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An economic analysis of multiple use forestry using FORPLAN-Version 2 Hackett, James Simpson 1989

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AN ECONOMIC ANALYSIS OF MULTIPLE USE FORESTRY USING FORPLAN - VERSION 2 by JAMES SIMPSON HACKETT B.S.F., University of British Columbia Vancouver, B.C., 1978 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTERS OF SCIENCE in THE FACULTY OF GRADUATE STUDIES (Department of Forestry) We accept this thesis as conforming to the required standard T H E U N I V E R S I T Y O F BRITISH C O L U M B I A November, 1989 ® Copyright by James Simpson Hackett 1989 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of The University of British Columbia Vancouver, Canada Date DE-6 (2/88) ABSTRACT This thesis examines a mathematical programming model called FORPLAN as a plan-ning tool for strategic analysis of forest management alternatives. This model uses economic efficiency as the objective of forest management planning. The dynamic theory of multiple use forestry is analyzed and expressed as a linear pro-gramming analogue in FORPLAN. The main weakness of this theory is that it focuses on single stand analysis. Even so, forest wide constraints applied to certain FORPLAN formulations compensate for this weakness. A strata-based forest management problem is developed to show the economic impli-cations of four forest management alternatives: (1) timber production; (2) timber production subject to a non-declining yield limitation; (3) timber and black-tailed deer (Odocolieus  hemionus columbianus) production; and (4) timber and black-tailed deer production, again including a non-declining yield of timber. Demand curves for two analysis areas and a supply curve for deer winter range are developed using parametric analysis. The ability of FORPLAN to address economic implications of current forest manage-ment policies is discussed. Economic analysis of forest management alternatives would play a useful role in forest planning in British Columbia. The need for such evaluation is underlined by the ever increasing number of resource conflicts caused by the dominance of the timber industry and the continually growing demand for other forest resources. Three conclusions are drawn from this study. First, FORPLAN has the technical capa-bility to be an effective tool for analyzing strategic multiple use plans under economic efficiency criteria. It does not have the timber bias of earlier models and the capability of FORPLAN to integrate area and strata-based variables makes it a very powerful model. i Second, parametric programming of F O R P L A N solutions provides marginal analysis for inputs and outputs. Comparative examination of these curves and their elasticities provide information about the relative importance of different analysis areas. Lastly, managing for timber and hunting services for black-tailed deer by preserving old growth winter range is not an economically viable management option. The relative value of the timber is significantly greater than the hunting services for the deer that it is just not worth managing for both. i i CONTENTS Page ABSTRACT i CONTENTS iii LIST OF TABLES v LIST OF FIGURES vi ACKNOWLEDGEMENTS vii CHAPTER 1 INTRODUCTION 1 CHAPTER 2 ECONOMIC EFFICIENCY AND M A R K E T FAILURE IN FORESTRY 5 2.1 Economic Efficiency 5 2.2 Market Failure in Forestry 8 2.3 Forest Planning and Economic Efficiency 12 CHAPTER 3 ECONOMIC THEORY OF MULTIPLE USE FORESTRY 14 3.1 Introduction 14 3.2 The Faustmann Model 14 3.3 The Multiple Use Faustmann Model 19 3.4 The Present Value Production Possibility Curve 21 3.5 Impact of Non-Timber Values in Practice 24 CHAPTER 4 T H E FORPLAN MODEL 27 4.1 Introduction 27 4.2 Problem Specification 30 4.3 Resource Data : 33 4.4 Marginal Values 37 4.5 Other Relationships 44 CHAPTER 5 APPLICATION AND RESULTS 47 5.1 Application 47 5.2 Results 48 5.3 Sensitivity Analysis of RHS Coefficients 52 iii C O N T E N T S Page C H A P T E R 6 DISCUSSION 58 C H A P T E R 7 C O N C L U S I O N 63 7.1 Strengths and Weaknesses of F O R P L A N 63 7.2 Opportunities for Improvement 67 7.3 Policy Implications of F O R P L A N 68 L I T E R A T U R E C I T E D 76 A P P E N D I X 1 Assumptions of the Faustmann Model 83 A P P E N D I X 2 Assumptions of a Linear Programming Model 84 A P P E N D I X 3 F O R P L A N Data and Yield Files 85 A P P E N D I X 4 L P . Specification of a Mixed Area Strata-Based Problem .. 91 iv LIST OF TABLES Table Page 1 Forest Inventory for the Tsitika River Watershed 34 2 Published Estimates of the Value of Hunting Black-Tailed Deer 41 3 F O R P L A N Results. Objective Function Value and Harvest per Period.... 