. The firms producing each product solve the optimization problems given by equation 5.58. (5.58) max/ = PIQI - C{'(Q{) i = 1, 2, 3 where C1'(Q1) = CL{QL) - XQ\ C2'(Q2) = C2(Q2) and C3'(Q3) = C*(Q3) The first order conditions are given in equations 5.59, 5.60 and 5.61. f.o.c. (5.59) p,1 = Q1 + (P1 - CQ + X)(Q\ + Q\v21) = 0 (5.60) A = Q2 + (P2 - c2Q)(Ql + qy2 + qy2) = 0 (5.61) p3 = q3 + (P3 - c3)(ql + qy3) = o These first order conditions correspond to the conditions of Case I when A equals zero (ie. there is no cost reduction due to joint production). Proposition III: If the reaction functions have positive slopes then a reduction in the marginal cost of producing a product reduces the equilibrium prices of all products. Proof: The effects of a reduction in the marginal cost of product 1 are found by totally differentiating the first order conditions in equations 5.59, 5.60 and 5.61. Chapter 5. Product Choice: A Model 103 u{ u\ 0 ' dP1' Axd\ (5.62) A A A dP2 + 0 o A A dp3 0 = 0 Note that the terms /z*- i,j = 1,2,3 are the same as the equivalent terms in the general model (ie. Case IV) when 9 is set equal to zero. Also note that this implies that A — 0- The determinant of the coefficient matrix, A, is also the same as before, with 9 = 0, and is represented as A = AAA ~ AAA ~~ AAA- The second order and stability conditions of the general model, with 9 = 0, can also used in this analysis and therefore are not redefined. Solving for the effects of a shift in marginal cost on the prices yields the following equations: (5.63) " dP1' 1 dP2 = A dP3 (AA - AA) -AA AA -A2A AA A2A3 -AA fi\dX 0 0 (5.64) -AA (AA - AA) Since u\ = (Q\ + Q\v2X) the previous expression can be rewritten as follows: (AA-AAm + QW1) dP1 d\ (5.65) dP2 _AA(Q\ + Q>21) _ r (5.66) dX dP3 ~dX < 0 2 1 < 0 dX AA(Q\ + QWl) = s2dP^ A T dX < 0 Certainly, the assumption that reaction functions have positive slopes (eg. r32 = —Al A — 0) implies that all prices are adjusted in the same direction. The necessary conditions for stability of the system, (ie. A and A a r e negative) imply that A *s positive. Since A i s positive, A must be negative, and the reaction functions slope upwards (eg. r 2 1 > 0) it implies that the term (AA ~ AA) l s positive. Finally, the first order conditions for product 1 imply that (Q\ + Q\v21) = —Q1/(P1 — CQ + A). Since the quantity demanded of product 1 is greater than zero and its price is greater than the Chapter 5. Product Choice: A Model 104 marginal cost the term (Q{ + Q\v21) must be negative. It can be concluded that a reduction in the marginal cost of producing product 1 (ie. A > 0) results in a reduction in the equilibrium prices of all products • The next step is to determine the effects of the shift in marginal cost on the profits that are generated by the three products. If reaction functions are upward sloping and firms do not overestimate the equilibrium response of other firms to a price change then a reduction in the marginal cost of producing a product increases the profits of that product but reduces the profits of all other products. The effect of the reduction in marginal costs is found by totally differentiating the profit function of product 1. (5.67) dir1 = [Q1 + (P1 - C Q + X)Q\] dP1 + Q1d\ + (P1 - CQ + \)Q\dP Recall that the first order condition for product 1 can be written as Ql + (P1 - C Q + X)Q\ = - ( P 1 - C\ + \)Qyi or as These terms are used in conjunction with (5.67) to define the effects of A on the profits of product 1. (5-68) ^  = (P 1 - CQ + A) dP2 dP1 Recall that Proposition III defined expressions for the terms dP1/d\ and dP2/d\. dP1 -(pipi-py2)(Q\ + Qyi) d\ A dP2 _ PIPKQ] + qy^) dX A -< 0 Chapter 5. Product Choice: A Model 105 (5.69) This allows (5.68) to be rewritten as equation 5.69. dir1 {Pl-CQ+\){Q\ + Q\v*) dX A Q\[p\pl + v2\p\p\ - p\p\)\ - A Recall that the second order condition for profit maximization is p\ + p\v21 < 0 or, alternatively, v21 < —p\/p\. Substituting this expression into the equation and recalling that A = p\p\p\ — AAA ~ AAA a U o w s equation 5.69 to be rewritten as follows: d-K1 (5-70) ~ > - ( P ' - C Q + X ) ( Q \ + Qyi) Ql A > o Again, positively sloped reaction functions imply that p\ is positive. Since Proposition III showed that (Q\ + Q\u21) is negative it follows that equation 5.68 is positive. Thus, sufficient conditions to ensure the that firms are profit maximizing also suggest that a reduction in the marginal cost of product 1 increases the equilibrium profits that accrue to that product. The effects of a change in marginal cost on the profits of the other firms can be determined in a similar manner. Using the first order conditions for these products and the total differentials of their profit functions yields the following relationships: (5-n)d£ = (P2-c2) dP1 (5.72) dTT^ ~dX (P3-C*)Q32( X dP2 -^dC) + Ql(dp3 .32 .23 A dP3 X dP2 X Recalling the expressions generated for dP1/dX, dP2/dX and dP3/dX by Proposition III allows (5.71) and (5.72) to be rewritten as equations 5.73 and 5.74 respectively. ( 5 . 7 3 ) ^ = ( P 2 - C 2 ) Ql(l-S2r2^+Q23(r32 dP2 < 0 This expression can be signed by recalling that the determinant of the coefficient matrix can be written as A = / x ^ ( r - 1 2 - - ^ ) < 0 . Chapter 5. Product Choice: A Model 106 This implies that (1 — u12r21) is greater than (1 — v12/r12) which is positive if the firm does not overestimate the response of the other firm. The same assumption is required of the firm's estimate the response of firm 3 (eg. r32 > u32). Since the equilibrium prices decline with an increase in A it follows that (5.73) is negative. J_3 Jp2 (5.74) ^  = (P 3 - C*)Ql(l - u23r32)d-j- < 0 Clearly, this term can also be signed by noting that the determinant of the coefficient matrix can be written as A = / x W 3 ( ^ 3 2 - ^ ) < 0 • Again, this implies that (1 — v23r32) is positive if the firm does not overestimate the response of the others (ie. r 2 3 > v23). Under these conditions it follows that an increase in the marginal cost of product 1 decreases the equilibrium profits of product 3. This analysis has been undertaken under the assumption that each product is pro-duced by a separate firm. The next step is to determine how the reduction in marginal cost affects profits if products 1 and 3 are produced by the same firm. This situation is investigated to determine if a firm which produces a product combination which allows a reduction in marginal cost will be able to capture higher profits than another firm which does not experience such cost reductions. Clearly, if P1 is not reduced the decrease in marginal cost will still increase the profits of that firm. The profits accrueing to the other products will not be altered because none of the equilibrium prices have changed. If the firm producing product 1 has consistent conjectures it has the option of reducing P1 only to the extent that the resulting increase in profits from product 1 exceed any decrease in profits from product 3. If the firm overestimates the response of the other firm it will not change the prices as much and will still receive the higher profits that arise from the decrease in marginal cost. If, however, the firm underestimates the response of the other firm it will decrease its price by more than an optimal amount, perhaps even to the point of reducing the combined profits of products 1 and 3 to a level below what they would have yielded if produced without a cost reduction. Bertrand assumptions Chapter 5. Product Choice: A Model 107 yield the same results under conditions in which the equilibrium price of product 2 is not greatly affected by the price of product 1 (ie. r 2 1 is close to zero). These results are also obtained in the case of demands being very elastic with respect to their own prices but very inelastic with respect to other prices. Thus, a decrease in marginal costs and the associated reduction in price create a large increase in profits of the product to experience the cost reduction but results in small effects on the demands of the other products. Thus, this analysis is not able to show that a reduction in marginal costs from the production of certain product combinations invariably leads to increased profits. On the other hand, if conjectures are consistent or firms are not greatly affected by the prices of other products, it can be concluded that the profits of the firm to experience the cost reduction will increase. Up to this point the analysis has dealt with the profitability of producing particular combinations of products. It is now necessary to relate these differences in profitability to the probability that a firm introduces a product combination. 5.3 Profitability and the Probability of Introduction The fundamental hypothesis of this section is that firms which have a greater potential to increase their profits due to the introduction of a new product consequently have greater incentives to undertake research effort. A higher level of research effort, in turn, results in a higher probability of actually making the introduction. A simple model is constructed to explore this hypothesis. The first part of the model relates the probability that a firm discovers a product to its equilibrium level of research effort and to the research effort of all other firms. The second part relates the expected profits that a firm would receive from introducing the product to the equilibrium level of research effort that this firm would assign to discov-ering the product. This provides the connection between the potential profitability of a product and the probability that a firm introduces that product. The empirical section Chapter 5. Product Choice: A Model 108 of this thesis checks whether the relationships between products, which are hypothe-sized to increase the profitability of producing certain combinations, actually increase the probability that these combinations are introduced by the same firm. Following the work of Loury (1979), Dasgupta and Stiglitz (1980), and Kamien and Schwartz (1982), it is assumed that the uncertainties faced by different research units are completely independent of one another. The search for insecticides has generally involved a trial and error search through hundreds of chemical compounds as if there were uniform and independent probabilities that any one could be of value (Heaton, 1986). The use of this type of screening procedure in the pharmaceutical industry has been modelled as a Poisson process (Gittins 1969, Davies 1962). A similar analysis is used here to predict the effects that the profitability of product combinations has on the probability that they are introduced by the same firm. The rate at which a firm, i, is expected to find suitable products at some time, t, is assumed to be dependent upon that firm's research effort (ie. p^E1)). The rate at which firm i is expected to find suitable products which have not been found by another firm also depends upon the research efforts of all other firms in the industry. In particular, there is a probability $l=QpT{E3)dT that a firm j has made the discovery by time t. Conversely, there is a probability 1 — /1L0PT(-E'"')dT that firm j has not made the discovery by time t. Since the research effort of each firm is independent, the probability that a suitable product has not been discovered by any competitor of firm i is just the product of the probabilities associated with each firm. Therefore, the rate at which firm i is expected to find suitable products which have not been found by another firm is given by N r P W R I - / pT{&)di • . L JT=O 3 £ i The probability, Pr%, that firm i ever finds the product before another firm is found by integrating over this density function as in equation 5.75. N (5.75) i V = / p\Ei)\\ \ - \ pr(E3)d Jt=o L JT=O dt j Chapter 5. Product Choice: A Model 109 Again following the work of Loury (1979), Dasgupta and Stiglitz (1980), and Kamien and Schwartz (1982), the discoveries are assumed to occur randomly (ie. with a Poisson distribution dependent upon the level of research effort). This assumption implies that pt(El) can be written as fl(El)e~f'(E'')t. This allows (5.75) to be rewritten as equation 5.76. iV r /•oo " rt (5.76) Pr1 = / ' ( F l e ^ ^ l ' T T 1 - fj(Ej)e-f^E^Tdr Jt=0 „•_, L JT=0 3-1 dt j ^i Integrating (5.76) yields the rather intuitive result in Equation 5.77 that the proba-bility of firm i ever making a discovery first is equal to the amount of its effective research effort (ie. ./*(£*)) relative to the total. (5.77) Pr' = fi{Ei) + Z-=1fi(EJ) The next step involves determining how the profitability of producing a product relates to the equilibrium level of research effort that a firm assigns to the discovery of that product. Recall that an earlier section of this chapter related the potential for local monopoly power or cost advantages to differences in the profitability of producing a product by various firms. A level of research effort (ie. the number of trials or experiments per time period) is assumed to be chosen by firm i to maximize the present value of expected profits, PVX. If the firm makes the discovery it will receive a profit stream which has a value of irl at the time of discovery. Recall that the rate at which firm i is expected to find suitable products which have not been discovered by other firms is given by N r P ' ( ^ ) II 1 - / Pr(Ej)d7 j=l 1 J T = ° Also recall that if discoveries can be described by a Poisson process this expression can be rewritten as equation 5.78. ' =fi(Ei)e-fi&*l[e-filEi* j+i (5.78)f ( ^ e - ' W ' f r 1 - / fj(Ej)e~f](E3)TdT / = 1 L Jr=0 Chapter 5. Product Choice: A Model 110 The term in (5.78) divided by (ie. e - ' W ' rj^ = 1 e - / W * ) i s the probability that the product has not been discovered by any firm prior to time t. Naturally, firms only undertake research effort, and its associated costs, cEl, if an appropriate product has not yet been discovered. The term fl(El) describes firmz's expected rate of discovery of appropriate products conditional on the product not being discovered prior to that time. The firm therefore expects to receive the returns from making the discovery at time t with the probability given by equation 5.78. These expected costs and returns at each time t indicate that the present value of undertaking research is given by equation 5.79. POO (5.79) PVl = / e-rt Jt=o dt j This expression is rewritten as equation 5.80 (5.80) FV< = t m ^ E l All further analysis is done under the assumption that there are two firms, 1 and 2, in the market. For instance, firm 1 seeks to maximize the returns to its research effort by solving the following problem: , x r , i fHE'y-cE1 It is also assumed that the firms possess conjectures, v12 and i/21, about the response of the other firm to a change in effort levels. As an example, v12 describes the conjectures of firm 2 about how E1 would be adjusted if it were to alter E2. The conjectured response of the other firm is believed to be taken into account when choosing a level of research effort to set the firm's perceived marginal profits equal to zero. Again, conjectures are not crucial to the analysis and can be set equal to zero (ie. Bertrand assumptions) if desired. Firm l's first order conditions are given in equation 5.82. Note that the arguements have been omitted for brevity and that subscripts denote partial derivatives. Chapter 5. Product Choice: A Model 111 f.o.c. (5.82) fi = (/> + / • + , ) • = ° In a manner similar to the previous models let the terms pl- denote the partial deriva-tive of the perceived marginal profits of firm i with respect to a change in E3. This allows the second order conditions for firm 1 to be expressed in the following manner: PI + PW1 < o Note that the "normal" response of firms to increased effort levels of other firms is likely to be a decrease in effort (ie. the reaction functions are expected to be downward sloping). This can be seen by noting that the effort of other firms enters into a firm's present value of effort (ie. equation 5.80) in a manner that similar to the discount rate. In both cases the firm puts little valuation on future discoveries. In one case there is a lower value because of more heavily discounted profits from future periods while in the other case there is a lower value because of a smaller chance that the discovery has not been made by another firm. Greater research efforts of other firms increase the probability that they will make the discovery first. This creates the incentive for the firm to respond by increasing its marginal returns to effort which is done by decreasing the amount of effort it chooses. The terms indicating the slopes of the reaction functions (eg. r2 1) are found by totally differentiating the first order conditions (ie. p^dE1 + p\dE2 = 0). Since the slope indicates the response of firm 2 to a change in the effort of firm 1 it can be written in the following manner: r = dE2 -p\ dE1 p\ Again, the conditions required for stability of the system are investigated under the assumption of a myopic adjustment process. The effort of firm i (ie. El) is expected to increase by some positive adjustment speed, sJ, if the firm increases its profits by doing so (ie. pl > 0). The rate of change of the effort, E%, is given by the following relation: Chapter 5. Product Choice: A Model 112 W = sifii This is shown for a linear approximation around the equilibrium points, Elx,E2*. (5.83) " El ' «VI ^A ' E1 -E1* E2 s2a\ s2n2 E2 - E2' Stability of the system requires that the coefficient matrix has eigenvalues with neg-ative real parts. The necessary conditions for this to hold are that the determinant of the coefficient matrix is positive and that the trace is negative. This holds for any values of the adjustment speeds if the terms, u\ and ix2,, are both negative and AA ~ AA xs positive. At this point, the model has been developed to indicate the necessary conditions for profit maximization and stability of the system. These conditions are used to determine the signs of the comparative statics results. The next step involves relating differences in the profitability of producing a product to differences in the probability of a particular firm introducing it. Proposition IV: A firm which would receive greater profits from producing a product undertakes greater research effort and has a higher probability of making the introduction. Proof: First, the total differentials are taken of the perceived marginal profits. 'A A dE1 + M i l A A . dE2 0 dTT1 = 0 This relationship can be rearranged in the following manner: (5.85) dE1 -1 A -A /4i dE2 AA - AA -A A _ 0 dir1 Chapter 5. Product Choice: A Model 113 The effects that a change in the potential profits of one firm has on both firms are given by equations 5.86 and 5.87. N dE1 - u W i 5.86 — = 1 2 > 0 OJTT1 pint -x dE2 u2u\ The terms can be signed by first noting that the term \L\I can be written as ( 5 8 8 K , = (p+p+rr — •• Recall that the first order condition indicates that the following relation holds: , f l , f 2 2^ ( / i V - ^ X / 1 +/'+'-) Substituting this into (5.88) yields c'E1 (£ ~ fi) (5.89)^- = ( / i + / 2 + T . ) ( / i 7 r i _ c i j E ; i ) Clearly, as long as the product yields positive profits (ie. Z 1^ 1 — c1E1 > 0) and the average product, f1/E1, exceeds the marginal product, /j 1 , it must hold that f i ^ is positive. Since stability requires that \i\ is negative and that — i s positive, an increase in the profits that a firm would receive upon making a discovery increases the effort that is devoted to making that discovery (ie. dE1/drr1 > 0). To determine the effects on the effort level of the other firm it is necessary to determine the sign of n\. Recall the expression for the slope of a reaction function (eg. r2 1). ™21 — dE2 _ -A dE1 ~ fi2 Chapter 5. Product Choice: A Model 114 The stability condition that \L\ is negative and the assumption that reaction functions slope downward imply that the term A is also negative. Therefore, an increase in the expected production profits of one firm decreases the research effort of the other. The effect that an increase in profits has on the probability of that firm actually making the introduction is explored next. First, totally differentiate the term describing the probability (5.77) that the introduction of a product is ever made by a particular firm (eg. firm 1). .p 1 fidE1 PUldE1 + ftdE*) _ fl/W - f / 2 W R (P + P) (p + py (p + py Substituting in the expressions describing the effects of the production profits on the equilibrium research effort (ie. (5.86) and (5.87)) yields the effect of these profits on the probability that the firm will ever make the introduction first. "rfPr1 - ^ i (PPA + f'ttA) > ( ] d*1 (AA-AA)(P + py ~ Recall that stability required that u\ is negative and (A A ~ A A) 1S positive. The term f i ^ was also shown to be positive and it can be expected that the total product of effort is positive (ie. / ' > 0) and has a positive marginal product (ie. /? > 0). Fi-nally, the assumption of downward sloping reaction functions implies that u\ is negative. Therefore, it can be concluded that an increase in the profits that a firm would receive from producing a product increases the probability that the firm will be responsible for the introduction of that product • The factors outlined by Propositions I, II and III indicated that the production of a good in combination with other goods which are neighbours or which yield cost advan-tages results in greater profits than would be possible if the good were produced alone. Proposition IV shows that these relationships between goods are expected to influence the probability that firms in such situations introduce a new product. There are un-doubtedly other mechanisms (eg. research backgrounds of the employees rather than Chapter 5. Product Choice: A Model 115 the firm or the firm's research interests in other branches of the chemical industry) that would alter the probability of introducing a product. The lack of available data on such influences make it difficult to undertake any empirical check of such hypotheses. Empirical estimation will be used in an attempt to verify whether neighbour relations or potential cost advantages do affect the probability of a firm introducing a product. The relative magnitudes of these influences in the insecticide industry will also be deter-mined. Recall that the special considerations of the use of characteristics theory makes it somewhat less likely to actually observe the pursuit of local monopoly power so any results to that effect provide even greater support for the hypothesis. On the other hand, observations of the choice of chemically similar products may include some products which were chosen since they could eliminate another good from the market rather than any cost advantages that resulted from the joint production of these goods. Up to this point the analysis has been concerned with the introduction of new products by multiproduct firms. The next section deals with the choice of products for production. 