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The regulation of the market for information in rental housing : a simulation study Mason, Gregory C. 1975

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THE REGULATION OF THE MARKET FOR INFORMATION IN RENTAL HOUSING: A SIMULATION STUDY by Gregory C. Mason B.A. , U n i v e r s i t y of B r i t i s h Columbia, 1970 M.A., Univ e r s i t y of B r i t i s h Columbia, 1972 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY I n t e r d i s c i p l i n a r y i n the Departments of Commerce Community and Regional Planning Economics We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA May 1975 In presenting th i s thesis in pa r t i a l fu l f i lment of the requirements for an advanced degree at the Univers i ty of B r i t i s h Columbia, I agree that the L ibrary sha l l make it f ree ly ava i l ab le for reference and study. I further agree that permission for extensive copying of th i s thesis for scho lar ly purposes may be granted by the Head of my Department or by his representat ives. It is understood that copying or pub l i ca t ion of th is thes is fo r f i nanc ia l gain sha l l not be allowed without my writ ten permission. Department of ^>L/^\OLAC^/I^MCUVL/ (7^~i^G^S The Univers i ty of B r i t i s h Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 Abstract Much of the d i r e c t i o n to recent proposals f o r consumer protection l i e s i n improving the q u a l i t y of pre-purchase information. As with much public p o l i c y the l e g i s l a t i o n frequently proceeds the t h e o r e t i c a l j u s t i f i c a t i o n . In the case of pre-purchase information the t h e o r e t i c a l basis stems from the economics of information. The main purpose of t h i s thesis i s to examine the demand and supply of information. In p a r t i c u l a r , a demand model f o r information i s con-structed, which unlike the ex i s t i n g theory, assumes that the searcher i s ignorant of the d i s t r i b u t i o n of o f f e r s and has l i m i t e d a b i l i t y to store market data. The use of an err o r - l e a r n i n g simulation model permits the study of problems such as decay i n the storage vector of market o f f e r s and problems due to oversearching and undersearching. It appears that the marginal rules of search are of l i t t l e use i n modelling the t r u l y ignorant consumer. In addition to analyzing the demand f o r information, t h i s essay investigates the supply of information. The r e n t a l housing market i s used as the i n s t i t u t i o n a l s e tting. Empirical analysis of t h i s market, along with a theory of the information broker i s integrated into the demand model to create a market model f or r e n t a l housing information. F i n a l l y , t h i s model i s subjected to some explorative p o l i c y t e s t s . In dealing with consumer ignorance the government can choose to do nothing, regulate, or n a t i o n a l i z e . The be n e f i t s , i n terms of reduced search costs, are simulated and compared. A f u l l scale cost-benefit simulation i s not possible because of l i m i t e d information of the costs of information production. i i i TABLE OF CONTENTS Page 1. CHAPTER ONE Introduction and Outline 1 Theo r e t i c a l Background 3 Information Costs and Brokerage 4 The Use of Simulation Studies i n Economics 8 Flowcharting 11 Information; Quantity and Quality 12 Outline ' 13 Footnotes 15 2. CHAPTER TWO The Demand f o r Information, a Simulation Study 16 The Basic Paradigm 16 A Simulation Model of the Demand for Information 22 The Model; A Verbal Description 23 The Model; A Mathematical Description 26 The Model;."Flowchart Explanation 31 Some Results 34 Modelling A l t e r n a t i v e Market Conditions 39 Problems of 'Oversearch' and 'Undersearch 1 41 The E f f e c t s of Undersearch 42 The E f f e c t s of Oversearch 44 Summary 45 Footnotes 46 3. CHAPTER THREE The Supply of Information 48 Rental Information Brokerage; An Overview 48 Casual Search 49 Professional Property Managers . 50 C l a s s i f i e d Advertisements 53 Modelling the Supply of Rental Information From the C l a s s i f i e d s 59 Some Results 60 Rental Information Agencies 64 Simulating the Rental Information Agency 69 A Simple Theory of Information Brokerage 70 The Structure of the Simulation Model of RIAs 73 S e n s i t i v i t y Analysis 77 Some Results 80 Summary - • 85 Footnotes 86 i v TABLE OF CONTENTS (continued) 4. CHAPTER FOUR The Market f o r Information 88 and I t s Regulation The Nature of Regulation 88 P o l i c y Tests 91 Summary of Tests 101 Extensions and Further Research 105 Footnotes 108 5. Appendix One 109 6. Appendix Two 115 7. Bibliography 123 LIST OF ILLUSTRATIONS Page 1. CHAPTER ONE Figure 1 - Transactions D i f f e r e n t i a t e d Demand and Supply Curves 6 Figure 2 - Flowchart Example 12 2. CHAPTER TWO Figure 3 - Marginal Cost and Returns to Search 18 Figure 4 - The Lognormal D i s t r i b u t i o n of Income 24 Figure 5 - Macro Flowchart of the Demand Model 32 Figure 6 - Micro Flowchart of the Demand Model 33 Figure 7 - The Relation Between Error Learning and Average Search Time 38 Figure 8 - Frequency D i s t r i b u t i o n of Search Time 38 Figure 9 - Vacancy Rate and Search 41 3. CHAPTER THREE Figure 10 - Supply of C l a s s i f i e d Information 57 Figure 11 - Values of JMAX 60 Figure 12 - Search Times and Storage 62 Figure 13 - Error Learning Rate and Search Time 63 Figure 14 - Vacancy Rates and RIA A c t i v i t y 69 Figure 15 - Vacancy Rate and L i s t i n g Per Day by Source 75 Figure 16 - Macro Demand-Supply Flowchart 81 Figure 17 - Vacancy Rate and Brokerage : 82 4. CHAPTER FOUR Figure 18 - The E f f e c t of D i f f e r e n t P o l i c i e s on the Frequency of Search Times 102 5. APPENDIX ONE Figure 19 109 Figure 20 - Micro Demand Supply Flowchart 116 v i LIST OF TABLES Page 1. CHAPTER ONE Table 1 - Owner-occupied and tenant-occupied dwelling units 1951-1971 2 2. CHAPTER TWO Table 2 - Results of T r i a l s with No Storage 36 Table 3 - A l t e r n a t i v e Market Conditions With Storage 40 Table 4 - E f f e c t s of Undersearch 42 Table 5 - E f f e c t s of Oversearch 43 3. CHAPTER THREE Table 6 - Information by Month 54 Table 7 - Co r r e l a t i o n Matrix f o r Column Inches 55 '.T o t a l Ads and Vacancy Rates Table 8 - E f f e c t s of V a r i a t i o n i n JMAXX on 61 Search Costs: No Storage Table 9 - Information i n C l a s s i f i e d s by C i t y 67 Table 10 - Vacancy Rates and RIA A c t i v i t y 68 Table 11 - S e n s i t i v i t y Analysis with the 79 Time Constraints Table 12 - S e n s i t i v i t y Analysis with Parameter of Brokerage Cost Function 80 Table 13 - Information Brokerage and Vacancy Rates 83 Table 14 - Redundancy i n Information and Search Costs 85 4. CHAPTER FOUR Table 15 - Free Market P o l i c y and Search Costs 91 Table 16 - Fee f o r Service and Search Costs 93 Table 17 - Re g i s t r a t i o n and Fee for Service and Search Costs 94 Table 18 - Public Information Agencies 98 Table 19 - Government Monopoly and Search Costs 101 v i i Acknowledgment s I wish to acknowledge f i r s t the contribution of my committee, and i n p a r t i c u l a r my advisor, Dr. M.A. Goldberg. But for h i s insistence that preliminary and imperfect d r a f t s be reworked resulted i n the thesis f i r s t being completed s i x months behind schedule, and second i t con-ferred what l i t t l e claim to q u a l i t y the thesis now possesses. I also wish to s i n g l e out Dr. David Donaldson, Dr. Stanley W. Hamilton and Dr. Maurice L e v i , a l l of whom I am sure recognize t h e i r own thinking i n the essay. Martin Schecter aided with the mathematics i n Appendix One. F i n a l l y I wish to thank the people at '5612' who provided me with a congenial home l i f e while the bulk of t h i s research was being com-pleted. CHAPTER ONE 1 Introduction and Outline The purpose of t h i s thesis i s to examine the brokerage of information i n the market f or urban r e n t a l housing. The procedure i s to construct a simulation model of the demand and supply f o r r e n t a l information, and thereby a model of the market f o r such information. Several i n t e r e s t i n g t h e o r e t i c a l problems, not i n the l i t e r a t u r e , are studied, and some tentative p o l i c i e s toward markets with imperfect information are evalu-ated. The study of markets with imperfect information i s important and i n t e r e s t i n g both t h e o r e t i c a l l y and for p o l i c y objectives. Academically, t h i s essay attempts to make headway on several f r o n t s . F i r s t , housing economics has been marked by a recurring controversy over the nature, extent, and importance of market imperfections. Many economists who have studied t h i s market remark on what they consider to be imperfections r e s u l t i n g from p e c u l i a r i t i e s i n the commodity such as i n d i v i s i b i l i t y , s p a t i a l uniqueness, and sluggish information markets. Some, such as Kirwan and Martin (1970) and Rodwin (1963), despair at what they consider a n a l y t i c i n t r a c t a b i l i t y , while others such as Smith (1964:), Muth (1960), and Olsen (1969), appear to-consider the market imperfections issue a red herring. This essay attempts to shed some l i g h t on the matter by examining the differ e n c e between perfect markets and perfect competition. Second, the issue of imperfect information i s d i r e c t l y r e l a t e d to models of consumer search recently constructed by S t i g l e r (1961), McCall (1970), and Rothschild (1973, 1974). These models have generally made extremely r e s t r i c t i v e assumptions i n order to f a c i l i t a t e the a p p l i c a t i o n 2 of a n a l y t i c solutions. The basic thrust of t h i s thesis i s to construct a l e s s r e s t r i c t i v e model of information markets. This removes the ' p o s s i b i l i t y of applying a n a l y t i c techniques, and neccessitates the a p p l i -cation of simulation methods, but the added i n s i g h t into the nature of search compensates for the loss i n a n a l y t i c elegance. Aside from i t s academic i n t e r e s t , t h i s essay attempts to contribute to current p o l i c y discussions. F i r s t , i t should be noted that the pro-portion of tenant to owner-occupied dwelling units has increased i n the past twenty years. In Table 1 t h i s i s demonstrated; note e s p e c i a l l y 2 the percentage change from 1961 to 1971. Table 1 % % 1951 Change 1961 Change 1971 Owner-occupied 2,236,955 34.4 3,005,587 21.0 3,636,925 Tenant-occupied 1,172,340 32.1 1,548,406 54.8 2,397,584 Owner-occupied and tenant-occupied dwelling units 1951 - 1971 Second, the r o l e of the information broker i s becoming very im-portant i n the modern consumption economy. There have been several excellent studies on brokerage i n the-freehold housing market such as Hempel (1969) and Becker (1972). However these studies do not separate the provision of services such as f i n a n c i a l and l e g a l assistance from the p r o v i s i o n of information about the commodity. Recent development i n the market for r e n t a l information, namely the rapid growth of r e n t a l i n -formation agencies, i s a good opportunity to study the r o l e of the i n -formation broker and the e f f e c t s t h i s agent has upon market imperfections. F i n a l l y , and r e l a t e d to the above point, t h i s study attempts to con-t r i b u t e to the growing l i t e r a t u r e on the economics of consumer protection. 3 Consumerism has become a f o c a l point f o r many p o l i t i c a l l y a c t i v e groups. These groups, ranging from informal l o c a l organizations to n a t i o n a l bodies such as the Consumer's Union, argue that the consumer needs to be pro-tected from rapacious corporate power. Recently tenant a c t i v i s t groups have argued for c e n t r a l i z e d government housing r e g i s t r i e s to prevent the e x p l o i t a t i o n that they a l l e g e , i s being perpetrated on low income tenants by r e n t a l information agencies. It should be emphasized that the p o l i c y tests are by no means con-c l u s i v e ; they are performed as an i n d i c a t i o n of the p o t e n t i a l of simula-t i o n i n the evaluation of government action i n r e c t i f y i n g market imper-f e c t i o n s , and to organize the discussion of p o l i c y . T h eoretical Background This essay uses old terminology i n ways that may be s l i g h t l y un-f a m i l i a r to the reader. The f i r s t important d i s t i n c t i o n i s between perfect competition and perfect markets. Although the growth of the l i t e r a t u r e i n t h i s area has been extremely rapid, the separation of the 3 two concepts i s r a r e l y made e x p l i c i t . Simply stated, perfect competition r e f e r s to the structure of the set of buyers or the set of s e l l e r s . A few large buyers indicates imperfect competition or monoposony i n the same way that a few large s e l l e r s indicates imperfect competition due to monopoly power. Pr i c e s may well diverge from the perfect competition optimum of p r i c e equalling marginal cost because of monopoly or monoposony power; i n other words because one side or the other has few a l t e r n a t i v e s . On the other hand, a perfect market r e f l e c t s a c e r t a i n condition i n the exchange between a buyer and a s e l l e r . In p a r t i c u l a r , Alchian 4 (1969) argues that perfect markets involve zero transactions costs. These exchange costs are normally thought to be composed of information costs (search or pre-purchase information a c q u i s i t i o n c o s t s ) , negotia-t i o n costs and contract enforcement costs. The l a s t two costs are merely subsets of information costs; with perfect information there would be no need to negotiate or enforce contracts. Perfect markets imply zero information costs. There i s no necessary connection between perfect markets and perfect competition. As S t i g l e r (1957) has argued, perfect markets tend to be more common to monopoly and monoposony than perfect compe-t i t i o n . With many atomistic s e l l e r s , no buyer can ever hope to know the complete set of p r i c e s . With p o s i t i v e costs of information a c q u i s i -t i o n i t i s l i k e l y that s e l l e r s may d e l i b e r a t e l y set prices which are d i f f e r e n t and the market p r i c e can diverge from marginal cost due to consumer ignorance. With monopoly, there i s only one p r i c e to know and perfect markets become possible. Information Costs and Brokerage Whenever a good or service involves economies of scale i n i t s production, and whenever s u f f i c i e n t demand for t h i s good or service e x i s t s , i t may pay someone to s p e c i a l i z e i n i t s production. Information a c q u i s i t i o n i s c o s t l y to the i n d i v i d u a l and there are probably s i g n i f i -cant economies i n c e n t r a l i z i n g the production, c o l l e c t i o n , and d i s t r i -bution of information. On a wide scale t h i s a c t i v i t y includes s c i e n t i -f i c and technological research, education, patents, copyright services, etc., but on a narrower focus, information on the p r i c e , q u a l i t y and l o c a t i o n of consumer goods and serivces i s obviously becoming a commodity 5 capable of sale. Various s p e c i a l i s t hobby magazines ranging from stereo to car journals, and stamps to quarter horse breeding, t e s t i f y to the ex-tent to which t h i s industry has grown. Adam Smith's dictum about the r e l a -tionship between the d i v i s i o n of labour and the extent of the market i s f u l l y demonstrated by the growth of the information industry. It i s possible to use a simple demand and supply analysis to i l l u s -4 t r a t e the basic economics of brokerage. F i r s t , the demand for brokerage services i n general i s a derived demand, which r e s u l t s from both buyers and/or s e l l e r s demanding the services of a market intermediary. Second, i t i s apparent that the fee charged by the broker must be les s than the cost of the buyer or s e l l e r performing the market service for themselves. In c e r t a i n cases i t i s possible f o r the broker to assume monopoly power and prevent the buyer or s e l l e r from performing these services without the help of the market agent. This i s the a l l e g a t i o n that i s often made about r e n t a l information agencies. They 'trap' the supply of information (to be explained i n Chapter 3), process t h i s information and then use the monopoly power to extract a rent from tenants who are searching for accommodation. But i n general brokers economise on market costs. Third, .brokerage fees can be s h i f t e d to one side of the market or the other as a function of the slopes of the demand and supply curves. The 'transaction cost d i f f e r e n t i a t e d supply and demand a n a l y s i s ' i s use-f u l i n i l l u s t r a t i n g the s h i f t i n g aid incidence of brokerage fees; t h i s analysis w i l l become important l a t e r when I examine the supply of r e n t a l housing information. ~* Quantity Figure 1 Transactions D i f f e r e n t i a t e d Demand and  Supply Curves In Figure 1 are drawn a conventional set of demand and supply curves. These r e l a t i o n s h i p s represent the demand and supply for buyers who are i n d i f f e r e n t to the l e v e l of service provided by market i n t e r -mediaries. For the sake of argument, imagine that a l l transactions between producers and consumers are handled by an agent. P a r t i c i p a n t s i n the market who demand market services, i n addition to the actual product and i t s d e l i v e r y , must pay a premium. Now suppose the buyer wishes to have a warranty, or equivalently exact information about the f a i l u r e of a product. The agent who provides such a service w i l l do so only i f rewarded. In other words, the p r i c e of the product charged to the buyer who demands t h i s service must s h i f t 7 upward f o r each unit offered by the agent, by an amount s u f f i c i e n t to cover the costs of producing t h i s information or warranty protection. This i s r e f l e c t e d by a s h i f t leftwards i n the supply curve from S' to S". A l t e r n a t i v e l y , suppose that i t i s the s e l l e r who demands some market service such as a c e r t i f i e d s e r v i c e centre for the product. The agent or r e t a i l e r w i l l be w i l l i n g to perform such a service only i f the p r i c e paid for the product i s lowered s u f f i c i e n t l y to cover the costs of t h i s market service. This i s r e f l e c t e d by a s h i f t leftward of the demand curve from D' to D". Of course, either the producer or consumer may decide that the premium demanded by the agent i s excessive and they may perform the market service themselves. The i n t e r s e c t i o n of the market service d i f f e r e n t i a t e d supply curve, S", and the o r i g i n a l pre-market or non-market service demand curve, D', y i e l d s the ask p r i c e . The i n t e r s e c t i o n of the market service d i f f e r e n - t i a t e d demand curve, D", and the non-market service d i f f e r e n t i a t e d supply curve, S', y i e l d s the b i d p r i c e . For market services demanded by the buyer, the market agent w i l l demand a higher than o r i g i -n a l p r i c e (P - P ), while f o r service demanded by the producer, the a e agent w i l l b i d a lower than o r i g i n a l p r i c e (P, - P. ) for the product. b e The spread between bid and ask p r i c e (P - P, ) r e f l e c t s the costs of a b transacting, given that there i s perfect competition p r e v a i l i n g amongst buyers and s e l l e r s . According to Demsetz (1968), the greater the b i d -ask p r i c e spread, the greater are the costs of transacting and hence, according to the above discussion, the greater are the market imper-fections . The s i m i l a r i t i e s of t h i s a nalysis with excise taxation are obvious, but there i s some d i f f i c u l t y i n the measurement of incidence i n the case 8 when both the demand and supply curves are s h i f t e d . Consider the case where only the buyer desires a market service. This r e s u l t s i n a s h i f t to the l e f t of the supply curve. As i n the case of excise taxation, both the buyer and the agent would share the costs of transacting, with the buyer's share being P - P ( r e f e r r i n g to Figure 1) and the agent's share a D being P - P . In the case where the producer alone desires market e x services, only the demand curve s h i f t s , and the proportion of trans-action charges borne by the s e l l e r i s given by P & - P^ and the portion of market costs borne by the s e l l e r i s given by P - P, . In the case y b where both curves s h i f t , the agent can generally s h i f t the market charges to both the buyer and s e l l e r . The buyer and s e l l e r then s p l i t the market costs; however, i t i s ambiguous whether the o r i g i n a l p r i c e P or the point P ' are the relevant benchmarks. P obviously d i s -e e e appears and equally obvious i s that P 1 never a c t u a l l y becomes an ob-served p r i c e , since as market imperfections decline and the demand for market services dwindles, both S" and D" s h i f t back to t h e i r o r i g i n a l p o s i t i o n s . I t i s probably safest to use an average point which l i e s between P and P ' , but t h i s point i s somewhat academic, e e It i s apparent that the incidence of brokerage fees (whether they f a l l on the buyer or s e l l e r ) i s a function of the r e l a t i v e demands for market services by buyers and s e l l e r s and the slopes of demand and supply f o r the product.'' The Use of Simulation Studies i n Economics The r e l a x a t i o n of the r e s t r i c t i v e assumptions of search theory, upon which the discussion of market imperfections r e s t s , necessitates the use of simulation, or Monte Carlo methods. This w i l l be j u s t i f i e d 9 inthe subsequent.chapter, but now I wish to ou t l i n e some important guidelines f o r the construction and use of these models. Simulation studies have p r o l i f e r a t e d i n the past decade. Doubt-less t h e i r contribution to economic methodology has been suspect. In a recent c r i t i q u e , Lee (1973) examines the r o l e of large scale simulation models and concludes that these large scale models have revealed l i t t l e about urban complexity i n r e l a t i o n to the i n s i g h t s obtained about how to b u i l d large scale models; as the s i z e of the model increases the returns to knowledge about the system being modelled decline, while there are increased returns to knowledge about the construction and use of large scale models. Lee proposes three guidelines f o r simulation studies: 1) "A balance should be obtained between theory, o b j e c t i v i t y and i n t u i t i o n . Excessive concern f o r theory r e s u l t s i n a loss of contact with the p o l i c y problem, but p o l i c y cannot be formulated w e l l without a strong t h e o r e t i c a l foundation. Over-emphasis on o b j e c t i v i t y i s one of the mistakes of the large models and r e s u l t s i n empty-headed empiricism; on the other hand most s o c i a l questions have a qua n t i t a t i v e com-ponent and require quantitative information to resolve..... 