49 v LIST O F F I G U R E S Figure Page 1(a) The Net Value Per Hectare - Even Aged Stand 16 1(b) The Present Value of Net Harvest Revenues 16 2 Faustmann Rotation vs Maximum Sustained Yield 18 3 The Trade-Off Between Timber and Hunting Present Values 22 4 The System Structure of F O R P L A N 29 5 Flow Chart of the F O R P L A N Analysis System 31 6 B.C. Wildlife Management Unit 1-10 42 7 Variation of Dual Variables of Constraints : 55 8 Winter Range in the Tsitika River Watershed 64 vi ACKNOWLEDGEMENTS I thank my research supervisor, Dr. Peter H . Pearse, for his support of this project. I also thank my supervisory committee, Dr. David Haley, Prof. F . L . C . Reed, and especially Dr. John Nelson for his technical knowledge of F O R P L A N and his interest in my work. My friends and colleagues at the Forest Economics and Policy Analysis Research Unit offered continuing technical and moral support for which I am grateful. I am especially indebted to Darcie Booth and Mike Fullerton for their never ending efforts to help me when I needed it. The initial support of Mr. Grant Ainscough, former Vice-President and Chief Forester, MacMillan Bloedel Limited, is acknowledged, as is the financial support of the Bradfield Graduate Fellowship, sponsored by Noranda Inc. A special thanks goes to Mr. Peter Kofoed, Resource Analyst, MacMillan Bloedel Limited, for his overall help, guidance and insight into relevant applications for F O R P L A N . Linda Harris and Alison Weir have done a tremendous job "processing the words". Laura Wilimovsky draughted the figures and I thank her for such a good job speedily done. Lastly, my wife Mary, and my friend, Huxley, were uncompromising in their support of this effort. vii PERSISTENCE Nothing in the world can take the place of persistence. Talent will not; Nothing is more common than unsuccessful men with talent. Genius will not; Unrewarded genius is almost a proverb. Education will not; The world is full of educated derelicts. Persistence and determination alone are omnipotent. The slogan "press on" has solved and always will solve the problem of the human race. Ansett viii CHAPTER 1 INTRODUCTION This thesis demonstrates an application of FORPLAN - Version 2 (Johnson etal., 1986) as a framework for analyzing the economics of multiple use forest planning. The purpose of this demonstration is to explain how FORPLAN can be used as an effective analytical tool within a comprehensive land management planning process in British Columbia. Multiple use forestry is frequently extolled as the means of mitigating conflicts on the forest land base. Despite some successes (e.g. in Europe) there are many clear examples where multiple use forestry has been difficult to implement in practice. This difficulty is due in part to the lack of a rigorous analytical framework. Examples of current land use conflicts in British Columbia are the Stein Valley, Meares Island, and the South Moresby archipelago. Land use conflicts became most apparent in the fall of 1985 when the provincial government appointed the Wilderness Advisory Committee to recommend areas for wilderness preservation. In its report, the Committee called for a new land use decision-making approach (W.A.C., 1986, p. 17). They cited weaknesses in the institutional framework for land use decision-making; lengthy delays in making decisions, resulting in community hardship caused by the uncertainty; poor communication from govern-ments, and agencies that made decisions without a long term strategy and without a coordinated effort implementing policies with those of other agencies. Another major deficiency in this effort, now widely acknowledged, is the lack of an economic framework for determining the appropriate compromises and modifications in forest land use plans that provide for other values. Pearse (1976) and the B.C. Forest Research Council (1983) have both documented their concern over the failure to adequately consider 1 economic values of other resources in forest development plans. Phillips etal. (1986) found the economics of integrated forest land use to be the most pressing topic in forest economics needing research effort. A concern from a slightly different perspective was expressed by Bowden (1986). He estimated the costs of environmental regulations on the B.C. forest industry at $700 million per year and then asked whether the benefits received at least met this figure. We simply do not know. Some economic analyses of land use decisions have been done (e.g. Ministries of Environment and Forests, 1983) but they are not enough. Consequently, an "on-line" economic framework that has the capability to analyze and determine resource trade-offs for forest development planning is required. Exactly what is multiple use forestry? Rowe and McCormack (1968) offer three common sense notions of multiple use: (1) different uses of adjacent subareas of one land unit which together form a composite multiple use area, (2) different uses on the same land unit through time, and (3) more than one use of a land unit at one time. In practice, multiple use often means "dominant use" management. Specific land areas are allocated to a primary purpose while the overall land use pattern provides multiple services. While