5.4 Profitability and the Probability of Production Recall that, in the case of introductions, it was assumed that each firm's potential profit from introducing a product would determine that firm's effort as a function of the effort levels of all other firms. A firm's equilibrium effort relative to the total effort then determines that firm's probability of making the introduction. The analysis of the production choices of multiproduct firms is somewhat different from the analysis of the introductions. The most significant difference is that there is no well defined equivalent to effort and any number of firms may actually produce a product rather than a single firm making an introduction. The analysis also differs since information is available each year that indicates the identities of firms which produce each product. Note that Brander and Eaton's (1984) results suggest that a variety of configurations of simultaneous product line selection can be Nash equilibria. However, this is not a simultaneous selection model. Presumably, firms enter into production sequentially and each firm continually questions whether it would be profitable to produce a particular product. If the firms possess Chapter 5. Product Choice: A Model 116 nonzero conjectural variation terms (ie. not using Nash assumptions) about the entry and exit of other firms then presumably they may enter into production of a good even if other firms already produce it. This would create a situation where combinations of products would be produced together according to a selection method in which the firms which have a greater profit potential from producing the goods would have a higher probability of doing so. For instance, assume that the decision to produce a particular pair of products is essentially a random process. The probability that a firm produces a particular pair of products is assumed to increase with the combined profits of the two products. If all firms were identical, assuming no collusion, no restriction of entry and no large fixed costs, it would be expected that firms would continue to enter into the production of a good as long as there were positive profits. If firms were not identical but could derive some degree of local monopoly, in geographic or characteristics space, which is not available to others then it would be expected that those firms with the greatest potential profit would enter into production as long as the least profitable of these could still expect positive profits. Even though a firm producing a highly profitable combination of products may be late at entering the production of a particular good, it would affect the profitability of all firms and increase the chances that a firm with a less profitable combination would exit. This relies upon the low fixed costs associated with producing any particular insecticide and thus easy entry and exit from the production of any good. Although information is not available on profitability of production of a good by each firm it is possible to determine conditions which would lead to local monopoly power or reduction in production costs. Propositions I, II and III in the previous sections indicate the effects of these factors on the profitability of producing certain product combinations. The empirical estimation in the next chapter indicates the effects of the various relationships between products on the probability that they are produced by the same firm. Chapter 5. Product Choice: A Model 117 5.5 Conclusion This chapter presented a number of mathematical models which related the connec-tions between products (eg. neighbouring or allowing the possibility of cost advantages from joint production) to the probability that the products would be introduced by the same firm. Admittedly, some of the relationships can not be shown for all values of the conjectural variation terms. However, it is felt that the analysis provides some indication of the influences of product relationships on the probability of a firm choosing certain combinations of goods. First, it was shown that equilibrium prices are higher if neighbouring products are produced by the same firm rather than all products produced by different firms. Fur-thermore, under Bertrand assumptions the prices are the same when nonneighbouring products are produced by the same firm as would be the case if all products were produced by separate firms. Next, as long as firms hold conjectures which do not overestimate the responses of other firms a product yields greater profits to the producer of a neighbouring product than it would to another firm. This advantage of a firm with a neighbouring product was also shown to decline as the time between introductions increases. The study of the effects of cost advantages suggested, at least for consistent conjec-tures or demand that is inelastic with respect to the prices of other products in the case of Bertrand assumptions, that a reduction in marginal costs increased the profits of that firm and decreased the profits of others. Finally, the potentially higher profits that would be generated by these relationships between products, or any other cause, were shown to increase the probability that the firm in question would introduce the product. The issue of which firms were likely to produce, rather than introduce, a product was explored using the same prediction of the impact on the relationship between products and their profitability. It also relied upon the ease of entry and exit which pertains to the production of any one good in the insecticide industry. Again it was felt that firms will produce the more profitable combinations of goods. Chapter 5. Product Choice: A Model 118 Thus, this chapter related the influence of firms having neighbouring products or products which could potentially yield cost advantages to the probability of such firms choosing particular products. Estimation is conducted in the following chapter to deter-mine if there is any empirical support in the insecticide industry for these predictions. Chapter 6 Product Choice: Empirical Results 6.1 Introduction This chapter discusses the procedure used in the empirical estimation of how the relationships between products, such as whether they are neighbours on the frontier, affect which combinations of products are introduced or produced by the same firm. The estimation is conducted in two sections. First, it is determined how the relationships between existing products and a new good are associated with the likelihood of the new good being introduced by the same firm as one of the existing products. Secondly, it is determined how these relationships between existing products are associated with the likelihood of certain combinations of these goods being produced by the same firm. In particular, this section looks at both the production of concentrates in every fifth year and the production of formulations in every tenth year. The chapter then presents the results of the estimations and relates these to the predictions of how relationships between products would influence the probability of being introduced or produced by the same firm. 6.2 Estimation Procedure This section of the chapter contains a discussion of the estimation procedure and the variables that are used. There are two subsections of this area. The first deals with the estimation of the influences of product interactions on the introduction of new products while the second deals with estimating the effects on the production of existing goods. 119 Chapter 6. Product Choice: Empirical Results 120 6.2.1 The Introduction of New Products Tests which would reveal a tendency of firms to introduce products with similar characteristics must be able to analyse information that is largely, if not entirely, of a qualitative nature. Despite a lack of information on the effective research effort that is allocated toward the development of particular insecticides, it still should be possi-ble to test the effects of the hypothesized causes of differentials in research effort (ie. cost advantages or potential for local monopoly power) on the ultimate effects of these differences (ie. the probable identity of the firm which introduces a product). The use of neighbour relations to describe the relative locations of products in char-acteristics space requires the use of a discrete metric1. As an alternative, restrictive as-sumptions would have to be made about the distribution and symmetry of preferences 2 . Potential methods of testing, therefore, must analyse the discrete forms of information that are generated by the neighbour relations and by identifying the firms which make the introductions. Possible procedures are basically restricted to discrete regression models, such as logit or probit, or to nonparametric testing with the use of contingency tables. There are three possible forms of discrete regression models which could be adopted: The dependent variable could be categorized by the identity of each firm, by the history of a firm's introductions, or by the relationships of firms responsible for each member of a group of goods. In broad terms, the idea behind the dependent variable is to attach some sort of identity to the firm that was responsible for the introduction of a product. The most obvious method is to use a multinomial logit model with separate categories for each firm. This is basically similar to the approach taken by West (1979, 1981a, 1981b) although he utilized contingency tables in his analysis rather than regressions. However, the use of separate categories for each firm is not valid in this case because firms entered and exited the industry during the period of study. Furthermore, it is not known which 2For example, by studying competition in geographic space rather than characteristics space, West (1979, 1981a, 1981b) found it necessary to assume directional symmetry of preferences and transportation costs. for neighbouring products for other products Chapter 6. Product Choice: Empirical Results 121 firms could have potentially introduced any product. There may have been companies which, although they devoted effort to introducing a product, never actually won a patent. Finally, many of the firms which have existed throughout the study period have been extensively involved in many aspects of the pharmaceutical, plastic and industrial chemical industries. The use of independent variables to describe a firm (eg. total assets or total research expenditures) bear little relation to that firm's incentives to develop a particular chemical in a particular branch of the agricultural chemicals industry. An alternative to the use of firm specific categories is to classify companies by the history of their introductions. Of course, this approach would require a model similar to McFadden's (1974) conditional logit model since the properties of each firm and prod-uct would be taken into account. The intuition behind the use of McFadden's model is that different categories of firms have different probabilities of introducing different types of products. The major difficulty with this application of the approach is that the introduction of a product affects the entire insecticide market and, therefore, affects the incentives for another product to be introduced. This is significantly different from the application of McFadden's technique in models concerned with the choice of products for consumption, since it is generally assumed that such choices are made independently of past consumption. Although Morey (1981) did use such history-dependent choices, he could treat different individuals' choices of ski sites as independent observations. Since each insecticide has only been introduced once, the use of a history-dependent estimates of which firm would introduce a product would result in only one observation in most categories. There would have to be a category for firms which had not introduced any products, another for firms which had introduced a good which was in a particular lo-cation relative to each other good of the same chemical type, and more categories to describe products which have been introduced by the same firm. The analysis would become extremely complex if each product's chemical type and position relative to other products were taken into account (eg. twenty products would require 210 categories to describe all their relative locations). A more general classification system is obviously required. Chapter 6. Product Choice: Empirical Results 122 The final alternative requires a reassessment of the underlying ideas about the rela-tionships that are to be tested. The first proposal outlined above involved calculating the probabilities that a particular company would make an introduction based upon how well the product fits into each firm's portfolio. The second only differed by defining the identity of the firm by the record of the products it had already introduced. Based upon the knowledge of which firm introduced which product, it should also be possible to uti-lize the chemical and locational (in characteristics space) relations between products to provide some information about probable connections between the firms that introduced them. As an example, if firms showed a strong tendency to introduce goods which neigh-bour one another, it is likely that a new product would be introduced by the firm that introduced the products it neighbours. This is based upon an assumption that all firms act identically in equivalent situations rather than the idea that a particular firm acts in the same manner in all situations. Any analysis which concentrates on relationships between goods must use groups of goods as the units of observation. To determine if products are similar to one another, it is necessary to judge them in pairs or, perhaps, larger groups. When discussing the firms responsible for the introduction of a group of goods, the most obvious relationship that the companies may have is that they are the same firm. The dependent variable, (FIRM)3, is set equal to one if the same firm introduced both products and set equal to zero otherwise. Before discussing the independent variables themselves some mention is made of the intuition behind the use of these variables and possible problems of using this type of estimation procedure. The intuition behind the effects of the independent variables on the probability of a firm introducing a new product proceeds as follows: Each firm's potential profit from introducing a product determines that firm's effort as a function of the effort levels of all other firms. The firm's relative amount of effort in equilibrium then determines its probability of making the introduction. Each existing product is assumed to have an independent effect upon the probability that the firm which introduced it will 3Variable names are given in parentheses. Chapter 6. Product Choice: Empirical Results 123 also introduce the new product. The total probability that a particular firm makes an introduction is found by summing the probabilities that are generated by each of the products which it had already introduced. Furthermore, the overall probability of any existing firm making the introduction can be found by taking the sum of the probabilities associated with each firm. , Since only one firm is assumed to make an introduction the relative probabilities as-sociated with each firm, conditional on the introduction being made by any existing firm, can be found by proportionately dividing all joint probabilities. As an example, imagine three consecutively introduced products, 1, 2, and 3. Let there be a 20% probability that a product is introduced by the same firm as an existing neighbouring product and a 10% probability of being introduced by the same firm as a nonneighbouring product. In other words, product 3 has a 20% chance of being introduced by the same firm as product 2 and a 10% chance of being introduced by the same firm as product 1. Thus, product 3 has an overall probability of 28% (ie. 0.1 + 0.2 - 0.1 x 0.2 = 0.28) that it is introduced by the firms that either introduced product 1 or 2. The assumption that only one firm introduces a product implies that the term describing the probability of joint introduction (ie. 0.1 x 0.2 = 0.02) must be divided among firm 1 and 2. For instance, the probability of joint introduction (ie. 0.02) is multiplied by the relative probability of a firm making the introduction (eg. the weight used for firm 2 is 0.2/(0.1 + 0.2)). Thus, the conditional probability (ie. conditional on the product being introduced by either firm 1 or firm 2) the product is introduced by firm 2 is Similarly, it can be shown that the conditional probability of firm 1 making the intro-duction is 0.3333. Note that as the probability of joint introductions increases (ie. the discovery of insecticides deviates from a Poisson process) the numerators deviate from the actual probability but the ratio of conditional probabilities remains the same as the ratio of actual probabilities (ie. 0.2/0.1). Since information is not available on all of the firms which may attempt to introduce a good the estimation must rely upon comparing the influences of the firms which had introduced the existing products. Obviously, this Chapter 6. Product Choice: Empirical Results 124 analysis can not be used to determine the actual magnitude of the effect of a neighbour-ing product on the probability of the same firm introducing both. It should, however, indicate the proportional difference that such a relationship makes on the probability that such a firm would make the introduction. Note that a rather strong assumption of the analysis is that each product has an independent effect on the probability of that firm also introducing the new product. In fact, there may be additional effects if a firm has a number of existing products (eg. there may be a special advantage to local monopoly power over a facet of the frontier which exceeds the effects of each of the pairwise relationships). These effects will be taken into account to some degree by using variables to indicate the total number of existing products, the number that are neighbouring the new good, and the number that have the potential for cost advantages. The analysis also generates a possible source of bias due to an inability to distinguish if one of a firm's existing products created all of the incentive for the firm to introduce the new good. Instead, the approach attributes the incentives to all of the firm's existing products. As an example, a firm which introduced products 1 and 2 may wish to intro-duce product 3 to take advantage of local monopoly power resulting from goods 2 and 3. However, the approach attributes the incentives for introducing product 3 to the con-nections between goods 1 and 3 and between 2 and 3. The estimation relies upon overall association between the connections and the probability of causing the introduction to distinguish whether 1 or 2 is more likely to have created the incentives to introduce prod-uct 3. Any biases which are created by these effects are, hopefully, relatively minor since there are only six out of 221 observations in which the wrong product could be concluded to have caused the introduction. The independent variables used in the estimation are chosen to differentiate the factors which may influence the probability of a particular firm introducing a product. Choice is somewhat limited by the requirement that product pairs are treated as observations. As was previously mentioned, the similarity of the characteristics mixes offered by a group of products will be determined by noting the goods' neighbour relations. This is Chapter 6. Product Choice: Empirical Results 125 treated as a dummy variable, (NEI), that is set equal to one if the products neighbour each other and zero otherwise. If a firm controls the production of two neighbouring products, it possesses some degree of monopoly control over consumers who wish to purchase a convex combination of characteristics that are available from these products. The previous chapter indicated that a firm with a neighbouring product has a higher probability of introducing a good in comparison to a firm without a neighbouring product. This would suggest that this variable has a positive coefficient. Although a greater degree of monopoly power would be possible if a firm controlled an entire facet (ie. three neighbouring products), checking product pairs allows a more sensitive study of the pursuit of monopoly power rather than concentrating on its achievement. Unfortunately, it is not possible to observe which combinations of products have the potential for cost advantages from their joint production. Instead, the chemical similar-ity of products is used as an indicator of which combinations have this potential for cost advantages. This choice is based upon the observation that chemically similar products generally share common inputs and have similar manufacturing processes. Chemical sim-ilarity of products is represented with another dummy variable, (CHEM), which equals one if each product is a member of the same chemical group (eg. organophosphates, cyclodienes) and equals zero otherwise. Recall that the previous chapter indicated that a firm with a product which would yield cost advantages in combination with the new good has a higher probability of introducing the good. Thus, the variable (CHEM) is also predicted to have a positive coefficient. Other variables are included in the analysis to provide further information on the conditions which provide a firm with a comparative advantage in introducing new prod-ucts. An increased number of years between the introductions of neighbouring products, (NEI*YRS), is predicted to have a negative coefficient since there is a reduction in the value of simultaneous patent protection on both products. Since neighbouring products exert relatively less influence on the introduction of a good it must imply that non-neighbouring products exert relatively more. This suggests that the variable indicating an increased number of years between nonneighbouring products, (YRS), has a positive Chapter 6. Product Choice: Empirical Results 126 coefficient. The effect of increased time between the introductions of chemically similar products, (CHEM*YRS), is uncertain since the value of any cost advantage is not pre-dicted to change over time. If anything, this variable would have a negative coefficient to reflect a firm's loss of comparative advantage as the production technology for a class of chemicals becomes more widely known. Finally, variables indicating the number of neighbouring products, (NNE), the number of chemically related products, (NCH), and the total number of products (TOTAL) are used in an effort to weight the influence of each observation of a neighbouring pair of products or a chemically similar pair. In other words, if there are only two products in the market the influence of each of these is expected to be greater than the influence of a product when there are many goods in the market. The empirical estimation is done using logit and probit regressions with the SHAZAM econometric package. The applications of this program are briefly outlined by White (1987) with a more detailed account of the program's capabilities given by White (1988). The independent variables enter into the regression as a general second-degree equation since there are no a priori beliefs about the functional form. The procedure that is used in conducting the regressions proceeds as follows: Origi-nally, all variables are included in the equations. After a regression is run the variable (ie. one of the terms in the second-degree equation composed of the previously mentioned independent variables) with the lowest asymptotic t-ratio associated with its coefficient is eliminated from the equation and the regression is rerun. This procedure is repeated until all remaining variables have t-ratios which are significantly different from zero. Note that each elimination of a variable is checked using the likelihood-ratio test. This concludes the discussion of the estimation procedure used for the introduction of new products. The following section reviews the procedure for the estimation of the effects of product interactions on the choices made in the production of existing products. The results of the regressions are discussed in a later section of this chapter. Chapter 6. Product Choice: Empirical Results 127 6.2.2 The Production of Existing Products The analysis of the production choices of multiproduct firms is somewhat different from the analysis of the introductions. The principal differences are that more than one firm may actually produce a product rather than a single firm making an introduction and that there is no well-defined equivalent to effort which serves as a link between the profitability