2) Start with a p a r t i c u l a r p o l i c y problem that needs solving, not a methodology that needs applying 3) Build only very simple models. Complicated models do not work very well i f at a l l , they do not f i t r e a l i t y very w e l l , and they should not be used i n any case because they w i l l not be understood ".8 This i s not the place to go into a prolonged discussion of simu-l a t i o n methodology; there are several' excellent texts (cf. Naylor, T.H. et. a l . 1971), however, several points need s t r e s s i n g . F i r s t , simulation studies should not be pursued as an end. The use of simu-l a t i o n i n t h i s essay i s necessitated, simply because the theory of search uses p r o b a b i l i t y theory. But theory can only be applied i f c e r t a i n r e s t r i c t i v e assumptions are made about human behaviour. Once these assumptions are relaxed, as they must i f various p o l i c i e s are to be examined, then le s s elegant methods are necessary. Simulation, i n t h i s case the use of random number generators, becomes an essen-t i a l device for exploring new areas i n the economics of information. Second, as with a l l research methodology, simulation has assump-tions that must be accepted before any progress can be made. One of the debating points between 'simulators and anti-simulators' i s the nature of v e r i f y i n g the equations used i n the model. Computers are exact. Just any monotonically increasing function w i l l not do; i t must be a p r e c i s e l y s p e c i f i e d algebraic or l o g i c a l equation. This required p r e c i s i o n has lead many c r i t i c s to argue that the model holds only f o r the s p e c i f i e d set of equations; vary the equations and i t i s l i k e l y that the model outputs gibberish. Any analyst who has worked with simulation models r e a d i l y concedes t h i s , but there are procedures which can be used to reduce the l i k e l i h o o d that the model i s l i m i t e d to a p a r t i c u l a r set of equations. F i r s t , models should be kept simple. The p r o b a b i l i t y of perverse output increases dramatically with a d d i t i o n a l separate r e l a t i o n s and v a r i a b l e s . In addition, as the number of equations used i n a simula-t i o n model are increased, analysts f i n d that they must use more a r b i -t r a r y assumptions i n order to l i n k various parts of the model; c a l i -b r ation or 'fudge f a c t o r s ' seem to grow exponentially with the number of equations and v a r i a b l e s . Second, the equations used i n the model must be t h e o r e t i c a l l y sound and must be v e r i f i e d using acceptable empirical techniques. Parameters obtained from regression analysis that have passed tests of s i g n i f i c a n c e can generally be used with confidence. Third, even those parameters which either f a i l to be v e r i f i e d with any high degree of confidence or for which adequate data i s unavailable can be evaluated using s e n s i t i v i t y a n a l y s i s . This i s one of the powers of simulation methodology. By repeated t r i a l and error, i t i s possible to evaluate the output of a model using many values of a given parameter. It i s at t h i s point that t h e o r e t i c a l judgment i s used to decide what values of the parameter ought to be employed. Flowcharting An important t o o l used throughout the essay i s the flowchart. The simulation model i s described and documented at four l e v e l s -verbal, mathematical, flowchart and program l i s t i n g s . The f i r s t and second forms of de s c r i p t i o n are common to economics, the l a s t pre-supposes a knowledge of FORTRAN IV, however the t h i r d i s very simple, even though i t may be unfamiliar to the reader. Rather than give an out l i n e of the theory of flowcharting, i t i s simpler to present the flowchart used by a noted economist to describe the process of getting 9 up. 12 I SET ALARM • • [TURN OFF ALARM]  [GROAN} Figure 2 Flowchart Example Information: Quantity and Qualtly The f i n a l background required i s a b r i e f examination of information as an economic commodity. S u p e r f i c i a l l y i t i s apparent that more i n -formation i s better than l e s s , but upon r e f l e c t i o n t h i s i s often un-true. Searchers have l i m i t s to t h e i r a b i l i t y to process market data. In addition, information has quantity and q u a l i t y aspects which are frequently r e l a t e d . It i s possible to conceive of the information a c q u i s i t i o n process as having both an extensive and an inte n s i v e margin. If commodities are composed of separate c h a r a c t e r i s t i c s , then information can be extensively acquired by considering more and more relevant a t t r i b u t e s about the product (price, l o c a t i o n , number of rooms e t c . ) . More information can mean gaining information on more a t t r i b u t e s . The extensive margin occurs at the point where the marginal returns to expanding search to one more a t t r i b u t e i s matched by the marginal costs. The intensive margin occurs for the a t t r i b u t e which i s best known by the consumer. The intensive margin occurs at the point when the marginal returns from more information about a p a r t i c u l a r c h a r a c t e r i s -t i c i s matched by the marginal costs of obtaining t h i s data. Obviously, i n d i v i s i b i l i t i e s and the problems inherent i n i d e n t i -f y i n g appropriate c h a r a c t e r i s t i c s d i s t o r t t h i s neat picture. Economists have employed two methods of quantifying and modelling information a c q u i s i t i o n . Some have attempted to weld information and mathematical communication theory d i r e c t l y onto economic theory (cf. Marshak, 1968). Others have used the process of sampling from a d i s t r i b u t i o n of p r i c e s as an analogue (simulation) of the information a c q u i s i t i o n process. In both cases i t has been presumed that a l l the consumer i s examining i s p r i c e . Quality a t t r i b u t e s of the commodity are ignored. Obviously t h i s i s a gross s i m p l i f i c a t i o n , however extensions r e s u l t i n extreme complications. Outline The next two chapters present the demand and supply models of information a c q u i s i t i o n i n the r e n t a l housing market. The demand model (Chapter Two) moves d i r e c t l y from the basic paradigm developed by 14 S t i g l e r (1961) and modifies t h i s theory by incorporating e r r o r - l e a r n i n g , storage and decay. These modifications r e s u l t i n complexities which are conventiently handled by simulation. Chapter Three extends the work of Chapter Two by integr a t i n g supply elements into the basic demand model. Empirical evidence i s presented f o r some of the sources of information ( c l a s s i f i e d s and r e n t a l information agencies); unfor-tunately the supply model cannot be extended into other important areas such as casual search (street signs, word of mouth) and property management, due to lack of data. Supply i s modelled as a function of the vacancy rate and the model i s run to show how v a r i a t i o n s i n the vacancy rate a l t e r the supply of information and provoke d i f f e r e n t search behaviours. The chapter concludes with a s e n s i t i v i t y a n a l y s i s . The f i n a l chapter presents some explorative and p a r t i a l p o l i c y t e s t s . The three general p o l i c i e s examined are free markets, regulation of p r i c e and q u a l i t y , and government monopolies. The nature of the simulation i s such that only comparisons -of benefits are possible; there i s no provision f o r examining the d i r e c t (administrative costs) of these p o l i c i e s and t h i s chapter should not be viewed as a f u l l blown cost-benefit examination. Extensions and q u a l i f i -cation of the model close the t h e s i s . 15 FOOTNOTES - CHAPTER ONE 1. These are but a few of the th e o r i s t s who have published work i n area recently. Since the essay attempts a substan-t i a l r e v i s i o n to the e x i s t i n g theory by r e v i s i n g assumptions common to the vast majority of the published works and since the l i t e r a t u r e i s vast, only a few c e n t r a l a r t i c l e s w i l l be mentioned and surveyed. 2. Source: Canada Year Book 1973, p. 610. It should be noted that these f i g u r e s omit the recent s i g n i f i c a n t r i s e i n con-dominium home ownership. Present day figures would probably reveal a higher proportion of fee simple and s t r a t a - t i t l e ownership than i s indicated i n Table 1. 3. See Rothschild (1973) for an excellent survey of t h i s l i t e r a -ture. 4. This analysis and the diagram are adapted from Demsetz (1968). 5. See Demsetz (1968) f o r the use of 'time d i f f e r e n t i a t e d demand and supply r e l a t i o n s h i p s ' i n the analysis of stock brokerage. In t h i s case the market service performed by the broker i s r e s t r i c t e d to providing immediacy of purchase or sale to both buyers and s e l l e r s . 6. Note that only prices and not quantities are relevant here. 7. See Appendix One for a d d i t i o n a l d e t a i l s . 8. Lee (1973), p. 176. 9. Baumol (1973), p. 605. CHAPTER TWO The Demand for Information Recently economists have become interested i n the economics of information. An important part of t h i s l i t e r a t u r e i s the theory of search which i s nothing more than the theory of the demand for information. The l i t e r a t u r e begins with S t i g l e r ' s seminal a r t i c l e ( S t i g l e r , 1961) and continues with the work of authors such as McCall (1970), Mortensen (1971), Kihlstrom (1973), and Rothschild (1973, 1974). S t i g l e r ' s model i s s t i l l very representative and pro-vides a convenient vantage from which recent work may be evaluated. It should be stressed that the simulation proceeds on the c r i t i c i s m of t h i s model, but does not r e l y upon any of the s p e c i f i c points."'" The Basic Paradigm Two c r i t i c a l assumptions are made by S t i g l e r and a l l subsequent work i n t h i s area (except for Rothschild whose work p a r a l l e l s , i n 2 part, the amendments undertaken i n t h i s chapter). F i r s t , search i s likened to sampling without replacement from a d i s t r i b u t i o n for which the mean and variance are known by the searcher p r i o r to undertaking search. Second and equally c r i t i c a l l y , i t i s assumed that searchers have two options with regard to accepting o f f e r s . They either must accept immediately or they can procrastinate i n d e f i n i t e l y ; i n other words there i s no decay or instantaneous decay i n the stored o f f e r s . These two assumptions permit the a p p l i c a t i o n of p r o b a b i l i t y theorems to derive marginal rules f or optimal search. Searchers who are forced into c o s t l y search w i l l search u n t i l the expected marginal costs of search. are equal to the expected returns f o r an extra unit of search. S t i g l e r uses simple p r o b a b i l i t y d i s t r i b u t i o n s to evaluate some of the implications of c o s t l y search. The uniform and normal d i s t r i -butions are used along with the assumption that the wage rate approxi-mates the time spent i n search. Needless to say, time costs are an important element of the unit cost of search. Expected returns from search are developed using the properties of cumulative d i s t r i b u t i o n s of o f f e r s or wages or rents. If F(x) i s the emulative d i s t r i b u t i o n of the set of o f f e r s , x, then the expected minimum i s given by the formula E (M) = /" (1-F(x)) ndx ,Q where n i s the number of un i t s of search undertaken and E(M) i s the 3 expected minimum p r i c e a f t e r n units of search. For the uniform and standard normal d i s t r i b u t i o n s , S t i g l e r shows that t h i s expression i s concave which ensures that as n increases E(M) decreases. The expected return from an a d d i t i o n a l unit of search i s given by the differ e n c e between n and n+1 units of search, or co -n M =m - m. . = / (l-F(x)J F(x)dx pn n n+1 0 As shown i n Figure 3, as long as t h i s function (M ) increases pn at a decreasing rate, and as long as the marginal costs of search (MC) are zero (the t o t a l costs of search are constant per unit of where m > m ,, n n+1. search), then the optimal number of units of search w i l l be f i n i t e . I n f i n i t e search occurs when the returns to an a d d i t i o n a l unit'of search are increasing The proof that search must stop before i n f i n i t y r e s t s upon the p a r t i c u l a r from of the d i s t r i b u t i o n of prices and sets the optimum number of units of search p r i o r to even beginning to sample. This obviously i s quite u n r e a l i s t i c , however a n a l y t i c methods are not s u f f i c i e n t l y powerful to model c e r t a i n c r i t i c a l features of search such as v a r i a t i o n s i n the a b i l i t y to store o f f e r s and the phenomena of oversearch and undersearch. xi a u rt cu c/> 13 c cd cn C U u CD Pi Units of Search Figure 3 Marginal Cost and Returns to Search Second, i t i s assumed that t h i s d i s t r i b u t i o n remains stable over time. The consumer i s presumed to know not only the form of the d i s -t r i b u t i o n of p r i c e s , but also how i t changes over time. This dynamic aspect of optimal search procedure w i l l not concern us i n t h i s essay, however the a p p l i c a t i o n of error learning i s straightforward. F i n a l l y , i n the l i t e r a t u r e , i t i s assumed that searchers have either complete storage and can act upon o f f e r s at t h e i r l e i s u r e , or that they have no storage a b i l i t y and o f f e r s must be accepted or rejected as soon as they are received.^ I t seems apparent that a model that permits v a r i a b l e degree of storage i n the search process permits greater in s i g h t into the complex in t e r a c t i o n s that characterize market processes. Decay i n the vector of stored o f f e r s can i n t u i t i v e l y be demon-strated using the optimal stopping paradigm. This aspect of search theory i s derived from the simple rules developed by Stigler., except that the decision when to stop i s somewhat more complex. The optimal stopping problem can best be characterized by the search for a parking l o t . As one approaches the destination, for example the theatre, the number of a v a i l a b l e parking spaces begins to dwindle. The decision that must be made i s when to stop, given that one knows the d i s t r i b u -t i o n of o f f e r s (vacant parking spaces), the unit cost of search and the l o c a t i o n of the parking spaces previously given up. With i n f i n i t e storage or no decay the searcher can simply turn around the block and choose a previous spot; with no storage or i n f i n i t e l y rapid decay, t h i s p o s s i b i l i t y does not e x i s t . Stopping r u l e problems can be structured i n the following way. The o f f e r s (x..O are random v a r i a b l e s from a known d i s t r i b u t i o n . It i s assumed that the highest o f f e r i s retained so that the return to stopping a f t e r n periods i s (3) g = max(x , x x )-nc n ± z n where max (x^, x„,....,x ) i s the best o f f e r received a f t e r n periods, 1 z n assuming complete storage, and c i s the constant cost for one unit of search. The stopping r u l e problem i s to formulate a strategy that maximizes the value of g^. If f(x) i s the optimal return received when an o f f e r x i s received, then a f t e r searching n periods the optimal return i s given by f( x ) = max(x.,x., )-nc = m = nc (4) n 1 2 In other words we are seeking a procedure that maximizes the expected value of f ( x ) . L e t t i n g t h i s be y then, E ( f ( x ) ) = y = E(max(m,y) - c (5) gives the expected gain from any p a r t i c u l a r unit of search. The optimal p o l i c y i s to continue search i n the event that the expected return from an a d d i t i o n a l -searchfy) exceeds the value of the best o f f e r received (m); otherwise stop. In other words, continue to examine the next parking spot for vacancy i f the expected u t i l i t y of being closer to the theatre (the p r o b a b i l i t y of vacancy times i t s u t i l i t y ) i s greater than the u t i l i t y of the best spot already examined. In the case of searching for a house, the r u l e i s to continue searching i f the expected gain w i l l r e s u l t i n an o f f e r better than the one already received. In e f f e c t , m i s the best o f f e r already received from the vector of o f f e r s (x.,x , ,x ) examined; to stop i s to receive m. The o p t i -1 z n mal stopping r u l e i s to p e r s i s t i n one extra unit of search as long as the expected gain l e s s the cost i s greater than the best o f f e r already received. Of course t h i s formulation i s very close to that of S t i g l e r except that optimal stopping permits what McCall c a l l s a 'myopic' approach to search. In the p r i o r search model of S t i g l e r , the searcher decides before s t a r t i n g , how many un i t s of search to undertake. In the se-quential rules developed by McCall the searcher proceeds and evaluates the value of an a d d i t i o n a l search while i n the process of examining various o f f e r s . There i s a subtle, but r e a l d i s t i n c t i o n between the two methods. The optimal stopping r u l e framework s u f f e r s from the same general defects as the p r i o r search models. The d i s t r i b u t i o n i s assumed to be known and unchanging, and the searcher i s assumed to have complete storage a b i l i t i e s . The stopping r u l e problem can be varied to admit the p o s s i b i l i t y that the vector of stored o f f e r s i s subject to instan-taneous decay, i n which case the problem collapses to a p r i o r search type problem where the searcher w i l l examine o f f e r s u n t i l the accumu-lated search costs outweigh the expected gains from search. The s o l u t i o n procedures for discovering the optimal number of searches are not t r i v i a l . Breiman (1964) evaluates l i n e a r and dynamic programming procedures f o r models with r e l a t i v e l y simple a n a l y t i c structures while McCall (1970) presents the s o l u t i o n i n the form of i n t e g r a l equations. The amendments that I propose to the basic search paradigm (error-learning to deal with ignorance about the basic d i s t r i -bution and decay i n the storage vector) preclude the p o s s i b i l i t y of any straightforward s o l u t i o n procedure. For t h i s reason simulation methods are chosen as an a t t r a c t i v e a l t e r n a t i v e to analyze the consumer search problem.^ A Simulation Model of the Demand for Information There are three c r i t i c a l elements to the simulation of the demand for r e n t a l information. F i r s t , there i s the notion of a reservation p r i c e . ^ This concept has been widely used i n the study of labour markets. It i s hypothe-sized that the searcher s t a r t s by s e t t i n g a wage below which employment w i l l not be accepted. The higher the reservation p r i c e (wage) i n r e l a -t i o n to the average or market p r i c e , the longer the search. Second, i t has been hypothesized (Mortensen, 1971) that f a i l u r e to f i n d employment r e s u l t s i n amendments to the reservation p r i c e . In t h i s case the reservation p r i c e c l o s e l y resembles the r u l e of thumb as developed by Baumol and Quandt (1964). In f a c t these two authors have introduced the r u l e of thumb as the decision method of the entre-preneur and developed simple simulation models to mimic fir m behaviour under various assumptions about the state of demand. They set out several simple c r i t e r i a f o r the r u l e of thumb, such as measurability and savings obtained from t h e i r use. The concept of e r r o r - l e a r n i n g i s the t h i r d basic element of the demand model. The a p p l i c a t i o n of adaptive processes has had a modest, yet impressive r o l e i n economics. Meiselman (1962) used e r r o r - l e a r n i n g to explain the term structure of i n t e r e s t rate; Arrow (1962) developed the concept of learning by doing; and f i n a l l y Rothschild (1974) and A x e l l (1974) have very recently introduced the notion into search theory. The basic notion of e r r o r - l e a r n i n g i s simple. If a c e r t a i n action (rule of thumb) r e s u l t s i n greater welfare, the p r o b a b i l i t y r i s e s that i t w i l l be repeated i n future decisions. If a r u l e r e s u l t s i n lower welfare, the opposite happens; the p r o b a b i l i t y increases that the r u l e w i l l be modified. These concepts are,of c o u r s e , l i t t l e more 9 than elementary p r o b a b i l i t y matching and learning theory. The Model; A Verbal Description The searcher i s assumed to be ignorant of general market condi-tions; i . e . , the d i s t r i b u t i o n of actual house rents i s unknown. In addition, searchers are assumed to be homogeneous except with respect to income. This s i m p l i f i c a t i o n reduces the complexity of the model at the expense of ignoring many i n t e r e s t i n g hypotheses such as the r e -l a t i o n s h i p between socio-economic c h a r a c t e r i s t i c s and the degree of r i s k aversion. Obviously, t h i s would have an important bearing on the degree to which a searcher would p e r s i s t i n the face of unfavour-able market conditions. This behaviour would be modelled by d i f f e r e n t rates of reformulating the e r r o r - l e a r n i n g r o l e . The actual search process commences With the searcher s e t t i n g time constraints to search. For the sake of s i m p l i c i t y these con-s t r a i n t s are assumed to be equal for everyone. F i r s t , there i s the maximum period of search which i s assumed to be t h i r t y days; tenants t y p i c a l l y give notice before f i n d i n g an a l t e r n a t i v e dwelling and t y p i c a l l y have one month to f i n d s u i t a b l e accommodation. There are, i n addition, two intermediate time constraints. F i r s t , there i s a time constraint that governs when the searcher a l t e r s the extensive margin of search and acquires information on more dwellings (widens the scope of search). Second, there i s the time constraint, which when v i o l a t e d w i l l cause the searcher to modify the r u l e of thumb. De t a i l s on these constraints are given i n the next section. Each searcher i s s t r a t i f i e d by income. The income of searcher ' i 1 i s calculated from a lognormal p r o b a b i l i t y generator that i s av a i l a b l e i n FORTRAN IV. The actual process of c a l c u l a t i n g these numbers i s not germane. The use of the lognormal d i s t r i b u t i o n f o r