such a scheme may be appealing because of its simplicity, it is totally devoid of any economic content. British Columbia's provincial forests are patterned this way and agencies such as the Forest Research Council of B.C. (1983, p.25-34) have found this form of land use allocation inadequate. Economics, concerned with social choices among products and alternative ways of producing them, offers a definition based on concepts established in the theory of the multi-product firm. In this light Bowes and Krutilla (1989, p.32) define economic multiple use management to be the allocation of land to its highest valued use, whether single or multiple purpose. The land manager's objective is to select from the set of all possible land management 2 activities those that will maximize the discounted net present value from the resulting flow of goods and services. The latter must include both marketed and non-marketed goods and services. This definition of multiple use management is used in this thesis. FORPLAN, which is a large linear programming system, offers the economic frame-work designed to address these problems. FORPLAN has been the center of an extensive effort of the U.S. Forest Service, in their very ambitious planning program on U.S. National forests. The program was designed to fulfill requirements of the National Forest Management Act of 1976 (NFMA). FORPLAN became the primary analytical tool used to weigh the economic benefits of alternative comprehensive plans for all National forests. The documented need for such a tool in British Columbia coupled with this huge planning effort proved timely to analyze the capability of FORPLAN for use in British Columbia. The main objective of this thesis was conceived in discussion with analysts of the Forest Economics and Policy Analysis Research Unit (F.E.P.A.). It is to develop and demonstrate the use of FORPLAN for analyzing the trade offs between two forest resources, timber and amenity services for hunting black-tailed deer. The problem is chosen because data was readily available. The idea is to focus on a relatively straightforward problem as a stepping stone to further application. This study begins with a review of the economic theory of resource allocation when information is lacking, and the problems associated with non-marketed goods exist. FORPLAN is presented as a linear programming analogue of a Hartman (1976) problem, that focuses on the optimum age to harvest the forest. The weak link of this theory is its focus on single stand analysis, but FORPLAN embodies procedures that compensate for this problem. This thesis distinguishes FORPLAN, the model, from FORPLAN, the planning system. The point is that FORPLAN in the United States has become synonymous with an entire 3 procedure that encompasses more than just the model itself. Even though a brief discussion of the system is presented in s.4.1, at issue here are the capabilities of F O R P L A N to analyze multiple use planning problems. Much of this thesis is devoted to analyzing the results and policy implications of the F O R P L A N problem. 4 CHAPTER 2 ECONOMIC EFFICIENCY AND MARKET FAILURE IN FORESTRY 2.1 Economic Efficiency Why is a model like F O R P L A N needed? Consider this. Suppose there were perfect markets for all forest resources. Owners of the resource(s) would still need a model such as F O R P L A N to help determine the optimum allocation of resources on the land base. The reason is the inherent complexities associated with multiple use allocation. Therefore, one of the benefits of F O R P L A N is the analytical framework necessary to examine these types of problems. A second rationale for F O R P L A N is the existence of market failures in forestry. A market failure is a situation where a private market fails to achieve allocative efficiency. This provides a rationale for government intervention in the economy. A fundamental tenet for government intervention is enhancement of the public interest. Discussion of what exactly the public interest is, lies beyond the scope of this thesis. The assumption made here is that minimizing economic waste is a proxy for the public interest. Other government objectives include economic stabilization and social equity. Boadway and Wildasin (1984) and Musgrave (1959) provide a thorough review of the subject. Krutilla et ah (1981) and Krutilla and Haigh (1978) offer a briefer review within a forestry context. Three different concepts of economic efficiency are used in the economics literature: production efficiency, exchange efficiency and overall efficiency. Economic efficiency is based on a fundamental concept of welfare economics: Pareto optimality, named for the Italian economist, Vilfredo Pareto (1848-1923). A Pareto optimum is defined as a state of affairs such that no one can be made better off without at the same time making at least one other person worse off (Boadway and Wildasin, 1984 p. 15). Within an 5 economic context this