of a combination and the probability that a firm chooses such a combination. As mentioned earlier, predictions of which firms produce a good rely upon the easy entry and exit of firms in the production of any particular product to ensure that these goods are produced by firms which find them most profitable. As in the section on introductions, estimation of the production decisions utilizes pairwise comparisons of products to determine the factors that influence the probability of a firm producing both. Since a number of firms may produce each product, the influence of each of these firm-specific versions, hereafter referred to as a "brand", is treated separately. Each product-pair consists of the product that is to be predicted and a brand of the other good. This is done in an effort to distinguish each brand's influence on the identities of the firms that produce the product. The dependent variable, (FIRM), is set equal to one if the product-pair is produced by the same firm and is set equal to zero if produced by different firms. As an example, if three firms produce brands of a good which could result in local monopoly power if produced with a particular product then the three firms are credited with having an equal probability of producing the other good. Note that some degree of local monopoly power is still possible when discussing the production of existing goods since the firm may be able to develop monopoly control of the production of a certain combination of products in a specific geographic market. Unfortunately, information is not available on the locations of production facilities so the influence of monopoly power in geographic space can not be tested. The overall probability of a firm producing a product is found by summing the prob-abilities associated with each of their brands being produced by the same firm as the product of interest. Firms are then ranked according to their probabilities of producing the good. If there are N firms which actually produce the product the N highest ranked Chapter 6. Product Choice: Empirical Results 128 firms are predicted to be the producers. As an example, there may be ten firms in the market and each is assigned a probability of producing a particular good. If only two firms actually produce the good then only the two firms with the highest probabilities are predicted to be the producers of the good. Rankings are used rather than some cutoff probability (eg. all firms with a probability greater than 0.8 could have been predicted to produce the good) to allow for differences in the demand and production costs of particu-lar products. In other words, although a good may have a large number of neighbouring products which would result in each of the respective firms having a high probability of producing the good a low demand for this good may imply that only one firm can actually undertake production. The analysis of the production of concentrates is run as cross-sectional estimations at five year intervals from 1952 to 19824. The estimations about the production of formulations are run at ten year intervals during the same period. The lack of available data for other years and the rapid rate of entry and exit in the production of each product preclude the use of a combined time-series/cross-sectional estimation. As in the case of introductions, dummy variables are set equal to one if the products (ie. the product/brand pair) are neighbouring (NEI) or chemically similar (CHEM) and set to zero otherwise. Again, the previous chapter suggests that the pursuit of local monopoly power or the potential for cost advantages should cause these variables to have positive coefficients. However, recall that since formulators generally add water to con-centrates and repackage them there is little reason to believe that the chemical structure of the products influences costs or the probability of chemically similar combinations. There is also some doubt about the ability of formulators to exercise any monopoly con-trol over particular combinations of products due to their large numbers and the simple technology employed in mixing the formulations. The estimations also use a variable to indicate the number of years between the introductions of the products, (YRS). The influence of simultaneous patent protection on two concentrates is opposite to what it is for the firms which introduced the products. 4Since data for 1957 are not available an estimation of 1956 production decisions is conducted instead. Chapter 6. Product Choice: Empirical Results 129 Presumably expiry of a patent means that a firm is no longer able to exert monopoly control over the production of a product (eg. licensing certain other firms to produce it). Therefore, there is an increased probability that any firm which finds the production of that good profitable is likely to undertake production. Since it is predicted that both firms with neighbouring products and chemically similar products increase the profitability of a good the variables, (NEI*YRS) and (CHEM*YRS), are predicted to have positive coefficients. Conversely, there is a reduced probability that other products are produced in conjunction with the good in question causing (YRS) to have a negative coefficient. Since the formulations of the products are mixed by many firms for local markets there is no indication that the period between introductions of two products affects a firm's decisions to formulate either neighbouring or chemically similar products. The influence of patent protection on the products is also captured by a term indicat-ing the number of years since the second introduction, (LAST). Finally, terms are also introduced to indicate the number of firm-specific products (ie. brands) that neighbour either product, (EITH), and the number that neighbour both, (BOTH), in an effort to weight the effects of product interactions. The empirical estimations are conducted using logit regressions with the SHAZAM econometric package. Again, the variables enter into the regression as a general second-degree equation. To facilitate the comparison of different years of the analysis, the results of the estimations of general second-dgree equations are presented first. The sensitivity of the regressions to their exact specification is indicated by eliminating variables with insignificant coefficients. Although these results do not allow year to year comparisons, they do indicate which terms can be concluded to influence the probability of producing a product pair (ie. the null hypotheses would be that the variables have no effect). The same procedure is used for eliminating variables from the equation as is used in the estimation of the introductions. Note that there is severe multicollinearity between a number of variables in the estimation of the production of concentrates in 1972 and later years. This precludes the estimation of the entire general second-degree equation during this period. Chapter 6. Product Choice: Empirical Results 130 The next section reviews the estimation results indicating which factors influence the introduction of new products, the production of concentrates and the production of formulations. 6.3 Empirical Results This portion of the chapter presents the results of the regressions on product choice. The first section deals with the introduction of new products and a later section deals with the production of existing products. There is a discussion of how well the empirical results correspond to the predictions of the previous chapter and how well the estimated equations fit the data. 6.3.1 The Introduction of New Products The results of both the logit and probit analyses of the introductions of new products are given in Table 6.1. All other variables of a general second-degree equation are not significant and have been eliminated from the estimation. A reminder and summary of the definitions of the basic variables is provided in Table 6.2. Chapter 6. Product Choice: Empirical Results 131 Table 6.1: Products Introduced by the Same Firm (asymptotic t-ratios in parentheses) n = 221 Variable Logit Probit CHEM 3.905 (3.62) 2.168 (3.72) NEI 16.968 (3.06) 9.344 (3.00) YRS 2.723 (2.50) 1.454 (2.53) TOT 0.604 (2.49) 0.331 (2.51) NNE 5.218 (2.16) 2.810 (2.15) NEI*YRS -1.238 (-2.58) -0.651 (-2.61) NEI*NNE -2.153 (-2.54) -1.199 (-2.45) YRS*TOT -0.145 (-2.31) -0.077 (-2.32) YRS 2 -0.032 (-2.31) -0.017 (-2.33) NNE 2 -0.386 (-2.00) ' -0.205 (-2.04) CONSTANT -32.173 (-3.19) -17.632 (-3.20) Chapter 6. Product Choice: Empirical Results 132 Table 6.1 cont'd (Measures of Goodness of Fit) Statistic Logit Probit Cragg-Uhler R2 0.568 0.574 Prediction Success(%) 94.6 94.1 LL(0) -57.4 -57.4 LLF -28.5 -28.1 Note that the signs of the coefficients for (NEI) and (CHEM) correspond to the predictions of the model. As expected, both neighbouring products and chemically similar products have a higher probability of being introduced by the same firm. However, note that confirmation that firms appear to pursue local monopoly power does not imply that they actually achieve it. Of the four firms which introduced three or more products only one introduced all the products forming a facet of the frontier. The coefficients of (YRS) and (NEI*YRS) also correspond to the predictions of the model. The relative influence of the neighbouring product declines over time (ie. (NEI*YRS) has a negative coefficient) and the relative influence of other products in-creases (ie. (YRS) has a positive coefficient). Also note that the small negative value for (YRS2) does not change the slopes during the period of the study. It should be emphasized that the regressions are merely designed to search for correlations between the independent and dependent variables. Bearing this in mind, the magnitudes of the coefficients should be interpreted with caution since they are not representative of any underlying structural equation. Their signs merely indicate whether higher values of the independent variables are positively or negatively associated with the dependent variable. Thus, although the results of the regressions can be used to determine if the correlations predicted in the last chapter actually occur, the inability to estimate any structural equation precludes the use of the regressions to predict future occurrences. Chapter 6. Product Choice: Empirical Results 133 Table 6.2: Variable Definitions: Introductions Variable Definition (dependent variable) FIRM Both products introduced by the same firm (independent variables) NEI Products are neighbours on the market opportunity frontier when the second is introduced CHEM Products are in the same chemical category YRS Number of years between the introductions TOT Total number of existing products at the time of the introduction NNE Number of neighbouring products at the time of the introduction NCH Number of products in the same chemical group at the time of the introduction Chapter 6. Product Choice: Empirical Results 134 In addition to the close correspondence between the signs of the coefficients and the predicted results the regressions also fit the data fairly well. Refer to Maddala (1983) for a discussion of the Cragg-TJhler R2. This is actually a pseudo-i?2 designed to take into account the maximum possible value of the likelihood function. However, care must be taken in interpreting particular measures of goodness of fit. The rather high percentage of observations that are predicted correctly is due to the small number of observations in which the dependent variable is equal to one (ie. both products introduced by the same firm). Any model which assigns a low probability to the possibility of a firm introducing both products could achieve this type of prediction success. Another indication, although still inadequate, of the power of the model is the percentage of times that it correctly predicts that a firm would actually introduce both products of the product pair rather than the percentage of times that it correctly predicts any observation. The prediction success in cases where both products are introduced by the same firm, 16 cases in all, is 50% in both the logit and probit analyses. These estimates, however, only illustrate the effects of relationships between product pairs. The same problem also arises from the use of the R2 measure of the goodness of fit. Since a new product is influenced by all existing goods, little weight should be given to either type of prediction success mentioned so far. A better measure of goodness of fit is the ability to predict which firm does or does not introduce a particular product based upon the influences of all the product relationships. In addition to this, the power of the test rests in its ability to predict which firms introduce which products. Predictions of the overall probability that a firm introduces a particular product are found by taking the sum of the probabilities associated with the new product being introduced by the same firm as any of that firm's existing products. The probabilities associated with each firm are then added to determine the overall probability that the new product is introduced by any firm which had introduced an existing good. The results for each product are listed under the heading "Any Existing Firm (%)" in Table 6.3. As an example, when Methoxychlor is introduced the model assigns a 41.35% probability that it is introduced by either ICI, Geigy or Velsicol, the companies which had already Chapter 6. Product Choice: Empirical Results 135 introduced products in this market. The probability, conditional upon the product being introduced by any of the firms with existing products, of any particular firm making the introduction is listed in the row corresponding to that firm. Again, using Methoxychlor as the example, if either ICI, Geigy or Velsicol were to introduce Methoxychlor a 77.44% probability is attached to the likelihood of Geigy being the firm to make the introduction. As was explained earlier, these probabilities are calculated by adding the probabilities associated with each of the existing goods of that firm. Each firm's conditional probability of making the introduction is found by proportionately dividing all joint probabilities of introduction and is based upon the assumption that a patent will be granted to a single firm. If no probability is calculated for a particular firm it is because that firm has not introduced any goods prior to the year that the product in question was introduced. A predictions of which firm is likely to make an introduction is decided by the firm with the highest, conditional, probability. These predictions should be compared to the identity of the firm which actually made the introduction which is listed under the term "Successful Firm". Note that the model is unable to make predictions about firms that have not yet introduced a product into the market. This is because all of the information on the firms is based upon the products they have in the market. Chapter 6. Product Choice: Empirical Results 136 Table 6.3: Predicted Introductions of New Products (Logit) Probabilities Conditional on Introduction by Any Existing Firm (%) Products: DDT Chlordane Methoxychlor Parathion Any Existing Firm (% ) 9.86 32.75 41.35 5.95 Firms: ICI 100.00 9.91 7.43 19.79 Geigy 90.09 77.44 72.33 Velsicol 15.12 7.88 Successful Firm: Geigy Velsicol Geigy Am Cyan. Products: Aldrin Dieldrin Heptachlor Toxaphene Any Existing Firm (% ) 62.91 63.91 68.94 65.69 Firms: ICI 0.45 0.74 7.18 14.66 Geigy 1.86 2.00 33.28 49.08 Velsicol 4.68 7.77 21.43 36.13 Am. Cyanamid <0.01 0.03 0.92 0.12 Hyman 93.01 89.45 5.89 0.01 Hercules <0.01 0.01 31.31 — Successful Firm: Hyman Hyman Velsicol Hercules Products: Allethrin M.-Parathion Malathion Demeton Any Existing Firm (% ) 5.37 1.85 72.26 98.53 Firms: ICI 8.50 8.02 0.12 0.03 Geigy 85.46 31.05 0.09 0.36 Velsicol 2.00 30.83 0.05 5.26 Am. Cyanamid 0.22 5.80 85.39 38.73 Hyman 0.14 0.69 0.01 1.32 Hercules 0.07 13.15 <0.01 0.45 Bayer 3.60 — 0.39 53.37 Sumitomo — 10.46 13.95 0.47 Successful Firm: Sumitomo Bayer Am. Cyan. Bayer Chapter 6. Product Choice: Empirical Results 137 Of nineteen common insecticides introduced since 1940 (botanicals such as Rotenone and Pyrethrum were used prior to the turn of the century) eleven were introduced by firms which had already introduced another of the products. The model is successfully able to predict seven out of eleven of these introductions (ie. 63.6%). Furthermore, in three of the remaining cases the model ranks the firms which actually made the introductions as second out of eight existing firms. In the final case, the firm to make the introduction is ranked third out of six. This rate of success is especially noteworthy in light of the lack of available data on the research efforts of the firms. The result suggests that the use of product interactions to determine the differentials in incentives is a viable approach to the analysis of introductions by multiproduct firms. At this point some mention should be made of the contribution of characteristics theory to this analysis. In particular, how do the results differ if the variables generated by the characteristics approach, (NEI) and (NNE), are not included? When a logit regression is run under these conditions all variables except (CHEM*TOT) and the constant are eliminated. These variables merely indicate that the influence of being a chemically similar product pair grows as the total number of products increases. The elimination of the variables generated by the characteristics approach reduces the model's ability to predict observations of firms introducing a product pair to zero. Furthermore, it only allows the correct prediction of the firm to introduce a product in four out of eleven cases. Thus, the loss of significance of most of the variables in the analysis and the reduced ability to fit the data suggest that failure to recognize the interactions of these products in characteristics space eliminates much of the usefulness of this approach to studying product introductions. The next section of this chapter discusses the estimation results for the production of existing products. Chapter 6. Product Choice: Empirical Results 138 Table 6.3 cont'd. Probabilities Conditional on Introduction by Any Existing Firm (%) Products: Endrin Chlorthion Diazinon Azinphos-M Any Existing Firm (% ) 92.98 94.25 92.75 87.08 Firms: ICI 2.57 <0.01 <0.01 0.04 Geigy 3.57 27.66 22.12 15.99 Velsicol 5.54 0.06 6.46 0.84 Am. Cyanamid 2.18 35.94 17.47 23.90 Hyman 84.28 1.34 1.99 1.50 Hercules 0.38 1.06 1.01 0.52 Bayer 1.26 33.87 50.29 56.69 Sumitomo 0.22 0.08 0.66 0.53 Successful Firm: Hyman Bayer Geigy Bayer Products: Dimethoate Aldicarb Carbofuran Any Existing Firm (% ) 97.76 1.50 0.89 Firms: ICI 0.28 <0.01 <0.01 Geigy 13.65 21.72 13.68 Velsicol 2.98 — — Am. Cyanamid 32.33 12.63 33.23 Hyman 4.30 <0.01 <0.01 Hercules 1.65 <0.01 2.49 Bayer 44.79 48.40 17.51 Sumitomo 0.02 <0.01 4.17 FMC 17.25 — Union Car bide — 28.92 Successful Firm: Am . Cyan. U Carb FMC Chapter 6. Product Choice: Empirical Results 139 6.3.2 The Production of Existing Products The results of the logit estimation of the production of concentrates in a general second-degree equation are given in Table 6.4. Note that the development of high de-grees of correlation between certain terms of a general second-degree equation precluded the use of this functional form during the 1970s and 1980s. The appropriate variable def-initions are provided in Table 6.5. Following this, Table 6.6 lists the results of estimating the same equations when variables with insignificant t-ratios are eliminated. These re-stricted equations were generated' by first estimating the entire general second-degree equation and by rerunning the estimation with the least significant coefficient restricted to equal zero (ie. the variable was omitted from the estimation). The variable with the least significant coefficient was dropped from the estimation during each iteration of this procedure until all coefficents had significant t-ratios at the 90confirmed that each of the omitted variables was not significant by conducting a liklihood ratio test. Although the resulting estimates are not comparable, the fact that the alternative specification of the model has not produced different signs for the coefficients suggests that the results are reasonably robust. Chapter 6. Product Choice: Empirical Results 140 Table 6.4: Concentrates Produced by the Same Firm (Logit): I 1952 1956 1962 1967 NEI 3.366 (1.71) 3.000 (2.27) 1.385 (0.87) 0.971 (0.52) CHEM -2.628 (-1.10) 0.463 (0.42) 1.400 (1.46) - -0.134 (-0.09) YRS -0.032 (-1.01) -0.057 (-2.33) -0.096 (-4.80) -0.051 (-2.30) LAST -1.287 (-2.39) -0.088 (-0.37) -1.009 (-5.10) -0.460 (-2.69) EITH -0.465 (-0.43) -0.046 (-0.10) -1.079 (-3.86) -0.707 (-2.20) BOTH 0.063 (0.06) -0.199 (-0.34) -1.649 (-2.28) -0.527 (-0.63) NEI*CHEM 2.519 (3.41) -0.450 (-1.38) -0.631 (-1.76) -0.034 (-0.07) NEI*YRS 0.028 (1.50) 0.009 (0.77) 0.023 (1.53) 0.003 (0.19) NEITAST -1.061 (-4.98) -0.206 (-1.94) -0.174 (-1.83) -0.209 (-2.33) NEI*EITH 0.089 (0.47) -0.088 (0.65) 0.040 (0.44) 0.179 (1.66) NEI*BOTH 0.428 (0.92) -0.077 (-0.25) 0.526 (1.48) 0.873 (2.14) CHEM*YRS -0.035 (-1.74) 0.003 (0.23) -0.030 (-1.96) -0.0002 (-0.009) CHEM*LAST 0.244 (1.25) -0.091 (-1.04) 0.050 (0.83) 0.054 (0.81) Chapter 6. Product Choice: Empirical Results 141 Table 6.4 cont'd. 1952 1956 1962 1967 CHEM*EITH 0.222 (0.81) 0.005 (0.04) -0.151 (-1.95) -0.022 (-0.27) CHEM*BOTH -0.587 (-1.30) 0.194 (0.88) -0.279 (-1.02) -0.143 (-0.50) YRS*LAST 0.001 (0.81). 