income has been well v e r i f i e d i n the l i t e r a t u r e ; (see -A-itCihisQn, 1973). The parameters that were used were a mean of $5000 and a variance of 2.0. Mean = 5000 Variance = 2.0 2000 30000 INCOME Figure 4 The Lognormal D i s t r i b u t i o n of Income Once the searcher has been s t r a t i f i e d by income, the model commences the actual search process. On the f i r s t day searcher ' i ' examines a c e r t a i n number of dwellings. P r i o r to search a very simpl r u l e i s developed. Along with each dwelling comes a b i d and ask rent C a l c u l a t i o n of the b i d and ask rents is'/ performed by a random number generator which produces random v a r i a t e s from the uniform d i s t r i b u -t i o n . The bid rents are re l a t e d to the income of the searcher, while the ask rents are independent of the searcher's income. No attempt was made to examine the r e a l i t y of the d i s t r i b u t i o n of o f f e r s or bids and the use of the uniform d i s t r i b u t i o n follows established p r a c t i c e i n t h i s f i e l d . If the di f f e r e n c e between the bid and ask rents i s s u f f i c i e n t l y high to s a t i s f y the r u l e of thumb, the vacancy i s accepted; i f the di f f e r e n c e does not s a t i s f y the r u l e of thumb, but i t i s p o s i t i v e that vacancy i s stored; i f the di f f e r e n c e i s negative (ask rent greater than b i d re n t ) , the vacancy i s rejected immediately. At the beginning of each day the searcher sets both the decision r u l e and the maximum number of dwellings to be searched. With each dwelling searched, money costs are incremented. Once the maximum number of dwellings per day has been examined the day counter i s incremented and the process begins anew for the next day. The model incorporates e r r o r - l e a r n i n g at three l e v e l s . Once the f i r s t time constraint i s v i o l a t e d the searcher w i l l then increment the number of l i s t i n g s (dwellings) examined on each day. This process of incrementation continues for each day beyond the f i r s t time con-s t r a i n t u n t i l a maximum number of l i s t i n g s i-s> being examined. The second l e v e l of error-l e a r n i n g occurs once the second time constraint i s reached (and once the maximum l i s t i n g s per day are being examined). The ru l e of thumb i s relaxed. In other words the d i f f e r -ence between the bid and ask rents i s no longer required to be as high. With each r e l a x a t i o n the searcher scans the stored vacancies (those that previously f a i l e d the r u l e of thumb) to discover whether there are any stored vacancies that now s a t i s f y the revised r u l e . F i n a l l y , t h i s storage vector i s subject to decay. The rate of decay i s introduced by a random s e l e c t i o n of elements i n the storage vector. For any given searcher, the proportion of o f f e r s or vacancies that are retained throughout the search period i s d i r e c t l y r e l a t e d to the vacancy rate. At high vacancy rates the searcher finds that the storage vector i s subject to l e s s decay than at low vacancy rates. Of course the vacancy rate i s an exogenous v a r i a b l e . The t h i r d l e v e l of e r r o r - l e a r n i n g keys off the rate of decay i n the storage vector. It i s reasonable to suppose that consumers who discover that they have l i t t l e a b i l i t y to store o f f e r s w i l l r e v i s e t h e i r search strategy. In t h i s case the s i m p l i f y i n g assumption i s made that the r u l e of thumb i s once again revised. In r e a l i t y , consumers probably check the s t o r -age vector frequently and most l i k e l y would respond to decay i n i t i a l l y by widening the scope of search, however, the model i s kept simple. The Model; A Mathematical Description The basic elements of the model are set out i n order of t h e i r appearance. (1) Time Constraints: There are three time constraints used i n the demand model. The f i r s t , designated by IDAYMX, i s the maximum number of days (in t h i s case 30), search may continue for any p a r t i c u l a r searcher."^ The second time constraint indicates the number of days before searchers w i l l a l t e r the scope of search. The scope of search indicates the percentage of t o t a l l i s t i n g s examined per day and has a maximum value of 1.00. This value, designated as IDYCRl"; i s set a r b i t r a r i l y since no empirical work was undertaken to v e r i f y the p a r t i -cular value used; however, i t was subjected to considerable s e n s i t i v i t y a n a l y s i s . F i n a l l y the t h i r d time constraint, IDYCR2, indicates the time required before searchers w i l l begin to a l t e r the r u l e of thumb and permit the accepted or reservation rent to r i s e . Once er r o r -learning has begun the t h i r d time constraint i s revised upon each r e v i s i o n according to the following r e l a t i o n , IDYCR2 t + 1 = IDAYMX - IDYCR2 t + I D y c R 2 2.0 t where t of course r e f e r s to the p a r t i c u l a r day of search and can vary between the values of 1 and 30. Of course these constraints are quite a r b i t r a r y and are set l a r g e l y as a matter of modelling convenience. To a c t u a l l y v e r i f y t h e i r values i s the subject f o r a research e f f o r t beyond the scope of t h i s essay. The a l l o c a t i o n of time i s one of the more i r r a t i o n a l aspects of economic behaviour, replete with r i s k aversion dependent upon complex socio-economic f a c t o r s . A tentative step might be to make the time con-s t r a i n t s , IDYCR1 and IDYCR2, functions of income under the assumption that higher income searchers are l e s s r i s k averse, but t h i s i s a digression from the main purpose of t h i s essay. (2) Supply of Information: Pending further refinement to be i n t r o -duced i n the next chapter, the supply of information i s modelled as a simple l i n e a r function of the vacancy rate. The maximum number of l i s t i n g s that any searcher can examine on any given day i s given by, JMAXX = BETA*VACANT (7) where VACANT i s the vacancy rate, an exogenous v a r i a b l e and BETA i s a c a l i b r a t i o n parameter."'"2 The percentage of l i s t i n g s examined by a searcher i s i n i t i a l i z e d according to the formula, JMAX = PER*JMAXX (8) where PER i s an adjustment f a c t o r that has a value between 0 and 1 and i s incremented each day (to the maximum value of 1) each day a f t e r the time constraint (IDAYCR1) i s exceeded, and JMAXX i s the maximum number of l i s t i n g s each day. t i l (3) Income: Income for the i searcher i s generated by a random 13 number generator sampling from a lognormal d i s t r i b u t i o n . The l o g -normal d i s t r i b u t i o n i s truncated to produce values l y i n g between 2000 and 30000 d o l l a r s . L e f t unattended, the random number generator could conceivably produce a searcher with an income of $1,000,000 or 57c which would surely d i s t o r t the simulation. (4) Error-Learning: E r r o r - l e a r n i n g i s the heart of the demand model. Time costs are the c r i t i c a l elements which govern the points at which searchers w i l l adjust t h e i r search behaviour. Since the d i r e c t money costs are r e l a t i v e l y small f o r tenants (except those with very low incomes) the time constraint as the binding b a r r i e r seems warranted. As outlined above, there are two c r i t i c a l values of the time constraint. The f i r s t governs the point at which search i s widened to include more l i s t i n g s per day. A second constraint then governs the point at which error-le a r n i n g commences and i s assumed to have a greater value than the f i r s t constraint. Money costs are incremented for each l i s t i n g examined according to the r e l a t i o n , COST. = COST. , + ALPHA2. (9) i t i t - 1 j t where COST, i s the cost for day t for searcher i and ALPHA2. i s the i t 3 • j t cost of the l i s t i n g s examined on day t. Once t exceeds the f i r s t c r i t i c a l time constraint (IDYCR1.), the scope of search i s widened according to PER ± t = (P + 1) / PMAX; PER i t <; 1.00 (10) where P E R i t i s the percentage of l i s t i n g s per day examined by searcher i on day t. The r u l e of thumb i s set by the following r e l a t i o n s h i p , If SURP.. > BP.. / GAMMA accept (11a) i j - i j If SURP.. < BP.. / GAMMA store ( l i b ) i j - I J If SURP.. < 0 r e j e c t (11c) i j -where SURP.. i s the d i f f e r e n c e between the bid and ask rents of the i j i * " * 1 searcher and the j 1 " * 1 l i s t i n g (BP.. - CP..) and GAMMA i s the para-meter that i s used to adjust t h i s r u l e . In e f f e c t , the r u l e states that the excess of bid "rent over ask rent must be greater than the bid rent divided by the adjustment f a c t o r . This i s the simplest e r r o r -learning r u l e that could be adopted. I t conforms to the requirements of a r u l e of thumb i n that i t i s simple, measurable and requires only that the consumer be able to place a subjective value on the worth of a p a r t i c u l a r vacancy. If,the vacancy (bid-ask rent combination) f a i l s the r u l e , but i s p o s i t i v e , that l i s t i n g i s stored; i f the surplus i s negative, the l i s t i n g i s rejected outright. Once the second time constraint (IDYCR2) i s exceeded, GAMMA i s incremented and the required surplus i s reduced. At each r e l a x a t i o n of the ru l e the stored l i s t i n g s are examined to discover i f any s a t i s f y the newly revised r u l e . The storage vector i s subject to decay. Competition f o r housing implies that o f f e r s are removed from the storage vector i n d i r e c t r e l a t i o n to the vacancy rate. This decay process i s simulated using a random number generator which removes c e r t a i n l i s t i n g s at random; the number of l i s t i n g s removed per period depends upon the vacancy rate. Low vacancy rates imply excess demand and high rates of decay while high vacancy rates imply greater a b i l i t y to store o f f e r s . At vacancy rates below .5% there i s almost no storage while at vacancy rates higher than 7% there i s complete a b i l i t y to store. Obviously t h i s i s a s i m p l i -f i c a t i o n , but i n general i t i s r e a l i s t i c . The exact process of removing these stored o f f e r s i s that the percentage of stored o f f e r s to be r e -moved each day i s a function of the vacancy rate, PERSTO ± t = (VACTES - VACANT)/VACANT (12) where VACTES = .07 and VACANT i s , of course, the exogenous vacancy rate. The f i r s t PERSTO^ l i s t i n g s on searcher i ' s storage vector are removed on day t, once er r o r - l e a r n i n g has commenced. Each time the storage vector i s consulted, the r u l e i s revised as a simple function of PERSTO. . This merely indicates that the i t searcher learns not only from f a i l i n g to f i n d accommodation a f t e r a given time, but also adjusts as a r e s u l t of d i r e c t market information (such as returning to f i n d an apartment has been rented). GAMMA i s incremented according to the r e l a t i o n , GAMMA. = GAMMA. , + (1-PERST0. ) / 1. (13) i t i t - 1 i t In other words higher values of PERSTO (lower values of the vacancy rate) cause more rapid r e v i s i o n of the r u l e . (5) Generation of Bid and Ask Rents: The l a s t point i s c l a r i f i c a t i o n on the method of generating the ask and bid rents. Both are generated from uniform d i s t r i b u t i o n of the form BP = l/(a-b) a > x < b (14) = 0 elsewhere where a = 0 and b = (..1)*(INCOME ). The bid rent i s t i e d to income, implying that higher income households tend to make higher bids than * lower income searchers; t h i s i s straightforward. A more r e a l i s t i c bid process would have the bids t i e d to objective c h a r a c t e r i s t i c s of 14 the house, but t h i s i s beyond the scope of the model. Ask rents are generated i n an analogous manner, except that b i s constrained to be equal to (.1)*(INC0MX) where INCOMX i s equal to 30000 the maximum income allowed i n the model. Of course, ask rents would not be d i r e c t l y t i e d to the income of the searcher, except i n the case where there was a s e l f s e l e c t i n g process and low income house-holds bid only on low rent dwellings and v i c e versa. The mathematical explanation of the demand model i s complete. It must be stressed that while the actual r e l a t i o n s are simple, the model derives i t s power and complexity from the number of times the b i d ask rents can be calculated (about 1000 for any i n d i v i d u a l searcher), and the l o g i c a l loops that test f o r constraint v i o l a t i o n s , r u l e r e v i -sions, state of the storage vector, etc. To appreciate t h i s aspect of the model the flowchart i s required. The Model; Flowchart Explanation Figures 5 and 6 present a macro and a micro flowchart. The macro flowchart can be examined i n r e l a t i o n to the verbal d e s c r i p t i o n of the model, while the micro flowchart would make most sense i f i t i s studied i n r e l a t i o n to the mathematical explanation. The macro flowchart needs l i t t l e a d d i t i o n a l c l a r i f i c a t i o n since i t i s a p i c t o r a l representation of the verbal d e s c r i p t i o n . In the same way, the micro flowchart i s an elaboration of the mathematical d e s c r i p t i o n . 32 1=1+1 Generate <— Subroutine INCOME(I) MONEY Set Constraints J = l Generate Bids —" \ passed Store Accept Data Update Time Cost Widen yes IDAY+1 no Rule • < < T Relax? Adjust Storage IDAY+1 passed Accept Data ->-Figure 5 Macro Flowchart of the Demand Model Storage Subroutine LIST Update tine,money cost Decay J=J+1 •^ JMAXX \TMAXX IDAY=IDAY+1 ilDYCRl Scope adj. PER=1. ItltJK K=l GAMMA Adjust empty Storage's^ K+K+l Find Best I Gener jte Find t fax. Some Results In t h i s section some i n i t i a l r e s u l t s are presented which demon-st r a t e the e f f e c t of er r o r - l e a r n i n g and decay upon the average search times and money costs of search. Throughout the t e s t i n g and experimentation with the model, average search times and money costs are used as i n d i c a t o r s of the costs of search. Comparative savings from alternate p o l i c i e s w i l l be used to evaluate the benefits from these p o l i c i e s . Also, the model r e s u l t s are presented as the r e s u l t of t r i a l s . Each t r i a l summarizes the search time and money costs for 1000 searchers, each d i f f e r e n t i a t e d only by the v a r i a b l e INCOME^. The words t r i a l and run are used interchangeably. F i n -a l l y , these t r i a l s represent d i f f e r e n t values i n the vacancy rate (VACANT), rates of scope adjustment or percentage of l i s t i n g s examined per day (PER^) and error adjustment (GAMMA). R e c a l l also that the subscript i r e f e r s to one p a r t i c u l a r searcher. The f i r s t set of experiments deal with evaluating the impact of d i f f e r e n t rates of error-learning upon search times and costs. For these runs i t i s assumed that there i s no p o s s i b i l i t y of storing various o f f e r s ; the searcher must accept an o f f e r when presented. Later t h i s condition w i l l be relaxes to simulate a l t e r n a t i v e market conditions. The following table (Table 2) presents the r e s u l t s of four t r i a l s which model the r e s u l t s of 1000 searchers. INUM i s an exo-genous v a r i a b l e ; 1000 i s generally used since with t h i s number of • runs a reasonable s t a t i s t i c a l sample can be generated upon which tests may be performed to gain an idea of the performance of a l t e r n a t i v e conditions and hypotheses. The rate of err o r - l e a r n i n g i s governed by the rate at which the ru l e of thumb i s relaxed; t h i s i s c o n t r o l l e d by the rate at which GAMMA i s incremented. Since storage i s suppressed i n these i n i t i a l t r i a l s , GAMMA i s incremented only as time runs out for the searcher; l a t e r r e s u l t s with storage a b i l i t y w i l l be even more s e n s i t i v e to erro r - l e a r n i n g . Aside from relaxing the r u l e of thumb the searcher also can vary search at the extensive margin; i n other words the searcher can choose to examine more vacancies per day. Table 2 i s a p a r t i a l view of what i s termed a response surface. Response surfaces have been applied to the simulation of physi c a l processes, e s p e c i a l l y simulations i n chemical engineering, and are only j u s t beginning to be applied to simulation studies i n the s o c i a l sciences."'""' The response surface can be depicted as a matrix which shows v a r i a t i o n s i n a key output v a r i a b l e for d i f f e r e n t values of input or exogenous v a r i a b l e s . In t h i s case the input v a r i a b l e s are the rate of error-le a r n i n g (GAMMA) and the rate of scope adjustment (PER). More complex response surfaces are presented i n the next chapter when they are used extensively i n the s e n s i t i v i t y analysis of the model. The r e s u l t s i n Table 2 are straightforward. As the response to search i s adjusted by changing the rates of error-le a r n i n g and scope adjustment, time and money costs vary i n a predictable manner. To 36 Table 2 Results of T r i a l s with No Storage INUM (number of searchers per t r i a l ) = 1000 Case One RULE; There i s no erro r - l e a r n i n g ( i . e . GAMMA i s not incremented i n the event of time running out, and the scope of search i s not responsive to time!) MARKET; There i s no storage a b i l i t y ( i . e . the market i s at the polar extreme 'tightness'.) Case Two RULE; GAMMA i s incremented by 1.5 each time the r u l e i s revised. The scope of search i s incremented by 1 l i s t i n g per day once the f i r s t time con-s t r a i n t i s exceeded.* MARKET; There i s no storage. Case Three RULE; GAMMA i s incremented by 2.0 each r e v i s i o n of the ru l e ; the scope of search i s as i n two. MARKET; As above. Case Four RULE; GAMMA is' incremented by 2.0 each r e v i s i o n and the scope of search i s incremented by 2.0 l i s t i n g s per day. MARKET; As above. * Note the scope of search increases u n t i l 100% of possible l i s t i n g s are examined. Case Average Search Times (days) Average Money Costs Average Surplus (BP(J) - CP(J)) 1 21.65 21.30 21.67 2 10.41 15.39 35.29 3 7.17 12.73 14.66 4 5.87 11.53 17.52 increase the rate of learning i s to reduce the average search time • and money cost; the same i s true when the number of l i s t i n g s per day are incremented. I n t e r e s t i n g l y , the surplus, or d i f f e r e n c e between bid and ask rents, seems to be unaffected by adaptive search pro-cedures. Undoubtedly t h i s i s due to the simple r e l a t i o n s that govern the s e t t i n g of time constraints and the creation of b i d rents. More sophisticated models where income and s o c i a l class were included e x p l i c i t l y would a l t e r t h i s . In addition, the i n a b i l i t y to store would a f f e c t the average surplus. Considering only the time aspect of search, i t i s possible to show the r e l a t i o n between learning and the average time of search. This i s shown i n Figure 7. R e c a l l that the r u l e of thumb adjustment r e f e r s to the minimum dif f e r e n c e between the b i d and ask rents that i s accepted by the searcher and i s governed by the v a r i a b l e GAMMA. Scope adjustment r e f e r s to the percentage of the maximum d a i l y l i s t i n g s that are a c t u a l l y examined by a searcher, where t h i s maximum i s given by the v a r i a b l e JMAXX, the actual number examined i s given by JMAX and the percentage examined or JMAX/JMAXX i s given by the v a r i a b l e PER. R e c a l l also that the time constraints ensure that scope adjustment preceeds r u l e adjustment and i s a necessary precondition to e r r o r - l e a r n i n g of the r u l e of thumb. An a l t e r n a t i v e way of measuring the response of the model i s to p l o t the frequency d i s t r i b u t i o n of search times for a l t e r n a t i v e learning hypotheses. This i s presented i n Figure 8 for the four cases presented i n Table 2. .2 .4 .6 1.0 ' 1.4 1.8 2.0 Rate at which GAMMA i s * rates of incrementation incremented i n the percentage of l i s t i n g s examined on any 0 5 " . 1 0 15 20 25 Time (days) Figure 8 Frequency D i s t r i b u t i o n of Search Time 39 Modelling A l t e r n a t i v e Market Conditions A l t e r n a t i v e market conditions are modelled by allowing the searcher to store p o t e n t i a l l y a t t r a c t i v e o f f e r s . A p o t e n t i a l l y a t t r a c t i v e o f f e r i s any o f f e r f or which the bid rent exceeds the ask rent. Every o f f e r which does not pass the decision r u l e for acceptance and which has a p o s i t i v e surplus i s placed i n a storage vector and p e r i o d i c a l l y examined when the r u l e of thumb i s relaxed. This storage vector decays at a rate l i n e a r l y r e l a t e d to the vacancy rate. For purposes of examining the r e l a t i o n between various performance i n d i -cators of the model and the vacancy rate, assume that the Case Four s i t u a t i o n of Table 2 holds. Table 3 presents the r e l a t i o n between the vacancy rate and the performance i n d i c a t o r s used previously i n Table 2. Each t r i a l uses a d i f f e r e n t vacancy rate and the number of searchers per t r i a l r e -mains 1000. The r e l a t i o n s h i p between the vacancy rate and the average surplus i s p o s i t i v e f o r two reasons. F i r s t , the searcher can more e a s i l y store o f f e r s at higher vacancy rates, and second, the r u l e of thumb i s adjusted f a s t e r at lower vacancy rates (in e f f e c t the model con-verges to a s o l u t i o n f a s t e r when the vacancy rate i s low). A model which incorporated longer-run supply e f f e c t s (supply of housing, not information) would have to also incorporate the e f f e c t s of housing shortages upon the surplus paid and the general rent l e v e l . Since t h i s i s only a model of the market for information, the surplus i s the appropriate concept. 40 Table 3 Al t e r n a t i v e Market Conditions with Storage Case Four RULE; GAMMA (rate of r u l e adjustment) i s incremented by 2.0 per r e v i s i o n ; scope of search i s incremented by 2.0 l i s t i n g s per day to a maximum value. MARKET; Represented by d i f f e r e n t l e v e l s of the va r i a b l e VACANT. Vacancy Rate Average Average Average (VACANT) Search Time Money Costs Surplus (days) 6.0 2.65 5.24 67.90 5.0 2.79 6.11 61.35 4.0 3.15 6.71 52.96 3.0 4.86 8.34 37.31 2.0 4.89 8.20 21.68 1.0 5,62 10.39 15.69 0.0* 6.01 10.78 16.37 * Note, t h i s i s an equivalent run to the previous case four. The r e l a t i o n between the vacancy rate and the d i s t r i b u t i o n of searchers can be graphed using the frequency d i s t r i b u t i o n of search times as the response i n d i c a t o r . This i s shown i n Figure 9. 