condition has been very hard to apply because of the necessity for inter-personal comparisons between gainers and losers. So economists have found ways to relax this condition in application, by demonstrating a potential Pareto improvement. A n efficient allocation of resources is defined as a Pareto-optimal one. For this tenet to hold, gainers from an exchange must be able to, in principle, compensate the losers and still be better off. The concept of economic efficiency derived from the Pareto principle is commonly classified into the three conditions, production efficiency, exchange efficiency and overall efficiency, mentioned above. These conditions are technical in nature and independent of both institutions and resource allocation mechanisms (Boadway and Wildasin, 1984). Production efficiency deals with the supply side of the economy. It holds that if it is not possible to reallocate factors of production among various users in such a way as to increase the output of one good without at the same time reducing the output of some other good (Boadway and Wildasin, 1984, p.24). That is, in the traditional Edgeworth box paradigm, if all isoquants are assumed to be convex to the origin, then factor inputs have diminishing marginal products and firms minimize their production costs, then production efficiency holds where the marginal rate of technical substitution between any two factors of production is the same in all industries (Boadway and Wildasin, 1984, p.26). When these conditions hold, then factor prices are the marginal values of inputs to the firm. In contrast, exchange efficiency examines the demand side of the economy. Exchange efficiency holds if it is not possible to reallocate goods to make one person better off while at the same time making another worse off (Boadway and Wildasin, 1984). This condition is abstracted from the supply side of the economy, taking any production of goods X and Y as given. This efficiency condition simply ensures that, once produced, a given output of X and Y is allocated efficiently. Again, in the Edgeworth box paradigm, if all individuals have continu-6 cms, convex indifference curves, and they wish to maximize their utility, then, when the marginal rate of substitution of any one good for another is the same for all consumers, exchange efficiency holds (Boadway and Wildasin, 1984, p. 19). Overall efficiency brings the demand side and the supply side of the economy together. It is synonymous with Pareto efficiency. Production and exchange efficiency are necessary conditions. Pareto efficiency holds when efficiently produced combinations of goods are efficiently distributed among consumers. When overall efficiency holds, prices measure the marginal opportunity cost of the resources used to produce the commodity and the marginal benefits to consumers when exchange efficiency conditions hold. This interpretation of market prices as measures of marginal benefits and costs is a property of an efficiently running economy. In a later chapter, this principle will be a critical assumption used in modelling the example in F O R P L A N . For overall efficiency conditions to be satisfied, the markets for all goods must be competitive (Boadway and Wildasin, 1984). All producers must be price-takers and face the same market prices for each commodity as other producers. In addition, producers must face the same set of relative prices for all commodities as other producers. And, in turn, all consumers are price-takers as well and face the same set of relative commodity prices as other consumers. Then, profit maximizing firms and preference maximizing consumers will set their marginal rates of substitution such that they are equal. A competitive market pricing system will therefore ensure that Pareto efficiency conditions are met. This brief exposition is a necessary forerunner to a discussion of market failures in forestry. There are situations where private markets do not function efficiently and, therefore, are said to fail. In some cases these departures are so severe that government intervention can improve the situation. In forest management, market failures provide forest managers with 7 great difficulty deciding what the optimum amount and composition of forest production should be. The remainder of this section examines the sources of market failure in forestry and ties this reasoning to the need for F O R P L A N . 