0.001 (1.03) 0.005 (6.47) 0.001 (1.85) YRS*EITH -0.003 (-0.83) 0.0003 (0.19)--0.006 (-4.17) -0.002 (-1.73) YRS*BOTH -0.004 (-0.58) 0.0009 (0.19) 0.006 (1.02) 0.002 (0.46) LAST*EITH 0.176 (2.54) 0.019 (0.80) 0.113 (6.12) 0.050 (3.26) LAST*BOTH 0.153 (1.62) 0.030 (0.54) 0.171 (3.41) 0.061 (1.36) EITH*BOTH -0.096 (-0.80) 0.0004 (0.006) -0.077 (-2.23) -0.064 (-1.62) YRS 2 0.0003 (2.07) 0.0003 (2.63) 0.0004 (4.04) 0.0003 (2.70) LAST 2 0.020 (4.52) 0.001 (0.72) -0.0003 (-0.19) 0.003 (1.82) EITH 2 -0.016 (-0.24) -0.008 (-0.32) -0.016 (-1.62) -0.010 (-0.99) BOTH 2 0.031 (0.20) 0.047 (0.50) 0.076 (0.76) -0.085 (-0.69) CONSTANT 2.389 ' (0.48) -0.328 (0.14) 10.309 (4.34) 5.43 (1.91) n = 1056 1781 2430 1616 Chapter 6. Product Choice: Empirical Results 142 Table 6.4 cont'd. (Measures of Goodness of Fit) 1952 1956 1962 1967 Cragg-Uhler R2 0.146 0.093 0.124 0.095 LL(0) -580.3 -1132.5 -1413.2 -859.6 LLF -526.2. -1070.7 -1305.0 -807.6 I: All Product Pairs (%) 77.4 67.8 73.1 78.3 II: Pairs by Same Firm (%) 10.3 16.9 4.6 7.2 III: If Firm Produces/Not (%) 83.3 83.0 87.2 85.4 IV: If Firm Produces (%) 55.4 58.9 57.7 51.1 Chapter 6. Product Choice: Empirical Results 143 Variable Table 6.5: Variable Definitions: Production Definition (dependent variable) FIRM Both products produced by the same firm (independent variables) NEI Products are neighbours on the market opportunity frontier CHEM YRS LAST EITH BOTH Products are in the same chemical category Number of years between the introductions Number of years since the last product was introduced Number of brands neighbouring either of the products Number of brands neighbouring both of the products Chapter 6. Product Choice: Empirical Results 144 Table 6.6: Concentrates Produced by the Same Firm (Logit): II (asymptotic t-ratios in parentheses) 1952 1956 1962 1967 1972 1977 1982 NEI 3.241 (6.20) 1.168 (4.08) 5.664 (4.21) -12.940 (-3.67) 7.821 (3.26) CHEM 1.400 (3.15) 1.212 (4.63) YRS -0.042 (-3.51) -0.045 (-5.50) -0.159 (-6.71) -0.081 (-3.49) 0.181 (4.43) 0.577 (4.55) LAST -0.697 (-3.11) 0.156 (5.13) -0.906 (-6.39) -0.242 (-2.40) -1.383 (-3.08) EITH -0.551 (-2.84) -2.88 (-6.61) -1.295 (-3.41) -5.762 (-2.96) -0.875 (-6.23) BOTH -3.836 (-3.75) -7.400 (-2.88) NEPCHEM 0.992 (3.29) -0.697 (-2.71) 34.724 (3.58) NEPYRS 0.013 (2.69) 0.033 (2.60) NEPLAST -0.638 (-5.63) -0.110 (-3.40) -0.187 (-3.90) -0.020 (-2.09) -0.175 (-2.23) NEPEITH 2.062 (3.86) NEPBOTH 0.486 (3.00) CHEM*YRS -0.037 (-2.57) Chapter 6. Product Choice: Empirical Results 145 Table 6.6 cont'd. 1952 1956 1962 1967 1972 1977 1982 C H E l v r L A S T CHEM*EITH C H E M * B O T H YRS*LAST YRS*EITH LAST*EITH LAST*BOTH YRS2 LAST 2 BOTH 2 CONSTANT 0.124 (3.62) -0.190 (-3.83) 0.0003 (3.41) 0.012 (5.01) 0.074 (2.47) 1.460 -1.769 (1.12) (-7.61) 0.0.71 (3.98) -0.206 (-3.30) 0.022 (3.22) 0.0004 (4.34) 24.257 (6.21) -0.306 (-2.18) 0.001 (2.27) 0.005 (6.82) -0.005 (-3.61) 0.104 0.038 (6.58) (3.29) 0.142 (3.93) 0.0002 (3.15) 7.251 (5.75) -0.017 (-3.81) 0.005 (2.49) -0.0007 (-4.01) -3.793 (-8.85) -1.258 (-3.43) -0.060 (-4.16) 0.196 0.010 (2.87) (2.85) 0.210 (2.44) -0.0021 (-4.49) 37.535 (2.95) 0.857 (130) 1056 1781 2430 1616 825 408 403 Chapter 6. Product Choice: Empirical Results 146 Note that the signs of the coefficients of (NEI) and (CHEM) in both Table 6.4 and 6.6 confirm the predictions that they are positive. The only exception, (NEI) in 1977 in Table 6.6, corresponds to a rather large value (ie. 34.74) of the coefficient for the choice of products which are neighbouring and chemically similar (ie. NEI*CHEM). These results correspond to the observation that during the 1970s the portfolios of products of most firms were greatly reduced. This may have been due to restrictions placed on the use of a number of products (eg. DDT) or could also be due to the effects of rising energy costs. The greater importance of recent products and the botanicals, discovered before World War II, results in the only positive value of the coefficient for the effects of an increased period between introductions (YRS). A large percentage of the firms that remained in the market were those that specialized in the short-lived botanicals or in organophosphates. Consequently, these firms held portfolios of products which were generally neighbouring and chemically similar. As mentioned in the analysis of introductions, confirmation of the pursuit of local monopoly power does not imply that it is achieved. For example, in 1962 a total of 23 firms produced three or more products. Only 11 (ie. 48% ) of these firms actually produced all the products on a facet of the frontier. This, however, represents a greater success rate than in the case of introductions and may be due to the greater certainty associated with producing an existing product. It should also be emphasized once again that the regressions only indicate correlations between the independent and dependent variables. The magnitudes of the coefficients are not discussed since they are not indica-tive of any underlying structural equations. As in the case of introductions, little weight should be given to the traditional mea-sures of goodness of fit since they only describe the goodness of fit associated with ob-servations of individual pairs of products. Various measures of the percentage of correct predictions are also given in Table 6.4 and Table 6.6. The first measure (ie. I: All Product Pairs (% )) lists the percentages of all observations that were correctly predicted. Again, these values are large since the model correctly predicts that most product pairs are not introduced by the same firm. The second measure is of the percentages of times that Chapter 6. Product Choice: Empirical Results 147 Table 6.6 cont'd. (Measures of Goodness of Fit) 1952 1956 1962 1967 1972 1977 1982 Cragg-Uhler R2 0.121 0.087 0.118 0.082 0.139 0.393 0.301 LL(0) -580.3 -1132.5 -1413.2 -859.6 -275.8 -135.3 -151.1 LLF -535.7 -1074.6 -1310.7 -814.8 -247.0 -92.1 -116.3. I: All Product Pairs (%) 76.5 67.3 73.2 77.8 90.2 90.4 88.8 II: Pairs by Same Firm (%) 6.3 13.2 5.8 1.7 9.3 28.6 28.0 III: If Firm Produces/Not (%) 83.7 83.7 87.6 87.0 91.7 92.8 91.7 IV: If Firm Produces (%) 56.6 60.5 60.6 52.4 52.6 60.9 62.5 Chapter 6. Product Choice: Empirical Results 148 the equation correctly predicts that the product pair is produced by the same firm. As was mentioned in the section on introductions, these cases do not reflect the combined influences of products on the identities of firms that actually produce a good. The third measure (ie. Ill: If Firm Produces/Not (% )) gives the model's overall ability to predict that a firm does or does not produce a good. This is calculated by taking the sum of the probabilities that the product in question is produced by the same firm as each of the brands produced by a particular firm. Finally, the fourth measure indicates the ability of the model to predict which firms produce which products. Since there is little value to knowing which firms do not produce a product, it is the final case which gives the best indication of the predictive power of the approach. In summary, the estimates of product choice in the production of concentrates yields rather similar results to the estimates about product introductions. Both generally in-dicate that there is a greater probability that a product is chosen by a firm with a neighbouring product rather than a nonneighbouring good. Similarly, chemically simi-lar products have a greater probability of being selected by a firm rather than dissimilar products. Furthermore, although the two models have different abilities to predict the in-fluence of individual product pairs, both have about a 50 to 60% success rate in matching the data by predicting which firm introduces or produces a product. The large number of formulators and the ease of entry and exit into the production of formulations result in somewhat lower expectations that these firms choose product combinations that yield some degree of local monopoly power in characteristics space. Unfortunately, lack of available data makes it impossible to determine whether these firms do exercise local monopoly power in geographic space rather than in characteristics space. The results of the logit regressions on the production of formulations using general second-degree equations are given in Table 6.7. Again, the robustness of the results to the specification of the estimated model is illustrated by eliminating the insignificant variables as in Table 6.8. Note that these regressions maintain the same coefficient signs as those that resulted from the use of the entire general second-degree equations. Also note that the predictive power of the estimation is not changed by the elimination of the Chapter 6. Product Choice: Empirical Results 149 variables. These estimates do not correspond as well as the previous regressions to the predictions of the model. Again, the major discrepancy occurs during the 1970s and may be due to the increased reliance on botanicals and other short-lived insecticides. This would also explain the positive signs on the coefficients of (YRS) and (LAST) during 1972 and 1982. Despite an inability to detect whether firms actually pursue local monopoly power there is some evidence that they do have some success in producing all products on a facet of the frontier. Again using 1962 as an example, all products forming at least one facet of the frontier were produced by 57 of the 104 firms (ie. 55% ) producing at least three products. This result does not contradict the inability of the analysis to detect the pursuit of local monopoly power but merely reflects the tendency of formulators to produce a large number of products (ie. an average of five products per firm). This necessarily increases the probability of producing adjacent products and reduces the ability of the regression to determine if the choices reflect the pursuit of local monopoly control of a facet. Chapter 6. Product Choice: Empirical Results 150 Table 6.7: Formulations Produced by the Same Firm (Logit): I 1952 1962 1972 1982 NEI 1.259 (1.20) 1.042 (1.26) -2.199 (-3.14) 1.426 (0.91) CHEM 1.301 (1.10) -0.662 (-1.51) -1.321 (-2.53) 2.408 (2.10) YRS 0.038 (2.48) -0.038 (-6.76) -0.002 (-0.30) 0.017 (1.84) LAST -0.693 (-2.30) -0.353 (-3.84) 0.144 (1.97) 0.506 (5.99) EITH 1.131 (2.10) -0.343 (-2.70) -0.203 (-1.58) 1.758 (6.52) BOTH 1.354 (2.22) -1.492 (-4.31) 0.287 (1.00) 0.376 (0.98) NEI*CHEM 0.326 (0.84) -0.422 (-2.63) -0.369 (-1.88) 0.470 (0.74) NEPYRS -0.018 (-2.38) 0.0004 (0.054) -0.007 (-0.96) -0.010 (-0.94) NEPLAST -0.158 (-1.45) -0.052 (-1.04) 0.023 (0.70) -0.015 (-0.27) NEPEITH 0.237 (2.34) 0.019 (0.48) 0.181 (3.51) -0.048 (-0.39) NEPBOTH -0.998 (-4.23) -0.040 (-0.24) 0.216 (1.21) -0.283 (-1.09) CHEM*YRS -0.023 (-1.64) -0.036 (-1.70) 0.040 (1.46) -0.012 (-1.02) CHEM*LAST -0.170 (-1.77) 0.048 (1.69) 0.063 (2.37) -0.144 (-2.43) Chapter 6. Product Choice: Empirical Results 151 Table 6.7 cont'd. 1952 1962 1972 1982 CHEM*EITH 0.129 (0.84) 0.082 (2.68) -0.031 (-0.76) -0.192 (-1.83) CHEM*BOTH -0.768 (-3.18) -0.329 (-2.81) 0.426 (3.87) 0.006 (0.03) YRS*LAST -0.0001 (-0.089) 0.002 (5.57) -0.001 (-1.99) -0.001 (-3.60) YRS*EITH -0.004 (-2.41). 0.0004 (1.17) -0.00003 (-0.08) -0.002 (-2.87) YRS*BOTH -0.004 (-1.23) -0.004 (-2.52) -0.002 (-1.22) -0.003 (-1.91) LAST*EITH 0.131 (3.54) 0.027 (3.34) 0.007 (0.99) -0.036 (-3.67) LAST*BOTH 0.024 (0.50) 0.081 (3.28) -0.023 (-1.51) 0.009 (0.53) EITH*BOTH -0.100 (-1.53) 0.047 (3.15) 0.031 (1.31) -0.149 (-3.72) YRS 2 -0.0001 (-0.98) 0.00002 (0.89) 0.0001 (1.73) 0.0001 (2.16) LAST 2 0.003 (1.34) 0.0002 (0.20)--0.001 (-2.13) -0.003 (-6.76) EITH 2 -0.109 (-3.49) -0.012 (-2.99) -0.001 (-0.17) -0.075 (-5.47) BOTH 2 -0.087 (-1.08) 0.003 (0.07) -0.168 (-3.50) 0.426 (5.18) CONSTANT -5.174 (-2.00) 5.595 (5.00) -1.278 (-1.33) -11.659 (-8.05) n = 3070 10790 7480 3250 Chapter 6. Product Choice: Empirical Results 152 Table 6.7 cont'd. (Measures of Goodness of Fit) 1952 1962 1972 1982 Cragg-Uhler R2 0.124 0.074 0.079 0.143 LL(0) -2002.4 -7471.4 -4541.0 -1978.5 LLF -1857.4 -7164.9 -4326.1 -1805.9 I: All Product Pairs (%) 64.2 61.1 70.3 71.0 II: Pairs by Same Firm (%) 27.0 72.9 6.0 13.1 III: If Firm Produces/Not (%) 80.0 80.8 80.7 78.9 IV: If Firm Produces (%) " 63.4 72.3 59.2 57.2 Chapter 6. Product Choice: Empirical Results 153 Table 6.8: Formulations Produced by the Same Firm (Logit): II 1952 1962 1972 1982 NEI 1.111 -2.061 (3.84) (-6.22) CHEM -1.831 5.637 (-2.75) (3.77) YRS -0.030 0.031 (-8.29) (2.44) LAST -0.573 -0.326 0.245 0.661 (-8.44) (-5.68) (10.12) (7.53) EITH -0.324 -0.110 2.605 (-3.01) (-7.31) (7.59) BOTH 0.403 -1.521 (7.10) (-5.56) NEPCHEM -0.379 0.957 (-2.74) (4.36) NEI* YRS -0.027 (-5.50) NEI*LAST -0.051 (-2.59) NEI*EITH 0.333 0.227 (8.07) (6.19) NEI*BOTH -0.976 (-5.62) CHEM*YRS -0.038 -0.025 (-2.11) (-4.21) CHEM*LAST -0.228 0.049 -0.138 (-6.46) (2.16) (-3.53) Chapter 6. Product Choice: Empirical Results 154 Table 6.8 cont'd. 1952 1962 1972 1982 CHEM*EITH 0.339 (7.92) 0.092 (4.99) -0.269 (-4.03) CHEM*BOTH -0.627 (-4.99) -0.391 (-4.01) 0.252 (3.06) YRS*LAST 0.002 (6.13) -0.0005 (-4.43) -0.0009 (-3.19) YRS*EITH -0.003 (-4.49) YRS*BOTH -0.004 (-3.50) LAST*EITH 0.120 (9.15) 0.027 (4.34) -0.040 (-5.16) LAST*B0TH 0.084 (4.20) 0.013 (2.53) EITH*BOTH 0.047 (4.14) -0.148 (-4.65) YRS 2 0.0001 (3.43) 0.0001 (3.20) LAST 2 ' -0.002 (-7.73) -0.004 (-8.35) EITH 2 -0.047 (-8.06) -0.012 (-3.26) -0.074 (-6.34) B O T H 2 -0.056 (-3.31) 0.397 (5.88) CONSTANT" -0.238 (-1.19) 5.185 (6.34) -5.191 (-9.70) -23.500 (-8.64) n = 3070 10790 7480 3250 Chapter 6. Product Choice: Empirical Results 155 The proportions of times that the model successfully predicted which firms produce the formulations are also given in Tables 6.7 and 6.8. As in Tables 6.4 and 6.6, the first measure indicates the success of predicting whether a product pair is produced by the same firm, including the success of predicting when they wouldn't. The second gives the success at predicting which pairs actually are produced by the same firm. As before, the third and fourth measures take the influences of all products into account by summing the probabilities of all brands produced by a firm. Using the firms' overall rankings to predict whether a firm produces or doesn't produce a product gives the third measure of prediction success (ie. Ill: If Firm Produces/Not (% )). Finally, the success at predicting the identities of the firms which actually produce a product are given in the final row. This measure, more than anything else, reveals the predictive power of the model. As an example, during 1982 there were 74 companies which produced the products in this study. On average, eighteen firms produced each product and the model fits the data well enough to predict ten of them. Thus, the estimation of the production of formulations is able to fit the observations of which firms produce which goods about as well as the other estimations. Despite this, it does considerably worse at fitting the data for the influences of individual product pairs and does not indicate a general tendency for firms to choose either neighbouring products or chemically similar products. Unfortunately, information is not available which would indicate whether these firms possess any local monopoly control over geographic space. 6.4 Conclusion This chapter presented the procedure that was used to determine the effects of the interactions between products on the probability that a firm introduces or produces cer-tain combinations of goods. This approach was applied both to the empirical estimation of the introduction of new products and the production of existing goods. All predictions made about the signs of coefficients were supported by the results of the estimations conducted on the introductions of new products. In other words, it was shown that a firm is more likely to introduce a product if it has already introduced a Chapter 6. Product Choice: Empirical Results 156 Table 6.8 cont'd. (Measures of Goodness of Fit) 1952 1962 1972 1982 Cragg-Uhler R2 0.117 0.073 0.076 0.140 LL(0) -2002.4 -7471.4 -4541.0 -1978.5 LLF -1865.5 -7168.3 -4335.3 -1809.4 I: All Product Pairs (%) 63.9 61.1 70.0 71.0 II: Pairs by Same Firm (%) 25.2 72.9 3.3 13.1 III: If Firm Produces/Not (%) 80.2 81.0 79.9 78.7 IV: If Firm Produces (%) 63.8 72.7 57.6 56.8 Chapter 6. Product Choice: Empirical Results 157 neighbouring product rather than a nonneighbouring good. It was also shown that a firm is more likely to introduce a product if it has already introduced a product of the same chemical type, presumably since it would yield a cost advantage. Finally, the estimated equation fit the data well enough to be able to predict the firms which introduced seven of the eleven products introduced by firms already in the market. The firms responsible for three of the remaining introductions were assigned probabilities that were second highest out of eight existing firms. The final introduction assigned the third highest probability, out of six firms, to the firm which made the introduction. The estimation of the production of concentrates also produced coefficients that gen-erally correspond with the predictions of the previous chapter. Furthermore, it was able to fit the observations of which firms produced which products with a 50 to 60% accu-racy. The estimation of the production of formulations was also able to generate the same degree of accuracy but did not yield consistent results for the effects of neighbour-ing products or chemically similar products on the probability of a firm producing a pair of formulations. This result, however, is largely expected due to the large number of formulators and the ease with which a firm may enter into production of formulations. The approach that has been illustrated of studying product interactions to explain product choice by multiproduct firms is particularly appealing due to its minimal data requirements. The use of the prices and characteristics of products would have yielded few results in traditional economic analysis but has been able to both fit the data to a reasonable degree and support predictions about how relationships between products influence product choice. Above all, it shows that a characteristics approach can be used in empirical applications. Chapter 7 Conclusions This thesis was intended to demonstrate an approach for analysing product choice by multiproduct firms. In particular, it was shown that detailed information, such as the level of research effort that various firms assign to the development of a particular product, is not required in order to derive a consistent method of determining which firms introduce which products. The underlying idea of this thesis is that a product may yield greater profits when produced in combination with particular other goods. Certain combinations of goods are thought to capture some degree of local monopoly power or have the potential for cost advantages in the production of goods requiring similar inputs and processes. The greater profitability of the combinations is thought to increase the probability that firms choose these goods. Characteristics theory was important to this analysis for a number of reasons. First, it easily allows for the introduction of new products without any requirement to redefine preferences over a larger space. It also allows a large number of products to be represented in a few dimensions. Finally, and most importantly, it predicts that competition is localized among adjacent products on the market opportunity frontier. This suggests one of the principal hypotheses of the thesis, that the pursuit of local monopoly power may encourage firms to choose products that are adjacent on the frontier. In order to illustrate that the use of characteristics theory is practical in this context the approach was applied to the market for insecticides. First, the twenty-five most com-mon insecticides were described using only the three characteristics that are routinely mentioned in the industry literature. Next, the fifteen of these products with available 158 Chapter 7. Conclusions 159 price data provided the first empirical support for the principal prediction of character-istics theory, that all products are priced on a convex market opportunity frontier. All products were shown to be on the frontier during fifteen years of the forty-four year study period. Incidents of products within the frontier during the other years were due to one product and could be accounted for by measurement errors of the characteristics. Characteristics theory was also used to derive a method of determining the implicit prices of characteristics. These prices were calculated for each facet of the frontier during every year of the study period. As expected, negative prices were assigned to the toxicity to mammals, positive prices were assigned to toxicity to insects and persistence had both positive and negative prices depending upon the combination of products used. The use of the characteristics approach provides an alternative to hedonic price analysis for cases of divisible and combinable goods and can also be used to determine the bounds on the possible prices of other goods. Perhaps the most important application of the characteristics approach is that it was used to determine the neighbour relations of twenty-three products over a forty-four year period. Since this indicated how competition was localized it was possible to simplify the analysis of these products by concentrating on the interactions of neighbouring goods. This thesis has shown that interactions between products can be used to determine which combinations of goods are likely to be introduced or produced by the same firm. These interactions were determined by noting which products are chemically similar and, with the use of characteristics theory, noting which were in direct competition and thus which could potentially yield some degree of local monopoly power. It was predicted that a product has a greater probability of being introduced or pro-duced by a firm which has a neighbouring product rather than a firm which has no products on the market. Furthermore, under Bertrand assumptions there is a greater probability of the product being introduced of produced by a firm with a neighbour-ing product rather than by a firm with a nonneighbouring product. The advantages of producing neighbouring products are also predicted to decline as the time between in-troductions increases. Finally, if conjectures are consistent the model also predicted that Chapter 7. Conclusions 160 combinations of products which yield cost advantages have a greater probability of being introduced or produced by the same firm. The real value of the model was its ability to use the observations of relationships between products and knowledge of which other products are in each firm's portfolio to predict, with about a 60% accuracy, the identity of the firm to introduce a particular good. For instance, of the eleven products that were introduced by firms with other products in the market, the model was able to predict the firm that introduced seven of them. Furthermore, in three of the remaining cases it ranked the firms that actually made the introduction as second out of eight existing firms. In the final case it gave the firm that made the introduction the third rank out of six existing firms. In the case of production the model also was able to predict the firms which produced the products with about a 50% accuracy. For example, in 1982 there were seventy-four firms producing insecticide formulations of the products being studied. On average each product was produced by eighteen firms. The model was able to predict eleven of the eighteen firms that produced an average product. In addition to this ability to fit the data the empirical sections, primarily -the sections on introductions and the production of concentrates, confirmed the predictions that a product has a greater probability of being introduced or produced by a firm with a neighbouring good or a good which yields a cost advantage. I believe that this thesis has shown that it is both practical and productive to use characteristics theory to analyse groups of products. The approach of studying product interactions is particularly appealing due to the ability to achieve results with minimal data requirements. Characteristics theory also provides a method of determining the implicit prices of characteristics and of determining how competition is localized. As such, it allows for the empirical analysis of interfirm competition that is rarely possible using traditional economic analysis. Appendix A Insecticide Names This appendix lists the twenty-five insecticides that are dealt with in this thesis by their common names (with other common names listed in parentheses). The insecticides are commonly divided into six groups according to their chemical makeup. These groups are the organophosphates, the carbamates, the organochlorines (which includes the cyclodienes as a distinct subgroup), the pyrethoids and the rotenoids. The last two categories are occasionally treated as one group; the botanicals. The chem-ical group that each product belongs to is listed in square brackets, [ ], after the name. The following lines provide the chemical names of these products using the nomen-clature that is based upon the rules of the International Union of Pure and Applied Chemistry (IUPAC) as cited by Worthing (1987). 1. Aldicarb (Temik) [Carbamate] 2-methyl-2-(methylthio)propionaldehyde O-methylcarbamoyloxime 2. Aldrin [Cyclodiene] (lR,4S,4aS,5S,8R,8aR)-l,2,3,4,10,10,-hexachloro--l,4,4a,5,8,8a-hexahydro-l,4:5,8--dimethanonapthalene 3. Allethrin [Pyrethroid] (RS)-3-allyl-2-methyl-4-oxocyclopent-2-enyl (lRS,2RS;lRS,2SR)-2,2-dimethyl-3-(2-methylprop-l-- enyl) cy cloprop anecarb oxylat e 161 Appendix A. Insecticide Names 4. Azinphos-methyl (Guthion) [Organophosphate] S-3,4-dihydro-4-oxo-l,2,3-benzotriazin-3-ylmethyl. 