20 Time(Days) Figure 9 Vacancy Rate and Search Time Problems of 'Oversearch' and 'Undersearch' Frequently one encounters the statement; " i f I knew then what I know now". This i s an example of undersearch. Other common examples are buying a commodity, then discovering that another place had the i d e n t i c a l item on sale f or h a l f the p r i c e . Oversearch, a more subtle problem for the consumer to discover, r e s u l t s from pr o c r a s t i n a t i o n . A dwelling may be removed from the market even though the searcher had considered the dwelling as a possible a l t e r n a t i v e . Jobs may be snapped up i n times of high unem-ployment and the searcher who dithers loses the opportunity. Both these aspects of search can be demonstrated within the con-text of t h i s model. Undersearch i s modelled by running each searcher, noting the point at which an o f f e r i s accepted (and the time and money costs associated with the acceptance) and then extending the model u n t i l IDAYMX i s exceeded. During t h i s extension the best a l t e r n a t i v e (the vacancy with the highest surplus) i s noted and compared with the vacancy that was i n t i a l l y accepted. This t r i a l f o r the model operating under Case Four assumptions Is presented i n Table 4 for various l e v e l s of vacancy rate. Table 4 The E f f e c t s of Undersearch Vacancy Rate (VACANT) ^ Difference i n I n i t i a l and Subsequent Best Surplus 6.0 -3.97 5.0 1.74 4.0 2.48 3.0 9.49 2.0 15.91 1.0 29.59 0.0 48.67 Oversearch can also be modelled. In t h i s case the best o f f e r that a searcher stores i n the storage vector i s retained and compared with the f i n a l o f f e r accepted. This best o f f e r can e a s i l y be removed by ti g h t markets and the searcher who tends to 'learn' about the market at a slower rate. Therefore two axes are needed to portray oversearch. Table 5 presents a matrix; the v e r t i c a l axes shows the vacancy rate as i n Table 4 while the h o r i z o n t a l axes shows the various l e v e l s of GAMMA incrementation governing the rate of rul e adjustment. The entries i n the matrix show differences between the f i n a l o f f e r accepted and the best o f f e r examined and stored by the s e a r c h e r . ^ Table 5 The E f f e c t s of Oversearch GAMMA Increments (decreasing dithering) VACANT i 6.0 36.21 32.73 29.45 24.67 23.19 17.20 5.0 42.91 41.16 40.11 37.75 31.62 29.11 4.0 49.61 41.62 40.21 36.49 36.48 31.01 3.0 57.32 56.21 55.31 50.28 45.31 31.48 2.0 60.28 59.57 56.69 50.10 46.13 37.37 1.0 67.39 62.11 56.73 52.49 46.99 39.72 The E f f e c t of Oversearch and Undersearch These simple experiments can hardly be regarded as conclusive, however they do i n d i c a t e an aspect of search theory that has h i t h e r t o been ignored by the l i t e r a t u r e . There are d i r e c t implications f o r the structure of industry and the extent -to which consumers search f o r p r i c e s . For example, p r i c e dispersion can lead to increased search. Consumers who encounter p r i c e v a r i a t i o n are l i k e l y to en-gage i n search while no p r i c e v a r i a t i o n i s l i k e l y to l i m i t search to infrequent, casual checks on a l t e r n a t i v e s . In s p a t i a l markets, of which housing must be considered a prime example, competition i s fostered by p r i c e v a r i a t i o n , where;, o l i g o p o l i s t s are l i k e l y to set common pr i c e s , i n part to avoid p r i c e wars amongst themselves, but also to l i m i t search and preserve t h e i r market shares. 45 Summary In t h i s chapter, several s i g n i f i c a n t modifications to the demand for information have been presented. F i r s t , e r r o r - l e a r n i n g was i n t r o -duced as a useful paradigm f o r the search process. Second, the searcher was assumed to store p o t e n t i a l l y a t t r a c t i v e o f f e r s . These o f f e r s were i n turn subject to decay. The rate of decay was a function of the vacancy rate and i n turn caused the rate of error-learning to be modified. This model only considers 'negative' e r r o r - l e a r n i n g . The p o s s i b i l i t y that rules of thumb might become more stringent i n the face of favourable, market evidence i s not considered. F i n a l l y , the phenomena of undersearch and oversearch were introduced. Simulation provided a convenient means for evaluating these aspects of h i t h e r t o unconsidered search behaviour. The most s e n s i t i v e aspect of t h i s model i s the r e l a t i o n between the vacancy rate and the average search times and money costs. The vacancy rate operates i n two ways. F i r s t , by governing the supply of information (number of l i s t i n g s ) and second, be governing the rate of decay on the storage vector. The next chapter examines the r e l a t i o n between the supply of information and the vacancy rate and presents a model of the supply of information. 46 FOOTNOTES - CHAPTER TWO 1. Once again t h i s survey i s not exhaustive since the l i t e r a t u r e r e l i e s upon common assumptions which are dropped i n the proposed model. 2. In addition to Rothschild (1974), A x e l l (1974) also incorporates er r o r - l e a r n i n g i n the theory of search, but within the context of a simulation model. These two works became known to the author only as the f i n a l manuscript was being prepared. In any event neither a r t i c l e attempts to deal with v a r i a t i o n i n the a b i l i t y of searchers to store o f f e r s , the problem of oversearch and under-search and the supply of information through brokers. 3. See Appendix One for proof. 4. See Appendix One for proof. 5. McCall (1970) does consider the p o s s i b i l i t y of v a r i a t i o n i n the storage a b i l i t y of searchers, but sets the problem aside due to an a l y t i c i n t r a c t i b i l i t y . 6. Telser (1973) uses simulation models to analyze the search f o r the lowest p r i c e , but once again he does not consider the types of problems which are of i n t e r e s t here. 7. Mortensen (1971) gives a good account of reservation wages i n r e l a t i o n to job search. 8. Cross (1973) has applied stochastic learning theory to economic theory i n general. 9. See Estes (1972) for a review of the l i t e r a t u r e on psychological learning theory. 10. Throughout the re s t of the paper the va r i a b l e s are presented i n the form they appear i n the computer code i n Appendix Two. 11. See Linder (1971) for a discussion of the r e l a t i o n s h i p s between time intensive a c t i v i t i e s such as search and r e a l income. 12. * i s from FORTRAN IV and denotes the action of m u l t i p l i c a t i o n . 13. See Figure Four for the form of t h i s function. 14. A bid p r i c e model of housing demand was constructed i n the author's Mast ers Thesis (Mason, 1972). In addition see Kihlstrom (1973) for an attempt to evaluate the demand for information on product q u a l i t y . In general the use of hedonic p r i c e indices and Lan-caster's consumer theory has met with l i m i t e d success. For a d e t a i l e d explanation of response surfaces see Naylor, e t . a l . (1971). Note that oversearch i s impossible with no decay i n the storage vector. CHAPTER THREE The Supply of Information In the previous chapter the supply of d a i l y information was modelled as a maximum number of vacancies that could be examined by a searcher. I t i s the purpose of t h i s chapter to disaggregate t h i s supply v a r i a b l e (JMAX) into i t s component parts, analyze the r e l a t i o n between the supply of information from various sources and general market forces ( i . e . the vacancy r a t e ) , and thereby construct a supply model of information. Rather than constructing a separate model of information supply, these elements are grafted onto the demand model through the disaggre-gation of the v a r i a b l e JMAX. This technique avoids the problem of constructing l i n k i n g models to unite demand and supply and thereby re-duces both computer time used i n the model and the time required to understand the action of the model. Several alternate suppliers of information are considered sequentially; they are analyzed using a a p r i o r i reasoning, or more substantive empirical measures where possible. F i n a l l y , these various elements are incorporated into the model. Rental Information Brokerage; An Overview There are four general sources of information that can be tapped by the searching tenant, which can, to varying degrees, be i s o l a t e d and e m p i r i c a l l y studied. F i r s t there i s what Hempel (1970) r e f e r s to as the casual i n f o r -mation source. This consists of fr i e n d s , p r o f e s s i o n a l colleagues and other acquaintances. In addition, s t r e e t a d vertising i s also included i n t h i s category."'" Second, there are dwellings managed by pro f e s s i o n a l property managers which consist l a r g e l y of r e a l estate companies. T y p i c a l l y these firms provide free information about the properties they manage. Third, and most importantly, there are c l a s s i f i e d adver-tisements i n major d a i l y newspapers. Fourth, there are r e n t a l i n f o r -mation agencies (RIAs). These firms are common to England, well established i n the United States and a recent phenomenon to Canada:.-Casual Search Data on t h i s aspect of housing search i s extremely d i f f i c u l t to obtain. Only wide-ranging studies of the a l l o c a t i o n of resources within the household could begin to reveal the nature of t h i s aspect of housing search. Some inroads into the nature of the process can be i n f e r r e d using studies completed by Hempel (1970) f o r the home ownership market i n Connecticut. These studies indicated that there i s a hierarchy of information a c q u i s i t i o n . A considerable proportion of searchers begin by f i r s t consulting casual sources, then a f t e r ' f e e l i n g out' the market, move on to more formal information sources such as newspapers and r e a l estate brokers. A s i g n i f i c a n t proportion, however, tend to by-pass the casual sources of information and proceed d i r e c t l y to 50 u t i l i z a t i o n of brokers. There tends to be a p o s i t i v e c o r r e l a t i o n between l e v e l of education, professional status and the elimination of casual information sources of market data. Hempel's studies do not investigate the extent to which casual search was the only source of information. In the home purchase process, where investment motives play an important r o l e , i t i s u n l i k e l y that many of the searchers could gain s u f f i c i e n t market knowledge without r e s o r t i n g to formal sources of information. In the r e n t a l housing market the amount of information required i s much smaller and casual sources, i f a v a i l a b l e , can often y i e l d u s eful information. At any rate, empirical v e r i f i c a -t i o n of the r e l a t i o n between market conditions and the amount of i n f o r -mation from casual sources i s extremely involved and beyond the scope of t h i s paper. Professional Property Managers Many firms o f f e r management services to landlords. These services include maintenance, rent c o l l e c t i n g and l o c a t i n g s u i t a b l e tenants. The number of firms s p e c i a l i z i n g i n t h i s form of brokerage v a r i e s widely from c i t y to c i t y . There seems to be great regional v a r i a t i o n i n the corporate structure of these firms. For example, i n Vancouver much of the property i s managed by r e a l estate firms, while i n Winnipeg and Montreal there are many firms which appear to s p e c i a l i z e i n the management of large apartments. These firms employ a v a r i e t y of information dissemination techniques to secure tenants. Aside from casual search ( e s p e c i a l l y signs i n front of the b u i l d i n g and c l a s s i f i e d ads, these firms appear to employ a system of waiting l i s t s whereby prospective tenants r e g i s -ter i n order to be considered p r i o r to general a d v e r t i s i n g . Of course, the firms are interested i n t h i s system since i t lowers t h e i r informa-t i o n costs and permits a c e r t a i n amount of con t r o l over the type of tenant. The major r e a l estate firms which advertise property management services were surveyed by telephone i n order to gain some notion of t h e i r quantitative impact on the supply of information i n the r e n t a l housing market. A l l firms were either reluctant to divulge information or could not take the time to provide data on the number of r e n t a l suites handled, the advertising devices employed or the revenues obtained from property management. Some crude concept of the number of suites handled by property management firms can be i n f e r r e d , however There are two large trade associations of apartment owners. F i r s t , there i s the Greater Vancouver Apartment Owners Association with approximately 6,000 members c o n t r o l l i n g some 40,000 suites and second, there i s the P a c i f i c Apartment Owners Association with approxi-mately 600 members and 20,000 suit e s . Property management firms t y p i -c a l l y belong to the second organization. Since there are approximately 100,000 r e n t a l suites i n the Vancouver area, property managers (large ones who manage i n excess of twenty suites) who tend to use waiting l i s t s account for 20% of the supply. However t h i s overstates the influence of waiting l i s t s as a source of information for two reasons. F i r s t , only the very large management firms would f i n d i t v i a b l e to employ a waiting l i s t . Smaller firms would undoubtedly employ casual search techniques such as placing a sign i n the front of the 52 b u i l d i n g . In recent public hearings the president of the Greater Vancouver Apartment Owners Association stated that casual search and 2 c l a s s i f i e d ads were the predominant form of adv e r t i s i n g . Second, i t i s apparent that the usefulness of waiting l i s t s depends on market conditions. At low vacancy rates they are highly favoured by landlords since advertising costs are low and the deluge of i n q u i r i e s that tends to occur with excess demand is'.avoided." . At higher vacancy rates more aggressive marketing i s required. The lack of empirical data (since even firms do not keep t h i s information) precludes any t e s t s of these hypotheses. There appears to be no f e a s i b l e empirical measure of the r e l a t i o n s h i p between the vacancy rate and the use of casual and property management source of information. There are two choices i n regard to simulation. F i r s t , some assumptions can be made about the d i r e c t i o n and form of the r e l a t i o n s h i p between the vacancy rate; and the number of vacancies that are obtained from casual search and waiting l i s t s . I t would then be possible to write some l i n e a r r e l a t i o n s h i p s into the simula-t i o n model to generate values' of JMAXX which would then be used as 3 part of the supply of l i s t i n g a v a i l a b l e to the searcher. Using some assumed cost and time functions i t would then be possible to generate values of money and time costs spent i n acquiring informa-t i o n from these sources. The second procedure i s to ignore t h i s aspect of search and concentrate upon the other dimensions of r e n t a l housing search ( c l a s s i f i e d ads and r e n t a l information agencies) which can be more r e a d i l y quantified. This second course i s taken, the j u s t i f i c a t i o n being that a p a r t i a l model, e m p i r i c a l l y v e r i f i e d (using s t a t i s t i c a l t e s t s ) , has more v a l i d i t y than a complete model which i s only par-t i a l l y v e r i f i e d . Of course t h i s means that important aspects of search are omitted, and t h i s w i l l surely temper the r e s u l t s of the model. C l a s s i f i e d Advertisements At vacancy rates of 2-3%, c l a s s i f i e d advertisements are the most important source of information f o r the r e n t a l housing market. Casual empiricism suggests that for vacancy rates i n excess of 3% casual search techniques a d v e r t i s i n g become important, while the analysis to be described l a t e r indicates that- for vacancy rates below 2%, the r e n t a l information agency becomes an important supplier of information. Low vacancy rates have characterized the housing market i n both North America and Europe and show l i t t l e i n c l i n a t i o n to r i s e . For t h i s reason both the empirical analysis and t h e o r e t i -c a l models concentrate upon t h i s ' t i g h t ' market s i t u a t i o n . In order to judge the r o l e of c l a s s i f i e d s i n providing i n f o r -mation some proxy f o r information as a quantity i s needed. This 4 point was examined i n an e a r l i e r chapter. Information has been modelled i n the previous chapter as a p a r t i c u l a r bid-ask p r i c e com-bination. The vast majority of information a c q u i s i t i o n models take t h i s undimensional view of information; searching f o r the lowest p r i c e i s considered to be the objective of the buyer. C l a s s i f i e d s obviously contain more information than p r i c e alone. Quality aspects are also included, such as distance from various urban f a c i l i t i e s , number of bedrooms, etc. There appears to be no successful method for including t h i s aspect of information into the analysis. A proxy v a r i a b l e that comes the clos e s t i s the number of column inches weighted by the number of ads. As t h i s r a t i o r i s e s i t could be argued that the informational content of the advertisement i s i n -creasing. Unfortunately i t i s apparent that the measure i s subject to bias. Advertising and persuasion play an important r o l e i n the length of the advertisement. In addition, the same landlord saves by l i s t i n g several properties i n the same space normally occupied by one ad. Even so, i t i s possible to use t h i s type of data to obtain some reasonably s i g n i f i c a n t r e l a t i o n s h i p s between the vacancy rate and information i n r e n t a l housing. Table 6 presents column inches and t o t a l ads for r e n t a l housing that appeared i n the Vancouver Sun from June 1971 to June 1974. June and December were chosen since these are the months for which the Central Mortgage and Housing Corporation publish vacancy rates. C l a s s i f i e d Ad Table 6 Information By Month Month Column Inches 1 To t a l Ads 2 Column Inches To t a l Ads Vacancy Rates June 1971 12047 24633 .489 4.1 Dec. 1971 9226 15354 .601 2.8 June 1972 11206 22564 .497 2.4 Dec. 1972 6272 12312 .509 .6 June 1973 11767 17424 .676 1.0 Dec. 1973 8541 9526 .896 .4 June 1974 9657 10557 .915 .2 There appears to be a straightforward r e l a t i o n s h i p between the decline i n column inches and t o t a l ads placed and the vacancy rates. Not so understandable i s the inverse r e l a t i o n between vacancy rates and the r a t i o of column inches to t o t a l advertisements. When r e n t a l informa-t i o n agencies are analyzed, a p l a u s i b l e explanation i s provided i n that these firms tend to achieve economies of space by placing many vacancies within one advertisement. As w i l l be shown, the propor-t i o n of t o t a l r e n t a l housing ads purchased by these agencies has sharply r i s e n i n the recent past. Using time ser i e s analysis these r e l a t i o n s h i p s may be more formally analyzed. The general trend i s cl e a r , however, more p r e c i -sion i s required since the regression parameters w i l l be used i n the simulation study. Since t o t a l ads and column inches are obviously correlated, (see Table 7) only one can be used as the dependent v a r i a b l e . T o t a l ads was chosen since i t corresponds more c l o s e l y to the l i m i t e d conception of information used i n the model and also r e s u l t s i n better s p e c i f i c a t i o n . Table 7 Corr e l a t i o n Matrix for Column Inches, T o t a l Ads and Vacancy Rates Column Inches To t a l Ads Vacancy Rate Column Inches (COLINC) 1.000 .7462 (s = .027) .5846 (s = .007) Tota l Ads (TOTADS) .7462 (s = .027)* 1.000 Vacancy Rate (VACRAT) .8546 (s = .007) .5559 (s = .098) 1.000 * Figures i n bracket i n d i c a t e l e v e l of s i g n i f i c a n c e .5559 (s = .098) Regression analysis r e s u l t s i n the following set of equations; COLINC = 8546.81 + 772.90 (VACRAT) R 2 = .30908 (15) (2.237) TOTADS = 10491.89 + 3384.94 (VACRAT) R 2 = .73026 (16) (13.536)* * S i g n i f i c a n t at .01 l e v e l Aside from v a r i a t i o n i n the t o t a l number of ads that r e s u l t s from f l u c t u a t i o n s i n the vacancy rate (hardly a s u r p r i s i n g f i n d i n g ) , c l a s s i f i e d s exhibit a pronounced d a i l y cycle that has a marked e f f e c t on search behaviour. Examples of t h i s v a r i a t i o n are shown i n Figure 10. Apparently Mondays are the low point i n the supply of c l a s s i f i e d s while Saturdays are the high point. I t i s d i f f i c u l t to know a p r i o r i whether landlords are second-guessing searchers and placing ads when they believe searcher w i l l be most responsive, or whether landlords are attempting to c o n t r o l the responses of searchers. In p a r t i c u l a r , t h i s second l i n e of reasoning would argue that i n times of low vacancy rates landlords would r e s t r i c t t h e i r a dvertising e f f o r t simply to reduce the amount of time spent i n dealing with searchers once the dwelling has been rented. There i s evidence that some landlords have received up to 300 a p p l i c a t i o n s for one s u i t e i n Vancouver. A test of t h i s would be to measure the v a r i a t i o n i n d a i l y ads and examine the r e l a t i o n s h i p betweeen t h i s v a r i a t i o n and the vacancy rate. If there i s a p o s i t i v e c o r r e l a t i o n ( i . e . , i f the v a r i a t i o n grows as the vacancy rate grows) the hypothesis i s rejected, otherwise i t remains p l a u s i b l e to argue that searchers respond to v a r i a t i o n i n the supply of c l a s s i f i e d s , rather than landlords are catering to the schedules of searchers. Undoubtedly a pronounced inverse r e l a t i o n s h i p would indi c a t e that i n times of t i g h t markets searchers are faced with 57 0 Figure 10 Supply of C l a s s i f i e d Information Days of the month 58 highly v a r i a b l e supplies of information and must adjust to t h i s . Two measures of v a r i a t i o n were computed. F i r s t absolute v7 v a r i a t i o n (ABSVAR) i s calculated according to the formula, Max - Min — ^ a d7) Min m where Max and Min are the greatest and l e a s t number of d a i l y m m column inches that appear i n the month i . The average v a r i a t i o n . (AVGVAR) i s computed according to the formula, E Max /p - Z Min /n p=l k n=l 1 (18) E Min In n=l where k i s the values of the peaks, p the number of peaks, 1 the value of the troughs and n the number of troughs during a given month.