2.2 Market Failure in Forestry Rezende (1982) specifies three reasons why markets fail in forestry: (1) the joint nature of production and the large number of outputs from forests that are poorly understood because of problems of measurement and little knowledge of transformation curves or production functions; (2) uncertainty about input and output values due primarily to the fact that many forest outputs are public goods and not priced in a typical market setting; and (3) the long production period of many forest outputs complicates selection of the correct discount rate for investment analysis. Earlier contributors (e.g. Hall, 1963; Zivnuska, 1961; Clawson, 1978) offer similar discussions. Forestry is a typical example of joint production. A single forest may produce a multitude of outputs and, along with it, two problems. First, quantifying outputs is difficult. While it is relatively easy to measure timber output in cubic meters, it is not so easy to quantify recreational and amenity services. Even more difficult is the accurate valuation of outputs in dollar terms. Second, production functions and corresponding transformation curves between prod-ucts are poorly understood. Growth functions are commonly used as approximations to describe timber production, and even these, at least for British Columbia coniferous species, are poorly understood. For non-timber benefits, relationships between inputs and outputs are simply not known. Multiple or joint production exists in two forms, fixed or variable proportions. With a fixed process, one product is determined solely by the amount produced of the other, whereas 8 with variable proportions, one output is not contingent only on the production of the other. Products produced in variable proportions can be further subdivided into: (1) competitive, (2) complementary, and (3) independent products. Most forestry production is variable in nature. Jointly produced goods are competitive when an increase in the output of one is made at the expense of the other. The classic example is timber production at the expense of wilderness recreation. In cases where the change in output of one good leads to a change in the other, and in the same direction, then these goods are said to be complementary. A typical example is increased water flow with timber production. Runoff increases because there are fewer trees to transpire water. Where output from one product does not affect the production of the other, goods are said to be independent of each other. It is important to put these definitions in context. One must refer to a specific tract of land when defining all outputs. Scale or the size of the land base is also important, because of the related issue of intensity. In a watershed of say 20,000 hectares, timber production and wilderness recreation might be very compatible if the logging activity is localized and the timber production is low relative to the land available for recreation. But as more timber is cut, what was at first complementary production becomes an increasingly competitive situation, as more logging is done at the expense of less wilderness activity. Incomplete information about the relationship of jointly produced goods leads to the problem of common costs. When two products are produced in variable proportions and they are competitive in nature, in theory, a socially optimum output of both can be determined. What is needed are the joint production function of both forestry outputs, the trade-off among all outputs, and the marginal benefits and costs of each output (Rezende, 1982, p.44). The difficulty in determining the marginal benefits arises partly from the fact that many 9 outputs are either public goods or externalities, which are discussed in greater detail below. The difficulty in determining the marginal costs of different outputs is due to the interdependence of the cost and production functions. Both the average and marginal cost of producing an amenity such as dispersed recreation and timber cannot be easily separated. Krutilla (1987), when asked to comment on the use of market receipts to justify below cost timber sales, said: "If critics have in mind determining the cost of timber management and harvest when the cost of other multiple use forest outputs are netted out, the answer is, unambiguously and conclusively, it can't be done. Joint multiple use outputs have common costs, and while from management data it may be possible to glean separable costs by output, the problem of how common costs are to be treated remains. Because allocation of common costs is purely arbitrary, it cannot be used to determine an economically justified full-cost estimate." Krutilla's argument is open to debate. Schuster (1988) describes three different methods for allocating costs, but shows that each method can yield completely different results. Paredes and Brodie (1988) argue that all that is needed is output from the linear programming simplex tableau, which allocates joint costs evaluated as the marginal revenues of resources used in the production process. In any event, the issue is contentious and beyond the scope of this thesis to attempt to resolve. It is, however, at the heart of many multiple use issues, especially when timber values on their own are marginal. The common occurrence of externalities in forestry has been recognized by Duerr (1960) and Gregory (1972). Externalities exist when an activity undertaken by an individual or firm yields benefits or costs to other individuals or firms in addition to the