0,0-dimethyl phosphorodithioate 5. Carbaryl (Sevin) [Carbamate] 1-naphthyl methylcarbamate 6. Carbofuran [Carbamate] 2,3- dihydro- 2,2- dimet hylbenzofuran- 7-yl methylcarbamate 7. Chlordane [Organochlorine] l,2,4,5,6,7,8,8-octachloro-2,3,3a,4,7,7a-hexahydro--4,7-methanoindene 8. Chlorthion [Organophosphate] 0-3-chloro-4-nitrophenyl 0,0-dimethyl phosphorothioate 9. DDT (pp'-DDT) [Organochlorine] l,l,l-trichloro-2,2-bis(4-chlorophenyl)ethane 10. Demeton (Systox) [Organophosphate] 0,0-diethyl O-2-ethylthioethyl phosphorothioate / 0,0-diethyl S-2-ethylthioethyl phosphorothioate 11. Diazinon [Organophosphate] 0,0-diethyl 0-2-isopropyl-6-methylpyrimidin-4-yl phosphorothioate 12. Dieldrin [Cyclodiene] (lR,4S,4aS,5R,6R,7S,8S,8aR)-l,2,3,4,10,10--hexachloro-1,4,4a,5,6,7,8,8a-octahydro-6,7--epoxy-l,4:5,8-dimethanonapthalene Appendix A. Insecticide Names 163 13. Dimethoate (Cygon, Rogor) [Organophosphate] 0,0-dimethyl S-methylcarbamoylmethyl phosphorodithioate 14. Endosulfan (Thiodan) [Organochlorine] (l,4,5,6,7,7-hexachloro-8,9,10-trinorborn-5-en-2,3--ylenebismethylene) sulphite 15. Endrin [Cyclodiene] (lR,4S,4aS,5S,6S,7R,8R,8aR)-l,2,3,4,10,10--hexachloro-1,4,4a,5,6,7,8,8a-octahydro-6,7--epoxy-l,4:5,8-dimethanonapthalene 16. Heptachlor [Organochlorine] l,4,5,6,7,8,8-heptachloro-3a,4,7,7a-tetrahydro-4,7--methanoindene 17. Isodrin [Cyclodiene] (lR,4S,5R,8S)-l,2,3,4,10,10,-hexachloro--1,4,4a,5,8,8a-hexahydro-l,4:5,8--dimethanonapthalene 18. Lindane (Gamma Benzene Hexachloride, Gamma-HCH) [Organochlorine] (1,2,3,5/4,6)-hexachlorocyclohexane 19. Malathion [Organophosphate] Diethyl(dimethoxyphosphinothioylthio)succinate 20. Methoxychlor [Organochlorine] l,l,l-trichloro-2,2-bis(4-methoxyphenyl)ethane 21. Methyl-Parathion [Organophosphate] 0,0-dimethyl O-4-nitrophenyl phosphorothioate Appendix A. Insecticide Names 22. Parathion [Organophosphate] 0,0-diethyl 0-4-nitrophenyl phosphorothioate 23. Pyrethrum (Pyrethrin I, Pyrethrin II, Cinerin I, Cinerin II, Jasmolin I, Jasmolin II) [Pyrethroid] (Pyrethrin I) (Z)-(S)-2-methyl-4-oxo-3-(penta-2,4--dienyl)cyclopent-2-enyl(lR,3R)-2,2-dimethyl-3--(2-methylprop-l-enyl)cyclopropanecarboxylate 24. Rotenone [Rotenoid] (2R,6aS,12aS)-l,2,6,6a,12,12a-hexahydro-2--isopropenyl- 8,9-dimethoxychromeno[3,4--b]furo[2,3-h]chromen-6-one 25. Toxaphene (Camphechlor) [Organochlorine] A reaction mixture of chlorinated camphenes containing 67-69% chlorine Appendix B Characteristics Data B.l Data Selection Data on the characteristics of insecticides were collected from a variety of articles concerned with the toxicology, effectiveness and persistence of insecticides. Original data are used whenever possible and any data from summary articles are clearly indicated. Results listed as ranges or inequalities are not used. The data reported in three papers (out of 113) are not used since they differ by several orders of magnitude from all other sources. These articles are by Marsh and Eden (1955), Oliver and Eden (1955), and Sun and Johnson (1960). All articles and books providing the data are listed at the end of this appendix. B.2 Characteristics Data All averages are recorded with two significant figures (for later manipulations) while the actual number of significant figures are given in parentheses { }. Many of the observations of persistence were listed in units of weeks or years (although they are recorded in terms of days) and have few significant digits. 165 Appendix B. Characteristics Data 166 Table B.l: Aldicarb Characteristics a) Toxicity to Mammals: Acute oral LD5o Rat (mg/kg) 0.8 (M) Gaines (1969) 0.65 (F) Gaines (1969) 0.96 (F) Metcalf (1972) 0.80 {1} b) Toxicity to Insects: Topical LD50 to the House Fly (pg/g) 5.5 Metcalf et al. (1967) 5.5 {2} c) Persistence: Soil half-life (days) 4 Andrawes et al. (1971) 7 Coppedge et al. (1967) 4 Bull et al. (1970) 7 Bull et al. (1970) 5.5 {1} Appendix B. Characteristics Data 167 Table B.2: Aldrin Characteristics a) Toxicity to Mammals: Acute oral LD50 Rat (mg/kg) 59.6 (M) Ball et al. (1953) 52.3 (F) Ball et al. (1953) 39 (M) Gaines (1960) 60 (F) Gaines (I960) 49 (M) Treon and Cleveland (1955) 45.9 (F) Treon and Cleveland (1955) 51 {1} b) Toxicity to Insects: Topical LD50 to the House Fly (pg/g) 2.3 Sun (1972) 1.15 Sun and Pankaskie (1954) 2.25 Metcalf (1972) 1.5 Brooks (1966) 1.8 {2} c) Persistence: Soil half-life (days) 324 Bess and Hylin (1970) 38 Castro and Yoshida (1971) 1826 Nash and Woolson (1967) 3287 Nash and Woolson (1967) 287 Bollen et al. (1958) 94 Lichtenstein et al. (1962) 142 Lichtenstein and Polivka (1959) 329 Lichtenstein and Schulz (1959) 197 Lichtenstein and Schulz (1959) 73 Lichtenstein and Schulz (1959) 307 Bess and Hylin (1970) 52 Castro and Yoshida (1971) 112 Lichtenstein and Schulz (1961) 222 Lichtenstein and Schulz (1965) 74 Lichtenstein and Schulz (1965) 166 Lichtenstein and Schulz (1960) 470 {1} Appendix B. Characteristics Data 168 Table B.3: Allethrin Characteristics a) Toxicity to Mammals: Acute oral LD^o Rat (mg/kg) 920 (M) Carpenter et al. (1950) 900 (F) Carpenter et al. (1950) 340 Carpenter et al. (1950) 680 Hayes (1963)  710 {1} b) Toxicity to Insects: Topical LDt i 0 to the House Fly (/zg/g) 10 Elliott (1970) 10. {1} c) Persistence: Half-life in sunlight and air (days) OA Chen and Casida (1969) 0.10 {1} Appendix B. Characteristics Data 169 Table B.4: Azinphos-methyl (Guthion) Characteristics a) Toxicity to Mammals: Acute oral LD50 Rat (mg/kg) 16.4 (F) DuBois et al. (1957) 11 Edson (1960) 13 (M) Gaines (1960) 11 (F) Gaines (I960) 13 {2} b) Toxicity to Insects: Topical LD50 to the House Fly (pg/g) 2J Metcalf (1972) 2.7 {2} c) Persistence: Soil half-life (days) 88 Yaron et al. (1974) 13 Yaron et al. (1974) 12 Schulz et al. (1970) 10 Iwata et al. (1975) 25 Iwata et al. (1975) 10 Iwata et al. (1975) 30 Iwata et al. (1975) 80 Iwata et al. (1975) 70 Iwata et al. (1975) 15 Iwata et al. (1975) 65 Iwata et al. (1975) 80 Iwata et al. (1975) 42 {1} Appendix B. Characteristics Data 170 Table B.5: Carbaryl (Sevin) Characteristics a) Toxicity to Mammals: Acute oral LD5o Rat (mg/kg) 744 Boyd and Boulanger. (1968) 510 Carpenter et al. (1961) 610 (F) Carpenter et al. (1961) 561 (F) Carpenter et al. (1961) 310 (M) Carpenter et al. (1961) 400 Edson et al. (1966) 850 (M) Gaines (1960) 500 (F) Gaines (I960) 290 (F) Weiss and Orzel (1967) 255 (F) Weiss and Orzel (1967) 230 (F) Weiss and Orzel (1967) 540 (F) Metcalf (1972) 480 {1} b) Toxicity to Insects: Topical LD50 to the House Fly (fig/g) 810 Busvine and Iwuala (1975) 900 Metcalf (1972)  860 {1} c) Persistence: Soil half-life (days) 8 Lafleur (1976) 8.0 {1} Appendix B. Characteristics Data 111 Table B.6: Carbofuran Characteristics a) Toxicity to Mammals: Acute oral LD50 Rat (mg/kg) 4.0 Metcalf (1972) 4.0 {2} b) Toxicity to Insects: Topical LD50 to the House Fly (pg/g) 6.5 Metcalf et al. (1967) 4.6 Metcalf (1972) 5.6 {2} c) Persistence: Soil half-life (days) 46 Caro et al. (1973) 46 {2} Appendix B. Characteristics Data 172 Table B.7: Chlordane Characteristics a) Toxicity to Mammals: Acute oral LD5o Rat (mg/kg) 590 Ambrose et al. (1953) 490 Carpenter et al. (1961) 283 Edson et al. (1966) 335 (M) Gaines (1960) 430 (F) Gaines (I960) 311 (M) Boyd and Taylor (1969) 410 {2} b) Toxicity to Insects: Topical LD50 to the House Fly (pg/g) 8.2 Bruce and Decker (1950) 4.2 Bruce and Decker (1950) 4.0 Kearns et al. (1949) 5.5 {2} c) Persistence: Soil half-life (days) 500 Bess and Hylin (1970) 390 Fleming and Maines (1954) 1600 Lichtenstein and Polivka (1959) 2922 Nash and Woolson (1967) 475 Bess and Hylin (1970) 400 Edwards (1964) 385 Fleming and Maines (1954) 335 Wilson and Oloffs (1973) 350 Fleming and Maines (1954) 1461 Hermanson et al. (1971) 880 {1} Appendix B. Characteristics Data 173 Table B.8: Chlorthion Characteristics a) Toxicity to Mammals: Acute oral LD^o Rat (mg/kg) 1500 (F) DuBois et al. (1953) 880 (M) Gaines (1960) 980 (F) Gaines (I960) 625 Schrader (1961) 1000 {2} b) Toxicity to Insects: Topical LD50 to the House Fly (iig/g) 11.5 Metcalf (1972) 12 {3} c) Persistence: Soil half-life (days) 36 36 {2} Menzie (1972) ***(a summary article) Appendix B. Characteristics Data 174 Table B.9: DDT Characteristics a) Toxicity to Mammals: Acute oral LD50 Rat (mg/kg) 406 Carpenter et al. (1961) 300 Edson (1960) 113 (M) Gaines (1960) 118 (F) Gaines (I960) 217 (M) Gaines (1969) 368 (M) Boyd and DeCastro (1968) 180 Philips and Gilman (1946) 150 Smith et al. (1946) 230 . {1} b) Toxicity to Insects: Topical LD5o to the House Fly (/ig/g) 16.8 Bruce and Decker (1950) 8.96 Bruce and Decker (1950) 13 Busvine and Iwuala (1975) 20.5 Kearns et al. (1949) 9.4 Lindquist and Dahm (1957) 11.8 Sun (1972) 2.0 Metcalf (1972) 60 Sun and Pankaskie (1954) 18 {1} c) Persistence: Soil half-life (days) 572 Bess and Hylin (1970) 3835 Nash and Woolson (1967) 1205 Edwards (1963) 1095 Edwards (1964) 2922 Fleming and Maines (1953) 513 Bess and Hylin (1970) 598 Lichtenstein and Schulz (1959) 283 Lichtenstein and Schulz (1961) 1461 Hermanson et al. (1971) 1400 {1} Appendix B. Characteristics Data 175 Table B.10: Demeton Characteristics a) Toxicity to Mammals: Acute oral LD^o Rat (mg/kg) 4 Edson (1960) 6.2 ' (M) Gaines (1960) 2.5 (F) Gaines (I960) 10.40 (M) Boyd and Krupa (1969) 1.7 DuBois et al. (1956) 5.0 {1} b) Toxicity to Insects: Topical LD50 to the House Fly (fig/g) 0.75 Metcalf (1972)  0.75 {2} c) Persistence: Soil half-life (days) 54 Menzie (1972) **(a summary article) 54 {2} Appendix B. Characteristics Data 176 Table B . l l : Diazinon Characteristics a) Toxicity to Mammals: Acute oral LD50 Rat (mg/kg) 466 (M) Boyd and Carsky (1969) 354 Carpenter et al. (1961) 108 (M) Gaines (1960) 76 (F) Gaines (I960) 250 (M) Gaines (1969) 285 (F) Gaines (1969) 235 Gasser (1953) 250 {2} b) Toxicity to Insects: Topical LD50 to the House Fly (pg/g) 4.8 Busvine and Iwuala (1975) 2.95 Metcalf (1972) 3.9 {2} c) Persistence: Soil half-life (days) 35 Getzin (1968) 32 Getzin and Rosefield (1966) 9 Malone et al. (1967) 10 Konrad et al. (1967) 12 Konrad et al. (1967) 6 Konrad et al, (1967) 17 {1} Appendix B. Characteristics Data 177 Table B.12: Dieldrin Characteristics a) Toxicity to Mammals: Acute oral LD50 Rat (mg/kg) 46 (M) Gaines (1960) 46 (F) Gaines (I960) 63.5 (M) Heath and Vandekar (1964) 50.8 (F) Heath and Vandekar (1964) 142 Carpenter et al. (1961) 40 Edson (1960) 47 (M) Treon and Cleveland (1955) 38.3 (F) Treon and Cleveland (1955) 83 (F) Weiss and Orzel (1967) 71 (F) Weiss and Orzel (1967) 69 (F) Weiss and Orzel (1967) 63 {1} b) Toxicity to Insects: Topical LD50 to the House Fly (fig/g) 1.1 Bruce and Decker (1950) 0.87 Bruce and Decker (1950) 0.75 Sun and Pankaskie (1954) 0.81 Sun (1972) 0.95 Metcalf (1972) 1.0 Brooks (1966) 0.91 {2} c) Persistence: Soil half-life (days) 400 Bess and Hylin (1970) 2557 Nash and Woolson (1967) 416 Bess and Hylin (1970) 892 Bollen et al. (1958) 1643 Stewart and Fox (1971) 821 Edwards (1964) 4748 Hermanson et al. (1971) 1600 {1} Appendix B. Characteristics Data 178 Table B.13: Dimetlioate (Cygon, Rogor) Characteristics a) Toxicity to Mammals: Acute oral LD50 Rat (mg/kg) 215 (M) Gaines (1969) 245 (F) Gaines (1969) 230 {3} b) Toxicity to Insects: Topical LD5Q to the House Fly (/ig/g) 0.8 Seume and O'Brien (1960) 0.55 Metcalf (1972) 0.58 Yates and Sherman (1970) 0.64 {1} c) Persistence: Soil half-life (days) 4 Bohn (1964) 4.0 {1} Appendix B. Characteristics Data 179 Table B.14: Endosulfan (Thiodan) Characteristics a) Toxicity to Mammals: Acute oral LD50 Rat (mg/kg) 43 (M) Gaines (1969) 18 (F) Gaines (1969) 35 Edson (1960) 121 (M) Boyd and Dobos 54 {2} b) Toxicity to Insects: Topical LD$0 to the House Fly (ug/g) 6.0 Barnes and Ware (1965) 6.7 Lindquist and Dahm (1957) 4.15 Metcalf (1972) 5.6 {2} c) Persistence: Soil half-life (days) 90 Stewart and Cairns (1974) 90. {1} Appendix B. Characteristics Data 180 Table B.15: Endrin Characteristics a) Toxicity to Mammals: Acute oral L D 5 0 Rat (mg/kg) '27.24 (M) Boyd and Stefec (1969) 17.8 (M) Gaines (1960) 7.5 (F) Gaines (I960) 28.8 (M) Treon and Cleveland (1955) 16.8 (F) Treon and Cleveland (1955) 20. {2} b) Toxicity to Insects: Topical LD50 to the House Fly (pg/g) 0.68 Sun (1972)  0.68 {2} c) Persistence: Soil half-life (days) 1461 Hermanson et al. (1971) 3975 Nash and Woolson (1967) 338 Castro and Yoshida (1971) 1900 {1} Appendix B. Characteristics Data 181 Table B.16: Heptachlor Characteristics a) Toxicity to Mammals: Acute oral LD50 Rat (mg/kg) 40 Edson (1960) 100 (M) Gaines (1960) 162 (F) Gaines (I960) 100 {1} b) Toxicity to Insects: Topical LD50 to the House Fly (fig/g) 1.95 Sun (1972) 2.25 Metcalf (1972) L0 Brooks (1966) 1.7 {2} c) Persistence: Soil half-life (days) 369 Bess and Hylin (1970) 388 Bess and Hylin (1970) 485 Young and Rawlins (1958) 293 Young and Rawlins (1958) 1087 Nash and Woolson (1967) 329 Edwards (1964) 1461 Hermanson et al. (1971) 245 Lichtenstein and Schulz (1960) 369 Lichtenstein and Schulz (1965) 510 {1} Appendix B. Characteristics Data 182 Table B.17: Heptachlor Epoxide Characteristics a) Toxicity to Mammals: Acute oral LD5Q Rat (mg/kg) 60 Brooks (1974) **(a summary article) 6d{T} b) Toxicity to Insects: Topical LD50 to the House Fly (/zg/g) 1.0 Brooks (1966) 1.0 {2} c) Persistence: Soil half-life (days) 483 Miles et al. (1971) 1038 Stewart and Fox (1971) 847 Stewart and Fox (1971) 444 Lichtenstein and Schulz (1965) 38 Lichtenstein and Schulz (1965) 140 Lichtenstein and Schulz (1960) 794 Lichtenstein and Polivka (1959) 289 Bess and Hylin (1970) 333 Bess and Hylin (1970) 490 {1} Appendix B. Characteristics Data 183 Table B.18: Isodrin Characteristics a) Toxicity to Mammals: Acute oral LD50 Rat (mg/kg) 15.5 (M) Gaines (1960) 7.0 •(F) Gaines (I960) 27.8 (M) Treon and Cleveland (1955) 16.4 (F) Treon and Cleveland (1955) 17 {2} b) Toxicity to Insects: Topical L D 5 0 to the House Fly (fig/g) 2.2 Winteringham (1969) **(a summary article) 3.0 Brooks (1974) **(a summary article) 2^ 6 {2} c) Persistence: Soil half-life (days) 1868 Nash and Woolson (1967) 1900 {1} Appendix B. Characteristics Data 184 Table B.19: Lindane Characteristics a) Toxicity to Mammals: Acute oral LD50 Rat (mg/kg) 157 (M) Boyd and Chen (1968) 107 Carpenter et al. (1961) 200 Edson et al. (1966) 88 (M) Gaines (I960) 91 (F) Gaines (I960) 230 Klosa (1950) 177 Woodward et al. (1947) 150 {1} b) Toxicity to Insects: Topical LD50 to the House Fly (ug/g) 1.7 Bruce and Decker (1950) 2.2 Bruce and Decker (1950) 2.9 Lidov et al. (1950) 1.5 Sun (1972) - 4 Sun and Pankaskie (1954) 0.85 Metcalf (1972) 2.2 {1} c) Persistence: Soil half-life (days) 279 Bess and Hylin (1970) 290 Bess and Hylin (1970) 495 Edwards (1964) 273 Lichtenstein and Schulz (1959) 330 {1} Appendix B. Characteristics Data 185 Table B.20: Malathion Characteristics a) Toxicity to Mammals: Acute oral LD50 Rat (mg/kg) 1090 (M) Boyd and Tanikella (1969) 2590 Carpenter et al. (1961) 1400 (F) DuBois et al. (1953) 1400 Frawley et al. (1957) 1375 (M) Gaines (1960) 1000 (F) Gaines (I960) 1500 (M) Hagan (1953) 1200 (F) Hagan (1953) 369 (M) Hazleton and Holland (1953) 739 (F) Hazleton and Holland (1953) 1156 (M) Hazleton and Holland (1953) 480 (M) Holland et al. (1952) 1200 {1} b) Toxicity to Insects: Topical LD50 to the House Fly (/ig/g) 28 Busvine and Iwuala (1975) 70 Georghiou and Metcalf (1962) 13.0 Seume and O'Brien (1960) 26.5 Metcalf (1972) 34 {1} c) Persistence: Soil half-life (days) 1 Konrad et al. (1969) 1 Lichtenstein and Schulz (1964) 1 Paschal and Neville (1976) 1.0 {1} Appendix B. Characteristics Data 186 Table B.21: Methoxychlor Characteristics a) Toxicity to Mammals: Acute oral LD5Q Rat (mg/kg) 6000 (M) Hayes (1963) 5000 Hodge et al. (1950) 7000 Smith et al. (1946) 6000 {!} b) Toxicity to Insects: Topical LD50 to the House Fly (/zg/g) 49.95 Bruce and Decker (1950) 50.0 Bruce and Decker (1950) 45 Metcalf et al. (1971) 9.0 Metcalf (1972) 38 {2} c) Persistence: Soil half-life (days) 96 Wallner et al. (1969) 96 {2} Appendix B. Characteristics Data 187 Table B.22: Methyl Parathion Characteristics a) Toxicity to Mammals: Acute oral LD50 Rat (mg/kg) 11 Carpenter et al. (1961) 12 Edson (1960) 14 (M) Gaines (1960) 24 (F) Gaines (I960) 12.5 Schrader (1961) 15. {2} b) Toxicity to Insects: Topical LD50 to the House Fly (/ig/g) 1.3 Metcalf and March (1953) 12 Metcalf (1972)  L3 {2} c) Persistence: Soil half-life (days) 6 Lichtenstein and Schulz (1964) 6 {1} Appendix B. Characteristics Data 188 Table B.23: Parathion Characteristics a) Toxicity to Mammals: Acute oral LD50 Rat (mg/kg) 23.4 (M) Boyd et al. (1969) 8.1 Carpenter et al. (1961) 3.50 (F) Deichmann et al. (1952) 9.7 (F) Deichmann et al. (1952) 14.8 (F) Deichmann et al. (1952) 27.0 (F) Deichmann et al. (1952) 11.0 (F) Deichmann et al. (1952) 4.03 (F) Deichmann et al. (1952) 4.41 (F) Deichmann et al. (1952) 15 (M) DuBois et al. (1949) 6 (F) DuBois et al. (1949) 30.0 (M) Frawley et al. (1952) 3.0 (F) Frawley et al. (1952) 13 (M) Gaines (1960) 3.6 •(F) Gaines (I960) 5.0 (M) Hazleton and Holland (1950) 1.75 (F) Hazleton and Holland (1950) 8.5 (M) Nishizawa (1962) 10.0 •(F) Nishizawa (1962) 2.10 (F) Weiss and Orzel (1967) 1.80 (F) Weiss and Orzel (1967) 4.70 (F) Weiss and Orzel (1967) 9.6 {1} b) Toxicity to Insects: Topical LD50 to the House Fly (ug/g) 0.9 Metcalf and March (1949) 1.4 Metcalf and March (1953) 1^ 2 {1} : ~ c) Persistence: Soil half-life (days) 69 18 44 {2} Ginsburg et al. (1949) Lichtenstein and Schulz (1964) Appendix B. Characteristics Data 189 Table B.24: Pyrethrum Characteristics a) Toxicity to Mammals: Acute oral LD50 Rat (mg/kg) 1870 (M) Carpenter et al. (1950) 820 (F) Carpenter et al. (1950) 200 Hayes (1963) 570 Edson et al. (1966) 870 {1} b) Toxicity to Insects: Topical LD50 to the House Fly (iig/g) 56.8 Bruce and Decker (1950) 49.1 . Bruce and Decker (1950) 15 Elliott (1970)  40. {2} c) Persistence: Half-life in sunlight and air (days) 0.0025 Chen and Cassida (1969) 0.0025 {1} Appendix B. Characteristics Data 190 Table B.25: Rotenone Characteristics a) Toxicity to Mammals: Acute oral LD50 Rat (mg/kg) 25 Lightbody and Mathews (1936)  b) Toxicity to Insects: Topical LD50 to Oncopeltus faciatus (pg/g) 2.5 Menusan (1948) *(Oncopeltus faciatus) 2.5 {2} c) Persistence: Half-life in sunlight and air (days) 1.5 Subba and Pollard (1951)  1.5 {2} Appendix B. Characteristics Data 191 Table B.26: Toxaphene Characteristics a) Toxicity to Mammals: Acute oral LD50 Rat (mg/kg) 220 (M) Boyd and Taylor (1971) 123 Carpenter et al. (1961) 283 Edson et al. (1966) 90 (M) Gaines (1960) 80 (F) Gaines (I960) 160 {1} b) Toxicity to Insects: Topical LD50 to the House Fly (/ig/g) 29.16 Bruce and Decker (1950) 32.2 Bruce and Decker (1950) 11.0 Metcalf (1972)  24 {3} c) Persistence: Soil half-life (days) 1461 Hermanson et al. (1971) 4018 Nash and Woolson (1967) 731 Adams (1967) 292 Adams (1967)  1600 {1} Appendix B. Characteristics Data 192 B.3 Characteristics Data Sources Adams, R.S. (1967), "The Fate of Pesticides in Soil," Minnesota Academy of Science Journal, 34 Ambrose, Anthony M., Herbert C. Christensen, and Dorothy J. Robbins (1953), "Phar-macological Observations on Chlordane," Federation of American Societies for Ex-perimental Biology; Proceedings, 12, 298 Andrawes, Natham R., William P. Bagley, and Richard A. Herrett (1971), "Fate and Carryover Properties of Temik Aldicarb Pesticide [2-Methyl-2-(methylthio)propionaldehyde 0-(Methylcarbamoyl)oxime] in Soil," Journal of Agricultural and Food Chemistry, 19, 727-730 Ball, W.L., Kingsley Kay and J.W. Sinclair (1953), "Observations on Toxicity of Aldrin," Archives of Industrial Hygiene and Occupational Medicine, 7, 292-300 Barnes, William W. and George W. Ware (1965), "The Absorption and Metabolism of C 1 4 - Labeled Endosulfan in the House Fly," Journal of Economic Entomology, 58, 286-291 Bess, Henry A., and J.W. Hylin (1970), "Persistence of Termiticides in Hawaiian Soils," Journal of Economic Entomology, 63, 633-638 Bohn, W.R. (1964), "The Disappearance of Dimethoate from Soil," Journal of Economic Entomology, 57, 798-799 Bollen, W.B., J.E. Roberts and H.E. Morrison (1958), "Soil Properties and Factors Influencing Aldrin-Dieldrin Recovery and Transformation," Journal of Economic Entomology, 51, 214-219 Boyd, E.M. and M.A. Boulanger (1968), "Augmented Susceptibility to Carbaryl Tox-icity in Albino Rats Fed Purified Casein Diets," Journal of Agricultural and Food Chemistry, 16, 834-838 Boyd, Eldon M. and Eva Carsky (1969), "Kwashiorkorigenic Diet and Diazinon Toxic-ity," Acta Pharmacologica et Toxicologica, 27, 284-294 Boyd, Eldon M. and CP. Chen (1968), "Lindane Toxicity and Protein-Deficient Diet," Archives of Environmental Health, 17, 156-163 Boyd, Eldon M., CP. Chen, and S.J. Liu (1969), "The Acute Oral Toxicity of Parathion in Relation to Dietary Protein," Archiv fur Toxikologie, 25, 238-253 Appendix B. Characteristics Data 193 Boyd, Eldon M. and Elvira S. DeCastro (1968), "Protein-Deficient Diet and DDT Tox-icity," Bulletin, World Health Organization, 38, 141-150 Boyd, E.M. and I. Dobos (1969), "Protein Deficiency and Tolerated Oral Doses of Endosulfan," Archives Internationales de Pharmacodynamic et de Therapie, 178, 152-165 Boyd, Eldon M. and Vincent Krupa (1969), "The Acute Oral Toxicity of Demeton in Albino Rats Fed from Weaning on Diets of Varying Protein Content," Canadian Journal of Pharmaceutical Sciences, 4, 35-40 Boyd, Eldon M. and Jitka Stefec (1969), "Dietary Protein and Pesticide Toxicity; with Particular Reference to Endrin," Canadian Medical Association Journal, 101, 335— 339 Boyd, Eldon M. and T.K. Tanikella (1969), "The Acute Oral Toxicity of Malathion in Relation to Dietary Protein," Archiv fur Toxikologie, 24, 292-303 Boyd, Eldon M. and Frances I. Taylor (1969), "The Acute Oral Toxicity of Chlordane in Albino Rats," Industrial Medicine and Surgery, 38, 42-49 Boyd, Eldon M. and Frances I. Taylor (1971), "Toxaphene Toxicity in Protein-Deficient Rats," Toxicology and Applied Pharmacology, 18, 158-167 Brooks, G.T. (1966), "Progress in Metabolic Studies of the Cyclodiene Insecticides and its Relevance to Structure-Activity Correlations," World Review of Pest Control, 5, 62-84 Brooks, G.T. (1974), Chlorinated Insecticides; Volume II, Biological and Environmental Aspects, CRC Press, Cleveland, Ohio Bruce, W.N. and G.C. Decker (1950), "House Fly Tolerance for Insecticides," Soap and Sanitary Chemicals, 26, 122-125 Bull, D.L., R.A. Stokes, J.R. Coppedge and R.L. Ridgeway (1970), "Further Studies of the Fate of Aldicarb in Soil," Journal of Economic Entomology, 63, 1283-1289 Busvine, James R. and Moses O.E. Iwuala (1975), "Effects of Mode of Testing on Sus-ceptibility to Various Insecticides of Adult or Larvae of Lucilia sericata, Chrysomya putoria and Musca domestica L.," Pesticide Science, 6, 481-490 Caro, Joseph H., Horatio P. Freeman, Dwight E. Glotfelty, Benjamin C. Turner, and William M. Edwards (1973), "Dissipation of Soil-Incorporated Carbofuran in the Field," Journal of Agricultural and Food Chemistry, 21, 1010-1015 Appendix B. Characteristics Data 194 Carpenter,"CP., C.S. Weil, P.E. Palm, M.W. Woodside, J.H. Nair and H.F. Smyth (1961), "Mammalian Toxicity of 1-Naphthyl-N-methylcarbamate (Sevin Insecti-cide)," Journal of Agricultural and Food Chemistry, 9, 30-39 Carpenter, CP., C.S. Weil, U.C. Pozzani, and H.F. Smyth (1950), "Comparative Acute and Subacute Toxicities of Allethrin and Pyrethrins," Archives of Industrial Hy-giene and Occupational .Medicine, 2, 420-432 Castro, Teresita. F., and Tomio Yoshida (1971), "Degradation of Organochlorine In-secticides in Flooded Soils in the Philippines," Journal of Agricultural and Food Chemistry, 19, 1168-1170 Chen, Yuh-Lin and John E. Casida (1969), "Photodecomposition of Pyrethrin 'I, Al-lethrin, Phthalthrin, and Dimethrin," Journal of Agricultural and Food Chemistry, 17, 208-215 Coppedge, J.R., D.A. Lindquist, D.L. Bull and H.W. Dorough (1967), "Fate of 2-Methyl-2-(methylthio)propionaldehyde 0-(Methylcarbamoyl)oxime (Temik) in Cot-ton Plants and Soil," Journal of Agricultural and Food Chemistry, 15, 902-910 Deichmann, William B., William Pugliese and James Cassidy (1952), "Effects of Dimethyl and Diethyl Paranitrophenyl Thiophosphate on Experimental Animals," Archives of Industrial Hygiene and Occupational Medicine, 5, 44-51 DuBois, Kenneth P., John Doull, Jere Deroin, and Oda K. Cummings (1953), "Studies on the Toxicity and Mechanism of Action of some New Insecticidal Thionophos-phates," Archives of Industrial Hygiene and Occupational Medicine, 8, 350-358 DuBois, Kenneth P., John