^ Both these measures y i e l d a serie s of s i x numbers that range between 0 and 1 (zero i n d i c a t i n g no v a r i a t i o n , 1 i n d i c a t i n g extreme v a r i a t i o n ) . These s e r i e s were regressed against the vacancy rate i n a test of the hypothesis that the degree of v a r i a t i o n increased as the vacancy rate declined. The r e s u l t s f o r both measures appear as follows. ABSVAR = .53121 - .06421 (VACRAT) R 2 = .53401 (19) (5.730) 1558 (VAX (2.81388)* AVGVAR = .46274 - .03 8 (VACRAT) R 2 = .36011 (20) * F r a t i o s From these r e s u l t s i t appears that the hypothesis has been supported, although the r e l a t i o n i s neither pronounced, nor the s t a t i s t i c a l tests 59 t e r r i b l y conclusive. However, coupled with i n t u i t i o n , i t can be argued that tenants are passive i n the p r o v i s i o n of information and landlords place ads to optimise the flow of tenants. This may appear to be picayune however, as i f the use of e r r o r - l e a r n i n g i s to be continued, the searcher as a passive responder to the environment must be demonstrated. If the flow of information was i n turn affected by searcher behaviour, the i n t e r a c t i o n s of the model would quickly become unmanageable. Modelling the Supply of Rental Information From the C l a s s i f i e d s The supply of r e n t a l housing information i s e a s i l y integrated into the basic demand model. A step function i s used to simulate both the v a r i a t i o n i n d a i l y l i s t i n g s and the average number of l i s t i n g s . In other words the l e v e l of the step function i s made a function of the vacancy rate. For the moment the exact l e v e l i s a r b i t r a r y ; however, i n the next section when r e n t a l information agencies are considered i n d e t a i l , a more e x p l i c i t formulation w i l l be provided. The step function i s coded as a ser i e s of FORTRAN statements that appear i n the subroutine CYCLE (see appendix 2); a representa-t i v e step function appears i n fi g u r e 11 below. 60 15 Day(IDAY) 30 Figure.11 Values of JMAX Some Results To avoid a plethora of output at the end of the chapter i t i s now us e f u l to present some r e s u l t s that demonstrate the e f f e c t of varying the supply of information on search times and costs. One i n t e r e s t i n g phenomenon of h e u r i s t i c models that employ error-l e a r n i n g i s the phenomenon of 'tracking'. The output of the model w i l l begin to mimic the environment as the rate of learning increases; t h i s i s c l o s e l y r e l a t e d to the point made by Day (1967) that rules of thumb and erro r - l e a r n i n g w i l l lead to a convergence of s a t i s f y i n g behaviour to marginal behaviour. The behaviour of the simulated e r r o r - l e a r n i n g searcher w i l l converge to the behaviour of a marginal r u l e using searcher. The step function of Figure 11 i s used to repeat the t r i a l s of the previous chapter which examined the e f f e c t s of alternate e r r o r -learning rules on search. In Table 8 the top figures are repeated from Table 2. Table 8 E f f e c t s of V a r i a t i o n i n JMAXX on Search Costs: g No Storage Case Average Average Average jSearch Times Money Costs Surplus (Days) 1 21.65 21.30 21.67 28.07 38.22 25.49 2 10.41 15.39 35.29 19.35 25.41 24.61 3 7.17 12.73 14.66 12.47 16.29 14.09 4 5.87 11.53 17.52 9.45 14.31 26.47 The v a r i a t i o n i n the d a i l y l i s t i n g produced from the subroutine CYCLE has affected that average search times and costs. Of course a l t e r i n g the step function so that the minimum value of l i s t i n g s per day was very high would produce completely d i f f e r e n t r e s u l t s . In t h i s respect the r e s u l t s produced by t h i s p a r t i a l model are not s t r i c t l y comparable with the r e s u l t s produced i n the previous chapter. If the a b i l i t y to store o f f e r s i s now 'turned on' and the same 62 step function i s employed to produce v a r i a t i o n i n the d a i l y l i s t i n g s , i t i s possible to analyze the phenomenon of tracking. R e c a l l that the a b i l i t y to store o f f e r s was d i r e c t l y r e l a t e d to the vacancy rate. Figure 12 shows the frequency d i s t r i b u t i o n f o r case 4 (high rates of error adjustment, both i n scope of search and r u l e adjustment) fo r the s i t u a t i o n storage and no storage. Note that the a b i l i t y to store (assuming a vacancy rate of 3.0%) smoothes the f l u c t u a t i o n s i n the number of searchers located for any given day. 10 20 Days 30 Figure 12 Search Times and Storage 63 The e f f e c t s of storage on the 'smoothness' of the frequency d i s t r i b u t i o n can be seen i n Figure 13 where case 4 and case 1 (fast c and slow error-learning) are compared f or a vacancy rate of 3.0%. Of course varying the vacancy rate a f f e c t s storage and as a r e s u l t the degree to which search behaviour w i l l mimic or track the supply of l i s t i n g s . Figure 13 Error Learning Rate and Search Time The basic outlines of the p a r t i a l market model of information are now c l e a r . V a r i a t i o n i n the supply of information a f f e c t s the time and money costs of search considerably. The rate of er r o r -learning i s d i r e c t l y r e l a t e d to these time and money costs with higher rate of e r r o r - l e a r n i n g being associated with lower l e v e l s of search costs. Rental Information Agencies Rental information agencies are a recent phenomenon to the Vancouver area, however, they have been incorporated i n North America 9 and England f o r at l e a s t a decade. These firms operate as pure information brokers while the other sources of information ( c l a s s i -f i e d and property managers) o f f e r t h e i r information j o i n t l y with other services, which tends to obscure the marketing of information. By providing a free a dvertising service to buyers or s e l l e r s , these r e n t a l information agencies (RIAs) assemble a l i s t which i s offered, for a front-end fee, to the opposite side of the market. During times of excess demand, s e l l e r s are organized and the l i s t of vacancies sold to tenants; during times of excess supply, tenants are organized and a l i s t of tenants sold to landlords. It seems reasonable to suppose that there i s some 'grey' area of market condition (perhaps vacancy rates between 2-6 percent) where neither side could be p r o f i t a b l y organized. Recently r e n t a l housing markets i n North America have been characterized by excess demand (low vacancy rates) and RIAs have entered, offered free a dvertising to landlords or i n some other way obtained a l i s t of vacancies, and sold the r i g h t to examine t h i s l i s t to tenants. The r i g h t to examine the l i s t l a s t s f o r a year and costs approximately $25-$35. The RIA does not permit the removal of the l i s t and l i m i t s the time spent i n examination. P o l i c i n g costs are r e l a t i v e l y high since information tends to have very low transactions costs. With a free advertising s e r v i c e , landlords face l i t t l e constraint i n s p e cifying the a t t r i b u t e s of the desired tenant or the a t t r i b u t e s of the dwelling i n some d e t a i l . There i s some evidence to suggest that private information agencies aid i n the process of f a c i a l , sexual and ethnic d i s c r i m i n a t i o n , however I found no evidence to support t h i s . Searchers become aware of the existence of the RIAs either through word of mouth or through the c l a s s i f i e d ads. Most of the RIAs placed ads (known as 'teasers') i n the c l a s s i f i e d ads which ou t l i n e the general a t t r i b u t e s of properties on the l i s t and then i n v i t e the searcher to come to the c e n t r a l o f f i c e where the complete information on the property i s a v a i l a b l e (for the front-end f e e ) . Teasers never supply enough information that the searcher can contact the landlord without paying for a d d i t i o n a l information possessed by the RIA. The front-end fee i s s l i g h t i n comparison to brokerage charges imposed on home buyers, however there are two points to emphasize. F i r s t , the aggregate transfer from tenant to RIA i s considerable (as i s the aggregate transfer from home buyer to r e a l estate broker). A recent study for the Consumer A f f a i r s Department of the c i t y of Seattle estimated that $300,000 had been paid to RIAs i n that c i t y during 1973. A s i m i l a r estimation made by the S o c i a l Services Com-mittee of the c i t y of Vancouver estimated the aggregate transfer as $800,000 for the same year. Second, the transactions charge borne by homeowners are simultaneously a consumption and investment cost. Well spent, they enhance not only current consumption but future investment gains. In the r e n t a l housing market, brokerage charges, even i f they are well spent, only enhance the current and future consumption l e v e l s . Rent and search costs can never be recaptured i n future land and b u i l d i n g values by tenants. At issue i n recent p o l i t i c a l debates has been the actual c o n t r i -bution made by these firms to the economic welfare of tenants. Various consumer a c t i v i s t groups have alleged that the information provided by these firms tends to be wrong, duplicated by other firms, and has diverted r e n t a l housing information from low cost c l a s s i f i e d s to these higher cost p r i v a t e information agencies. Since the q u a l i t y of i n f o r -mation cannot be inspected p r i o r to i t s consumption by the searcher (since t h i s would leave the RIA with nothing to s e l l ) , i t has been alleged that tenants can be trapped into paying the front end fee out of desperation ( i n markets with very low vacancy rates) and end up getting nothing for t h i s money. Since the front-end fees are not scaled i n accordance with incomes i t i s argued that t h i s bears heavily on low income tenants. These a l l e g a t i o n s are quite d i f f i c u l t to t e s t . Naturally these firms are extremely circumspect about releasing information on t h e i r current l i s t i n g s so the a l l e g a t i o n of d u p l i c a t i o n cannot be evaluated. S i m i l a r l y the charge that they often l i s t vacancies which have been f i l l e d i s extremely d i f f i c u l t to treat since that would require the inve s t i g a t o r to have complete market knowledge and the complete l i s t s provided by these firms. The a l l e g a t i o n that l i s t i n g s have been diverted from c l a s s i f i e d s to RIAs can be tested by using the teasers as a measure of RIA a c t i v i t y . Cross-section analysis i s a convenient way of t e s t i n g the r e -la t i o n s h i p between the vacancy rate and the l e v e l of RIA a c t i v i t y . Table 9 presents data which indicates that there tends to be an inverse r e l a t i o n between the vacancy rate and the l e v e l of RIA a c t i v i t y . Table 9 Information i n C l a s s i f i e d s By Cit y C i t y Montreal Toronto Winnipeg Calgary Edmonton Vancouver Vacancy Rate (Dec. 1973) 2.0 1.5 3.5 7.9 5.3 .4 Level of RIA a c t i v i t y * ADACT .17 .25 .05 .10 .12 .40 * Column inches of ads placed by RIAs divided by t o t a l column inches of r e n t a l housing advertising (monthly averages f o r the largest evening newspaper) Regressing a d v e r t i s i n g a c t i v i t y on the vacancy rate r e s u l t s i n the following r e l a t i o n , ADACT = .29479 = .03295 (VACRAT) R 2 = .51971 (21) It i s probable that the usage of RIAs i s affected by the population of an area and the average incomes. C e r t a i n l y small v i l l a g e s with very low vacancy rates are u n l i k e l y to induce any one to enter into i n f o r -mation brokerage. Also, as average incomes r i s e , the Linder Theorem (Linder, 1971) suggests that time intensive a c t i v i t i e s are dropped from consumption. In other words, brokers who o f f e r saving i n search time are u t i l i z e d to a greater extent. Introducing these v a r i a b l e s into the regression improves the s p e c i f i c a t i o n somewhat. ADACT = .38956 - .03112 (VACRAT) + 10.3452 (POP) (4.226)* (5.385)* + .06831 (INCOME) (2.035) * S i g n i f i c a n t at .05 l e v e l R* .63963 (22) Before these r e s u l t s can be used i n the simulation models more det a i l e d analysis of information brokerage i s necessary. In p a r t i -cular the 'Linder' e f f e c t i s open to considerable question. The d i v e r s i o n of information from low cost c l a s s i f i e d s to higher cost RIAs can be seen from the following table. The time ser i e s was computed only for Vancouver since . i t was d i f f i c u l t to obtain complete data for other c i t i e s (since the l i b r a r y did not have a complete c o l l e c t i o n ) . This information i s presented i n graphical form i n Figure 14. Table 10 Month June 1970 Dec. 1970 June 1971 Dec. 1971 June 1972 Dec. 1972 June 1973 Dec. 1973 June 1974 * Rentex enters the market Vacancy Rate 3.1 2.3 4.1 2.8 2.4 .6 1.0 .4 .2 Percent of C l a s s i f i e d s Space Purchased by RIAs 0 0 0 1 5* 11 20 26 31 50 Dec. Dec. Dec. Dec. 1970 1971 1972 1973 Figure 14 Vacancy Rates and RIA A c t i v i t y Simulating the Rental Information Agency One method of simulating the RIA i s simply to use the regression equations i n the previous section to generate the l i s t s from RIAs that can be expected at various l e v e l s of vacancy rate. The course followed i s more ambitious and re s t s upon making some assumptions that are not v e r i f i e d . The r e s u l t i s a model which i s more robust and captures some features of information brokerage that are not normally mentioned. The procedure used i s c l o s e l y r e l a t e d to models of the firm constructed by Baumol and Quandt (1974), Cyert and March (1963) and Day, Morley and Smith (1974). Combining these simple simulation models of the firm with some i n s i g h t s into nature of information brokerage permits the modelling of entry and e x i s t mechanisms for RIAs. In t h i s way the e f f e c t of various regulatory procedures can be more f u l l y explored. A Simple Theory of Information,.Brokerage Brokers derived t h e i r revenue from both sides of the market. Both buyers and s e l l e r s consume brokerage services, and the extent of the transactions charge borne by a buyer or a s e l l e r i s a function of the r e l a t i v e e l a s t i c i t i e s of demand for the actual commodity. Informa-t i o n i s an unusual commodity and requires a p e c u l i a r environment to support i t s sale. F i r s t , information requires s t r i c t c o n t r o l . In many ways i t i s a public good which can exhibit very low marginal costs of production, making i t hard to exclude free r i d e r s . Patent and copyright laws are evidence of c o n t r o l l i n g f or free r i d e r s . For these reasons firms s p e c i a l i z i n g i n the sale of information can be required to bear p o l i -cing costs to c o n t r o l the sale and r e s a l e of t h e i r commodity. Second, because of the requirement of p o l i c i n g , information i s very hard to evaluate p r i o r to consumption. Of course t h i s d i f f i c u l t y i n evaluation i s not j u s t because of the p o l i c i n g . Some information, such as the s p e c i f i c a t i o n s of stereo, equipment, requires a c e r t a i n l e v e l of t e c h n i c a l competence. These aspects of information brokerage can imply that consumers of a product or service often have to deal with two or more l e v e l s of 70 71 uncertainty. F i r s t there i s uncertainty about the q u a l i t y of informa-t i o n provided by the market intermediary and second there i s the un-ce r t a i n t y about the commodity to be consumed. Imperfect information about brokerage can e a s i l y compound the imperfection that may e x i s t i n the market without these brokerage services. Generally, brokers function to reduce these transactions costs and un c e r t a i n t i e s , but i t i s easy to devise a simple model to the contrary. This model i s based upon some work by Balderston (1957). Assume that there are ( i = 1, 2, ,n) s e l l e r s and (j = 1,2 ,m) buyers as indicated by n m Assume also that each buyer sends a message to each s e l l e r and v i c e versa. This implies that there are a t o t a l of mn messages per period. If the cost per message i s 'a' then the t o t a l costs of information i s given by, TC = 2amn. Average costs are 2amn/mn. Brokers enter and p o s i t i o n themselves between buyers and s e l l e r s i f they can reduce the message costs f o r either buyers or s e l l e r s . Obviously, a l l they have to do i s p r i c e message costs l e s s than 'a' per message; assuming that there i s perfect information on brokerage services, every buyer and s e l l e r w i l l now send one message to the broker instead of many messages to the other side of the market. This s i t u a t i o n could appear as follows; Assume that only one broker has entered. If broker's message costs are 'b' per message i t can be seen that the t o t a l costs of messages i n t h i s system are given by TC = (a+b) (m+n) and the average costs are AC = (a+b). The average message costs with a monopoly broker are considerably l e s s than the previous average costs without a broker. If a second broker enters the market and assuming that each has i d e n t i c a l p r i c e s j t h e n each w i l l share the market. T o t a l costs are now TC = (a+b) (m+n) + (a+b)/2(m+n) with average costs given by AC = <, 3(a+b)Ii. These r e s u l t s depend upon the assumption that some buyers and some s e l l e r s w i l l patronize the wrong broker and f a i l to make con-tact with the appropriate member of the opposite side. In t h i s case information costs must be incurred again with the other broker. In general, with the assumption that the market i s exactly shared, and that a c e r t a i n percentage of buyers and s e l l e r s w i l l have to r e -peat message transmissions (in some cases many times) i n order to contact the appropriate opposite party, i t can be shown that the aver-age costs of search w i l l be, N + l(a+b) ; N odd AC = , (23) 2(N+1)(a+b)/N ; N even where N i s the number of brokers. (See appendix 1). 12 Of course t h i s i s an extremely simple model. I t i s reasonable to expect that brokers have cost functions and that the theory of the fi r m w i l l apply. The point of the exercise i s to underline the notion of imperfection i n the brokerage market and to i n d i c a t e that the average cost of message transmission increases as the number of brokers increases; t h i s may be a case where monopoly rather than perfect competition i s the appropriate structure of industry. The Structure of the Simulation Model of RIAs Several basic assumptions are made. F i r s t , searchers are assumed to choose randomly from the brokers. Of course, i n theory, a d v e r t i s i n g e f f o r t , competitive p r i c i n g and other factors are l i k e l y to be impor-tant, however incorporation of these aspects i s beyond the scope of t h i s paper. Second, the vacancy rate i s d i r e c t l y r e l a t e d to the s h i f t i n g of brokerage fees. At low vacancy rates most of the fee i s s h i f t e d to tenants ( f u l l s h i f t i n g below 1.5%) and at higher vacancy rates the 13 fee i s s h i f t e d to landlords. Third, i t i s assumed that the cost structure of each RIA i s i d e n t i c a l , as are the revenue curves. A c t u a l l y , measuring cost functions i s extremely d i f f i c u l t ; t h i s problem i s compounded by the fa c t that information brokerage must, by nature, be a rather s e c r e t i v e operation. By using standard 'u' shaped cost curves and downward sloping demand r e l a t i o n s a crude mechanism for entry and e x i t i s pos-s i b l e . th Fourth, i t i s assumed that the i searcher w i l l consult a broker under several conditions. F i r s t , a money cost constraint i s set up. If the d i f f e r e n c e between t h i s maximum value (1% of income) and the present search cost i s greater than the brokerage charges s h i f t e d to tenants, then the r u l e of thumb has been adjusted more than f i v e times a broker i s consulted. F i n a l l y , i f the time spent i n search i s greater than 20 days a broker i s consulted. Given these conditions a searcher w i l l pay for the a d d i t i o n a l information possessed by a broker. This sequence i s somewhat a r b i t r a r y , but i t i s the only way that a simulation can be accomplished. Once again i n t u i t i o n would suggest that searchers do i n f a c t u t i l i z e lower cost forms of informa-t i o n f i r s t and then more c o s t l y information i n the event of f a i l u r e . F i n a l l y , i t i s assumed that brokers are of equal s i z e ; each supplies the same amount of information and services an equal number of searchers and landlords. Once the d e c i s i o n to consult a broker has been made, the f i r s t step i n the model i s to increment the costs of search by the amount of the brokerage fee according to the formula, COST. ,, = COST. + FIXED1 (24) i t+1 i t where FIXED1 i s the brokerage charge passed on to the tenant, and COST^. i s the present money costs accumulated by search i at time t. The model calc u l a t e s two brokerage charges according to the formulas, FIXED1 = BETAl*VACANT_ (25a) FEXED2 = BETA2*VACANT (25b) where for vacancy rates i n excess of 5%, FIXED1 i s set to zero and f o r rates below 1.5%, FIXED2 i s set to zero. It i s important to devise a mechanism for separating the various sources of information. This i s accomplished by the following set of formulas, LISBRO k t = (ALPHA3/VACANT ) / k (26a) JMAXX,. = f (VACANT,.) (26b) TOTLIS^ = (LISBRO*k) + JMAXXfc (26c) t h where LISBRO i s the l i s t i n g s c a r r i e d by the k firm, JMAXX i s the K. r e s u l t from the step function and TOTLIS i s the sum of the d a i l y l i s t i n g s from both sources. TOTLIS w i l l vary and exhibit the c y c l i c a l tendencies of JMAXX, however these w i l l be attenuated by the e f f e c t s of LISBRO. The supply of l i s t i n g s from brokerage does not exhibit as extreme a v a r i a t i o n as the supply of information from c l a s s i f i e d ads. From regression equations 16 and 21, JMAXX i s the average d a i l y l i s t i n g s from c l a s s i f i e d s and LISBRO i s the number of l i s t i n g s handled by RIAs which i s always constrained to be less than or equal to TOTLIS. The r e l a t i o n between TOTLIS, JMAXX, LISBRO and the vacancy rate i s shown i n 14 Figure 15. 0. 