benefits or costs accruing to the emitting party (Boadway and Wildasin, 1984, p.60). When they occur, markets do not allocate resources efficiently because no transaction is involved (Rezende, 1982, p.46). There is no transaction because there are no property rights to transfer. Therefore, there is 1 0 market failure; markets become inefficient and a Pareto optimum is not generated. Externalities may be either beneficial or detrimental. Economic agents not rewarded for the economies (benefits) they cause will produce less than is socially desirable while those agents not penalized for the diseconomies (costs) they provide will overproduce them. A typical example of a diseconomy is air and water pollution produced by a pulp mill. The mill will produce more effluent than that which is socially desirable. The point is, given that externalities exist, economic efficiency will not be achieved because of the wedge driven between private and social values (Ellis and Fellner, 1943). Rezende (1982) provides a review of solutions to this problem. Public goods are prevalent in forestry and are important causes of market failure. A pure public good is a commodity such that, for a given output, additional consumption by one person does not imply reduced consumption by another and, therefore, all consumers have the same potential consumption (Layard and Walters, 1978). Musgrave (1969a) called this joint con-sumption characteristic "non-rivalrous". However, public goods may or may not be non-excludable (Boadway and Wildasin, 1984, p.57). It may be possible to exclude individuals from the consumption of existing outputs of public goods. Both these properties create difficulties for efficient market pricing to work. When markets operate properly, they exclude those consumers who are not willing to pay the market price. In this way markets ensure the quantity available is rationed to those who value it the most. When a good is nonexcludable, sellers are unable to exact a price from users since they can consume it free of charge anyway. And since a voluntary price cannot be imposed on rational individuals, one must be enforced by coercive means, such as a tax. The failure of the private market pricing mechanism due to nonexcludability is called the free-rider problem (Boadway and Wildasin, 1984, p.57). 1 1 Even if nonexcludability was not an issue, the market pricing mechanism would still have difficulty because, although individuals consume the same amount of a public good, both total and marginal benefits across individual consumers would vary. And even if individuals could be excluded from consuming a public good, they probably should not because the marginal cost of doing so is zero. Therefore, excluding people from consumption would be economically inefficient. Impure public goods embody a property of partial rivalness which is called congestion in the economics literature. Examples are parks, highways, and police protection (Rezende, 1982, p.64). In the absence of congestion, all public goods are pure public goods. For most public goods subject to congestion, excludability is possible. The salient point is that nonrivalry in consumption means that demand curves are added vertically for public goods rather than horizontally, as are private goods (Musgrave, 1969b). Not all forms of market failure warrant government intervention in the economy, but failures can provide a normative rationale for intervention in the management of forest resources, in general. And in British Columbia in particular, government ownership of the land and resources is perhaps the most important reason for government intervention. According to Krutilla et al.,(1981) public agencies responsible for forest management ought to engage in land use planning to achieve efficiency in resource allocation. In the presence of market failures this planning will provide a wider level of services than would otherwise be produced. F O R P L A N is one useful analytical tool for identifying and quantifying the desired level of services. 2.3 Forest Planning and Economic Efficiency The linkage between economic efficiency and broad planning objectives of the U.S. Forest Service is derived from the legislative mandate of the National Forest Management Act 12 (1976), which directs the Forest Service to use economic principles in evaluation of land management planning alternatives. This has been more rigorously interpreted to mean economic efficiency criteria are used to develop national forest plans (Krutilla et al, 1981, Krutilla and Haig, 1978, Iverson and Alston, 1986), but not without some debate as to the legislative intent of the Act (Teeguarden, 1985). Nevertheless, there is a focus on the analysis of supply and demand and on the systematic comparison of costs and benefits among alternative production possibilities. In British Columbia, government intervention in the provincial econ-omy includes continued retention of the forest land base in public ownership. Pearse (1976, 1988) has suggested reasons for this. Therefore, the issue addressed here is the utility of FORPLAN as a comprehensive analytical tool, used in much the same way as it is in the United States, to measure the costs and benefits of alternative land management decisions over time, on Timber Supply Areas and Tree Farm Licences, as an attempt to identify desired products, services and production levels of various forest products. 