Doull, Paul R. Salerno, and Julius M. Coon (1949), "Studies on the Toxicity and Mechanism of Action of p-Nitrophenyl Diethyl Thionophos-phate (Parathion)," Journal of Pharmacology and Experimental Therapeutics, 95, 79-91 DuBois, Kenneth P., Sheldon D. Murphy, and Donald R. Thursh (1956), "Toxicity and Mechanism of Action of Some Metabolites of Systox," Archives of Industrial Health, 13, 606-612 DuBois, Kenneth P., Donald R. Thursh, and Sheldon D. Murphy (1957), "Studies on the Toxicity and Pharmacologic Actions of the Dimethoxy Ester of Benzotriazine Dithiophosphoric Acid (DBD, Guthion)," Journal of Pharmacology and Experi-mental Therapeutics, 119, 208-218 Edson, E.F. (1960), "Applied Toxicology of Pesticides," The Pharmaceutical Journal, 15, 361-367 Appendix B. Characteristics Data 195 Edson, E.F., D.M. Sanderson, and D.N. Noakes (1966), "Acute Toxicity Data for Pes-ticides (1966)," World Review of Pest Control, 5, 143-151 Edwards, C A . (1963), "Persistence of Insecticides in the Soil," New Scientist, 19, 282-284 Edwards, C A . (1964), "Factors Affecting the Persistence of Insecticides in Soil," Soils and Fertilizers, 27, 451-454 Elliott, M. (1970), "The Relationship between the Structure and the Activity of Pyrethroids," Bulletin of the World Health Organization, 44, 315-324 Fleming, Walter E. and Warren W. Maines (1953), "Persistence of DDT in Soils of the Area Infested by the Japanese Beetle," Journal of Economic Entomology, 46, 445-449 Fleming, Walter E. and Warren W. Maines (1954), "Persistence of Chlordane in Soils of the Area Infested by the Japanese Beetle," Journal of Economic Entomology, 47, 165-169 Frawley, John P., Henry N. Fuyat, Ernest C. Hagan, Jane R. Blake, and 0. Garth Fitzhugh (1957), "Marked Potentiation in Mammalian Toxicity from Simultaneous Administration of Two Anticholinesterase Compounds," Journal of Pharmacology and Experimental Therapeutics, 121, 96-106 Frawley, John P., Ernest C. Hagan, and 0. Garth Fitzhugh (1952), "A Comparative Pharmacological and Toxicological Study of Organic Phosphate - Anticholinesterase Compounds," Journal of Pharmacology and Experimental Therapeutics, 105, 156-165 Gaines, Thomas B. (1960), "The Acute Toxicity of Pesticides to Rats," Toxicology and Applied Pharmacology, 2, 88-99 Gaines, Thomas B. (1969), "Acute Toxicity of Pesticides," Toxicology and Applied Phar-macology, 14, 515-534 Gasser, Von R. (1953), "Uber ein neues Insektizid mit breitem Wirkungsspektrum," Zeitschrift fur Naturforschung, 8b, 225-232 Georghiou, G.P. and R.L. Metcalf (1962), "Carbamate Insecticides: Comparative In-sect Toxicity of Sevin, Zectran, and Other New Materials," Journal of Economic Entomology, 55, 125-127 Appendix B. Characteristics Data 196 Getzin, L.W. (1968), "Persistence of Diazinon and Zinophos in Soil: Effects of Auto-claving, Temperature, Moisture, and Acidity," Journal of Economic Entomology, 61, 1560-1565 Getzin, L.W. and I. Rosefield (1966), "Persistence of Diazinon and Zinophos in Soils," Journal of Economic Entomology, 59, 512-516 Ginsburg, J.M'., R.S. Filmer, J.P. Reed, and A.R. Paterson (1949), "Recovery of Parathion, DDT and Certain Analogs of Dichlorodiphenyl-Dichloroethane fron Treated Crops," Journal of Economic Entomology, 42, 602-611 Hagan, Ernest C. (1953), "Acute Toxicity of 0,0-dimethyl dithiophosphate of diethyl mercaptosuccinate (4049)," Federation of American Societies for Experimental Bi-ology; Proceedings, 12, 327 Hayes, Wayland J. (1963), Clinical Handbook of Economic Poisons, United States De-partment of Health, Education and Welfare Publication 476, Public Health Service, Communicable Disease Center, Toxicology Section, Atlanta, Georgia Hazleton, Lloyd W. and Emily G. Holland (1950), "Pharmacology and Toxicology of Parathion," in Agricultural Control Chemicals, American Chemical Society, Ad-vances in Chemistry Series, 1, 31-38 Hazleton, Lloyd W. and Emily G. Holland (1953), "Toxicity of Malathion," Archives of Industrial Hygiene and Occupational Medicine, 8, 399-405 Heath, D.F. and M. Vandekar (1964), "Toxicity and Metabolism of Dieldrin in Rats," British Journal of Industrial Medicine, 21, 269-279 Hermanson, Harvey P., Francis A. Gunther, Lauren D. Anderson, and Morris J. Garber (1971), "Installment Application Effects upon Insecticide Residue Content of a California Soil," Journal of Agricultural and Food Chemistry, 19, 722-726 Hodge, Harold C , Elliott A. Maynard, Joan F. Thomas, H.J. Blanchet Jr., W.G. Wilt Jr., and Karl E. Mason (1950), "Short-Term Oral Toxicity Tests of Methoxychlor in Rats and Dogs," Journal of Pharmacology and Experimental Therapeutics, 99, 140-148 Holland, Emily G., Lloyd W. Hazleton, and Dorothy L. Hanzal (1952), "Toxicity of Malathion (0,0-dimethyl dithiophosphate of diethyl mercaptosuccinate)," Federa-tion of American Societies for Experimental Biology; Proceedings, 11, 357 Iwata, Yutaka, Margarete E. Dusch, William E. Westlake, and Francis A. Gunther (1975), "Behaviour of Five Organophosphorus Pesticides in Dust Derived from Appendix B. Characteristics Data 197 Several Soil Types," Bulletin of Environmental Contamination and Toxicology, 14, 49.-56 Kearns, C.W., Carl J. Weinman, and George C. Decker (1949), "Insecticidal Properties of Some New Chlorinated Organic Compounds," Journal of Economic Entomology, 42, 127-134 Klosa, Josef (1950), "Diskussionen zur Toxikologie der Hexachlorcyclohexane," Die Pharmazie, 5, 615-616 Konrad, J.G., D.E. Armstrong, and G. Chesters (1967), "Soil Degradation of Diazinon, a Phosphorothioate Insecticide," Agronomy Journal, 59, 591-594 Konrad, J.G., G. Chesters, and D.E. Armstrong (1969), "Soil Degradation of Malathion, a Phosphorodithioate Insecticide," Soil Science Society of America; Proceedings, 33, 259-262 LaFleur, Kermit S. (1976), "Movement of Carbaryl through Congaree Soil into Ground Water," Journal of Environmental Quality, 5, 91-92 Lichtenstein, E.P., O H . Mueller, G.R. Myrdal, and K.R. Schulz (1962), "Vertical Dis-tribution and Persistence of Insecticidal Residues in Soils as Influenced by Mode of Application and a Cover Crop," Journal of Economic Entomology, 55, 215-219 Lichtenstein, E.P. and J.B. Polivka (1959), "Persistence of Some Chlorinated Hydrocar-bon Insecticides in Turf Soils," Journal of Economic Entomology, 52, 289-293 Lichtenstein, E.P. and K.R. Schulz (1959), "Breakdown of Lindane and Aldrin in Soils," Journal of Economic Entomology, 52, 118-124 Lichtenstein, E.P. and K.R. Schulz (1959), "Persistence of Some Chlorinated Hydrocar-bon Insecticides as Influenced by Soil Types, Rate of Application and Tempera-ture," Journal of Economic Entomology, 52, 124-131 Lichtenstein, E.P. and K.R. Schulz (1960), "Epoxidation of Aldrin and Heptachlor in Soils as Influenced by Autoclaving, Moisture, and Soil Types," Journal of Economic Entomology, 53, 192-197 Lichtenstein, E.P. and K.R. Schulz (1961), "Effect of Soil Cultivation, Soil Surface and Water on the Persistence of Insecticidal Residues in Soils," Journal of Economic Entomology, 54, 517-522 Lichtenstein, E.P. and K.R. Schulz (1964), "The Effects of Moisture and Microorganisms on the Persistence and Metabolism of Some Organophosphorus Insecticides in Soils, with Special Emphasis on Parathion," Journal of Economic Entomology, 57, 618— 627 Appendix B. Characteristics Data 198 Lichtenstein, E.P. and K.R. Schulz (1965), "Residues of Aldrin and Heptachlor in Soils and their Translocation into Various Crops," Journal of Agricultural and Food Chemistry, 13, 57-63 Lidov, Rex E., Henry Bluestone, S. Barney Soloway, and Clyde W. Kearns (1950), "Alkali-Stable Polychloro Organic Insect Toxicants, Aldrin and Dieldrin," in Agri-cultural Control Chemicals, American Chemical Society, Advances in Chemistry Series, 1, 175-183 Lightbody, Howard D. and Joseph A. Mathews (1936), "Toxicology of Rotenone," fn-dustrial and Engineering Chemistry, 28, 809-811 Lindquist, Donald A. and Paul A. Dahm (1957), "Some Chemical and Biological Ex-periments with Thiodan," Journal of Economic Entomology, 50, 483-486 Malone, OR., A.G. Winnett, and K. Helrich (1967), "Insecticide-Induced Responses in an Old Field Ecosystem: Persistence of Diazinon in the Soil," Bulletin of Environ-mental Contamination and Toxicology, 2, 83-89 Marsh, M.W. and W.G. Eden (1955), "Relative Toxicity of Six Insecticides to Two Strains of the House Fly," Journal of Economic Entomology, 48, 610-611 Menusan, H. (1948), "Comparative Toxicity of Insecticides Administered in Various Ways to Several Species of Insects," Journal of Economic Entomology, 41, 302-313 Menzie, Calvin M. (1972), "Fate of Pesticides in the Environment," Annual Review of Entomology, 17, 199-222 Metcalf, R.L. (1972), "Development of Selective and Biodegradable Pesticides," in Pest Control Strategies for the Future, National Academy of Science, Washington, D:C, 137-156 Metcalf, Robert L., Inder P. Kapoor, and Asha S. Hirwe (1971), "Biodegradable Ana-logues of DDT," Bulletin of the World Health Organization, 44, 363-374 Metcalf, Robert L. and Ralph B. March (1949), "Studies of the Mode of Action of Parathion and Its Derivatives and Their Toxicity to Insects," Journal of Economic Entomology, 42, 721-728 Metcalf, Robert L. and Ralph B. March (1953), "The Isomerization of Organic Thionophos-phate Insecticides," Journal of Economic Entomology, 46, 288-294 Metcalf, R.L., M.F. Osman, and T.R. Fukuto (1967), "Metabolism of C14-Labeled Car-bamate Insecticides -to C 1 402 in the House Fly," Journal of Economic Entomology, 60, 445-450 Appendix B. Characteristics Data 199 Miles, J.R.W., C M . Tu, and CR. Harris (1971), "Degradation of Heptachlor Epoxide and Heptachlor by a Mixed Culture of Soil Microorganisms," Journal of Economic Entomology, 64, 839-841 Nash, Ralph G. and Edwin A. Woolson (1967), "Persistence of Chlorinated Hydrocarbon Insecticides in Soils," Science, 157, 924-927 Nishizawa, Yoshihiko, Saichiro Kuramoto, Tadaomi Kadota, Junshi Miyamoto, Keimei Fujimoto, and Hideo Sakamoto (1962), "Studies on Organophosphorus Insecti-cides," Agricultural and Biological Chemistry, 26, 257-264 Oliver, A.D. and W.G. Eden (1955), "Toxicity of Several Insecticides to Two Strains of the House Fly," Journal of Economic Entomology, 48, 111-112 Paschal, Daniel C. and M.E. Neville (1976), "Chemical and Microbial Degradation of Malaoxon in an Illinois Soil," Journal of Environmental Quality, 5, 441-443 Philips, Frederick S. and Alfred Gilman (1946), "Acute Toxicity of DDT Following Intravenous Injection in Mammals with Observations on the Treatment of Acute DDT Poisoning," Journal of Pharmacology and Experimental Therapeutics, 86, 213-221 Schrader G. (1961), "Zur Kenntnis neuer, wenig toxischer Insektizide auf der Basis von Phosphorsaureestern," Angewandte Chemie, 73, 331-334 Schulz, K.R., E.P. Lichtenstein, T.T. Liang, and T.W. Fuhremann, "Persistence and Degradation of Azinphosmethyl in Soils as Affected by Formulation and Mode of Action," Journal of Economic Entomology, 63, 432-438 Seume, F.W. and R.D. O'Brien (1960), "Potentiation of the Toxicity to Insects and Mice of Phosphorothionates containing Carboxyester and Carboxyanide Groups," Toxicology and Applied Pharmacology, 2, 495-503 Smith, M.I., H. Bauer, E.F. Stohlman, and R.D. Lillie (1946), "The Pharmacologic Action of Certain Analogues and Derivatives of DDT," Journal of Pharmacology and Experimental Therapeutics, 88, 359-365 Stewart, Donald K.R. and Kenneth G. Cairns (1974), "Endosulfan Persistence in Soil and Uptake by Potato Tubers," Journal of Agricultural and Food Chemistry, 22, 984-986 Stewart, D.K.R. and C.J.S. Fox (1971), "Persistence of Organochlorine Insecticides and Their Metabolites in Nova Scotian Soils," Journal of Economic Entomology, 64, 367-371 Appendix B. Characteristics Data 200 Subba, Rao N.V. and A.G. Pollard (1951), "Photo-Decomposition of Rotenone in Spray-Deposits III - Kinetics of the Photo-Decomposition," Journal of the Science of Food and Agriculture, 2, 462-472 Sun, Yun-Pei (1972), "Correlation of Toxicity of Insecticides to the House Fly and to the Mouse," Journal of Economic Entomology, 65, 632-635 Sun, Yun-Pie and Elmer R. Johnson (1960), "Synergistic and Antagonistic Actions of Insecticide - Synergist Combinations and Their Mode of Action," Journal of Agricultural and Food Chemistry, 8, 261-266 Sun Yun-Pei, and Joe E. Pankaskie (1954), uDrosophila, a Sensitive Insect, for the Microbioassay of Insecticide Residues," Journal of Economic Entomology, 47, 180-181 Treon, Joseph F. and Frank P. Cleveland (1955), "Toxicity of Certain Chlorinated Hy-drocarbon Insecticides for Laboratory Animals, with Special Reference to Aldrin and Dieldrin," Journal of Agricultural and Food Chemistry, 3, 402-408 Treon, Joseph F., Frank P. Cleveland, and John Cappel (1955), "Toxicity of Endrin for Laboratory Animals," Journal of Agricultural and Food Chemistry, 3, 842-848 Wallner, W.E., N.C. Leeling, and M.J. Zabik (1969), "The Fate of Methoxychlor Applied by Helicopter for Smaller European Elm Bark Beetle Control," Journal of Economic Entomology, 62, 1039-1042 Weiss, L.R. and R.A. Orzel (1967), "Some Comparative Toxicologic and Pharmaco-logic Effects of Dimethyl Sulfoxide as a Pesticide Solvent," Toxicology and Applied Pharmacology, 11, 546-557 Wilson, D.M. and P.C. Oloffs (1973), "Persistence and Movement of alpha- and gamma-Chlordane in Soils Following Treatment with High-Purity Chlordane," Canadian Journal of Soil Science, 53, 465-472 Winteringham, F.P.W. (1969), "Mechanisms of Selective Insecticidal Action," Annual Review of Entomology, 14, 409-442 Woodward, Geoffrey and Ernest C. Hagan (1947), "Toxicological Studies on the Iso-mers and Mixtures of Isomers of Benzene Hexachloride," Federation of American Societies for Experimental Biology; Proceedings, 6, 386 Worthing, Charles R. (Ed.) (1987), The Pesticide Manual: A World Compendium (8th ed.), Croydon, England: The British Crop Protection Council Appendix B. Characteristics Data 201 Yaron, Bruno, Bruria Heuer, and Yehudith Birk (1974), "Kinetics of Azinphosmethyl Losses in the Soil Environment," Journal of Agricultural and Food Chemistry, 22, 439-441 Yates, J.R. and Martin Sherman (1970), "Latent and Differential Toxicity of Insecticides to Larvae and Adults of Six Fly Species," Journal of Economic Entomology, 63, 18-23 Young, William R. and W.A. Rawlins (1958), "The Persistence of Heptachlor in Soils," Journal of Economic Entomology, 51, 11-19 Appendix C Prices of Insecticides (annual) The insecticide prices that are used are based upon weekly price quotations in $ U.S./lb. for the largest quantities (ie. tankcars, carloads etc.) recorded in the newspaper, The Chemical Marketing Reporter (weekly). Yearly averages of these price quotations were calculated and are also available in a summary publication of the newspaper, Chem-ical Pricing Patterns (1966), and in the U.S. Department of Agriculture publication, The Pesticide Review (annual). The quantities and values, and the calculated unit values, of annual sales of a few of the products can be found in a publication of the U.S. Tariff Commission, Synthetic Organic Chemicals (annual), and correspond well with the yearly averages of prices from The Chemical Marketing Reporter. 202 Appendix C. Prices of Insecticides^ (annual) 203 Table C.l : Insecticide Prices ($U.S./lb.) Aldrin Allethrin Chlordane DDT Dieldrin 1945 0.53 1946 0.50 1947 1.60 0.45 1948 1.50 0.36 1949 1.44 0.36 1950 1.72 45.00 0.76 0.38 1951 1.79 49.25 0.65 0.51 3.40 1952 1.55 38.06 0.65 0.46 2.89 1953 0.97 32.01 0.65 0.27 2.09 1954 0.90 32.19 0.65 0.30 2.00 1955 0.90 32.03 0.65 0.30 2.00 1956 0.90 32.06 0.65 0.28 2.00 1957 1.00 32.06 0.65 0.25 2.00 1958 1.03 32.06 0.65 0.24 2.02 1959 1.07 32.06 0.65 0.26 2.06 1960 1.11 32.06 0.65 0.26 2.06 1961 1.11 32.06 0.65 0.23 2.06 1962 1.11 32.06 0.65 . 0.23 2.06 1963 1.11 32.06 0.65 0.19 2.06 1964 1.11 32.06 0.65 0.18 2.06 1965 1.11 32.06 0.65 0.19 2.06 1966 1.11 32.06 0.65 0.20 2.06 1967 1.11 32.06 0.60 0.20 1.85 1968 1.17 . 32.06 0.59 0.19 1.83 1969 1.18 32.06 0.59 0.20 1.83 1970 1.18 32.06 0.59 0.24 1.83 Appendix C. Prices of Insecticides (annual) 204 Insecticide Prices ($U.S./lb.) cont'd. Aldrin Allethrin Chlordane DDT Dieldrin 1971 1.18 32.06 0.59 0.24 1.83 1972 1.18 32.06 0.59 0.24 1.83 1973 1.18 32.06 0.61 0.24 1.83 1974 1.33 32.06 0.64 0.30 2.16 1975 1.54 32.06 0.71 0.38 2.60 1976 1.54 42.01 1.00 0.38 2.60 1977 1.54 45.00 1.05 0.38 2.60 1978 1.54 45.00 1.05 0.38 2.60 1979 45.00 1.05 0.38 1980 45.00 1.55 0.38 1981 51.15 3.00 0.38 1982 55.00 3.60 0.38 1983 55.00 3.60 1984 3.60 1985 3.60 1986 3.60 Appendix C. Prices of Insecticides (annual) 205 Insecticide Prices ($U.S./lb.) cont'd. Endrin Heptachlor Lindane Malathion Methoxychlor 1949 1.30 1950 1.30 1951 5.75 1.29 1952 6.13 1.25 1953 3.40 1.25 1954 3.08 1.15 1.25 1955 3.75 3.10 1.04 1.25 1956 3.75 2.97 1.00 1.25 1957 3.75 2.95 1.00 1.25 1958 3.56 0.90 2.91 0.99 1.26 1959 3.38 0.94 2.40 0.99 1.35 1960 2.76 0.96 2.17 0.99 1.32 "1961 2.77 0.96 2.13 0.99 1.32 1962 2.77 0.96 2.13 0.99 1.32 1963 2.77 0.96 1.89 1.00 1:32 1964 2.73 0.96 1.85 1.00 1.32 1965 2.70 0.96 1.85 1.00 1.32 1966 2.70 0.96 1.85 1.00 1.32 1967 2.47 0.97 1.41 1.00 1.32 1968 2.45 1.00 1.30 0.98 1.32 1969 2.45 1.03 1.30 0.88 1.32 1970 2.45 1.03 1.30 0.88 1.32 1971 2.45 1.03 1.33 0.88 1.32 1972 2.45 1.04 1.37 0.88 1.62 1973 2.45 1.08 1.59 0.88 2.03 1974 2.49 1.13 2.04 0.99 2.03 1975 2.75 1.27 2.50 1.14 2.03 Appendix C. Prices of Insecticides (annual) 206 Insecticide Prices ($U.S./lb.) cont'd. Endrin Heptachlor Lindane Malathion Methoxychlor 1976 3.00 1.67 3.32 1.14 2.03 1977 3.00 1.75 3.45 1.14 2.03 1978 3.00 1.75 3.45 1.14 2.03 1979 1.75 3.45 1.14 2.03 1980 2.28 3.45 1.14 2.03 1981 3.88 6.87 1.50 2.03 1982 4.55 9.00 1.79 3.94 1983 7.78 4.55 9.00 . 1.80 4.10 1984 7.78 4.55 9.00 1.80 4.10 1985 7.78 4.55 9.00 1.80 4.10 1986 7.78 4.55 7.80 1.80 4.10 1987 7.78 6.50 1.80 4.10 Appendix C. Prices of Insecticides (annual) 207 Insecticide Prices ($U.S./lb.) cont'd. M-Parathion Parathion Pyrethrum Rotenone Toxaphe 1944 46.88 10^ 90 1945 46.88 11.93 1946 46.54 12.52 1947 46.38 20.49 1948 2.78 36.84 20.67 1949 2.60 49.31 19.98 0.26 1950 2.22 56.14 16.50 0.23 1951 1.76 77.48' 16.50 0.26 1952 1.67 57.91 . 16.50 0.25 1953 1.67 57.25 16.50 0.19 1954 1.79 49.96 16.50 0.19 1955 1.49 49.29 10.67 0.22 1956 1.49 49.96 11.20 0.23 1957 1.75 1.50 50.00 12.00 0.24 1958 1.46 1.41 50.00 12.00 0.24 1959 1.05 0.93 53.78 12.00 0.24 1960 1.05 . 0.93 55.88 11.67 0.24 1961 1.05 0.93 55.88 10.50 0.24 1962 * 1.10 0.93 55.88 10.50 0.24 1963 1.10 0.93 55.88 10.50 0.24 1964 1.10 0.96 55.88 10.50 0.24 1965 1.10 0.98 55.88 10.50 0.24 1966 1.10 0.98 56.48 10.50 0.24 1967 0.98 0.87 57.63 9.43 0.24 1968 0.78 0.69 55.72 9.00 0.24 1969 0.69 0.66 52.98 9.00 0.24 1970 0.69 0.66 49.62 9.00 0.24 Appendix C. Prices of Insecticides (annual) 208 Insecticide Prices ($U.S./lb.) cont'd. M-Parathion Parathion Pyrethrum Rotenone Toxaphi 1971 0.57 0.51 50.63 10.87 0.25 1972 0.58 0.50 51.18 11.00 0.26 1973 0.60 0.54 51.25 11.00 0.30 1974 0.61 0.57 55.48 13.13 0.32 1975 0.98 0.90 61.25 16.00 0.44 1976 1.20 0.97 61.25 20.63 0.45 1977 1.20 0.97 61.25 22.00 0.42 1978 1.20 0.97 61.25 22.00 0.42 1979 1.20 0.97 61.25 22.00 0.42 1980 1.27 1.19 61.25 22.00 0.42 1981 1.45 1.62 139.33 22.00 0.42 1982 1.68 1.82 188.13 22.00 0.42 1983 1.80 1.83 188.13 22.00 0.42 1984 1.90 1.83 188.13 22.00 0.42 1985 1.96 1.85 188.13 22.00 0.42 1986 2.06 1.94 188.13 22.00 0.42 1987 2.06 1.94 188.13 22.00 0.42 Appendix D Products Forming Facets and Implicit Prices of Characteristics D.l Introduction The check of the predictions of characteristics theory was conducted for each year of the study (ie. 44 years in total). This yields the identities of the products within the market opportunity frontier and the relative price that they would require to reach the frontier. It also indicates which combinations of products form facets on the market opportunity frontier. These combinations are "neighbours" on the frontier. Recall that the analysis was conducted by checking every group of three products, calculating the implicit prices of characteristics, and determining whether they formed a supporting plane to the frontier. If they did, the three products and the implicit prices they generated are listed since these goods form a facet of the market opportunity frontier. In the case that is studied, there is information available on the prices and characteristics of fifteen of the most common insecticides. D.2 Units of Measurement and Product Codes The implicit prices of the toxicity to mammals are presented in terms of the expen-diture that is made (in $ U.S.) to potentially place a 1000 kg. biomass of mammals at a 50% risk. The negative price indicates that the expenditure is made to remove this risk. The implicit prices of the toxicity to insects is similarly expressed as the expenditure that is made (in $ U.S.) to potentially place a 100 000 kg. biomass of insects at a 50% risk. Note that the positive values indicate that the expenditure is made to place the insects at risk. Finally, persistence or total exposure to the insecticides is measured as the expenditure (in $ U.S.) required for the generation of an exposure to one kilogram 209 Appendix D. Products Forming Facets and Implicit Prices of Characteristics 210 Table D.l: Product Codes 2 Aldrin 19 Malathion 3 Allethrin 20 Methoxychlor 7 Chlordane 21 Methyl- P arathion 9 DDT 22 Parathion 12 Dieldrin 23 Pyrethrum 15 Endrin 24 Rotenone 16 Heptachlor 25 Toxaphene 18 Lindane of the insecticides for one day. This measure is based upon the fact that the insecti-cides dissipate and degrade over time. The lack of a general tendency toward positive or negative values of this characteristic reflect the different uses of insecticides. The insecticides are indicated by the numbers used in Appendix A and repeated in Table D.l . Appendix D. Products Forming Facets and Implicit Prices of Characteristics 211 1945 CHARACTERISTICS PRICES PRODUCTS ON A FACET MAMMALS INSECTS PERSISTENCE 9 23 24 -0. 753E+02 0.760E+03 -0.463E+00 1946 CHARACTERISTICS PRICES PRODUCTS ON A FACET MAMMALS INSECTS PERSISTENCE 9 23 24 -0. 747E+02 0.754E+03 -0.460E+OO 1947 CHARACTERISTICS PRICES PRODUCTS ON A FACET MAMMALS INSECTS PERSISTENCE 7 9 24 0. 914E+00 0.218E+01 -0.207E-01 7 23 24 -0. 735E+02 0.747E+03 -0.926E+01 1948 CHARACTERISTICS PRICES PRODUCTS ON A FACET MA MM A L_ S INSECTS PERSISTENCE 7 9 22 -0. 927E-01 0.189E+01 0.717E-03 7 22 24 -0. 408E+01 0.522E+02 -0.644E+00 7 23 24 -0. .580E+02 0.591E+03 -0.733E+01 1949 CHARACTERISTICS PRICES PRODUCTS ON A FACET MAMMALS INSECTS PERSISTENCE 7 9 20 -0. 278E+02 -0.374E+01 0.612E+00 7 9 22 -0. 893E-01 0. 180E+01 0.891E-03 7 20 22 -0. . 270E+01 0.347E+02 -0.421E+00 9 22 25 -0. 459E-01 0. 126E+01 0.145E-02 20 22 24 -0. 393E+01 0.504E+02 -0.703E+00 20 23 24 -0. . 783E+02 0.795E+03 -0.140E+02 1950 CHARACTERISTICS PRICES PRODUCTS ON A FACET MAMMALS INSECTS PERSISTENCE 2 3 20 -0. 468E+02 0. 165E+03 -0.237E+01 2 3 24 -0. 105E+02 0.114E*03 -0.283E+01 2 7 9 -0 333E+00 0.716E+00 0.934E-02 2 7 20 -0. .109E+02 0.247E+02 -0.133E+00 2 9 25 -0 248E+00 0.611E+00 0.780E-02 2 22 24 -0 . 311E+01 0.403E+02 -0.102E+01 2 22 25 0. . 192E-01 0.347E+00 0. 105E-02 3 23 24 0 .611E+02 0.237E+03 -0.155E+05 7 9 20 -0 . 305E+02 -0.531E+01 0.674E+00 1951 CHARACTERISTICS PRICES PRODUCTS ON A FACET MAMMALS INSECTS PERSISTENCE 2 7 12 -0 662E+00 0.162E+01 0.775E-03 2 7 25 -0 204E+00 0.576E*00 0.696E-02 2 12 22 -0 .534F-01 0.115E+01 -0.184E-01 2 22 25 0. 787E-02 0.366E+00 0. 161E-02 3 18 20 -0. 407E+03 0.682E+03 -0.785E+01 3 18 24 -0. . 115E+02 0.125E+03 -0.101E+02 3 23 24 0. 904E+02 0.3O0E+03 -0.221E+05 7 9 20 -0, 307E+02 -0.565E+01 0.683E+00 7 9 25 -0. 488E+00 0.397E+00 0. 150E-01 7 12 20 -0. 135E+02 0.208E+02 -0.263E-01 12 18 20 -0. 221E+02 0.378E+O2 -0.247E+00 12 18 22 -0. 387E+00 0.546E+01 -0.20JE+00 18 22 24 -0. 266E+01 0.359E+02 -0.279E+01 Appendix D. Products Forming Facets and Implicit Prices of Characteristics 212 1952 CHARACTERISTICS PRICES PRODUCTS ON A FACET MAMMALS INSECTS PERSISTENCE 2 7 12 -0. 618E+00 0. 