3.0 6.0 Vacancy Rate Figure 15 Vacancy Rate and Li s t i n g ' P e r Day by Source 76 The f i n a l step i n simulating the r e n t a l information agencies i s the assumption that landlords only l i s t with one information source. Thus a landlord chooses to l i s t only with the c l a s s i f i e d s or a r e n t a l information agency. Furthermore the landlord w i l l only choose one agency. This i s of course quite r e s t r i c t i v e , however t h i s assumption w i l l be relaxed shortly. In addition searchers consult only one r e n t a l information agent. Once these input values have been calculated, the model i s run for one period. This permits the summation of the number of searchers who are going to use brokers; i t permits the c a l c u -l a t i o n of the s h i f t i n g of charges and the c a l c u l a t i o n of the number of landlords who are l i s t i n g with brokers. A f t e r a l l searchers have been s e t t l e d the monthly clock (m) i s incremented and the equilibrium number of brokers i s c a l c u l a t e d , for the next period. The c a l c u l a t i o n of the number of brokers i s accomplished simply. The revenues are computed according to the equation, REVENU (k) = ALIST (k)*FIXEDl + BLIST (k)*FIXED2 (27) where REVENUE(k) i s the revenue of the k firm, ALIST(k);' i s the percentage of searchers that use that firm, BLIST(k)^the percentage of landlords that use the f i r m and FIXED1 and FIXED2 the respective brokerage charges.^ The c a l c u l a t i o n of the equilibrium number of firms i s performed i n a stepwise manner. F i r s t , the revenue i s calculated as i f there were only one firm. This revenue i s compared with a cost function given by CC"? CCL COST(k) = A + CCl(ALIST(k)) + CC3(BLIST(k)) (28) where CCL-4 are parameters of the cost function. If a p o s i t i v e p r o f i t i s obtained and as long as the l e v e l of p r o f i t exceeds ten percent, the revenue function and the cost functions are r e - c a l c u l a t e d , but ALIST(k), and BLIST(k) are adjusted to r e f l e c t the assumption that searchers and landlords are i n d i f f e r e n t about whom they patronize and landlords only l i s t with one agency (when vacancy rates are low). Therefore when the number of firms increases to 2 the values of ALIST and BLIST are halved. This procedure i s followed u n t i l the number of firms that can be supported by the market i s calculated. The various parameters i n the revenue and cost function are calcu-lated using s e n s i t i v i t y analysis which i s explained shortly. Once the equilibrium number of r e n t a l information agencies has been established the model returns to the second month and a new batch of searchers. Each time these searchers consult a broker they obtain exactly LISBRO/k l i s t i n g s from which to attempt to s e l e c t a s u i t a b l e dwelling. The r u l e s for accepting t h i s dwelling are p r e c i s e l y those which are formulated i n the previous chapter. S e n s i t i v i t y Analysis Some of the parameters i n the brokerage sub-model and the c l a s s i f i e d s sub-model are not supported by empirical evidence. Other elements i n the basic demand model are also e m p i r i c a l l y un-supported. If a l l parameters were required to be v e r i f i e d with stringent confidence i n t e r v a l s , then i t i s safe to argue that no simulation models would ever be constructed. In many studies, these parameters are submerged and the authors appear to hope that no one w i l l notice that they have been slipped i n through the back door. The better models incorporate extensive s e n s i t i v i t y a n a l y s i s of the empi r i c a l l y u n v e r i f i e d parameters (and even the parameters for which the s t a t i s t i c a l evidence i s strong). The next section b r i e f l y o u tlines some simple s e n s i t i v i t y tests and presents some of the r e s u l t s . A complete s e n s i t i v i t y analysis would e a s i l y double the length of the thesis.^ S e n s i t i v i t y analyses are conceptually very simple. The model i s run for d i f f e r e n t values of the parameters, a response i n d i c a t o r or i n d i c a t o r s are chosen and the r e s u l t i n g output i s analysed for evidence of changes that appear to make l i t t l e sense. Very sophis-t i c a t e d tests have been devised, such as analysis of variance and factor analysis i n several dimensions, to test f o r p e r v e r s i t i e s i n the r e l a t i o n s h i p between changes i n a parameter and the r e s u l t i n g change i n the response i n d i c a t o r . For the present essay only simple examination of the output i s required since the model i s not espe-c i a l l y complex. An example of a t y p i c a l s e n s i t i v i t y 'run' i s presented i n Table 11. The two constraints or parameters to be evaluated are the time constraints that govern basic e r r o r - l e a r n i n g . R e c a l l that IDYCR1 was set to 10 days a f t e r which searchers would widen the scope of search, while IDYCR2 governed the point at which e r r o r -learning would commence. I t was asserted that varying these con-s t r a i n t s did not m a t e r i a l l y a l t e r the output from the model. This i s now demonstrated. Various l e v e l s of IDYCR2 are depicted h o r i z o n t a l l y , while down the columns are indicated various l e v e l s of IDYCR1. Moving to the r i g h t indicates that f o r any l e v e l of IDYCR1 (the dec i s i o n to widen the scope of search) the average time and money costs of search increase. For any l e v e l of IDYCR2 (the point at which the r u l e i s relaxed) and moving down increasing the value of IDYCR1 also increases the time and money costs of search. Extreme values of IDYCR1 and IDYCR2 r e s u l t i n very wild f i g u r e s ; however, i t i s important to stress that the d i r e c t i o n of change i s consistent and that for small changes i n these v a r i a b l e s the time and.money costs also change incrementally. Table 11 S e n s i t i v i t y Analysis with the Time Constraints IDYCR2 5 10 15 16 20 25 IDYCR1 1 .49* 1.37 1.49 3.69 8.75 24.09 9.59** 14.34 17.81 35.55 87.45 114.55 5 2.51 .4.88 6.72 9.41 17.41 25.66 11.02 15.12 18.91 39.51 110.39 140.54 11 3.61 4.92 6.91 11.30 21.44 26.07 12.46 17.20 21.49 41.66 127.66 151.02 12 3.67 4.96 6.77 11.51 23.81 25.98 13.41 16.87 24.62 44.09 139.54 163.78 20 6.9 8.11 9.75 13.82 24.61 38.93 15.90 21.63 39.01 67.32 167.37 200.78 VACANT =2.0 INUM = 1000 *average time costs ** average money costs A second example of the s e n s i t i v i t y output i s provided when the cost parameters are adjusted. For the sake of s i m p l i c i t y i f i t i s assumed that the exponents and c o e f f i c i e n t s are equal; i . e . CCI = CC3 and CC2 = CC4. The r e s u l t s from varying these parameters are indicated i n Table 12. In t h i s case the response i n d i c a t o r i s the number of brokers. These s e n s i t i v i t y tests were run with VACANT = 2.0 and for INUM = 1000. For any h o r i z o n t a l movement the cost curve s h i f t s upward, while f o r any v e r t i c a l movement the curves become more non-linear. Table 12 S e n s i t i v i t y Analysis with Parameter of Brokerage Cost Function CC1, CC3 1.0 1.2 1.4 1.8 2.0 2.5 CC2, CC4 .5 0 0 0 1 1 2 1.0 0 0 0 1 2 3 1.5 0 0 1 2 3 6 2.0 0 1 3 5 6 9 Apparently the number of brokers i s very s e n s i t i v e to the parameters of the cost function. The procedure i s to choose the set of parameters that allow the model to most c l o s e l y r e p l i c a t e r e a l i t y . Needless to say t h i s process of choosing the best combination of c o e f f i c i e n t s i s the outcome of many runs; t h i s i s what makes simula-t i o n expensive. Some Results The complete demand supply model i s presented i n macro flowchart form i n Figure 16. The e f f e c t s of c l a s s i f i e d s and RIAs i s presented i n r e l a t i o n to the simple version of the demand model introduced i n Chapter Two. The complete d e t a i l e d flowchart i s presented i n Appendix Two. Figure 16 Macro Demand Supply Flowchart The f i r s t i n t e r e s t i n g t e s t i s the r e l a t i o n between the number of brokers supported by a set of market conditions and the vacancy rate. Two such r e l a t i o n s h i p s are shown i n Figure 17. Obviously the number of searchers i s an important v a r i a b l e . It i s important to stress that the model r e s u l t s are s e n s i t i v e to the input v a r i a b l e s , however; although the magnitude of the change w i l l vary with the magnitude of the input v a r i a b l e s (number of searchers, for example), the d i r e c t i o n w i l l be consistent. In t h i s case, increasing the number of searchers w i l l always increase the number of brokers supported by given market. 0. 3.0 6.0 Vacancy Rate Figure 17 Vacancy Rate and Brokerage A second i n t e r e s t i n g r e l a t i o n i s the e f f e c t of segmenting the supply of information. Obviously the vacancy rate w i l l play an important r o l e . The conditions f or case four (the rate of r u l e of thumb r e v i s i o n equals 2.0 and the rate of scope r e v i s i o n i s 2.0) as presented i n the previous chapter w i l l be used for the remainder of the essay. It i s now possible to analyze the r e l a t i o n between search costs and the vacancy rate. This i s shown i n Table 13. ' Table 13 Information Brokerage and Vacancy Rates Vacancy Rate (VACANT) 6.0 5.0 4.0 3.0 2.0 1.0 Number of Brokers 0 0 1 1 3 4 Average Average Average Average Time Costs Money Costs Time Costs Money Costs (1) 3.25 3.31 4.01 4.97 5.66 6.43 (1) 5.98 6.58 10.56 15.62 18.35 23.67 (2) 2.65 2.79 3.15 4.86 4.89 5.62 (2) 5.24 6.11 6.71 8.34 8.20 10.39 (1) with brokerage (2) from table chapter 2 INUM = 1000; Case 4 error- l e a r n i n g Column 1 shows the time and money costs produced by the model when both brokerage and c l a s s i f i e d ads are suppliers of information; column 2 presents the output obtained from the simple demand model of Chapter Two. The higher costs imposed by information brokerage are i n s i g n i f i c a n t at high vacancy rates; however, i n times of excess demand they can become more s u b s t a n t i a l . 84 A l l of t h i s i s quite straightforward. I t i s more i n t e r e s t i n g to study the e f f e c t s of d u p l i c a t i o n of information. I t has often been alleged that the RIAs merely repeat each others' l i s t i n g s . Landlords, of course, have an incentive to l i s t with as many free agencies as possible. C l a s s i f i e d ads i n t h i s age of conglomerate firms w i l l often be i d e n t i c a l from newspaper to newspaper and the marginal costs of l i s t i n g i n extra c l a s s i f i e d s are often s l i g h t i n comparison with the t o t a l costs. The simulation model permits one to speculate about these e f f e c t s i n an a p r i o r i manner. It i s possible to simulate the e f f e c t of redundant information by using the same technique that was used to simulate the e f f e c t s of decay on the storage of o f f e r s . A v a r i a b l e (ZERT) i s made a simple l i n e a r function of the vacancy rate according to the expression ZERT = ALPHA* (VACANT) (29) As the vacancy rate declines ZERT increases. A random number i s generated each time a c l a s s i f i e d or RIA l i s t i s generated, and i f t h i s number (which i s between 0 and 1 as i s the value of ZERT) i s greater than ZERT, the values of the b i d and ask prices are l e f t unaltered. Otherwise they are set to zero and the searcher i s forced to consider another l i s t i n g . For the sake of argument (since t h i s section i s quite speculative) i t i s assumed that redundancy of information a f f l i c t s a l l sources of market data ( c l a s s i f i e d s and information brokers) equally; i . e . , as the vacancy rate declines the l i k e l i h o o d increases that any p a r t i c u l a r b i t of information (bid-ask rent combination) i s redundant or worthless. Of course t h i s compounds the problem of decay. In f a c t , 85 redundancy i n information would lead to increased rates or e r r o r -learning, however, t h i s aspect of search i s ignored simply because the model has become s u f f i c i e n t l y complex as i t stands. The e f f e c t s of redundancy are apparent i n Table 14. Table 14 Redundancy i n Information and Search Costs Vacancy Rate Average Average Average Average (VACANT) Time Costs Money Costs Time Costs Money Costs (1) (1) (2) (2) 6.0 3.25 5.98 3.54 6.01 5.0 3.31 6.58 3.78 7.32 4.0 4.01 10.56 4.86 13.69 3.0 4.97 15.62 6.38 21.76 2.0 5.66 18.35 9.62 29.12 1.0 6.43 23.67 11.17 29.22 (1) from table 15 INUM = 1000; Case 4 e r r o r - l e a r n i n g Summary The market model of information i s now complete. Since 1 important sources of information such as casual search (on-street-advertising, word of mouth etc.) and waiting l i s t s are omitted, no claim to complete-ness can be made; however, i t i s possible to analyze various regulations i n terms of the e f f e c t s these regulations have upon search times and money costs, and the number of brokers operating i n the market at any given period. In the next chapter several p o l i c i e s are examined which have recently been advanced to improve the welfare of tenants. FOOTNOTES - CHAPTER THREE 86 1. On-street advertising includes signs i n front of buildings and notices placed i n public areas such as supermarkets and laundromats. 2. Evidence given before the S o c i a l Services Committee of the c i t y of Vancouver August 2, 1974 by the president of the Greater Vancouver Apartment Owners Association. 3. R e c a l l that JMAXX i s the t o t a l number of l i s t i n g s a v a i l a b l e per day. 4. See Chapter 1 5. For the remainder of t h i s essay where c l a s s i f i e d ads are used the raw data was obtained from the major evening d a i l y . For Vancouver t h i s i s the Vancouver Sun. 6. Evidence for t h i s was also given before the S o c i a l Services Committee c i t e d i n footnote 2. 7. An alternate measure of v a r i a t i o n could be (Ads -Min )/(Max -Min ), where Ads measures the average value, m 8. Simply be adding a test statement, storage can be completely by-passed i n the model. 9. Rentex, the largest f i r m operating i n Vancouver during the summer of 1974, was f i r s t incorporated i n Delaware i n 1964, and i n Vancouver they obtained t h e i r business l i c e n c e to operate a franchise i n the summer 1972. The other two large firms, Timesavers and Homefinders are more recent. 10. Baake (1963) and Rees (1966) f i n d some evidence that p r i v a t e imployment agencies aid the process of sex, race, ethiiic^and age d i s c r i m i n a t i o n , however as i n most cases of di s c r i m i n a t i o n the empirical evidence i s meager. 11. See appendix 1 for further d e t a i l s . 12. An extension of error- l e a r n i n g might be possible at t h i s point. Instead of searchers randomly choosing t h e i r broker, they might use error-learning to se l e c t the broker which provides the best service (greater number of l i s t i n g s ) . Doubtless many services, such as medical and l e g a l services., are chosen, i n part, using an error- l e a r n i n g mechanism. The front end fee, however, i s an important b a r r i e r to extensive use of t r i a l and error s e l e c t i o n procedures. As a f i r s t approximation random s e l e c t i o n seems reasonable. 87 13. See appendix 1 for further d e t a i l s on the s h i f t i n g of fees. 14. Note that i n t h i s f i g u r e the c y c l i c a l nature of JMAXX i s not apparent. A three dimensional diagram i s required to portray t h i s . JMAXX represents the average value of JMAXX at various vacancy rates. 15. The revenue i s simply the value of FIXED2 times the number of searchers who patronize a p a r t i c u l a r broker. In addition i t should be noted that the number of landlords IUNIT i s an exogenous v a r i a b l e . Extensions of th i s aspect of the model are to be found at the end of the next chapter. CHAPTER FOUR The Market f or Rental Information and I t s Regulation This chapter presents some explorative p o l i c y t e s t s . These tests are accomplished by a l t e r i n g the l o g i c or algebra i n a way that i s completely analogous to s h i f t i n g simple demand and supply curves i n s t a t i c a n a l y s i s . In t h i s way alternate p o l i c i e s may at le a s t be conceptually compared. Before describing these tests a b r i e f aside i s presented on the nature of regulation. The Nature of Regulation Intervention i n the free market has been advocated f o r a v a r i e t y of reasons, the most common being that the priv a t e sector f a i l s to provide a s o c i a l l y optimal l e v e l of service at pr i c e s which are 'ju s t ' . Regulation can range from s e t t i n g q u a l i t y constraints on outputs or factor inputs (drug t e s t i n g requirements and dr i v e r ' s l i c e n c e s ) , p r i c e and quantity controls (rent c o n t r o l and farm quotas) or at the extreme, public provision of the good or service. Most economists have despaired of f i n d i n g an objective r u l e f o r intervening i n the economy. For example, i n the provision of pub l i c goods Buchanan writes; "Decisions on the demand and supply of public goods are made through p o l i t i c a l not market i n s t i t u t i o n s and there i s no analogue to competitive order that eases the a n a l y t i c a l task." 1 The consensus appears to be that economists ought to evaluate the costs and benefits for various p o l i c i e s and then permit the p o l i t i c a l process to choose, once f u l l y informed. This i s the p o s i t i o n taken i n 89 t h i s paper. One of the cases i n which government intervention i s deemed most appropriate i s f o r decreasing cost i n d u s t r i e s or 'natural mono-p o l i e s . ' I t i s thought by some authors that information q u a l i f i e s as a decreasing costs industry (Zeckhauser, 1970). The argument i s that the marginal costs of providing consumers with information are very low; average costs i n e v i t a b l y exceed marginal costs over wide ranges of output and monopoly tends to be the equilibrium structure of the information industry. This conclusion does not conform with casual empiricism. Many firms disseminate information and, while they are not p e r f e c t l y competitive, they are c e r t a i n l y not monopolies ( t e l e v i s i o n , newspapers, consumer t e s t i n g , magazines, e t c . ) . In addition to casual empiricism there are good reasons f o r supposing that information production does not tend toward monopoly. For example, i n the r e n t a l information industry the entry require-ments are very low. In addition, since information cannot be evaluated p r i o r to consumption, ignorance can e f f e c t i v e l y d i f f e r -entiate the product. Although t h i s d i f f e r e n t i a t i o n can lead to monopoly power and mon o p o l i s t i c a l l y competitive firms, i t does not lead to natural monopoly. Of course for some in d u s t r i e s such as newspapers, the c a p i t a l requirements are very large and there has been a tendency f o r concentration to increase i n the past decade. In a l l l i k e l i h o o d the impetus f o r t h i s i s due to conventional economies of scale that e x i s t i n producing newspapers, than i n the fact that information may have very low marginal costs. The argument that information production tends towards natural monopoly must be rejected. I t i s s t i l l possible t o condone i n t e r -vention on the grounds that the present l e v e l s of production are less than s o c i a l l y optimal. To estimate the value of a d d i t i o n a l i n -formation service may seem impossible, however i t i s easier (at le a s t conceptually) than i t f i r s t appears. Information i s an intermediate good, used by consumers to produce (along with the goods and services being 'researched') u t i l i t y . By postulating the consumer under various environments, with and without information, i t i s possible to i n f e r the net benefit of alternate p o l i c i e s that a f f e c t the supply of i n f o r -mation to the consumer. There are several important provisos that need to be e x p l i c i t . F i r s t , t h i s model does not evaluate u t i l i t y d i r e c t l y . The net benefit of an increase i n information i s indicated by change i n search costs (time and money). Second, t h i s model only examines the benefit aspect; costs of alternate p o l i c i e s are not calculated. F i n a l l y , i t should bev-pointed out that there may be some d i f f i c u l t y due to a v i o l a t i o n of 2 the Scitovsky c r i t e r i o n i n evaluation of p o l i c y changes. The d i s -t r i b u t i o n of welfare may not be symmetrical with respect to a p o l i c y change. This problem would a r i s e i n the model i n the event that p o l i c i e s were changed i n a short time span. With error- l e a r n i n g and an entry/exit process that may take several months to f u l l y work out, i t i s necessary to evaluate some p o l i c i e s over a long period of time. With these points i n mind i t i s possible to proceed. These tests w i l l be described, the changes i n l o g i c b r i e f l y explained and the resultant output evaluated. P o l i c y Tests There are three general ty,pes of p o l i c i e s evaluated i n t h i s model. (1) Free Market: Often the option of doing nothing i s ignored as a legitimate p o l i c y . In addition, the.free market option provides a bench-mark against which other p o l i c i e s may be compared. The free market run i s presented for d i f f e r e n t vacancy rates and for the f i r s t , s i x t h and twelfth month. Included i n the f i g u r e are average search times (top number), average search costs (middle number), number of information brokers (bottom number). Table 15 Free Market P o l i c y and Search Costs Vacancy Rate Month 2 Month 6 Month 12 3.41* 3.46 3.10 6.0 5.67** 5.94 5.49 0 *** 0 0 3.53 3.51 3.17 5.0 5.94 6.01 6.11 0 0 0 4.11 3.94 4.17 4.0 9.12 10.87 9.24 1 1 1 4.81 4.67 4.98 3.0 14.17 16.35 17.12 2 2 2 5.12 5.41 5.24 2.0 17.40 18.31 18.93 3 3 3 6.47 6.94 6.53 1.0 22.64 24.67 23.55 4 4 4 * Average Time Costs ** Average Money Costs *** Number of Brokers ( p r o f i t l i m i t set at 10%) (2) Regulation Regulation of the r e n t a l information market can be accomplished by several p o l i c i e s of varying degree. Three p o l i c i e s w i l l be examined; fee'.for service, r e g i s t E a t i o n fee plus fee f o r service, and l e g a l actions f o r f a l s e advertising. These p o l i c i e s are a l l aimed at r e n t a l information agencies and have been attempted by governments through-3 out North America. Unfortunately no studies have been done which evaluate t h e i r e f f e c t . (a) Fee for Service: This regulation has been advanced as an appro-p r i a t e form of regulation whenever the consumer cannot evaluate a service p r i o r to consumption. The notion i s simple; the firm cannot charge f o r a service before i t i s delivered to the consumer. In the case of RIAs t h i s would mean that consumers cannot be b i l l e d f o r examining a housing l i s t u n t i l they had been housed and can be charged only i f the fir m had provided them with information leading to that vacancy. This p o l i c y i s very simply tested i n the model by amending the incrementation of money search costs so that FIXED1 i s not added to search i ' s costs u n t i l searcher i i s housed and only i f a house was located through a l i s t provided by a broker. There i s some p o s s i b i l i t y for ambiguity once a vacancy i s added to a storage l