13 CHAPTER 3 ECONOMIC THEORY OF MULTIPLE USE FORESTRY 3.1 Introduction The Faustmann problem is to maximize the present value of receipts from a timber stand by the selection of a sequence of harvest dates (Faustmann, 1849). Hartman (1976) introduces multiple use values into the problem by assuming they are a function of stand age. Adding these values can lead to a change in the optimal time to harvest a stand of timber, but the direction and extent of the change depends on the nature and relative value of the amenities compared to the timber resource (Bowes and Krutilla, 1989). F O R P L A N is a linear programming analogue of the Hartman model. The literature on the economics of multiple use forestry in a static setting (i.e. without embodying time as a variable) is omitted from this discussion because it does not bear directly on the theory underlying F O R P L A N . The reader is referred to Gregory (1955), Muhlenberg (1964), Pearse (1969), Saastamoinen (1982), Bowes and Krutilla (1989), and Krutilla et aj. (1986) for expositions of this theory. 3.2 The Faustmann Model The classic problem in forest economics is the timing of harvests of a sequence of forest crops which are managed in perpetuity with prices, costs, interest rates, and stand productivity assumed to be known and constant. The basic unit of analysis is an even-aged stand of timber. The objective is to maximize the net present value of the future sequence of harvests. This is the capitalized value of the expected annual net income from the forest land. It is the opportunity cost of the land. The algorithm was first described by Faustmann (1849) and more recently by such authors as Pearse (1967), Anderson (1976), Samuelson (1976), Heaps and Neher (1979), Nautiyal and Fowler (1980), and Chang (1984). 14 This model can best be understood by starting with unstocked land, assuming regenera-tion costs per hectare are zero. Timber grows according to the volume function G(t). It reaches a merchantable volume per hectare at a given age t. At harvest time, a net revenue is obtained of the form PG(t), where P is the harvest price, net of harvesting costs. For simplicity, PG(t) = V(T). This cycle is repeated in perpetuity. Since prices, costs, interest rates, and land productivity are assumed constant over time, the harvest age is the same at the end of each cycle. The problem is determining the harvest age T such that the net present value from the sequence of harvest cycles of length T is maximized. The maximum value X*, is expressed as: where r is the interest rate and T is the harvest or rotation age. X* is the maximum net present value or the asset value of a hectare of bare land. The first order condition for maximization requires the selection of a rotation age T such that: Since it can be shown that the second order condition for maximization is met, the rotation age that maximizes the discounted net revenue from an infinite series of rotations occurs when the marginal increase in value V'(T) is just equal to the opportunity cost of delaying the harvest. This opportunity cost is the potential interest income on both X*, the asset value of bare land and V(T), the value of the stock of timber. As long as the growth rate in combined value of the land and the timber (the own rate of return) is greater than the interest rate on alternative investments, it pays the land owner to delay the harvest for another period. Figure 1(a) illustrates a typical value function V(T). With this value function the present value of net revenues from an infinite number of future harvests can be computed for various rotation ages. The curve X(T) in Figure 1(b) describes these net present values. The Faustmann (1) V'(T) = r[V(T)+X*] (2) 15 FIGURE 1 TF T Stand Age a. The Net Value Per Hectare - Even Aged Stand TF T Rotation Length' i . The Present Value of Net Harvest Revenues 16 rotation, T F is the rotation that maximizes the net present value of revenues from all future harvests cycles. Figures l(a and b) assume that the land owner starts with bare land. If the stand is already stocked with timber, the harvest solution remains unchanged, unless the stand has already passed the Faustmann age. Then, of course, the solution is to cut immediately and then follow the Faustmann rule. The Faustmann formula can be used to show the effect of changes in timber prices and regeneration costs on the optimal rotation. If regeneration costs were included in the formula, then the optimal rotation length would increase. Conversely, if timber prices