141E+01 0. 296E-02 2 7 25 -0. 245E+00 0.558E+00 0. 800E-02 2 12 22 -0. 405E-01 0.959E+00 -0. 153E-01 2 22 25 0. 109E-01 0.305E+00 0. 154E02 3 18 20 -0. 313E+03 0.524E*03 -0. 800E+01 3 18 24 -0. 867E+01 0.962E+02 -0. 769E+01 3 23 24 0. 870E+02 0.228E*03 -0. 164E+05 7 9 20 -0. 297E+02 -0.539E+01 0. 659E+00 7 9 25 -0. 396E+00 0.462E+00 0. 123E-01 7 12 20 -0. 131E+02 0.200E*02 -0. 234E-01 12 18 20 -0. 229E+02 0.395E+02 -0. 278E*00 12 18 22 -0. 430E+00 0.599E+01 -0. 228E+00 18 22 24 -o- 268E+01 0.3B0E+02 -0. 278E+01 1953 CHARACTERISTICS PRICES PRODUCTS ON A FACET MAMMALS INSECTS PERSISTENCE 2 7 9 -0. 399E+00 0.641E+00 0. 977E-02 2 7 12 -0. 668E+00 0. 126E+01 0. 615E-02 2 9 25 -0. 148E+00 0.332E+00 0. 521E-02 2 12 22 -0. 239E-01 0.752E+00 -0. 142E-01 2 22 25 0. 222E-01 0.164E+00 0. 919E-03 3 ia 20 -0. 268E+03 0.449E+03 -0. 510E+01 3 18 24 -0. 713E+01 0.807E+02 -0. 855E+0.1 3 23 24 0. 690E+02 0.211E+03 -0. 165E+05 7 9 20 -0. .295E+02 -0.519E+01 0. 653E+00 7 12 20 -0. 132E+02 0.199E+02 -0. 203E-01 12 18 20 -0. 185E+02 0.304E+02 -0. 15BE+00 12 18 22 -0. 213E+00 0.319E+01 -0. 117E+00 18 22 24 -0. 265E+01 0.357E+02 -0. 288E+01 1954 CHARACTERISTICS PRICES PRODUCTS ON A FACET MAMMALS INSECTS PERSISTENCE 2 7 9 -0. 401E+00 0.612E*00 0. 102E-01 2 7 12 -0. 877E+00 0.124E+01 0. 850E-02 2 9 25 -0. 201E+00 0.367E+00 0. 859E-02 2 12 22 -0. 195E-01 0.729E+00 -0. 142E-01 2 22 25 0. 285E-01 0.142E+00 0. 842E-03 3 18 19 -0. 416E+02 0.130E+03 -0. 641E*01 3 18 20 -0. 271E+03 0.452E+03 -0. 514E+01 3 19 24 -0. 669E+01 0.820E*02 -0. 111E+03 ._3._._ 23 24 0. 582Et02 ._0..J.93E±Q.3_ __-0.. ..142E*05 7 9 20 -0 .296E+02 -0.522E+01 0 .654E+00 7 12 20 -0 . 132E+02 0.199E+02 •0 . 199E-01 12 18 20 -0 . 179E+02 0.293E+02 -0 .142E+00 12 18 22 -0 . 184E+00 0.286E+01 -0 .104E+00 18 19 22 -0 .820E+00 0.113E*02 •0 .828E+00 19 22 24 ' -0 .558E+00 0.152E+02 -0 .102E+02 Appendix D. Products Forming Facets and Implicit Prices of Characteristics 213 1955 CHARACTERISTICS PRICES PRODUCTS ON A FACET MAMMALS INSECTS PERSISTENCE 2 7 9 -0 401E+00 0. 612E+00 0. , 102E-01 2 7 12 -0 .677E+00 0. 124E+01 0. 650E-02 2 9 25 -0 .158E+00 0. 314E+00 0. .581E-02 2 12 22 -0 .263E-01 0 734E+00 -0. . 140E-01 2 22 25 0 205E-01 0. ,137E+00 0. 130E-02 3 18 19 -0 .420E+02 0. ,130E*03 -0. 637E+01 3 18 20 -0 .269E+03 0. 450E+03 -0. .511E+01 3 19 24 -0. .702E+01 0 821E+02 -0 111E+03 3 23 24 0. 571E+02 0. 192E+03 -0. , 140E+05 7 9 20 -0. 296E+02 -0. 522E+01 0. 654E+00 7 12 20 -0. .132E+02 0. 199E+02 -0. . 199E-01 12 18 20 -0. .180E+02 0. 294E+02 -0. 143E+00 12 18 22 -0. 193E+00 0. . 289E+01 -0. , 105E+00 18 19 22 -0. 745E+00 0. 103E+02 -0. 732E+00 19 22 24 -0. 609E+00 0. 123E+02 -0. 580E+01 THE FACET THE PRODUCT RELATIVE PRICE 2 12 22 15 0.681E+00 1956 CHARACTERISTICS PRICES PRODUCTS ON A FACET MAMMALS INSECTS PERSISTENCE 2 7 9 -0 .408E+00 0 .630E+00 0. . 101E-01 2 7 12 -0 677E+00 0 .124E+01 0. 650E-02 2 9 25 -0 .110E+00 0 .263E+00 0. 470E-02 2 12 22 -0 263E-01 0 .734E+00 -0. , 140E-01 2 22 25 0 208E-01 0 .134E+00 0. . 139E-02 3 18 19 -0. .422E+02 0 . 130E+03 -0. 639E+01 3 18 20 -0. 270E+03 0. 451E+03 -0. 512E+01 3 19 24 -0 699E+01 0. 822E+02 -0. . 112E+03 3 23 24 0 581E+02 0. 194E+03 -0. 142E+05 7 9 20 -0 295E+02 -0. 520E+01 0. 653E+00 7 12 20 -0. 132E+02 0. 199E+02 -0. 199E-01 12 18 20 -0. . 177E+02 0. 289E+02 -0. 136E+00 12 18 22 -0. 182E+00 0 ,275E*01 -0. 991E-01 18 19 22 -0. .715E+00 0. 987E+01 -0. , 705E+00 19 22 24 -0. ,581E*00 0. 121E+02 -0. 618E+01 THE FACET THE PRODUCT RELATIVE PRICE 2 12 22 15 0.881E+00 Appendix D. Products Forming Facets and Implicit Prices of Characteristics 214 1957 CHARACTERISTICS PRICES PRODUCTS ON A FACET MAMMALS INSECTS PERSISTENCE 2 7 9 -0. 401E+00 0 .660E+00 0 .955E-02 2 7 12 -0. 618E+00 0 . 115E+01 0 .882E-02 2 9 25 -0. 41BE-01 0 .218E+00 0 .302E-02 2 12 22 -0. 227E-01 0 890E+00 -0 .122E-01 2 22 25 0. 190E-01 0 .158E+00 0 .149E-02 3 18 19 -0. 422E+02 0. .130E+03 -0 639E+01 3 18 20 -0. 270E+03 0 451E+03 -0 .512E+01 3 19 21 -0. 821E+01 0. 838E+02 -0. .108E+03 3 21 24 -0. 631E+01 0. 832E+02 -0 249E+03 3 23 24 0. 582E+02 0. 194E+03 -0. .142E+05 7 9 20 -0. 295E+02 -0. 517E+01 0. 852E+00 7 12 20 -0. 132E+02 0. 199E+02 -0. , 199E-01 12 18 20 -0. 177E+02 0. 288E+02 -0. 135E+00 12 18 21 -0. 271E+00 0. 286E+01 -0. 983E-01 12 21 22 -0. 250E-01 0. 720E+00 -0. .135E-01 18 19 21 -0. 125E+01 0. 114E+02 -0. 779E+00 21 22 24 0. 364E+01 -0. 286E+02 -0 216E+02 THE FACET THE PRODUCT RELATIVE PRICE 2 12 22 15 0.686E+00 1958 CHARACTERISTICS PRICES PRODUCTS ON A FACET MAMMALS INSECTS PERSISTENCE 2 7 9 -0. 399E+00 0. 669E+00 0. 937E-02 2 7 16 -0. 551E+00 0. .102E+01 0. 732E-02 2 9 25 -0. 236E-01 0. 208E+00 0. 256E-02 2 16 22 0. 943E-02 0 256E+00 -0. 695E-03 2 22 25 0. 163E-01 0 . 168E+00 0. 155E-02 3 18 19 -0. 423E+02 0. . 130E+03 -0. 639E+01 3 18 20 -0. 270E+03 0. 451E+03 -0. 512E+01 3 19 21 -0. 822E+01 0. 838E+02 -0. 108E+03 3 21 24 -0. 630E+01 0. 832E+02 -0. 250E+03 3 23 24 0. 582E+02 0. 194E+03 -0. 142E+05 7 9 20 -0. 298E+02 -0. 521E+01 0. 658E+00 7 12 18 -0. 738E+00 0. . 134E+01 0. 829E-02 7 12 20 -0. 133E+02 0. . 200E+02 -0. 202E-01 12 16 18 -0. 206E*01 0. 548E+01 -0. 999E-01 12 18 20 -0. 177E+02 0. 288E+02 -0. 133E+00 16 18 21 -0. 329E+00 0. 329E*01 -0. 133E+00 16 21 22 -0. 977E-02 0. 505E+00 -0. 123E-01 18 19 21 -0. 125E+01 0. , 113E+02 -0. 773E+00 21 22 24 0. 369E+01 -0. 291E*02 -0 . 219E+02 THE FACET THE PRODUCT RELATIVE PRICE 2 16 22 15 0.515E+00 Appendix D. Products Forming Facets and Implicit Prices of Characteristics 215 1959 CHARACTERISTICS PRICES PRODUCTS ON A FACET MAMMALS INSECTS PERSISTENCE 2 7 9 -0 .384E+00 0 .654E+00 0 .931E-02 2 7 16 -0 .546E+00 0 . 102E*01 0 .713E-02 2 9 25 -0 558E-01 0 .250E+00 0 .335E-02 2 16 22 -0. 320E-02 0. 287E+00 -0 .635E-03 2 22 25 0. 433E-02 0. ,191E*00 0 . 183E-02 3 18 19 -0. 423E+02 0. .130E*03 -0 .641E+01 3 18 20 -0. 272E+03 0. .454E+03 -0 .513E+01 3 19 21 -0. 824E+01 0. 839E+02 -0 . 108E+03 3 21 24 -0. 630E+01 0. 832E+02 -0. .252E+03 3 23 24 0. 638E+02 0. 203E+03 -0. . 154E+05 7 9 20 -0. 321E+02 -0. 589E*01 0. 709E+00 7 12 16 -0. 720E+00 0. 132E+01 0. 616E-02 7 12 20 -0. 143E+02 0. 216E+02 -0. .225E-01 12 16 18 -0. 173E+01 0. 449E+01 -0 750E-01 12 18 20 -0. 177E+02 0. 282E+02 -0. .109E+00 16 18 21 -0. 268E+00 0. 264E+01 -0. 103E+00 16 21 22 -0. 132E-01 0. 416E+00 -0. 667E-02 18 19 21 •0. 127E+01 0. 114E+02 -0. 801E+00 21 22 24 0. 376E+01 -0. 298E+02 -0. 223E+02 HE FACET THE PRODUCT RELATIVE PRICE ! 16 22 15 0.521E+00 1960 CHARACTERISTICS PRICES IDUCTS ON A FACET MAMMALS INSECTS PERSISTENCE 2 7 9 -0. 377E+00 0. 655E+00 0. 914E-02 2 7 16 -0. 527E+00 0. 998E+00 0. 712E-02 2 9 25 -0. 542E-01 0. 259E+00 0. 329E-02 2 16 22 -0. 327E-02 0. 287E+00 -0. 362E-03 2 22 25 0. 343E-02 0. 202E+00 0. 184E-02 3 18 19 -0. 423E+02 0. 130E*03 -0. 642E+01 3 18 20 -0. 272E+03 0. 454E+03 -0. 514E*01 3 19 21 -0. 824E+01 0. 839E+02 -0. 108E*03 3 21 24 -0. 633E+01 0. 832E+02 -0. 249E+03 3 23 24 0. B68E+02 0. 209E+03 -0. 161E*05 7 9 20 -0. 313E+02 -0. 553E*01 0. 692E+00 7 12 16 -0. 688E+00 0. 128E*01 0. 623E-02 7 12 20 -0. 140E+02 0. 211E+02 -0. 218E-01 12 18 18 -0. 156E+01 0. 402E+01 -0. 640E-01 12 18 20 -0. 169E+02 0. 268E+02 -0. 963E-01 16 18 21 -0. 233E+00 0. 233E+01 -0, 894E-01 16 21 22 •0. 132E-01 0. 416E+00 -0. 639E-02 18 19 21 -0. 127E+01 0. 114E+02 -0. 812E+00 21 22 24 0. 365E+01 -0. 289E+02 -0. 216E+02 THE FACET 2 16 22 THE PRODUCT RELATIVE PRICE 15 0.651E+00 Appendix D. Products Forming Facets and Implicit Prices of Characteristics 216 1B61 CHARACTERISTICS PRICES PRODUCTS ON A FACET MAMMALS INSECTS PERSISTENCE 2 7 9 -0. 388E+00 0. 681E+00 0. 899E-02 2 7 16 -0. 527E+00 0. 998E+00 0 712E-02 2 9 25 -0. 375E-02 0. . 209E+00 0 .202E-02 2 16 22 -0. .327E-02 0. 287E*00 -0 .362E-03 2 22 25 0 343E-02 0 .202E*00 0 .184E-02 3 18 19 -0 .423E+02 0 . 130E+03 -0. 642E+01 3 18 20 -0. 272E+03 0 .454E+03 -0. .514E+01 3 19 21 -0 824E+01 0 .839E+02 -0. .108E+03 3 21 24 -0 644E+01 0 .832E+02 -0. 241E+03 3 23 24 0 668E+02 0 .209E+03 -0. .161E+05 7 9 20 -0, 313E+02 -0 .550E+01 0. 891E+00 7 12 16 -0. 888E+00 0 . 128E+01 0. 623E-02 7 12 20 -0. , 140E+02 0. 211E+02 -0. 218E-01 12 16 18 -0. ,154E+01 0. 394E+01 -0. 621E-01 12 18 20 -0. 168E+02 0. 267E+02 -0. 943E-01 16 18 21 -0. 227E+00 0. 228E+01 -0. 872E-01 16 21 22 -0. 132E-01 0. 416E+00 -0. 839E-02 18 19 21 -0. 127E+01 0. 114E+02 -0. 814E+00 21 22 24 0. 327E+01 -0. 258E+02 -0. 194E+02 HE FACET THE PRODUCT RELATIVE PRICE ! 16 22 15 0.649E+00 1962 CHARACTERISTICS PRICES (DUCTS ON A FACET MAMMALS INSECTS PERSISTENCE 2 7 9 -0. 388E+00 0. 681E+00 0. 899E-02 2 7 16 -0. 527E+00 0. 998E+00 0. 712E-02 2 9 25 -0. 375E-02 0. 209E+00 0. 202E-02 2 16 22 -0. 327E-02 0. 287E+00 -0. 362E-03 2 22 25 0. 343E-02 0. 202E+00 0. 184E-02 3 18 19 -0. 423E+02 0. 130E+03 -0. 842E+01 3 18 20 -0 272E+03 0. 454E+03 -0. 514E+01 3 19 21 -0. 823E+01 0. 838E+02 -0. .108E+03 3 21 24 -0. 644E*01 0. 832E+02 -0, 241E+03 3 23 24 0. 668E*02 0. 209E*03 -0. .1B1E+05 7 9 20 -0 .313E+02 •0. 550E+01 0. 691E+00 7 12 16 -0 888E+00 0. , 128E+01 0 623E-02 7 12 20 -0 .140E+02 0. 211E+02 -0. 218E-01 12 16 18 -0 .154E+01 0. 394E+01 -0 .621E-01 12 18 20 -0 .168E+02 0. 287E*02 -0 .943E-01 16 18 21 -0 .225E+00 0. 228E+01 -0 872E-01 16 21 22 -0 .168E-01 0. . 460E+00 •0 .844E-02 18 19 21 -0 .127E+01 0. . 114E*02 -0 ,814E*00 21 22 24 0 .326E+01 -0 257E+02 -0 .193E+02 THE FACET THE PRODUCT RELATIVE PRICE 2 16 22 15 0.649E+00 Appendix D. Products Forming Facets and Implicit Prices of Characteristics 217 1963 PRODUCTS ON A FACET CHARACTERISTICS PRICES MAMMALS INSECTS PERSISTENCE 2 7 9 -0. 403E+00 0. 716E+00 0. 879E-02 2 7 16 -0. 527E+00 0. 998E+00 0. 712E-02 2 9 22 0. 219E-02 0. 218E+00 0. 143E-02 2 16 22 --0. 327E-02 0. 287E+00 -0. 362E-03 3 18 19 -0. 422E+02 0. 130E+03 -0. 644E+01 3 18 20 -0. 273E+03 0. 455E+03 -0. 515E+01 3 19 21 -0. 824E+01 n -n m o c * m 3 21 24 -0 .644E+01 0 .832E+02 -0 .241E+03 3 23 24 0 .668E+02 0 .209E*03 -0 . 161E+05 7 9 20 -0 .313E+02 -0 .546E+01 0 .690E*00 7 12 16 -0 .688E+00 0 .128E*01 0 .623E-02 7 12 20 -0 .140E+02 0 .211E+02 -0 .218E-01 9 22 25 0 259E-01 -0 .789E-01 0, .173E-02 12 16 18 -0. . 140E+01 0 . 350E+01 -0. 508E-01 12 18 20 -0. . 163E+02 0 .257E+02 -0. 823E-01 16 18 21 -0. . 190E+00 0 . 197E+01 -0. 739E-01 16 21 22 -0. 166E-01 0 .460E+00 -0. 844E-02 18 19 21 -0. 129E+01 0 . 115E*02 -0. 835E+00 21 22 24 0. . 326E+01 -0 .257E+02 -0. . 193E+02 HE FACET THE PRODUCT RELATIVE PRICE ! 16 22 15 0.649E+00 1964 CHARACTERISTICS PRICES (DUCTS ON A FACET MAMMALS INSECTS PERSISTENCE 2 7 9 -0. 407E+00 0. 724E+00 0. 874E-02 2 7 16 -0. 527E+00 0. 998E+00 0. 712E-02 2 9 22 0. 255E-02 0. 221E+00 0. 130E-02 2 16 22 -0. 256E-02 0. 286E+00 -0. 372E-03 3 18 19 -0. 422E+02 0. 130E*03 -0. 844E+01 3 18 20 -0. 273E+03 0. 455E+03 -0. 515E*01 3 19 21 -0. 824E+01 0. 839E+02 -0. 108E+03 3 21 24 -0. 644E+01 0. 832E+02 -0. 241E+03 3 23 24 0. 668E+02 0. 209E+03 -0. . 161E*05 7 9 20 -0. 313E+02 -0. 545E+01 0. 690E+00 7 12 18 -0. 688E+00 0. 128E+01 0. 623E-02 7 12 20 -0. ,140E+02 0. 211E*02 -0. 218E-01 9 22 25 0, 326E-01 -0. 155E+00 0. 169E-02 12 16 18 -0. 137E+01 0. . 342E+01 -0. 489E-01 12 18 20 -0. .183E+02 0. 258E+02 -0. 803E-01 16 18 21 -0, .184E+00 0. . 192E+01 -0. 716E-01 16 21 22 -0. .147E-01 0. 443E+00 -0. 770E-02 18 19 21 -0. .129E+01 0. , 115E+02 -0. 837E+00 21 22 24 0. 326E+01 -0. 257E+02 -0. . 193E+02 THE FACET 2 16 22 THE PRODUCT RELATIVE PRICE 15 0.661E+00 Appendix D. Products Forming Facets and Implicit Prices of Characteristics 218 1965 PRODUCTS ON A FACET CHARACTERISTICS PRICES MAMMALS INSECTS PERSISTENCE 2 7 9 -0. 403E+00 0 . 716E+00 0 .879E-02 2 7 16 -0. 527E+00 0 998E+00 0 .712E-02 2 9 22 0. 337E-02 0 218E+00 0 . 141E-02 2 18 22 -0. 209E-02 0 ,288E*00 -0 .379E-03 3 18 19 -0. 422E+02 0 . 130E+03 -0 .644E+01 3 18 20 -0. 273E*03 0 455E+03 -0 .515E+01 3 19 21 -0. 824E+01 0 839E+02 -0 . 108E+03 3 21 24 -0. 644E+01 0 832E*02 -0 .241E+03 3 23 24 0. 668E+02 0, 209E+03 -0 . 161E+05 7 9 20 -0. 313E+02 -0 .546E+01 0. 890E+00 7 12 16 -0. 688E+00 0 . 128E+01 0. 623E-02 7 12 20 -0. 140E+02 0 .211E*02 -0. 218E-01 9 22 25 0. 288E-01 -0 .747E-01 0. 171E-02 12 16 18 -0. 137E+01 0 .342E+01 -0. 489E-01 12 18 20 -0. 163E+02 0 .256E+02 -0. 803E-01 16 18 21 -0. 184E+00 0 .192E+01 -0. 716E-01 16 21 22 -0. 134E-01 0 432E+00 -0. 721E-02 18 19 21 -0. 129E+01 0 .115E*02 -0. 837E+00 21 22 24 0. 326E+01 -0 257E+02 -0. , 193E+02 HE FACET THE PRODUCT RELATIVE PRICE ! 16 22 15 0.671E+00 1966 CHARACTERISTICS PRICES •DUCTS ON A FACET MAMMALS INSECTS PERSISTENCE 2 7 9 -0. 399E+00 0. 707E+00 0. 884E-02 2 7 16 -0. 527E+00 0 998E*00 0. 712E-02 2 9 22 0. 371E-02 0 212E+00 0, . 152E-02 2 16 22 -0. 209E-02 0. 286E+00 -0. 379E-03 3 18 19 -0. 422E+02 0. .130E+03 -0. 644E+01 3 18 20 -0. 273E+03 0. 455E+03 -0. 515E+01 3 19 21 -0. 824E+01 0 839E+02 -0. . 108E+03 3 21 24 -0. 644E+01 0 832E*02 -0 241E+03 3 23 24 0. 677E*02 0 210E+03 -0 . 163E+05 7 9 20 -0. 313E+02 -0 547E+01 0 890E+00 7 12 16 -0. 688E+00 0 . 128E+01 0 623E-02 7 12 20 -0 .140E+02 0 211E+02 -0 .218E-01 9 22 25 0 203E-01 0 .386E-02 0 .174E-02 12 16 18 -0 .137E+01 0 .342E*01 -0 .489E-01 12 18 20 -0 .163E+02 0 .256E*02 -0 .803E-01 16 18 21 -0 .184E*00 0 . 192E+01 -0 .716E-01 16 21 22 -0 .134E-01 0 .432E+00 -0 .721E-02 18 19 21 -0 .129E+01 0 . 115E+02 -0 .837E+00 21 22 24 0 .326E+01 -0 .257E+02 -0 .193E+02 THE FACET 2 16 22 THE PRODUCT RELATIVE PRICE 15 0.671E+OO Appendix D. Products Forming Facets and Implicit Prices of Characteristics 219 1967 CHARACTERISTICS PRICES PRODUCTS ON A FACET MAMMALS INSECTS PERSISTENCE 2 7 9 -0 347E+00 0 643E+00 0 788E-02 2 7 12 -0 463E+00 0 907E+00 0 633E-02 2 9 22 0 113E-02 0 215E+00 0 157E-02 2 12 16 -0 444E+00 0 892E+00 0 575E-02 2 16 22 -0 S28E-02 0 297E+00 -0 530E-03 3 18 19 -0 422E+02 0 130E+03 -0 646E+01 3 18 20 -0 274E+03 0 457E+03 -0 517E+01 3 19 21 -0 824E+01 0 839E+02 -0 108E+03 3 21 24 -0 654E*01 0 .833E+02 -0 234E+03 3 23 24 0 693E+02 0 213E*03 -0 167E+05 7 9 20 -0 315E+02 -0 558E+01 0 695E+00 7 12 20 -0 140E+02 0 .211E+02 -0 223E-01 9 22 25 0 187E-01 -0 .545E-02 0 179E-02 12 16 18 -0 910E+00 0 .235E+01 -0 316E-01 12 18 20 -0 156E+02 0 .243E+02 -0 627E-01 16 18 21 -0 123E+00 0 135E+01 -0 467E-01 16 21 22 -0 124E-01 0 389E+00 -0 484E-02 18 19 21 -0 129E+01 0 116E+02 -0 859E+00 21 22 24 0 293E+01 -0 231E+02 -0 174E+02 THE FACET THE PRODUCT RELATIVE PRICE 2 16 22 15 0.726E+00 1968 CHARACTERISTICS PRICES PRODUCTS ON A FACET MAMMALS INSECTS PERSISTENCE 2 7 9 -0 329E+00 0 641E+00 0 739E-02 2 7 12 -0 413E+00 0 832E+00 0 626E-02 2 9 22 -0 487E-02 0 242E+00 0 151E-02 2 12 16 -0 381E+00 0 807E+00 0 525E-02 2 16 22 -0 967E-02 0 303E+00 -0 585E-04 3 18 19 -0 423E*02 0 130E*03 -0 646E+01 3 18 20 -0 274E+03 0 457E+03 -0 517E+01 3 19 21 -0 824E+01 0 839E+02 -0 108E+03 3 21 24 -0 658E+01 0 833E*02 -0 231E+03 3 23 24 0 685E+02 0 209E+03 -0 181E+05 7 9 20 -0 315E+02 -0 560E+01 0 696E+00 7 12 20 -0 141E+02 0 212E+02 -0 225E-01 9 22 25 0 224E-01 -0 993E-01 0 186E-02 12 16 18 -0 778E+00 0 205E+01 -0 267E-01 12 18 20 -0 154E*02 0 239E+02 -0 576E-01 16 18 21 -0 113E+00 0 121E+01 -0 394E-01 16 21 22 -0 106E-01 0 315E+00 -0 819E-03 18 19 21 -0 128E+01 0 114E*02 -0 847E+00 21 22 24 0 282E+01 -0 223E+02 -0 167E+02 THE FACET THE PRODUCT RELATIVE PRICE 2 18 22 15 0.734E+00 Appendix D. Products Forming Facets and Implicit Prices of Characteristics 220 1969 CHARACTERISTICS PRICES PRODUCTS ON A FACET MAMMALS INSECTS PERSISTENCE 2 7 9 -0 .323E+00 0. 632E+00 0 740E-02 2 7 12 -0 407E+00 0 823E+00 0 628E-02 2 9 22 -0 546E-02 0. 242E+00 0 . 164E-02 2 12 16 -0 345E+00 0. 775E+00 0. 431E-02 2 16 21 -0. 149E-01 0. 327E+00 -0. 407E-03 2 21 22 -0. 627E-02 0. 252E+00 0. 137E-02 3 18 19 -0. 428E+02 0. 131E+03 -0. 646E+01 3 18 20 -0. 274E+03 0. 457E+03 -0. 517E+01 3 19 21 -0. 823E+01 0. 839E*02 -0. 110E+03 3 21 24 -0. 658E*01 0. 833E+02 -0. 232E+03 3 23 24 0. 825E+02 0. 202E+03 -0. 152E+05 7 9 20 -0. 315E*02 -0. 5B1E+01 0. 696E+00 7 12 20 -0. 141E+02 0. 212E*0? -n ? ? R F - n i 9 22 25 0 .157E-01 -0 .232E-01 0 . 191E-02 12 16 18 -0 .729E+00 0 .198E+01 -0 .266E-01 12 18 20 -0 .154E+02 0 .239E+02 -0 .576E-01 16 18 21 -0 .115E+00 0 .120E+01 -0. 383E-01 18 19 21 -0 .115E+01 0 .102E+02 -0. . 755E+00 21 22 24 0. .284E+01 -0 .225E+02 -0. . 168E+02 THE FACET THE PRODUCT RELATIVE PRICE 2 16 21 15 0.732E+00 1970 CHARACTERISTICS PRICES PRODUCTS ON A FACET MAMMALS INSECTS PERSISTENCE 2 7 9 -0. . 308E+00 0, 598E+00 0. 761E-02 2 7 12 -0 .407E+00 0. . 823E+00 0. 628E-02 2 9 25 -0. .180E-01 0. 241E*00 0 234E-02 2 12 16 -0. 345E+00 0 . 775E+00 0 431E-02 2 16 21 -0. 149E-01 0. 327E+00 -0. 407E-03 2 21 22 -0. 627E-02 0. 252E*00 0. . 137E-02 2 22 25 -0. 435E-02 0. 228E+00 0. 200E-02 3 18 19 -0. 428E+02 0. .131E+03 -0. 646E+01 3 18 20 -0. 274E+03 0. 457E*03 -0 517E+01 3 19 21 -0. 823E+01 0. 839E+02 -0. . 110E+03 3 21 24 -0. 658E+01 0. 833E+02 -0. 232E+03 3 23 24 0. 576E+02 0. , 193E+03 -0. . 141E+05 7 9 20 -0. .315E+02 -0. 565E+01 0. 697E*00 7 12 20 -0. 141E+02 0. 212E+02 -0. 225E-01 12 16 18 -0. 729E+00 0. 198E+01 -0 266E-01 12 18 20 -0. .154E+02 0. .239E+02 -0. 578E-01 16 18 21 -0. 115E+00 0. , 120E+01 -0. 383E-01 18 19 21 -0. ,115E+01 0. , 102E+02 -0. 755E+00 21 22 24 0. 284E+01 -0. 225E+02 -0. 168E+02 THE FACET THE PRODUCT RELATIVE PRICE 2 16 21 15 0.732E+00 Appendix D. Products Forming Facets and Implicit Prices of Characteristics 221 1971 CHARACTERISTICS PRICES DUCTS ON A FACET MAMMALS INSECTS PERSISTENCE 2 7 9 -0. 308E+00 0. 598E+00 0. 761E-02 2 7 12 -0. 407E+00 0. 823E+00 0. 628E-02 2 9 22 -0. 760E-02 0. 228E+00 0. 216E-02 2 12 16 -0. 345E+00 0. 775E+00 0. 431E-02 2 16 21 -0. 196E-01 0. 334E+00 -0. 340E-03 2 21 22 -0. ,778E-02 0. 231E+00 0. 210E-02 3 18 19 -0. 428E+02 0. 131E+03 -0. 646E+01 3 18 20 -0. .274E+03 0. 457E+03 -0. 517E+01 3 19 21 -0. 823E+01 0. 839E+02 -0. .110E+03 3 21 24 -0 640E+01 0. 832E+02 -0, 246E+03 3 23 24 0 591E+02 0. .196E*03 -0 .144E+05 7 9 20 -0 .315E+02 -0 565E+01 0. 697E+00 7 12 20 -0 .141E*02 0 .212E+02 -0 225E-01 9 22 25 -0 .610E-02 0 210E+00 0 .218E-02 12 16 18 -0 747E+00 0 .203E+01 -0 .280E-01 12 18 20 -0 .155E+02 0 .240E*02 -0 .591E-01 16 18 21 -0 .124E+00 0 .125E+01 -0 .399E-01 18 19 21 -0 .115E+01 0 .102E*02 -0 .754E+00 21 22 24 0 .347E+01 -0 .278E+02 -0 •205E+02 THE FACET THE PRODUCT RELATIVE PRICE ! 16 21 15 0.709E+00 1972 CHARACTERISTICS PRICES IDUCTS ON A FACET MAMMALS INSECTS PERSISTENCE 2 7 9 -0. , 308E+00 0 .598E+00 0. 761E-02 2 7 12 -0. ,407E+00 0 .823E*00 0. 628E-02 2 9 22 -0. .783E-02 0 .229E+00 0. 216E-02 2 12 18 -0. .333E+00 0 .766E+00 0. 395E-02 2 18 21 -0 201E-01 0 .341E+00 -0. 529E-03 2 21 22 -0, 915E-02 0 .245E+00 0. . 173E-02 3 18 19 -0. 428E+02 0 .131E+03 -0. 646E+01 3 18 20 -0 276E+03 0 .460E+03 -0, .516E+01 3 19 21 -0, 823E+01 0 .839E+02 -0. , 110E+03 3 21 24 -0 .838E+01 0 .832E+02 -0 247E*03 3 23 24 0 599E+02 0 .197E+03 -0 . 146E+05 7 9 20 -0 392E*02 -0 .718E+.01 0. 866E*00 7 12 20 -0 . 174E+02 0 .262E+02 -0 296E-01 9 22 25 -0 .748E-03 0 .140E+00 0 225E-02 12 16 18 -0 754E+00 0 .208E+01 -0 298E-01 12 18 20 -0 . 189E+02 0 .292E+02 -0 682E-01 18 18 21 -0 .129E+00 0 .129E+01 -0 .418E-01 18 19 21 -0 .115E+01 0 .102E+02 -0 ,752E*00 21 22 24 . 0 .351E+01 -0 .279E+02 -0 .208E+02 THE FACET THE PRODUCT RELATIVE PRICE 2 16 21 15 0.714E+00 Appendix D. Products Forming Facets and Implicit Prices of Characteristics 222 1973 CHARACTERISTICS PRICES IDUCTS ON A FACET MAMMALS INSECTS PERSISTENCE 2 7 9 -0 .329E+00 0 .623E+00 0 .799E-02 2 7 12 -0 .422E+00 0 .835E+00 0. 674E-02 2 9 22 -0 689E-02 0 .227E+00 0, .214E-02 2 12 16 -0. 288E+00 0 .730E+O0 0. 251E-02 2 16 21 -0 229E-01 0 .371E+00 -0. .128E-02 2 21 22 -0. 790E-02 0 .240E+00 0. . 181E-02 3 18 19 -0 428E+02 0 .131E+03 -0. 645E+01 3 18 20 -0. 279E+03 0 .464E+03 -0 513E+01 3 19 21 -0. 823E+01 0 .839E+02 -0. . 110E+03 3 21 24 -0. 638E+01 0 .832E+02 -0. 247E+03 3 23 24 0. 600E+02 0 . 197E+03 -0. 146E+05 7 9 20 -0. 496E+02 -0 .923E+01 0. . 110E+01 7 12 20 -0. 220E+02 0 .330E+02 -0. 388E-01 9 22 25 0. 218E-01 -0 .132E+00 0. 251E-02 12 16 18 -0. 819E+00 0 .239E+01 -0. 401E-01 12 18 20 -0. 240E+02 0 .369E+02 -0. 890E-01 16 18 21 -0. 159E+00 0 .156E+01 -0. 527E-01 18 19 21 -0. ,115E+01 0 .102E+02 -0. 741E+00 21 22 24 0. 351E+01 -0 .279E+02 -0. 208E+02 THE FACET 2 16 21 THE PRODUCT RELATIVE PRICE 15 0.732E+00 1974 CHARACTERISTICS PRICES OUCTS ON A FACET MAMMALS INSECTS PERSISTENCE 2 7 9 -0. 310E+00 0 .616E+00 0. 825E-02 2 7 16 -0. 451E+00 0. 937E+00 0. 635E-02 2 9 21 -0. 813E-02 0 245E+00 0. 278E-02 2 16 21 •0. 206E-01 0 .354E+00 0. 204E-O3 3 18 19 -0. 423E+02 0 .130E+03 -0. 643E+01 3 18 20 -0. 278E+03 0 .462E+03 -0. 512E+01 3 19 21 -0. 825E+01 0 839E+02 -0. 108E+03 3 21 24 -0. 618E+01 0 832E+02 -0. 262E+03 3 23 24 0. 683E+02 0 208E+03 -0. , 180E+05 7 9 20 -0 495E+02 -0 .922E+01 0. . 109E+01 7 12 16 -0. 533E+00 0 .108E+01 0. 590E-02 7 12 20 -0 220E+02 0 .330E+02 -0. 393E-01 9 21 22 -0 674E-02 0 .233E+00 0 .278E-02 9 22 25 -0. .448E-02 0 .205E+00 0. 281E-02 12 16 18 -0 . 130E+01 0 .348E+01 -0 .556E-01 12 18 20 -0 .245E+02 0 .380E+02 -0 .105E+00 16 18 21 -0 223E+00 0 .211E+01 -0 .761E-01 18 19 21 -0 .130E+01 0 .115E+02 -0 822E+00 21 22 24 0 .421E+01 -0 .335E+02 -0 .249E+02 THE FACET 2 16 21 THE PRODUCT RELATIVE PRICE 15 0.769E+00 Appendix D. Products Forming Facets and Implicit Prices of Chara.cteristics 1975 CHARACTERISTICS PRICES PRODUCTS ON A FACET MAMMALS INSECTS PERSISTENCE 2 7 9 -0. 314E+00 0 844E+00 0. 913E-02 2 7 16 -0. 457E+00 0. 973E+00 0. 719E-02 2 9 22 -0. 209E-02 0. 282E+00 0. 347E-02 2 16 22 -0. ,103E-01 0. . 366E+00 0. 797E-03 3 18 19 -0. 415E+02 0. .129E+03 -0. 641E+01 3 18 20 -0. 277E*03 0. 461E+03 -0. 510E+01 3 19 21 -0. 827E+01 0. 839E+02 -0. , 106E+03 3 21 24 -0. 590E+01 0. 831E+02 -0. 281E+03 3 23 24 0. ,749E+02 0. . 222E+03 -0. 178E+05 7 9 20 -0. 493E+02 -0. 915E+01 0. 109E+01 7 12 18 -0. 808E+00 0. 158E+01 0. 525E-02 7 12 20 -0. 219E+02 0. , 329E+02 -0. 391E-01 9 22 25 0. 160E-01 0. 359E-01 0. 371E-02 12 16 18 -0. 174E+01 0. 449E+01 -0. 693E-01 12 18 20 -0. 249E+02 0. 390E+02 -0. 118E+00 16 18 21 -0. 269E+00 0. 263E+01 -0. 973E-01 16 21 22 -0. 112E-01 0. 378E*00 0. 229E-03 18 19 21 -0. 148E+01 0. 132E+02 -0. 937E+00 21 22 24 0. 5O9E+01 -0. 404E+02 -0. 301E+02 THE FACET THE PRODUCT RELATIVE PRICE 2 18 22 15 0.839E+00 1976 CHARACTERISTICS PRICES PRODUCTS ON A FACET MAMMALS INSECTS PERSISTENCE 2 7 9 -0 . 618E+00 0 .102E+01 0 . 147E-01 2 7 12 -0 .778E+00 0 . 138E+01 0 . 125E-01 2 9 22 -0 .442E-03 0 260E+00 0 344E-02 2 12 16 -0 .278E*00 0 .992E*00 -0 . 324E-02 2 16 21 -0 .388E-01 0 .B84E+00 -0 689E-02 2 21 22 -0 .222E-01 0 536E*00 -0, 367E-02 3 18 19 -0 .562E+02 0. 172E+03 -0. 839E+01 3 18 20 -0 . 358E+03 0. 597E*03 -0. 671E+01 3 19 21 -0. .108E+02 0. 110E+03 -0. 144E+03 3 21 24 -0 777E+01 0. 109E+03 -0. 366E+03 3 23 24 0. 702E+02 0. 243E*03 -0. 172E+05 7 9 20 -0 481E+02 -0. 849E+01 0. 106E+01 7 12 20 -0. 215E+02 0. 323E+02 -0. 313E-01 9 22 25 0. 225E-01 -0. 289E-01 0. 374E-02 12 18 18 -0. 157E+01 0. 503E+01 -0. 107E+00 12 18 20 -0. 265E+02 0. 422E+02 -0. 159E*00 16 18 21 -0. 363E*00 0. 350E+01 -0. 130E+00 18 19 21 -0. 146E+01 0. 131E+02 -0. 895E+00 21 22 24 0. 657E+01 -0. 522E+02 -0. 389E+02 THE FACET THE PRODUCT RELATIVE PRICE 2 16 21 15 0.921E+00 Appendix D. Products Forming Facets and Implicit Prices of Characteristics 224 1977 CHARACTERISTICS PRICES >DUCTS ON A FACET MAMMALS INSECTS PERSISTENCE 2 7 9 -0 .671E+O0 0 . 108E+01 0. 156E-01 2 7 12 -0 .814E+00 0 . 141E+01 0. 137E-01 2 9 22 -0 442E-03 0 .260E+00 0. 344E-02 2 12 16 -0. . 187E+00 0 .921E+00 -0. 611E-02 2 16 21 -0 440E-01 0 .726E+00 -0. 818E-02 2 21 22 -0. 222E-01 0 .536E+00 -0. 367E-02 3 18 19 -0. 606E+02 0 .185E+03 -0. 899E+01 3 18 20 -0. 383E+03 0 .838E+03 -0. 720E+01 3 19 21 -0. 115E+02 0 .118E+03 -0. 156E+03 3 21 24 -0. 833E+01 0 . 117E+03 -0. 392E+03 3 23 24 0. 687E+02 0 .249E+03 -0. 171E+05 7 9 20 -0. 479E+02 -0 .838E+01 0. 106E+01 7 12 20 -0. 215E+02 0 .322E+02 -0. 299E-01 9 22 25 0. 597E-02 0 .179E+00 0. 353E-02 12 18 18 -0. 151E+01 0 .507E+01 -0. 113E+00 12 18 20 -0. 268E+02 0. 427E+02 -0. 186E+00 16 18 21 -0. 378E+00 0. 363E+01 -0. 134E+00 18 19 21 -0. 146E+01 0. 131E+02 -0. 889E+00 21 22 24 0. 702E+01 0. 558E+02 -0. 