i s t ; i n t h i s case a p a r t i c u l a r bid-ask rent combination i s flagged to i d e n t i f y i t as o r i g i n a t i n g with a RIA. Of course RIAs are opposed to such regulation since i t would increase c o l l e c t i o n costs. Also';„revenue would probably drop i n the event that RIAs do not place everyone who signs a contract. I t i s probable that there w i l l be fewer firms i n such a regulated industry and landlords who hitherto l i s t e d e x c l u s i v e l y with RIAs would be forced to u t i l i z e c l a s s i f i e d s and other dissemination devices. The increase i n c o l l e c t i o n costs w i l l not be modelled; however, the decline i n revenues "can be demonstrated without changing the structure of the model. Table 16 presents a serie s of t r i a l s with exactly the same i n i t i a l conditions as Table 15. The reduction i n money costs i s apparent as i s the decline i n the number of firms that can earn an acceptable rate of return (10%). The p o l i c y tends to have l i t t l e e f f e c t at low vacancy rates, but as the vacancy rate declines money costs of search are s u b s t a n t i a l l y a l t e r e d . Times costs are unaffected and the number of brokers declines. Since t h i s i s a hypothetical s i t u a t i o n these r e s u l t s merely indi c a t e general tenden-4 c i e s , not exact responses. Table 16 Fee f o r Service and Search Costs Vacancy Rate Month 2 Month 6 Month 12 3.31* 3.50 3.17 6.0 5.49** 5.44 5.61 0 A** 0 0 3.33 3.57 3.54 5.0 5.87 5.74 6.03 0 0 0 4.21 3.87 4.06 4.0 6.98 6.84 5.99 0 0 0 5.42 5.38 5.51 3.0 9.27 10.38 8.79 0 0 0 5.24 5.41 5.39 2.0 11.32 10.93 10.97 0 1 1 6.35 6.29 6.41 1.0 14.33 12.49 15.67 1 1 1 * Average Times Costs ** Average Money Costs *** Number of Brokers ( p r o f i t l i m i t set at 10%) Number of searchers per run - 1000 94 j(b) R e g i s t r a t i o n Fee plus Fee for Service It has been pointed out that many services (lawyers) charge a retai n e r to ensure that the consumer pay for services as they are ren-dered. The simulation of a p r i c i n g structure which permits the charging of a r e g i s t r a t i o n fee (about 10% of the f u l l charge) and then c o l l e c t i o n of the remainder upon successful d e l i v e r y of the service, i s very s t r a i g h t -forward. Every time the searcher c a l l s upon an RIA, costs are i n i t i a l l y incremented by a small amount and the remainder of FIXED1 assigned when the consumer has been housed by an RIA. The r e s u l t s i n Table 17 are very s i m i l a r as i n Table 16, except that more brokers survive and search costs are higher. Table 17 Registration and Fee for Service and Search Costs Vacancy Rate 6.0 5.0 4.0 3.0 2.0 1.0 Month 2 3.29* 5.32** 0 *** 3.43 5.92 0 4:36 6.87 0 4.96 8.96 0 5.31 13.45 1 6.67 15.39 1 Month 6 3.57 5.29 0 3.42 5.72 0 4.41 6.95 0 5.45 11.54 1 5.49 12.69 1 6.47 16.98 1 Month 12 3.21 5.53 0 3.29 5.59 0 3.98 7.05 0 5.29 9.17 1 5.33 13.01 1 6.46 19.54 1 *Average Time Costs **Average Money Costs ***Number of brokers ( p r o f i t l i m i t set at 10%) Number of searchers per run = 1000 95 (c) Requirements on V a l i d i t y of Housing L i s t s : It i s commonly alleged by various consumer a c t i v i s t groups that r e n t a l information agencies, dance studios, correspondence schools etc., misrepresent the service they o f f e r . A p o l i c y that i s often advocated i s class actions that enable the consumer to f i l e s u i t i n the event that a service was not performed once a fee had been paid. Simulating t h i s p o l i c y i s impossible within the context of the model, however some points should be made about t h i s course of a c t i o n . F i r s t , i t i s extremely expensive. The r e s p o n s i b i l i t y of proving misrepresentation r e s t s on the consumer, and therefore i s l i k e l y to be i n e f f e c t i v e unless the state increases the l e v e l of s u r v e i l l e n c e on 'business e t h i c s ' . P r i c e regulation may have side e f f e c t s such as black markets, but t h e i r d i r e c t costs to tax-payers tends to be small i n comparison to l e g a l sanction. (3) N a t i o n a l i s a t i o n of Information Dissemination Economists have occasionally c a l l e d for c e n t r a l i z e d housing r e g i s t r i e s ( c f . Rodwin, 1963). Consumer A c t i v i s t groups also make th i s plea i n the face of current excess demand for housing. There are two polar p o s s i b i l i t i e s - government agencies that compete wtih the present p r i v a t e services and government monopoly that would eliminate a l l sources of information except for the public agency, (a) Public Agencies that Compete with the Private Sector Many argued that when the government entered the auto insurance business, they should do so i n d i r e c t competition with the p r i v a t e sector. P r i v a t e businesses argued that government monopoly was high-handed and a r b i t r a r y . They also alleged that the ' t y p i c a l ' i n e f f i -ciency of public enterprise would more than o f f s e t any economies due to streamlining the l i t i g a t i o n process. In t h i s model the addition of a new firm representing the public information agency, has an impact only i f i t charges a lower front-end fee than other p r i v a t e agencies. Provision has not been made for market share increasing techniques such as advertising or p r i c e cu t t i n g ; however, i n the event that the p r i c e charged by the p u b l i c f i r m i s l e s s than the p r i v a t e industry p r i c e (which i t would have to be given current p o l i t i c a l opinion), then i t i s reasonable to suppose that the public agency w i l l be the f i r s t broker to be con-sulted by housing searchers. I have simulated two a l t e r n a t i v e s of t h i s p o l i c y . The f i r s t , -models the p o s s i b i l i t y that the government underwrites the p u b l i c information agency and provides a free information service. The second version has the government fi r m set a break-even p r i c e which i s charged only i n the event that the tenant i s a c t u a l l y housed; i t i s u n l i k e l y that governments could use front-end fees. With the f i r s t version the searcher immediately consults the government l i s t (which i s formulated i n the same way that the various l i s t s f o r the private agencies were created). Once th i s has been exhausted on the f i r s t day, the vacancies with p o s i t i v e surpluses are stored and the searcher enters the usual search stream as i n the free market m o d e l . W i t h the second a l t e r n a t i v e the model i s run with the government agency s e t t i n g a break-even p r i c e l e v e l which i s calculated i t e r a v e l y . This process i s accomplished with the aid of several assumptions. F i r s t , i t as assumed that landlords are i n -d i f f e r e n t to information agencies as long as the p r i c e charged to them i s the same for a l l firms. Therefore the share of the market from the point of view of the number of landlords l i s t i n g with the firm i s equal for a l l brokers, pr i v a t e and p u b l i c . Second, i t i s assumed that searchers (consumers of information) are p r i c e s e n s i t i v e ; they w i l l patronize the firm that has the lowest p r i c e before others. The number of searchers a t t r a c t e d to the f i r m with the lowest p r i c e does not vary once i t has been established that the f i r m has the lowest p r i c e . It i s not necessary to c a l c u l a t e the complex r e l a t i o n -ship between number of consumers, p r i c e , t o t a l revenues, costs and p r o f i t s . A l l that i s r e a l l y required i s to run the model for a s e r i e s of months, decreasing the p r i c e of the government service u n t i l i t no longer earns a p o s i t i v e p r o f i t . This p r i c e i s then used i n the p o l i c y simulation and compared with the r e s u l t s of version 1. These r e s u l t s appear i n Table 18. Only Month 12 i s presented for each version. Table 18 Public Information Agencies and Search Costs Vacancy Rate 6.0 5.0 3.0 2.0 1.0 Version 1 3.28* 3.45** 1 *** 3.21 4.14 1 3.79 7.45 3 4.67 9.74 3 6.22 14.14 4 Version 2 3.12 3.62 1 3.29 4.65 1 4.01 10.56 3 6.25 16.69 3 8.43 20.44 4 Free Market (from Table 15) 3.10 5.49 0 3.17 6.11 0 4.17 17.12 3 5.24 18.93 3 6.53 23.55 4 * Average Time Costs ** Average Money Costs *** Number of Brokers ( p r o f i t l i m i t set at 10%) Month 12 Number of Searchers = 1000 It i s easy to see that the government agencies do cause a reduc-t i o n i n search costs of searchers (at le a s t within the context of t h i s model). The net benefits to searchers of a subsidized housing r e g i s -t r y , e s p e c i a l l y one which had monopoly power, are i n t u i t i v e . This model omits c e r t a i n features which undoubtedly q u a l i f y these conclusions, F i r s t , there i s some problem i n estimating the patronage of the government agency by both landlords and tenants. For example, landlords might be reluctant to l i s t with the government agency, given that other private agencies are free simply because they believe that the public agency would l i k e l y have welfare cases, si n g l e mothers, poor people and Indians are i t s most common c l i e n t s . Middle income tenants might w e l l f i n d as a r e s u l t that the av a i l a b l e l i s t i n g s provided by the public agency are unsuitable and end up going to p r i v a t e agencies. The pu b l i c agency could become an information broker f o r the landlords that provided slum type housing and could i n fact a id the r a c i a l , sex and ethnic discrimination process i n housing. Thus, public information agencies i n housing could end up being s i m i l a r to Canada Manpower i n t h e i r secondary e f f e c t s . Second, taxpayers could l e g i t i m a t e l y complain when t h i s informa-t i o n service was being used to a i d the discrimination process. Home owners might regard i t as a transf e r that should be paid by wealthy tenants, not owners of fee simple properties. In addition, there i s the problem that people could e a s i l y use the f a i l u r e of the public housing r e g i s t r y to provide information as synonomous with f a i l u r e s i n government housing p o l i c y to provide dwelling u n i t s . It could be a p o l i t i c a l l y treacherous exercise. F i n a l l y , i t i s i n t e r e s t i n g to note that the time costs of search tend to increase when the government enters into d i r e c t competition with the private sector. This may appear to be counter i n t u i t i v e , but the reasons are straightforward and re l a t e d to the arguments advanced for government monopoly i n car insurance. If i t i s assumed that there are a f i n i t e number of l i s t i n g s a v a i l a b l e to r e n t a l information agencies both public and priv a t e , then the creation of an a d d i t i o n a l agency means that the l i s t possessed by any one agency w i l l be smaller as a new firm enters; t h i s mechanism for increasing search times as the vacancy rate r i s e s tends to be obscured by the increase i n search times due to the u n a v a i l a b i l i t y of s u i t a b l e vacancies (low vacancy r a t e s ) . The i n c l u s i o n of public agencies which w i l l be used p r i o r to p r i v a t e agencies implies that the time required to search the i n f o r -mation possessed by agencies i n general increases as the vacancy rate declines. (b) Government Monopoly i n Information: This p o l i c y i s very simply i l l u s t r a t e d . The supply of information to the market i s now deriva-t i v e form only one source - government r e g i s t r i e s . There are two forms of the p o l i c y . Version one assumes that a l l rentals must be r e g i s -tered with :the c e n t r a l agency and other sources of information are eliminated, while Version two permits other forms of information dissem-i n a t i o n except for p r i v a t e r e n t a l information agencies. In the f i r s t case the model resembles the simple demand model i f there i s no d i r e c t charge for ~>the use of the :government agency. Th t h i s case the problems of h o r i z o n t a l equity are important. In the second case the government becomes a monopoly broker and the entry e x i t model i s constrained to one broker. The r e s u l t s are presented i n Table 19 for Month 6. 101 Table 19 Government Monopoly and Search Costs Vacancy Rate Version 1 Version 2 2.56* 2.79 6.0 5.01** 5.96 1 AAA 1 2.81 2.87 5.0 6.03 , 61.0 1 1 3.09 3.24 4.0 6.66 7.34 1 1 4.66 4.89 3.0 8.27 9.58 1 1 5.62 5.94 2.0 10.24 12.48 1 1 6.25 6.54 1.0 10.69 16.25 1 1 * Average Time Costs ** Average Money Costs *** Number of Brokers Number of Searchers f o r each run = 1000 Summary of P o l i c y Tests These p o l i c i e s can be summarized (except f o r l e g a l sanctions) on graphs. This i s done f or search times i n Figure 18. Within the framework of t h i s model i t i s apparent that n a t i o n a l i z a t i o n with complete subsidy to the searcher most reduces the costs of tenants i n searching for accommodation. I t was pointed out at the beginning of t h i s chapter that t h i s model cannot account f o r the d i r e c t costs of providing that service. Furthermore there are important problems of h o r i z o n t a l equity i n that homeowners and non-searching tenants are required to pay for such services even though they do not consume them. This burden w i l l vary depending upon the type of financing. I f general income taxes are used, then the burden i s d i s t r i b u t e d over tenants and homeowners. If financing for such agencies i s by municipal l e v e l s of government, the financing of such agencies comes l a r g e l y from property taxes. In th i s case homeowners bear a considerable, although c e r t a i n l y not the t o t a l , burden of the service. The exact c a l c u l a t i o n of the d i r e c t costs of such services requires an involved process, the costs of which probably outweigh the benefits. Since the d i r e c t costs of p r i c e regulation are much smaller i n comparison, i t i s between the free market and the p o l i c i e s suggested i n 2 (regulation) that a choice ought to be made. Some q u a l i f i c a t i o n s are needed. 30 Time CD ays). 15 Figure -18 The E f f e c t s of P o l i c i e s On Search Times F i r s t , i t i s clear that regulating the fee charged by brokers a f f e c t s the money costs, and to a much le s s e r extent the time costs of search. Since t h i s model does not examine the implications of r e n t a l information agencies that engage i n deceptive information practices (advertising dwellings which are no longer vacant) simply because evidence of these p r a c t i s e s i s only heresay, a case f o r intervention must be constructed on the assumption that a l l l i s t i n g s are exclusive and v a l i d . Second, i t should be apparent that the costs of obtaining i n f o r -mation r i s e dramatically during periods of high excess demand (low vacancy rates) as documented i n Chapter Three. Also, during these periods, firms s p e c i a l i z i n g i n the sale of information enter the market and s e l l information to consumers. I t seems obvious that i f these firms could place everyone who signed a contract, then i t would make l i t t l e d ifference whether the fee was assigned p r i o r to placement or subsequent to placement. Of course there are higher c o l l e c t i o n costs and i n e f f i c i e n t firms would be eliminated, but there i s a w e l l established l e g a l apparatus f o r securing small debts; a s e r i e s of well p u b l i c i z e d l e g a l decisions r e l a t i n g to the f a i l u r e of tenants to pay these i n f o r -mation fees would no doubt have a profound e f f e c t upon tenants who seek to avoid the brokerage charges. A p r i o r i , the objections of the industry bo fee for service l e g i s l a t i o n merely r a i s e s doubts about whether these firms o f f e r l i s t i n g s which are exclusive and up-to-date. F i n a l l y , the d i r e c t costs of such fee for service l e g i s l a t i o n (or the r e g i s t r a t i o n fee plus fee for service proposal) are r e l a t i v e l y 104 small. C e r t a i n l y t h i s i s true i n comparison to government housing agencies. Coupled with the observation that t r u l y e f f i c i e n t firms which o f f e r v a l i d and economically u s e f u l information would be r e l a t i v e l y unaffected by t h i s l e g i s l a t i o n , there seems to be a c l e a r case for such consumer protection. An objection to t h i s intervention can be advanced on the general grounds that modern mixed market economies already s u f f e r too much intervention and government co n t r o l . Recent submissions of the various i n q u i r i e s into i n f l a t i o n i n the United States appear to condemn govern-ment intervention and regulation as an important source of i n e f f i c i e n c y . Some economists al l e g e that were t h i s regulation eliminated, s u b s t a n t i a l increases i n growth and employment could be r e a l i z e d . Unfortunately the i estimates of such increased growth tend to s u f f e r from the same degree of u n s p e c i f i c i t y as do my estimates of the net benefit of intervention; as do the estimates of the benefits obtained by consumer protection i n general and indeed as do the studies that attempt to measure the costs of monopoly. The problem i s inherently p o l i t i c a l i n nature and we are forced to return to the quotation from Buchanan. In summary, i t seems c l e a r both from the model, and the s t a t i s t i c a l evidence presented i n Chapter Two that the government w i l l f i n d i t s e l f induced to strengthen the market for information i n some product markets. This essay has attempted to e s t a b l i s h the rules under which t h i s i n t e r -vention should occur. As i n the case of a n t i t r u s t regulations, the i n t e r -vention by the government proceeded by some t h i r t y years the economic j u s t i f i c a t i o n supplied by economists. In the same way, governments are 105 proceeding to supply information i n a wide v a r i e t y of product and factor markets to reduce the degree of market imperfection. This p o l i c y discussion i s explorative and incomplete. The main purpose was to e s t a b l i s h a framework for discussing the problem of p u b l i c i n t e r -vention into the production of market information. Extensions and Further Research There are several areas i n which the model may u s e f u l l y be extended. F i r s t , there are extensions to the e r r o r - l e a r n i n g framework. Throughout the essay I have balked at creating a more complicated model and de-ferred such embellishments for further e f f o r t s . There i s obviously a r e l a t i o n s h i p between the rate of e r r o r - l e a r n i n g and the benefits ob-tained from government action. The recognition, on the part of con-sumers, that caveat emptor may be a u s e f u l t o o l to use i n the purchase of information, may reduce the scope for government action. In other words the rate of e r r o r - l e a r n i n g may d i r e c t l y a f f e c t the benefits of various government p o l i c i e s ; i . e . , increases i n the rate of learning w i l l probably r e s u l t i n greater search cost savings. The actual error-learning process could be made more i n t e r e s t i n g by incorporating some e x p l i c i t socio-economic v a r i a b l e i n the rate of learning. For example, i t seems i n t u i t i v e that r i s k taking plays an important r o l e i n the rate of adjustment to uncertainty. If so, then these v a r i a b l e s should be included i n further extensions of the model. Related to the above point i s the more abstract problem of oversearch and undersearch. Ignorance of the underlying d i s t r i b u t i o n of prices and q u a l i t y a t t r i b u t e s may well induce the consumer to 106 undersearch. Therefore i t i s possible for firms who charge greater than marginal cost to survive simply because of consumer ignorance combined with c o s t l y search. In t h i s case increased information, provided either by the p u b l i c or p r i v a t e sector, could decrease the patronage of i n e f f i c i e n t firms or firms that are earning greater than normal p r o f i t s . In the event that firms i n a p a r t i c u l a r industry have d i f f e r e n t cost curves, increased information w i l l tend to reduce the number of firms. It i s even possible that perfect information may indeed lead to the lowest p r i c e paid by the consumer, but that only one f i r m would be able to survive. In t h i s extreme event i t i s pos-s i b l e f or the p r i v a t e sector and even firms whose prime business i s not the marketing of information to engage i n deliberate mis-informa-t i o n , which may create the need for government action. The model, by increasing the s o p h i s i t i c a t i o n of the brokerage submodel to include the choice of broker on p r i c e and advertising grounds, could shed some important i n s i g h t s i n t h i s area. F i n a l l y , and most s i g n i f i c a n t l y , the model should be extended into the fee simple market. Numerically, r e n t a l brokers are dealing with an increasing volume of business, however i n .terms of f i n a n c i a l t r a n s f e r s , i t i s apparent that the fee simple brokerage industry s t i l l commands the largest share "of housing brokerage business. For example, r e n t a l information agencies i n B.C. had a gross income of approximately $1,000,000 for the year of 1974, however i n terms of commissions alone the fee simple brokerage industry accounted for $90,000,000. Combined with t h e i r other charges the r e a l estate industry i n B r i t i s h Columbia i s e a s i l y a b i l l i o n d o l l a r a c t i v i t y . The extension of the model into the fee simple domain i s reasonably straightforward. The fee simple broker, i n addition to furnishing information, provides f i n a n c i a l , l e g a l and other market assistance. These would have to be acknowledged i n the construction of the model. In a d d i t i o n the actual f i r m structure i s no longer simple. Real estate brokerage firms range from simple one or two person operations which s e l l l i f e and car insurance i n addition to houses, a l l the way to extremely large and d i v e r s i f i e d corporations which engage brokerag service, and construction, mortgage financing etc., etc. Separating the function of the modern r e a l estate corporation i s not a t r i v i a l task. 108 FOOTNOTES - CHAPTER FOUR 1. Buchanan (1968), p.5. 2. The basis f o r Cost-Benefit analysis i s the Kaldor-Hicks c r i t e r i o n which affirms that a p o l c i y i s b e n e f i c i a l i n the event that those who gain could t h e o r e t i c a l l y compensate those who lose. Scitovsky pointed out that t h i s could lead to a paradoxical s i t u a t i o n where a p o l i c y and i t s repeal might simultaneously be viewed as s o c i a l l y desirable. 