416E+02 THE FACET 2 16 21 THE PRODUCT RELATIVE PRICE 15 0.944E+00 1978 CHARACTERISTICS PRICES DUCTS ON A FACET MAMMALS INSECTS PERSISTENCE 2 7 9 -0. 671E+00 0. 108E+01 0. 156E-01 2 7 12 -0. 814E+00 0. 141E+01 0. 137E-01 2 9 22 -0. 442E-03 0. 260E+00 0. 344E-02 2 12 16 -0. 187E+00 0. 921E+00 -0. 611E-02 2 16 21 -0. 440E-01 0. 726E+00 -0. 816E-02 2 21 22 -0. 222E-01 0. 536E+00 -0. 367E-02 3 18 19 -0. 606E+02 0. .185E+03 -0. 899E+01 3 18 20 -0 . 383E+03 0. 638E+03 -0. 720E+01 3 19 21 -0. . 115E+02 0. .118E+03 -0. , 156E+03 3 21 24 -0 833E+01 0 .117E+03 -0. 392E+03 3 23 24 0 687E+02 0 ,249E+03 -0. . 171E+05 7 9 20 -0 . 479E+02 -0 .838E+01 0, . 106E+01 7 12 20 -0 .215E+02 0 .322E+02 -0 .299E-01 9 22 25 0 .597E-02 0 .179E+00 0, 353E-02 12 16 18 -0 . 151E+01 0 .507E+01 -0 . 113E+00 12 18 20 -0 .268E+02 0 .427E+02 -0 . 166E+00 16 18 21 -0 . 378E+00 0 .363E+01 -0 . 134E+00 18 19 21 -0 . 146E+01 0 . 131E+02 -0 .889E+00 21 22 24 0 . 702E+01 -0 .558E+02 -0 .416E+02 THE FACET 2 16 21 THE PRODUCT RELATIVE PRICE 15 0.944E+00 Appendix D. Products Forming Facets and Implicit Prices of Characteristics 1979 CHARACTERISTICS PRICES PRODUCTS ON A FACET MAMMALS INSECTS PERSISTENCE 3 18 19 -0 .606E+02 0 . 185E+03 -0 .899E+01 3 18 20 -0 .383E+03 0 .638E+03 -0 . 720E+01 3 19 21 -0 . 115E+02 0 . 118E+03 -0 . 156E+03 3 21 24 -0 .833E+01 0 . 117E+03 -0 . 392E+03 3 23 24 0 .687E+02 0 . 249E+03 -0 .171E+05 7 9 16 -0 .518E+00 0 . 111E+01 0 .122E-01 7 9 20 -0 .479E+02 -0 .838E+01 0 .106E+01 7 16 18 -0 .635E+01 0 . 112E+02 -0 .201E-01 7 18 20 -0 .210E+02 0 . 330E+02 -0 .510E-01 9 16 22 -0 . 172E-01 0 .469E+00 0 .323E-02 9 22 25 0 .597E-02 0 .179E+00 0 .353E-02 16 18 21 -0 .378E+00 0 .3B3E+01 -0 . 134E+00 16 21 22 -0 .228E-01 0 .541E+00 -0 . 138E-03 18 19 21 -0 .146E+01 0 .131E+02 -0 .889E+00 21 22 24 0 .702E+01 -0 .558E+02 -0 .416E+02 1980 CHARACTERISTICS PRICES PROOUCTS ON A FACET MAMMALS INSECTS PERSISTENCE 3 18 19 -0, 606E+02 0 . 185E+03 -0 899E+01 3 18 20 -0 .383E+03 0 638E+03 -0 720E+01 3 19 21 -0. 115E+02 0 . 118E*03 -0. , 156E+03 3 21 24 -0. 833E+01 0. 117E+03 -0. 391E+03 3 23 24 0. 667E+02 0. 249E+03 -0. 171E+05 7 9 16 -0. 915E+00 0. 179E+01 0. 189E-01 7 9 20 -0. 460E+02 -0. 723E+01 0. 101E+01 7 18 18 -0. 597E+01 0. 105E*02 -0. 911E-02 7 18 20 -0. 204E+02 0. 320E+02 •0. 396E-01 9 18 21 -0 . 330E-01 0. 650E+00 0. 307E-02 9 21 22 -0 . 134E-01 0. 479E+00 0. 312E-02 9 22 25 0. 914E-02 0. 198E+00 0. 341E-02 16 18 21 -0. 350E+00 0. 341E+01 -0. 116E+00 18 19 21 -0. 146E*01 0. 131E+02 -0. 888E+00 21 22 24 0. 701E+01 -0. 557E*02 -0. 414E+02 1981 CHARACTERISTICS PRICES PRODUCTS ON A FACET MAMMALS INSECTS PERSISTENCE 3 18 19 -0. 679E*02 0. 209E+03 -0. 101E+02 3 18 20 -0. 428E+03 0. 713E*03 -0. 809E+01 3 19 21 -0. 131E+02 0. 134E+03 -0. 174E+03 3 21 24 -0. 976E+01 0. 133E+03 -0. 423E+03 3 23 24 0. 180E+03 0. 459E*03 -0. 418E+05 7 9 18 -0. 205E+01 0. 373E+01 0. 381E-01 7 9 20 -0. 403E+02 -0. 392E+01 0. 883E+00 7 16 18 -0. 129E+02 0. 224E+02 -0. 220E-01 7 18 20 -0. 181E*02 0. 302E+02 -0. 330E-01 9 16 21 -0. 915E-01 0. 121E+01 0. 279E-02 9 21 22 0. 288E-02 0. 390E+00 0. 301E-02 9 22 25 0. 153E-01 0. 234E+00 0. 317E-02 16 18 21 -0. 770E+00 0. 712E+01 -0. 253E+00 18 19 21 -0; 192E+01 0. 172E+02 -0. 106E+01 21 22 24 0. 898E+01 -0. 554E+02 -0. 412E+02 Appendix D. Products Forming Facets and Implicit Prices of Characteristic 1882 CHARACTERISTICS PRICES PRODUCTS ON A FACET MAMMALS INSECTS PERSISTENCE 3 18 19 -0. 721E+02 0. 223E+03 -0. 108E+02 3 18 20 -0. 468E+03 0. 781E+03 -0. 857E+01 3 19 21 -0. 142E+02 0. 144E+03 -0. 184E+03 3 21 24 -0. 107E+02 0. 143E+03 -0. 443E+03 3 23 24 0. 250E+03 0. 590E+03 -0. 570E+05 7 9 16 -0. 252E+01 0. 454E+01 0. 459E-01 7 9 20 -0. 867E+02 -0. 123E+02 0. 190E+01 7 16 18 -0. 174E+02 0. , 303E+02 -0. 367E-01 7 18 20 -0, 385E+02 0 617E+02 -0 812E-01 9 16 21 -0. . 110E+00 0 . 143E+01 0 257E-02 8 21 22 -0. 478E-03 0 .485E+00 0 282E-02 9 22 25 0. .182E-01 0 .251E*00 0 306E-02 16 18 21 -0, . 104E*01 0 ,956E*01 -0 .350E*00 18 19 21 -0 .230E+01 0 .205E+02 -0 .122E+01 21 22 24 0 .694E+01 -0 .550E+02 -0 .410E*02 1983 CHARACTERISTICS PRICES PRODUCTS ON A FACET MAMMALS INSECTS PERSISTENCE 3 18 19 -0 .720E+02 0 .223E+03 -0 . 108E+02 3 18 20 -0 469E*03 0 .782E+03 -0 .857E*01 3 19 21 -0 . 142E*02 0 . 144E+03 -0 . 184E+03 3 21 24 -0. 107E+02 0 . 143E+03 -0. 442E+03 3 23 24 0. 250E+03 0 . 590E+03 -0. 570E+05 7 16 18 -0. 174E+02 0 . 303E+02 -0. 367E-01 7 16 25 -0. 191E+01 0 . 348E+01 0. 494E-01 7 18 20 -0. 403E+02 0 . 643E + 02 -0. 850E-01 7 20 25 -0. 134E+03 -0 . 796E+02 0. 378E+01 16 18 21 -0. 104E+01 0 955E+01 -0. 350E+00 16 21 25 -0. 101E+00 0. . 139E+01 0. 423E-02 18 19 21 -0. 230E+01 0. 206E+02 -0. 123E+01 21 22 24 0. 692E+01 -0. 548E+02 -0. 409E+02 21 22 25 -0. 882E-02 0. 592E+00 0. 318E-02 THE FACET THE PRODUCT RELATIVE PRICE 16 21 25 15 0.964E+00 1984 CHARACTERISTICS PRICES DUCTS ON A FACET MAMMALS INSECTS PERSISTENCE 7 16 18 -0 .174E+02 0.303E+02 -0.367E-01 7 16 25 -0. .191E+01 0.348E+01 0.494E-01 7 18 20 -0. 403E*02 0.643E+02 -0.850E-01 7 20 25 -0. 134E+03 -0.796E+02 0.378E+01 16 18 21 -0 . 103E+01 0.955E+01 -0.350E+00 16 21 25 -0. 969E-01 0. 138E+01 0.414E-02 18 19 21 -0. 230E+01 - 0.206E+02 -0.123E+01 19 21 23 -0. . 287E+03 0.299E+04 -0.440E+04 21 22 24 0. 690E+01 -0.546E+02 -0.408E+02 21 22 25 -0. . 163E-01 0.686E+00 0.322E-02 21 23 24 -0. . 248E+03 0.281E+04 -0.585E+04 THE FACET 16 21 25 THE PRODUCT RELATIVE PRICE 15 0.970E+00 Appendix D. Products Forming Facets and Implicit Prices of Characteristics 227 1985 CHARACTERISTICS PRICES PRODUCTS ON A FACET MAMMALS INSECTS PERSISTENCE 7 16 18 -0 174E+02 0 . 303E+02 -0 .367E-01 7 16 25 -0 . 191E+01 0 348E+01 0 494E-01 7 18 20 -0. . 403E+02 0. 643E+02 -0. 850E-01 7 20 25 -0. , 134E+03 -0 796E+02 0 378E+01 16 18 21 -0. . 103E+01 0. 955E+01 -0 .350E+00 16 21 25 -0. 946E-01 0. .138E+01 0. 408E-02 18 19 21 -0. 230E+01 0. 206E+02 -0. .123E+01 19 21 23 -0. 287E+03 0. 299E+04 -0. 440E+04 21 22 24 0. 689E+01 -0. 545E+02 -0. 408E+02 21 22 25 -0. 194E-01 0. 730E+00 0. 322E-02 21 23 24 -0. 248E+03 0. 281E+04 -0. 585E+04 THE FACET THE PRODUCT RELATIVE PRICE 18 21 25 15 0.974E+00 1986 CHARACTERISTICS PRICES PRODUCTS ON A FACET MAMMALS INSECTS PERSISTENCE 7 16 18 -0 .146E+02 0 .254E+02 -0 209E-01 7 16 25 -0 .191E+01 0 .348E+01 0. 494E-01 7 18 20 -0 .405E+02 0 .640E+02 -0. 756E-01 7 20 25 -0 .134E+03 -0 . 798E + 02 0. 378E+01 16 18 21 -0 851E+00 0 .800E+01 -0. 283E+00 16 21 25 -0 908E-01 0 . 138E+01 0. 399E-02 18 19 21 -0. . 230E+01 0 .206E+02 -0. 129E+01 19 21 23 -0. , 287E+03 0 .299E+04 -0. 440E+04 21 22 24 0. 687E+01 -0 .544E+02 -0. 407E+02 21 22 25 -0. 207E-01 0 .769E+00 0. 318E-02 21 23 24 -0. 248E+03 0 .281E+04 -0. 585E+04 THE FACET THE PRODUCT RELATIVE PRICE 16 21 25 15 0.979E+00 1987 CHARACTERISTICS PRICES DUCTS ON A FACET MAMMALS INSECTS PERSISTENCE 15 18 21 -0, 527E*00 0.517E+01 -0.119E+00 15 18 25 -0. .114E+01 0.455E+01 0.287E-01 15 21 25 -0 952E-01 0.141E+01 0.404E-02 18 19 21 -0 230E*01 0.207E+02 -0.135E*01 18 20 25 -0 .166E+02 0.232E+02 0.412E*00 19 21 23 -0 287E*03 0.299E*04 -0.440E+04 21 22 24 0 .687E+01 -0.544E+02 -0.407E+02 21 22 25 -0 207E-01 0.789E+00 0.318E-02 21 23 24 -0 .248E+03 0.281E+04 -0.585E+04 Appendix E Bounds on Prices E.l Introduction Recall that information is available on the characteristics of ten products but not on their prices. Bounds are placed on the possible prices that these products could have if they are not priced so high as to be within the market opportunity frontier nor priced so low that they would force other products to be within the frontier. The calculated bounds are listed on the following pages. Note that no predictions could be calculated for the price of Carbaryl and that Isodrin was never introduced. 228 Appendix E. Bounds on Prices 229 Table E.l : Predicted Bounds on Chemical Prices (US$/lb.) 1946-1975 Azinphos-M Chlorthion Demeton Diazinon 1951 1952 1.54< 4.14< <87.80 1953 0.84< 1.73< <73.78 1954 0.75< 1.45< <68.39 1955 0.78< 1.47< <67.96 1956 0.75< 1.35< <67.98 1957 0.30< 0.74< 2.09< 1.33< <67.98 1958 0.48< 0.76< 2.15< 2.49< <67.96 1959 0.22< 0.61< 1.32< 2.29< <67.94 1960 0.22< 0.55< 1,32 < 1.06< <67.93 1961 0.22< 0.54< 1.32< 1.08< <67.93 1962 0.17< 0.54< . 1.27< 1.04< <67.93 1963 0.17< 0.47< 1.27< 1.04< <67.92 1964 0.2K 0.46< 1.35< 0.97< <67.92 1965 0.24< 0.46< 1.40< 0.91< <67:92 1966 0.24< 0.46< 1.40< 0.91< <67.92 1967 0.21< 0.34< 1.23< 0.53< <67.90 1968 0.16< 0.3K 0.97< 0.52< <67.88 1969 0.2K 0.31< 0.98< 0.47< <67.79 1970 0.2K 0.3K 0.98< 0.47< <67.79 1971 0.12< 0.31< 0.71< 0.56< <67.79 1972 0.10< 0.32< 0.68< 0.51< <67.79 1973 0.14< 0.38< 0.76< 0.49< <67.80 1974 0.17< 0.5K 0.82< 0.47< <67.92 1975 0.25< 0.63< 1.30< 0.51< <68.08 endix E. Bounds on Prices Predicted Bounds on Chemical Prices (US$/lb.) 1946-75 cont'd. Dieldrin Dimethoate Endosulfan Endrin Heptachlor 1950 1.90< <202.40 1.02< <120.70 1951 <10.90 1.15< <2.90 1952 <10.89 0.92< <2.66 1953 <6.68 0.43< <1.78 1954 <6.22 0.36< <1.68 1955 0.36< <1.49 1956 68.03< <0.30 0.37< <1.48 1957 77.52< <0.30 0.8K <1.48 1958 76.99< <0.29 1959 77.48< <0.20 1960 77.52< <0.21 1961 . 77.53< <0.21 1962 77.49< <0.21 1963 78.34< <0.21 1964 78.34< <0.21 1965 78.34< <0.21 1966 78.34< <0.21 1967 78.55< <0.20 1968 77.16< <0.17 1969 69.27< <0.16 1970 69.27< <0.16 1971 69.37< <0.14 1972 69.35< . <0.13 1973 69.29< <0.14 1974 77.95< <0.15 1975 89.48< <0.22 Appendix E. Bounds on Prices 231 Predicted Bounds on Chemical Prices (US$/lb.) 1946-75 cont'd. Lindane Malathion Methoxychlor Methyl-Parathion 1945 1946 1947 0.20< 1948 0.22< 1949 <349.82 1950 0.65< <142.39 <11.06 <72.70 1951 <11.67 <75.50 1952 <9.07 <64.48 1953 <7.65 <58.48 1954 <35.07 1955 <25.40 1956 <26.10 Appendix E. Bounds on Prices 232 Table E.2: Predicted Bounds on Chemical Prices (US$/lb.) 1976-87 Aldicarb Allethrin Aziriphos-M Carbofuran Chlorthion 1976 0.12< 0.84< 1977 0.12< 0.88< 1978 0.12< 0.71< 1979 0.12< 0.65< 1980 0.35< 0.65< 1981 1.69< 0.77< 0.6K 1.3K 1982 0.81< 1.72< 1983 0.70< 1.87< 1984 7.82< 0.60< 1.87< 1985 7.82< 0.56< 1.87< 1986 7.83< 0.59< 1.6K 1987 7.85< 0.59< 1.34< Appendix E. Bounds on Prices 233 Predicted Bounds on Chemical Prices (USS/lb.) 1976-87 cont'd. Demeton Diazinon Dimethoate Endosulfan Endrin 1976 1.27< 1.13< <88.90 89.10< <0.23 1977 1.27 < 0.97< <95.15 89.08< <0.24 1978 1.27 < 0.39< <95.15 89.08< <0.24 1979 1.23< <95.15 89.08< <0.27 <11.77 1980 1.73< <95.15 89.01< <0.30 <11.80 1981 2.66< 1.36< <108.47 116.83< <0.36 <22.86 1982 2.93< <116.87 139.29< <0.41 <29.80 1983 2.83.< 1.18< <116.88 139.98< <0.43 1984 2.73< 1.17< 139.88< <0.45 1985 2.71< 1.17< 139.83< <0.46 1986 2.84< 1.16< 139.99< <0.48 1987 2.84< 1.16< 140.27< <0.48 Bibliography [1] D'Aspremont, C , J. Jaskold Gabszewicz, and J.F. Thisse (1979) "On Hotelling's 'Stability in Competition'," Econometrica, 47, 1145-1150 [2] Adelman, I. and Z. Griliches (1961), "On an Index of Quality Change," American Statistical Association Journal, 535-548 [3] Archibald, G.C. and B.C. Eaton (1989), "Two Applications of Characteristics The-ory," in George Fiewel, ed., Essays in Honour of Joan Robinson, London: Macmil-lan and Co. [4] Archibald, G.C, B.C. Eaton and R.G. Lipsey (1986), "Address Models of Value Theory," in J.E. Stiglitz and E. F. Mathewson, eds., New Developments in the Analysis of Market Structures, Cambridge, Massachusetts: M.I.T. Press [5] Archibald, G.C. and G. Rosenbluth (1975), "The 'New' Theory of Consumer De-mand and Monopolistic Competition," Quarterly Journal of Economics, 89,569-590 [6] Archibald, G.C. and G. Rosenbluth (1978), "Production Theory in Terms of Char-acteristics: Some Preliminary Considerations," U.B.C. Discussion Paper, 1978-19 [7] Auld, Douglas A.L. (1972), "Imperfect Knowledge and the New Theory of De-mand," Journal of Political Economy, 80, 1287-1294 [8] Auld, Douglas A.L. (1974), "Advertising and the Theory of Consumer Choice," Quarterly Journal of Economics, 88, 480-487 [9] Bailey, D.R. (1956), "Burdening a Blast Furnace for Minimum Costs," Ironmaking Conference Proceedings, Metallurgical Society of the A.I.M.E., Ironmaking Com-mittee: 15, 79-94 [10] Bailey, E.E. and A.F Friedlander (1982), "Market Structure and Multiproduct Industries," Journal of Economic Literature, 20, 1024-1048 [11] Becker, Gary S. (1965), "A Theory of the Allocation of Time," Economics Journal, 75, 493-517 [12] Berndt, Ernst R. and David 0. Wood (1975), "Technology, Prices, and the Derived Demand for Energy," Review of Economics and Statistics, 57, 259-268 234 Bibliography 235 [13] Brander, James A. and Jonathan Eaton (1984), "Product Line Rivalry," American Economic Review, 74, 323-334 [14] Brown, J.N. and H.S. Rosen (1982), "On the Estimation of Structural Hedonic Price Models," Econometrica, 50, 765-768 [15] Canadian Agricultural Chemicals Association (1965), Pesticide Safety Handbook: A Guide for Users and Agriculturalists, Montreal: The Canadian Agricultural Chem-icals Association [16] Caplin, Andrew S. and Barry J. Nalebuff (1986),, "Multi-dimensional Product Dif-ferentiation and Price Competition," Oxford Economic Pavers, 38, 129-145 [17] Carlson, Gerald A. (1977), "Long Run Productivity of Insecticides," American Journal of Agricultural Economics, 59, 543-548 [18] Carson, Rachel (1962), Silent Spring, Boston: Houghton Mifflin [19] Chamberlin, Edward H. (1933), The Theory of Monopolistic Competition, Cam-bridge, Massachusetts: Harvard University Press [20] The Chemical Marketing Newspaper (The Oil, Paint & Drug Reporter) (1966), Chemical Pricing Patterns, New York: Schnell Publishing Company, Inc. [21] The Chemical Marketing Reporter, (The Oil, Paint & Drug Reporter, (weekly) 1944-1987 [22] Cowing, Thomas G. (1974), "Technical Change and Scale Economics in an En-gineering Production Function: The Case of Steam Electric Power," Journal of Industrial Economics, 23, 135-152 [23] Dasgupta, Partha and Joseph Stiglitz (1980), "Uncertainty, Industrial Structure, and the Speed of R & D," Bell Journal of Economics, 11, 1-28 [24] Davies, O.L. (1962), "Some Statistical Considerations in the Selection of Research Projects in the Pharmaceutical Industry," Applied Statistics, 11, 170-183 [25] Dixit, Avinash (1986), "Comparative Statics for Oligopoly," fnternational Eco-nomic Review, 27, 107-122 [26] Eaton, Curtis and Richard G. Lipsey (1979), "The Theory of Market Pre-emption: The Persistence of Excess Capacity and Monopoly in Growing Spatial Markets," Economica, 46, 149-158 [27] Economides, Nicholas (1984), "The Principle of Minimum Differentiation Revis-ited," European Economic Review, 24, 345-368 Bibliography 236 [28] Economides, Nicholas (1986a), "Minimal and Maximal Product Differentiation in Hotelling's Duopoly," Economic Letters, 21, 67-71 [29] Economides, Nicholas (1986b), "Nash Equilibrium in Duopoly with Products De-fined by Two Characteristics," Rand Journal of Economics, 17, 431-439 [30] Farm Chemicals Handbook (annual), Willoughby, Ohio: Meister Publishing Com-pany [31] Faulhaber, Gerald R. (1975), "Cross-Subsidization: Pricing in Public Enterprise," American Economic Review, 65, 966-977 [32] Fisher, R.A. (1935), The Design of Experiments, Edinburgh: Oliver and Boyd [33] Francis, Jack C. and Stephen H. Archer (1979), Portfolio Analysis, Englewood Cliffs, New Jersey: Prentice-Hall, Inc. [34] Gittins, J.C. (1969), "Optimal Resource Allocation in Chemical Research," Ad-vances in Applied Probability, 1, 238-270 [35] Goldsmith, E.B., C M . Harrison and A.J. Morton (1986), "Description and Anal-ysis of Vegetation," in Methods in Plant Ecology 2nd Ed., P.D. Moore and S.B. Chapman (eds.), Oxford: Blackwell Scientific Publications, pp.437 -524 [36] Goodman, A. (1978), "Hedonic Prices, Price Indices and Housing Markets," Jour-nal of Urban Economics, 5, 471-484 [37] Gorman, W.M. (1956/1980), "A Possible Procedure for Analysing Quality Differ-entials in the Egg Market," Review of Economic Studies, 47, 843-856 [38] Griliches, Z. (1961), "Hedonic Price Indexes for Automobiles: An Econometric Analysis of Quality Change," The Price Statistics of the Federal Government, Gen-eral Series, No.73, New York: National Bureau of Economic Re'search [39] Griliches, Z. (1971), "Introduction: Hedonic Prices Revisited,"Price Indexes and Quality Change, Ed. Z. Griliches. Cambridge, Mass.: Harvard University Press [40] Hay, D.A. (1976), "Sequential Entry and Entry-Deterring Strategies in Spatial Competition," Oxford Economic Papers, 28, 240-257 [41] Heaton, C.A. (1986), "Agrochemicals," in C.A. Heaton, ed., The Chemical Indus-try, Glasgow: Blackie and Son Ltd. [42] Hicks, J.R. (1956), A Revision of Demand Theory, Oxford: Oxford University Press Bibliography 237 [43] Hirsch, W. (1981), "Habitability Laws and the Welfare of Indigent Tenants," Review of Economics and Statistics, 63, 263-274 [44] Hotelling, Harold (1929), "Stability in Competition,"Economic Journal, 39, 41-57 [45] Houthakker, H.S. (1952), "Compensational Changes in Quantities and Qualities Consumed,"Review of Economic Studies, 19, 155-164 [46] Ironmonger, D.S. (1972), New Commodities and Consumer Behaviour, Cambridge: Cambridge University Press [47] Jevons, Stanley W. (1879), The Theory of Political Economy 2nd Edn., London: Macmillan and Co. [48] Kamien, Morton I. and Nancy L. Schwartz (1982), Market Structure and Innova-tion, Cambridge: Cambridge University Press [49] Kendall, Maurice and Alan Stuart (1977), The Advanced Theory of Statistics 4th Ed., London: Charles Griffin &; Company Limited, Vol. II, 566-592 [50] Kerr, William A. (1981), Micro Economic Approaches to Technical Change in the Canadian Beef Cattle Industry, University of British Columbia Ph.D. Thesis [51] Kuhr, Ronald J. and H. Wyman Dorough (1976), Carbamate Insecticides: Chem-istry, Biochemistry, and Toxicology, Cleveland: CRC Press [52] Lancaster, Kelvin J. (1966), "A New Approach to Consumer Theory," Journal of Political Economy, 74, 132-157 [53] Lancaster, Kelvin J. (1971), Consumer Demand: A New Approach, New York: Columbia University Press [54] Lancaster, Kelvin J. (1975), "Socially Optimal Product Differentiation," American Economic Review, 65, 567-585 [55] Lane, W.J. (1980), "Product Differentiation in a Market with Endogenous Sequen-tial Entry," Bell Journal of Economics, 11, 237-260 [56] Lichtenberg, Erik (1987), "Integrated versus Chemical Pest Management: The Case of Rice Field Mosquito Control," Journal of Environmental Economics and Management, 14, 304-312 [57] Lipsey, Richard G. and Gideon Rosenbluth (1971), "A Contribution to the New Theory of Demand: A Rehabilitation of the Giffen Good," Canadian Journal of Economics, 4, 131-163 Bibliography 238 [58] Loury, Glenn (1979), "Market Structure and Innovation," Quarterly Journal of Economics, 93, 395-410 [59] Lucas, Robert E.B. (1975), "Hedonic Price Functions,"Economic fnquiry, 13, 157-178 [60] Maddala, G.S. (1983), Limited Dependent and Qualitative Variables in Economet-rics, Cambridge: Cambridge University Press [61] Mansfield, E., J. Rapoport, A. Romeo, E. Villani, S. Wagner and F. Husic (1977), The Production and Application of New fndustrial Technology, New York: W. W. Norton &; Company, Inc. [62] McFadden, Daniel (1974), "Conditional Logit Analysis of Qualitative Choice Be-haviour," Frontiers in Econometrics, P. Zarumbka (ed.), New York: Academic, 105-142 [63] Matsumura, Fumio (1985), Toxicology of fnsecticides 2nd Ed., New York: Plenum Press [64] May, Kenneth 0. (1954), "Intransitivity, Utility and the Aggregation of Preference Patterns,"Econmetrica, 22, 1-13 [65] Menger, Carl (1871), Grundsdtze der Volkswirtschaftslehre, Wien: W. Braumuller, (Eng. trans, in Principles of Economics, by J. Dingwall and B.F. Hoselitz, Glencoe, Hlinois: The Free Press, 1950) [66] Metcalf, Robert L. (1972), "Development of Selective and Biodegradable Pesti-cides," in Pest Control Strategies for the Future, Agricultural Board, Division of Biology and Agriculture, National Research Coucil, Washington D . C : National Academy of Sciences, pp. 137-156 [67] Morey, Edward R. (1981), "The Demand for Site-Specific Recreational Activities: A Characteristics Approach," Journal of Environmental Economics and Management, 8, 345-371 [68] Morishima, Michio (1959), "The Problem of Intrinsic Complementarity and Sepa-rability of Goods," Metroeconomica, 11, 188-202 [69] Nelson, J. (1978), "Residential Choice, Hedonic Prices, and the Demand for Urban Air Quality," Journal of Urban Economics, 5, 357-369 [70] Panzar, John C. and Robert D. Willig (1981), "Economies of Scope," American Economic Review, 71, 268-272 Bibliography 239 [71] Pesticide Handbook (Entoma) (annual), College Park, Maryland: Entomological Society of America [72] Plapp, Frederick W. Jr. (1981), "The Nature, Modes of Action, and Toxicity of Insecticides," in Handbook of Pest Management in Agriculture Vol. Ill, David Pi-mental (ed.), Boca Raton, Florida: CRC Press Inc. [73] Prescott, E.C. and M. Visscher (1977), "Sequential Location among Firms with Foresight," Bell Journal of Economics, 8, 378-393 [74] Quandt, Richard E. and William J. Baumol (1966), "The Demand for Abstract Transport Modes: Theory and Measurement," Journal of Regional Science, 6, 13-26 [75] Regev, Uri, Haim Shalit and A.P. Gutierrez (1983), "On the Optimal Allocation of Pesticides with Increasing Resistence: The Case of Alfalfa Weevil," Journal of Environmental Economics and Management, 10, 86-100 [76] Rosen, S. (1974), "Hedonic Prices and Implicit Markets: Product Differentiation in Pure Competition," Journal of Political Economy, 82, 34-55 [77] Schmalensee, Richard (1978), "Entry Deterrence in the Ready-to-Eat Breakfast Cereal Industry," Bell Journal of Economics, 9, 305-327 [78] Sarhan, Mohamed E., Richard E. Howitt and Charles V. Moore (1979), "Pesticide Resistance Externalities and Optimal Mosquito Management," Journal of Envi-ronmental Economics and Management, 6, 69-84 [79] Shaw, R.W. (1982), "Product Proliferation in Characteristics Space: The UK Fer-tilizer Industry," The Journal of Industrial Economics, 31, 69-91 [80] Siegel, Sidney (1956), Nonparametric Statistics for the Behavioural Sciences, Toronto: McGraw-Hill Book Co. Inc., 96-104 [81] Stigler, George J. (1947), "Notes of the History of the Giffen Paradox," Journal of Political Economy, 55, reprinted in Essays in the History of Economics, by G.J. Stigler (1965), Chicago: University of Chicago Press, 374-384 [82] Strotz, Robert H. (1957), "The Empirical Implications of a Utility Tree," Econo-metnca, 25, 269-280 [83] Theil, H. (1952), "Qualities, Prices and Budget Enquiries,"Review of Economic Studies, 19, 129-147 Bibliography 240 [84] Tocher, K.D. (1950), "Extension of the Neyman - Pearson Theory of Tests to Discontinuous Variates," Biometrika, 37, 130-144 [85] United States Department of Agriculture, Agricultural Stabilization and Conser-vation Service, The Pesticide Review (annual), Washington: United States Depart-ment of Agriculture [86] United States Tariff Commission, Synthetic Organic Chemicals (annual), Washing-ton: United States Tariff Commission [87] Varian, Hal R. (1985), "Non-Parametric Analysis of Optimizing Behavior with Measurement Error," Journal of Econometrics, 30, 445-458 [88] White, K.J. (1987), "SHAZAM: A General Computer Program for Econometric Methods (Version 5)," American Statistician 41, 80 [89] White, K.J. (1988), SHAZAM: User's Reference Manual (Version 6.1), Toronto: McGraw-Hill Book Co. [90] Winteringham, F.P.W. (1969), "Mechanisms of Selective Insecticidal Action," An-nual Review of Entomology, 14, 409-442 [91] West, Douglas S. (1979), Market Preemption as a Barrier to Entry in a Growing, Spatially Extended Market, University of British Columbia Ph.D. Thesis [92] West, Douglas S. (1981a), "Testing for Market Preemption Using Sequential Loca-tion Data," Bell Journal of Economics, 12, 129-143 [93] West, Douglas S. (1981b), "Tests of Two Locational Implications of a Theory of Market Pre-Emption," Canadian Journal of Economics, 14, 313-326 [94] Worthing, Charles R. (ed.) (1987), The Pesticide Manual: A World Compendium 8th Ed., Croydon, England: British Crop Protection Council 

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0098243/manifest

Comment

Related Items