3. At t h i s time many states including Delaware, Hawaii, Colorado and Washington have passed l e g i s l a t i o n of t h i s v a r i e t y . 4. An alternate fee f o r service structure might be a d a i l y charge. 5. Here the free service r e s u l t s i n the agency being consulted at the outset, before any type of broker or information source i s u t i l i z e d . Appendix One  Mathematical Notes This appendix supplies some a d d i t i o n a l mathematical d e t a i l s to c e r t a i n propositions that appear i n the text. The notes are presented by chapter and the reader should have l i t t l e d i f f i c u l t y i n r e l a t i n g them to the main body of the essay. Chapter One An important part of t h i s chapter deals with the s h i f t i n g and incidence of the brokerage charges which was asserted to depend upon the amount of market services desired by buyers and s e l l e r s and the slopes-of the demand and supply curves. This i s now demonstrated more rigorously. Figure 19 i s repeated from Chapter One. Assume that the demand and supply r e l a t i o n s can be represented by the following equations, S' = c + dp S" = c + dp m D' = a - bp D" = a - bp m Quantity Figure 19 From these equations i t i s possible to c a l c u l a t e the value of P , P' , , P and P^. e e b P i s calculated at the i n t e r s e c t i o n of D' and S". This r e s u l t s i n a a - bp = c + dp m P a = a " °m (30a) b + d P' i s calculated at the i n t e r s e c t i o n of D" and S" which r e s u l t s i n e \ ~ cm (30b) b + d In the same way P = (a - c)/(b + d) and P = (a - c)/(b + d). b m e The s h i f t of brokerage charges to the buyers was shown to be ei t h e r P - P' or P - P depending on which equilibrium p r i c e (after or before markets.services have been rendered) was taken to be relevant. If P^ i s the relevant benchmark', then the s h i f t to buyers i s P - P' = (a-c )/(b+d) - (a -c )/(b+d) a e m m m = (a-a )/(b+d) (31) m The s h i f t to s e l l e r s i s P' - P, and i s e b = (c-c )/(b+d) (32) ' m Thus the s h i f t i n g of brokerage charges depends d i r e c t l y upon the degree of market services demanded by ei t h e r the buyer or s e l l e r , a-a and m c-c , re s p e c t i v e l y , and inversely upon the slopes of the demand and m supply curves (b and d). I t i s i n t e r e s t i n g to note that the incidence of brokerage charges borne by the s e l l e r i s dependent upon the slope" of the supply curve, as i s the incidence of market charges borne by the s e l l e r dependent upon the slope of the demand curve. If care i s taken i n t h e i r i n t e r p r e t a t i o n , these slopes can be viewed as crude measrues of e l a s t i c i t y . Chapter Two The proofs required f or t h i s chapter deal with the basic theorems i n the theory of search presented by S t i g l e r (1961). The f i r s t deals with the expected minimum value of a set pf pr i c e s a f t e r a c e r t a i n s p e c i f i e d number off searches. The other proof follows d i r e c t l y from t h i s theorem. Theorem Given that the set of prices can be presented by a s t r i c t l y p o s i t i v e set of numbers x^ (i=l,k) with a p r o b a b i l i t y density function f (x) , then the expected minimum p r i c e a f t e r n draws (units of search) i s given by the formula, m = i f (1-F(x)) ndx (33) n 0 where F(x) i s the cumulative frequency function of the p r i c e s . Proof The proof i s i n two stages. I; By the d e f i n i t i o n of a cumulative frequency function Assuming that the p r i c e s are independent l e t M be the minimum p r i c e a f t e r n draws, or F(x) = P(X < x). (34) M = min(X l 5 X, Since the X. are independent, P(M > x) P(X 1 > x)- P(X 2 > x). 5 • > P(X > x) n-(l-F(x)) n P(M < x) 1-(1-F(x)) n (35) I I ; For any s t r i c t l y p o s i t i v e random v a r i a b l e x, the expected value i s defined by the expression, CO E(X) = / xf(x)dx (36) 0 We proceed by i n t e g r a t i n g by parts. Let u = x, v = l-F(x) and dv = d/dx(l-F(x)) = -f(x)dx E(X) = - r x(-f(x))dx 0 oo = - f udv 0 I OO CO - / vdu 0 0 1 CO 00 = - x ( l - F ( x ) ) | + / 1-F(x)dx (37) •0 0 The f i r s t term of t h i s expression vanishes when evaluated for both zero and i n f i n i t y and we are l e f t with, oo . E(x) = fl 1-F(x)dx 0 The expected value of M defined i n part I above i s then simply substituted into the above expression to obtain E(M) = /" i - ( l - ( l - F ( x ) ) n ) d x 0 = /" (1-F(x)) ndx (38) 0 which i s the desired r e s u l t . This expression obviously deminishes f o r increasing values of nv The second expression used i n the chapter involves the expected gain from an a d d i t i o n a l unit of search. This i s the diffe r e n c e between the n*"*1" and the n ^ ' + l search or, oo n M = m f - m ^ = / (l-F(x)) F(x)dx (39) pn n " n+1 o Proof; m -,-m = f (1-F(x)) ndx - /°° ( l - F ( x ) ) n + 1 d x n i n+1 o 0 = I" (1-F(x)) ndx - r ( l - ( F ( x ) ) (1-F(x)) ndx 0 0 113 = (1-F(x)) ndx - r (1-F(x)) ndx +r ( l - F ( x ) ) n F ( x ) d x 0 0 0 = /°° ( l - F ( x ) ) n F ( x ) d x 0 The function M i s graphed i n f i g u r e 3 of Chapter Two. The conditions of concavity that are shown, requires that the f i r s t d e r i v a t i v e of egn.3.9 be greater than zero and the second d e r i v a t i v e be les s than zero. Obviously these conditions depend c r i t i c a l l y " upon the form of the d i s t r i b u t i o n of random v a r i a b l e s . Developing the precise form of the f i r s t and second order conditions f o r M i s not a t r i v i a l task and pn i s l e f t f o r the time being. Chapter Four Given that there are S ^ ( i = 1, 2,....n) s e l l e r s and B_. (j = 1, 2,...m) buyers with messages costs of 'a' between any buyer and s e l l e r , i f brokers enter with message costs of 'b' between a broker and eit h e r a buyer or s e l l e r , then the average message costs of the system with brokerage i s given by (n+1)(a+b) ; N odd AC = (40) 2(N+l)(b+b)/N ; N even where N i s the number of s e l l e r s . Proof; Assuming that the broker charges the r e c i p i e n t 'b' per message and assuming that the cost of sending a message to the broker remains at 'a', then f o r m buyers, n s e l l e r s and one broker the t o t a l costs of sending a message are TC = (a+b)(m+n) (41) 114 and average costs Ac = (a+b)(m+n+N) where N i s the number of brokers. If another broker enters and divides the market (messages sent to buyers and s e l l e r s ) with the e x i s t i n g broker and assuming that the buyers and s e l l e r s are ignorant of exactly how t h i s d i v i s i o n i s made, then a l l market p a r t i c i p a n t s w i l l have to send and receive at le a s t one message. But, there i s a f i f t y - f i f t y chance that a buyer or a s e l l e r w i l l f a i l to contact the desired party on the opposite side of the market and the message costs w i l l need to be repeated. Denoting as V the average costs f o r one broker, the average costs now are, For, three brokers a l l p a r t i c i p a n t s w i l l bear an i n i t i a l round of message costs, two thirds w i l l then repeat and out of that two th i r d s one t h i r d w i l l need to send message to a l l three brokers. The average costs are given by, This can be generalized into a serie s where the average costs are N+1/N(V) , N odd AC = 3/2(V) (42) AC = 2V. (43) AC = (44) 2(+l)/N(V) N even 115 Appendix Two This appendix presents the micro flowchart of the complete market model (Figure 20). In addition a program l i s t i n g i s presented. The program takes approximately 10 seconds of CPU time to compile, and approximately 11 seconds to complete one t r i a l of 1000 searchers. Undoubtedly to run t h i s model for extended periods of time would e n t a i l considerable computing expense; most of the comuting cost i s due to the many generations of random numbers (approximately 10,000) for an average. I t should be pointed out that the l i s t i n g i s merely one version of several used i n the various t r i a l s . Each p o l i c y and experiment required a d d i t i o n a l subprograms and statements. For t h i s reason the l i s t i n g may not "mesh" neatly with the flowchart. Dlmens ion Input I n i t i a l I z e 1 = ) Generate Income 1 = 1 + 1 Subrout ine Money Set Constraints PER-P/ PI I0AY=1 Figure 20 Demand -Supply Flowchart 117 L I ST ING OF F I L E F I LE1 0 9 : 2 2 A . M . MAY 13, 1975 ID=h 1 C A SIMULATION MODEL OF THE MARKET FOR INFORMATION 2 C IN RENTAL HOUSING MARKETS 3 C 4 C THIS MODEL INCORPORATES A SUPPLY SECTION WITH 5 C AND ENTRY AND EXIT MECHANSIM FOR RENTAL 6 C INFORMATION AGENCIES AND A SUBROUTINE TO 7 C SIMULATE THE SUPPLY OF CLASS IF I ED AD 8 C INFORMATION.THE DEMAND MODEL IS AN ERROR 9 C LEARNING MODEL OF CONSUMER DEMAND FOR INFORMATION 10 C 11 C THIS L I ST ING DOES NOT INCLUDE THE POLICY TESTS 12 C OR THE TESTS FOR REDUNDANCY.THESE ARE EXPLAINED 13 C IN THE TEXT AND ARE STRAIGHTFORWARD EXTENSIONS 14 C 15 IMPLICIT R E A L * 4 ( A - H , 0 - Z ) 16 REAL *4 INCOME 17 INTEGER TOTL IS 18 DIMENSION R E S ( 1 0 0 0 ) , C O S T ( 1 0 0 0 ) , T I M E ( 1 0 0 0 ) , I N C O M E ( 1 0 0 0 ) 19 * , S U R P ( 1 0 0 0 ) , B P ( 1 0 0 0 ) , C P ( 1 0 0 0 ) 20 * , B I D R ( 1 0 0 0 ) , A S K R ( 1 0 0 0 ) , S U R P P ( 1 0 0 0 ) , G A M ( 1 0 0 0 ) 21 * , P P ( 1 0 0 0 ) , J J J ( 1 0 0 0 ) , I S E A R ( 1 0 0 0 ) , J M A X X ( 3 5 ) , PROF I T ( 2 0 ) 22 * , R A T R E T ( 2 0 ) , R E V E N U I 20 ) ,T IME1 (20> 23 * , B P S T O R ( 1 0 0 0 ) , C P S T O R ( 1 0 0 0 ) , S R P S T O ( 1 0 0 0 ) 24 * * * * * * * * * * * 25 C DIMENSIONS SET*VAR IABLES TYPED 26 C * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 27 COMMON I N C O M E , I D A Y C R , R E S , S U R P , 8 P , J M A X , I D A Y , C O S T , T I M E , 2 8 * C O S T M X , T I M E M X , J , I , C P , C P M E A N , J M A X X , I D A Y M X , A D J , V A C A N T , T E S T 29 * , INUM,MONTH,TOTL I S ,K ,JMXTOT,L I SBRO,BROTOT ,F IXED1 30 # , F I X E D 2 , A G E N T , T 0 T B R 0 , R E V E N U , P R 0 F I T , R A T R E T 31 COMMON BPSTOR »C P S T O R , J J , P E R S T 0 , S R P S T O 32 C INUM SETS THE MAXIMUM NUMBER OF SEARCHERS 33 DATA T I M E 1 / 2 0 + 0 . / 34 TI MEK 1) = 1. 35 VACTES=7. 36 C THE MODEL BEGINS WITH MONTH SET TO 1 37 C THE EXOGENOUS VAR IABLE ,VACANT, GOVERNS 38 C ,THE NUMBER OF SEARCHERS,AND THE NUMBER 39 C OF L IST INGS THROUGH THE SUBROUTINES 40 C CYCLE AND ENTRY 1 41 DO 500 M0NTH=1,12 42 VACANT=1.0 43 WR ITE (6 ,516 ) VACANT,MONTH 44 516 F O R M A T ( « ' , ' V A C A N C Y RATE IS ' , F 5 . 3 , ' FOR THE MONTH » ,13 ) 45 IUNIT=200 46 INUM=1000 47 I F ( V A C A N T . L T . 2 . 0 ) GO TO 2 48 I F ( V A C A N T . G T . 7 . 0 ) GO TO 3 49 C THE SH IFT ING OF TRANSACTIONS CHARGES BY 50 C BROKERS IS CALCULATED AS A FUNCTION OF 51 C THE VACANCY RATE.F IXED1 IS THE CHARGE 52 C BORNE BY CONSUMERS WHILE F IXED2 IS THE 53 C CHARGE BORNE BY SUPPL IERS.FOR VACANCY RATES 54 C IN EXCESS OF 1% THE CHARGE IS BORNE ENTIRELY 55 C BY SUPPL IERS;FOR VACANCY RATES LESS THAN 2% 56 C THE CHARGE IS BORNE ENTIRELY BY CONSUMERS. 57 T0T1=INUM+IUNIT 58 BETA 1= 20*I UN IT L I S T I N G OF F I L E F I L E ! 118 0 9 : 22 A . M . MAY 1 3 , 1 9 7 5 ID=t-5 9 B E T A 2 = 2 0 * I N U M 6 0 F I X E D 1 = BETA 1 * V A C A N T 6 1 F I X E D 2 = B E T A 2 / V A C A N T 62 GO TO 1 6 3 2 F I X E D 2 = 2 0 . 6 4 F I X E D 1 = 0 . 6 5 GO TO 1 6 6 3 F I X E D 2 = 0 . 6 7 F I X E D 1 = 2 0 . 6 8 1 I DAYMX=30 6 9 C B E G I N T I M E P E R I O D S 7 0 B R O T O T = 0 . 7 1 P E R S T O = ( V A C T E S - V A C A N T ) / V A C A N T 7 2 C THE S U B R O U T I N E S C Y C L E AND ENTRY ARE NOW 7 3 C C A L L E D TO G E N E R A T E L I S T I N G S FOR CONSUMER 7 4 C ' 1 • ON DAY ' I D A Y * . 7 5 30 C A L L C Y C L E 7 6 C 7 7 C THE S E A R C H P R O C E S S I N NOW COMMENCED 7 8 C 7 9 DO 4 0 0 1 = 1 , I N U M 8 0 B R O K E R = 0 . 8 1 C THE S U B R O U T I N E MONEY I S C A L L E D 8 2 C TO G E N E R A T E AN E S T I M A T E OF 8 3 C INCOME FOR S E A R C H E R ' I ' 8 4 C A L L MONEY 8 5 A L P H A 3 = . 2 * I U N I T 8 6 A L P H A 2 = . l 8 7 C O S T E S = • 1 * I N C O M E ( I ) 8 8 C THE P A R A M E T E R S THAT G O V E R N THE T I M E 8 9 C AND MONEY C O N S T R A I N T S HAVE NOW B E E N 9 0 C B E E N S E T . 91 I D Y C R 1 = ( . 1 + . 0 0 0 0 0 3 4 ) * I N C 0 M E ( I ) * I D A Y M X 9 2 IDYC R 2 = ( . 1 5 + . 0 0 0 0 3 4 ) * I N C O M E ( I ) * I D A Y MX 9 3 C THE R U L E OF THUMB P A R A M E T E R ' G A M M A ' I S 9 4 C NOW I N I T I A L I Z E D 9 5 P = l . 9 6 P M A X = 5 . 9 7 C J M A X X , P , P M A X GOVERN THE NUMBER OF H O U S E S E X A M I N E D PER DAY 9 8 C O S T U ) = 0 . 9 9 T I M E ( I ) = 0 . 1 0 0 T E S T = 0 . 1 01 C 1 0 2 J J = 1 1 0 3 I DAY=1 1 0 5 C B E G I N S E A R C H FOR S E A R C H E R I 1 0 6 1 0 7 P E R = P / P M A X 1 0 8 2 0 I F { I D A Y . G T . 2 0 . A N D . C O S T ( I ) . G T . C O S T E S . A N D . C O S T I I ) 1 0 9 * . G T . F I X E D 1 . A N D . B R O K E R . E Q . O . ) GO TO 21 1 1 0 C D E C I S I O N R U L E TO CONSULT B R O K E R S 111 L I S B R O = 0 112 GO TO 22 1 1 3 21 C A L L E N T R Y 1 1 1 4 J M A X = P E R * J M A X X ( I D A Y ) 1 15 J M A X = P E R * J M A X X ( I D A Y ) 1 1 6 I T E S T = J M A X X ( I D A Y ) 119 L I ST ING OF F I L E F I L E 1 09 :22 A . M . MAY 1 3 , 1975 ID=h 117 I F ( J M A X . G T . I T E S T ) JMAX=ITEST 118 I F ( T E S T . G E . l . O ) GO TG 410 119 22 TOTLIS=LISBRO+JMAX 120 C GENERATE L IST INGS FROM CLASS IF I EDS 121 00 600 J = l i J M A X 122 CALL L I S T 123 C THE SUBROUTINE L IST GENERATES VALUES OF B P ( J ) ,CP<J) ,SURP<J) 124 C BY RANDOM SAMPLING FROM A 0,1 UNIFORM D ISTRIBUTION 125 I F ( S U R P ( J ) - B P ( J ) / G A M M A ) 7 0 0 , 7 0 1 , 4 0 2 126 C IF THE DECISION RULE IS PASSED THE VACANCY IS ACCEPTED(GO TO 4C 127 701 COSTJI ) -COST( I )+ALPHA2*C0STMX 128 B P S T O R ( J J ) = B P { J ) 129 CPSTOR{JJ ) = C P ( J ) 130 S R P S T O ( J J ) = BP{J ) - C P ( J ) 131 JJ=JJ+1 132 C VACANCY IS STORED 133 GO TO 600 134 700 C O S T d )=COST( I )+ALPHA2*C0STMX 135 600 CONTINUE 136 I F (P .GT .PMAX ) P=PMAX 137 IDAY=IDAY+1 138 I F ( I DAY .GT . IDAYMX) GO TO 100 139 I F ( I D A Y . L T . I D Y C R 1 ) GO TO 20 140 PER=(P+1)/PMAX 141 C SCOPE OF SEARCH WIDENEO.FIRST TIME CONSTRAINT EXCEEDED 142 I F ( I D A Y . G T . I D Y C R 2 ) GAMMA=GAMMA+{1+PERSTG)/1. 143 GAMMA= GAMMA + .2 144 CALL STORE 145 DO 300 LL=1,KK 146 I F ( S R P S T O { L L ) . G T . B P S T G R ( L L ) / G A M M A ) GO TO 420 147 300 CONTINUE 148 GO TO 20 149 420 B P ( J ) = BPSTOR(LL ) 150 CP (J )=CPSTOR{LL ) 151 SURP (J )=SRPSTO(LL ) 152 GO TO 402 153 100 SURPMX=0. 154 ITEST=JMAXX(IDAYMX) 155 DO 601 J = l , I T E S T 156 CALL L I ST 157 IF (SURP( J K G E . S U R P M X ) SURPMX=SURP ( J ) 158 601 CONTINUE 159 C THIS LOOP SEARCHES FOR THE BEST AVAL I ABLE HOUSES IF TIME COSTS 160 C EXCEED MAXIMUM TIME AVA ILABLE 161 C VACANCY ACCEPTED,PROCESSED FOR S T A T I S T I C A L ANALYSIS 162 402 B I D R U ) = BP( J ) 163 A S K R ( I ) = C P ( J ) 164 SURPP( I )=SURP(J ) 165 GAM(I)=GAMMA 166 PP ( I ) =P 167 I SEAR( I) = I DAY 168 J J J ( I ) = J M A X 169 GO TO 400 170 403 B IDR ( I ) =BP (J ) 171 A S K R ( I ) = C P ( J ) 172 SURPP( I ) = SURP(J ) 173 ISEAR( I )=IDAY 174 GO TO 400 L I S T I N G OF F I L E F I L E 1 120 0 9 : 2 2 A . M . MAY 13t 1 9 7 5 ID=r 1 7 5 4 1 0 MANTOT = MANTOT + 1 1 7 6 4 1 3 DO 4 1 1 J = l , 2 0 1 7 7 C A L L L I S T 1 7 8 I F ( S U R P ( J ) . G T . B P ( J ) / 2 . ) GO TO 4 1 2 1 7 9 4 1 1 C O N T I N U E 1 8 0 GO TO 4 1 3 1 8 1 4 1 2 B I D R { I ) = B P ( J ) 1 8 2 A S K R ( I ) = C P ( J ) 1 8 3 S U R P P ( I ) = S U R P ( J ) 1 8 4 C O S T U ) = 0 . 1 8 5 I S E A R ( I ) = 0 1 8 6 4 0 0 C O N T I N U E 1 8 7 C T H I S S E C T I O N COMPUTES S T A T I S T I C A L 1 8 8 C S U M M A R I E S OF THE S EARCH C G S T S T T I M E AND MONEY) 1 8 9 C FOR THE SET OF S E A R C H E R S R E P R E S E N T E D BY INUM 1 9 0 T 0 T 1 = 0 . 191 T 0 T 2 = 0 . 1 9 2 T 0 T 3 = 0 . 1 9 3 T Q T 4 = 0 . 1 9 4 T 0 T 5 = 0 . 1 9 5 T 0 T 6 = 0 . 1 9 6 DO 4 0 4 1 = 1 , I N U M 1 9 7 T 0 T 1 = B I D R ( I ) + T O T l 1 9 8 T 0 T 2 = A S K R ( I ) +T0T2 1 9 9 T 0 T 3 = S U R P P ( I ) + T 0 T 3 2 0 0 T 0 T 5 = I S E A R ( I J + T 0 T 5 2 0 1 4 0 4 T 0 T 6 = C 0 S T ( I ) + T 0 T 6 2 0 2 A V G C S T = T 0 T 6 / I N U M 2 0 3 A V G S E A = T 0 T 5 / I N U M 2 0 4 AVGR EN= TOT 1/ INUM 2 0 5 A V G S U R = T 0 T 3 / I N U M 2 0 6 W R I T E ( 6 , 4 5 ) A V G C S T , A V G S E A , A V G R E N , A V G S U R , M A N T O T , 8 R 0 T 0 T 2 0 7 4 5 FORMAT{ ' » , 4 F 1 2 . 2 , I 6 , F 7 . 0 ) 2 0 8 C THE T I M E AND MONEY COSTS FOR INUM S E A R C H E R S HAS NOW B E E N 2 0 9 C A G G R E G A T E D AND P R I N T E D OUT 2 1 0 W R I T E ( 6 , 5 0 1 ) MONTH 2 1 1 5 0 1 FORMA T ( • • ,•MONT H ' , I 4 ) 2 1 2 J M X T O T = 0 2 1 3 DO 5 0 2 I D A Y = 1 , I D A Y M X 2 1 4 J M X T O T = J M X T O T + J M A X X ( I D A Y ) 2 1 5 5 0 2 C O N T I N U E 2 1 6 T O T L I S = JMXTQT+ L I S B R C 2 1 7 W R I T E ( 6 , 5 0 5 ) T O T L I S , L I S B R O , J M X T O T 2 1 8 5 0 5 F O R M A T ( 1 ' , ' T O T A L L I S T I N G S ' , 3 1 1 0 > 2 1 9 W R I T E ( 6 , 5 1 0 ) A G E N T , M O N T H 2 2 0 5 1 0 F O R M A T ( ' • , F 6 . 0 , ' A G E N T S I N M O N T H ' , 1 3 ) 2 2 1 I F ( A G E N T . L E . O . ) GO TO 5 0 0 2 2 2 DO 5 1 1 1 = 1 , K 2 2 3 5 1 1 W R I T E ( 6 , 5 1 2 ) I , P R O F I T ( I ) , R A T R E T ( I ) , R E V E N U ( I ) 2 2 4 5 1 2 FORM A T ( ' • , ' B R O K E R ' , I 3 , ' H A S PROF I T * , F 1 2 . 2 , ' R E T U R N ' , F 6 .4 2 2 5 * • R E V E N U E ' , F 1 2 . 2 ) 2 2 6 5 0 0 C O N T I N U E 2 2 7 STOP 2 2 8 END 2 2 9 S U B R O U T I N E L I S T 2 3 0 C T H I S S U B R O U T I N E G E N E R A T E S V A L U E S OF 2 3 1 C B P ( J ) AMD C P U ) BY RANDOM S A M P L I N G 2 3 2 C FROM A U N I F O R M D I S T R I B U T I O N . ± Z 1 L I ST ING OF F I L E F I L E 1 0 9 : 2 2 A . M . MAY 13 , 1975 ID=H 233 IMPLIC IT R E A L * 4 ( A - H . O - Z ) 234 REAL * 4 INCOME,MAXY,MAXTIM 235 DIMENSION R E S ( 1 0 0 0 ) , C O S T < 1 0 0 0 ) , T I M E ( 1 0 0 0 ) , I N C O M E ( 1 0 0 0 ) 236 * , S U R P < 1 0 0 0 ) , B P ( 1 0 0 0 ) , C P ( 1 0 0 0 ) 237 COMMON INCOME, IDAYCR,RES ,SURP,BP ,JMAX, I D A Y , C O S T , T I M E , 238 * C O S T M X , T I M E M X t J t I 239 4 S=SCLOCK( 0.0) 240 X=RAND(S) 241 B P < J ) = F R A N D ( 0 . 0 ) * 5 0 0 . 242 I F ( B P ( J ) . G T . I N C 0 M E ( I ) * . 2 ) GO TO 4 243 C P ( J ) = F R A N D ( 0 . 0 ) * 5 0 0 . 244 SURP(J ) = B P ( J ) - C P ( J ) 245 I F ( S U R P ( J ) . G T . B P ( J ) ) GO TO 4 246 RETURN 247 END 248 SUBROUTINE MONEY 249 C THIS SUBROUTINE USSES A LOGNORMAL RANDOM NUMBER GENERATOR 250 C TO GENERATE VALUES OF INCOME U ) 251 IMPL IC IT REAL*4 ( A - H , 0 - Z ) 252 REAL #4 INCOME,MAXY,MAXTIM 253 DIMENSION R E S ( 1 0 0 0 ) , C O S T ( 1 0 0 0 ) , T I M E ( 1 0 0 0 ) , I N C O M E ( 1 0 0 0 ) 254 * , S U R P ( 1 0 0 0 ) , B P ( 1 0 0 0 ) , C P ( 1 0 0 0 ) 255 COMMON INCOME, I D A Y C R , R E S , S U R P , B P , J M A X , I D A Y , C O S T , T I M E , 256 *COSTMX,T IMEMX,J , I , CP ,CPMEAN 257 FM=.6 258 STD=2.0 259 S=SCLOCK(0 .0 ) 260 X=RANDL(S,FM,STD) 261 1 INCOME(I) = FRANDL (0 .0 )#1000Q. 262 I FUNCOME I I ) . G T . 3 0 0 0 0 . ) GO TO 1 263 I F ( I N C O M E ( I ) . L T . 2 0 0 0 . ) GO TO 1 264 RETURN 265 END 266 SUBROUTINE CYCLE 267 IMPL IC IT REAL*4 ( A - H , 0 - Z ) 268 REAL *4 INCOME 269 DIMENSION R E S ( 1 0 0 0 ) , C O S T ( 1 0 0 0 ) , T I M E ( 1 0 0 0 ) , I N C O M E ( 1 0 C 0 ) 270 * , S U R P ( 1 0 0 0 ) , B P ( 1 0 0 0 ) , C P ( 1 0 0 0 ) 271 * , B I D R ( 1 0 0 0 ) , A S K R ( 1 0 0 0 ) , S U R P P ( 1 0 0 0 ) , G A M ( 1 0 0 0 ) 272 * , P P ( 1 0 0 0 ) , J J J ( 1 0 0 0 ) , I S E A R ( I O O C ) , J M A X X ( 3 5 ) 273 COMMON INCOME, IDAYCR,RES,SURP,BP,JMAX,. I D A Y , C O S T , T I M E , 274 *COSTMX,T IMEMX,J , I , CP ,CPMEAN,JMAXX , ICAYMX,ADJ ,VACANT 275 IZETA=7 276 L= l 277 M=7 278 2 DO 1 I DAY= L,M 279 1 JMAXX(I DAY)=ADJ*VACANT 280 JMAXX( IZETA)=0 281 I BETA= IZETA-1 282 I BETA l= IB ETA -1 283 JMAXX( IBETA)=JMAXX( IBETAJ+5 284 JMAXX( IBETA1) = JMAXX(I B E T A l ) + 5 285 IZETA=IZETA+7 286 L=M+1 287 M=M+7 288 I F I M . G T . 3 5 ) GO TO 3 289 GO TO 2 290 3 RETURN L I S T I N G OF F I L E F I L E 1 0 9 : 2 2 A . M . MAY 13 , 1975 ID=r 291 END 292 SUBROUTINE ENTRY1 293 IMPL IC IT R E A L * 4 ( A - H , 0 - Z ) 294 REAL *4 INCOME 295 DIMENSION RES( 1000 ) , C O S T ( 1 0 0 0 ) , T I M E ( 1 0 0 0 ) , INCOME(10CO) 296 * , S U R P ( 1 0 0 0 ) , B P { 1 0 0 0 ) , C P ( 1 0 0 0 ) 297 * , B I D R ( 1 0 0 0 ) , A S K R ( 1 0 0 0 ) , S U R P P ( 1 0 0 0 ) , G A M ( 1 0 0 0 ) 298 * , P P ( 1 0 0 0 ) , J J J ( 1 0 0 0 ) , I S E A R ( 1 0 0 0 ) , J M A X X ( 3 5 ) , P R O F I T , 2 0 ) 299 * , R A T R E T ( 2 0 ) , R E V E N U ( 2 0 ) , T I M E 1 (20) 300 * , A L 1 S T ( 2 0 ) , B L I S T ( 2 0 ) , P E R T I M (20) 301 C * $ : « 4 $ : # : $ : * $ < « $ : $ 4 $ 302 C DIMENSIONS SET ,VAR IABLES TYPED 303 C * 304 COMMON INCOME , IDAYCR ,RES , SURP ,BP , JMAX , IDAY ,COST ,T IME , 305 * C O S T M X » T I M E M X , J , I , C P » C P M E A N , J M A X X , I D A Y M X , A D J , V A C A N T , T E S T 306 * , INUM, MONTH,TOTL I S ,K , JMXTOT,L I SBRO,BROTOT,F IX EDI 307 * , F I X E D 2 , A G E N T , T O T B R O , R E V E N U , P R O F I T ,RATRET ,T IME1 308 L I SBR0=.2* IUN IT 309 DO 22 K = l , 2 0 310 22 T I M E 1 ( K ) = 0 . 311 T IME1 (1 )=1 .0 312 DO 20 M0NTH=1,12 313 I F ( M O N T H . E Q . 2 . A N D . R A T R E K 1 ) . G T . . 1 0 ) TIME 1 (2 ) = 1.0 314 TOT IM=0. 315 DO 6 K=l,MONTH 316 6 TOTIM=T0TIM+TIME1(K) 317 DO 7 K = l , MONTH 318 7 PERT IM (K )=T IME1 (K ) /TOT IM 319 A=10. 320 C=.01 321 B= .01 322 DO 2 K=l,MONTH 32 3 A L I S T(K ) = P E R T I M(K)*L I S B R O 324 BL 1ST ( K ) =P ER TI M ( K ) *B ROTOT 325 REV ENU(K ) = F IXED1*AL I ST (K )+F IXED2*BL I ST (K) 32 6 C O S T S = A + B * ( A L I S T ( K ) * A L I S T ( K ) ) + C * ( B L I S T ( K ) * B L 1 S T ( K ) ) 327 PROF IT(K ) = REVENU(K ) -COSTS 328 RATRET (K ) = PROF IT (K ) /COSTS 329 2 CONTINUE 330 4 DO 8 K=l,MONTH 331 8 WR ITE (6 ,9 ) K ,REVENU(K) ,PROF I T ( K ) , R A T R E T ( K ) , T I ME1(K) 332 * , A L I S T ( K ) , B L I S T(K ) , L I S B R O , B R O T O T , P E R T I M ( K ) 333 9 FORMAT(• ' , 1 3 , ' BROKER • , 6 F 8 . 2 , 1 6 , 2 F 8 . 2 ) 334 DO 19 K=l,MONTH 335 TIME1(K)=M0NTH-K+1 336 WR ITE (6 ,17 )K ,T IME1 (K ) ,MONTH 33 7 17 FORMAT( • • , 1 3 , ' M O N T H ' , F 8 . 2 , ' T I M E « , 1 4 ) 338 19 CONTINUE 339 20 CONTINUE 340 I F ( R A T R E T ( K ) . G T . . 1 0 ) TOTBRO=TOT BRO+1. 341 RETURN 342 END 343 SUBROUTINE STORE 344 COMMON B P S T O R , C P S T O R , J J , P E R S T O , S R P S T O 345 DIMENSION BPSTORt1000) ,CPSTOR(IGGO) , SRPSTO(1000) 346 KK=PERSTO 347 RETURN 348 END BIBLIOGRAPHY 123 Alchian, A.A. (1969) Information Costs, Prices and Resource Unemploy- ment, Western Economic Journal, January. Aitchison, A.B. (1973)' Wealth, Income and Inequality; Selected Readings, London, Penguin. Arrow, K.J. (1963) The Economic Implications of Learning by Doing, Review of Economic Studies, June. A x e l l , Bo. (1974) P r i c e Dispersion and Information; An Adaptive Sequantial Search Model, Swedish Journal of Economics, March. Baake, E.W. (1963) A P o s i t i v e Labour Market P o l i c y , Columbus, Charles E. M e r r i l l Books. Balderston, F.H. (1957) Communication Costs i n Intermediate Markets, Management Science, November. Baumol, W.J. 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