decreased, the optimal rotation length will also increase. Both of these effects cause the curve representing the growth rate in net present value of an infinite series of harvests to shift up. A land owner must wait longer for the sum of all benefits to equal costs. The simplifying assumptions of the Faustmann model are described in Appendix 1. By comparison, maximum sustained yield is a policy that aims to provide the greatest average annual flow of timber per year. This is achieved at a rotation age when the maximum average yearly value V(T)/T is attained. This requires the following condition to be satisfied: V'(T) = V(T)/T (3) which means that a stand of timber shall be cut when the increment in value V'(T) falls to equal the maximum mean annual increment, V(T)/T. This is known as the culmination of mean annual increment, or the forester's solution to the rotation age problem. Comparative results of both the economic (Faustmann) and forester's solution are presented in Figure 2. The Faustmann solution requires a harvest age which satisfies the condition: V'(T) = r[V(T)+X*] (4) 17 FIGURE 2 Faustmann Rotation vs Maximum Sustained Yield Rotation Age T (yrs.) 18 Substituting X* from equation (1) gives: V'(T) = V(T)[r/(i-e r T)] (5) The maximum sustained yield solution is simply a special case of the Faustmann rotation where the interest rate, r, equals zero and volume and value growth rates are identical. At a positive interest rate the Faustmann rotation age is always less than the maximum sustained yield age. This is illustrated in Figure 2, where the function r/(l-e_rT) is everywhere greater than the corresponding function 1/T. Since the timber growth rate (V'/V) decreases with age, the Faustmann rotation age (T F) is less than the forester's rotation age (T m ) . 3.3 The Multiple Use Faustmann Model This section explains the economics of multiple use forestry over time. It was first described by Hartman (1976) as an extension of the Faustmann problem. Faustmann's (1849) formulation does not include the value of other goods and services that flow from a standing forest. Hartman (1976) provides an extension of the general model that includes multiple use values from a forest stand. His analysis also focuses on a single, even-aged stand of timber. He assumes that the flow of multiple use services is a function of stand age which holds for many, but not all cases. Management for joint production of timber and other non-market services is assumed. The solution to this problem is the rotation period that provides the most valuable combination of outputs over repeated rotations. Hartman (1976) formulates his problem by considering the flow of benefits from a hectare of standing stock a(n) at age n. The present value from the amenity service flows of the stand over repeated harvest cycles is: B(T)= } [a(n)e-™)dn/(l-eK) (6) 19 Referring back to equation (1), and combining it with (6) we have: H * = max U(T)+B(T) • T (7) = max \ V(T>- , T + ] [a(n)em]dn / ( l - e^ ) • T (8) where H * is the overall asset value of a hectare of land and X(T) is the timber value defined for the Faustmann problem in equation (1). Solving for the rotation age must satisfy the first order optimality condition: which says that the optimal rotation age is where the marginal increase in value from delaying the harvest V'(T) just equals the opportunity cost of the harvest delay. In other words, keep the stand of timber intact until the rate of growth in the total asset value of both land and timber stock is just offset by r, the rate of return on alternative investments. Equation (9) describes the kernel of the multiple use problem, that a harvest delay pro-vides the benefit of increased timber value plus the growth in amenity values, a(T), assuming that non-timber values increase with stand age. The solution will depend on the condition of neighbouring stands of timber. Theoretically correct estimates of H * , the site value of the land, assumes that management of neighbouring stands is the same. Generally, the Hartman rotation age will lie between the Faustmann age and the age which will maximize the present value of returns from amenity services alone (Bowes and Krutilla, 1989). The optimal rotation age will depend on both the total amenity benefits of a harvest cycle relative to the net timber receipts and on the relative growth rates of amenity and timber values. When amenity values of the standing stock are rising with stand age, the harvest solution will be longer than the Faustmann rotation age (Hartman, 1976; Heaps, 1985). If the amenity benefits, a(T), are sufficiently large and increasing with stand age, the correct solution V'(T)+a(T)=r[V(T)+H*] (9) 20 may be to leave the stand uncut forever. The rotation age becomes infinitely long. If an old growth stand is inherited, the existing high flow of amenity services might also be sufficient to preserve the stand. For it to be economic to preserve the older stand, the present value of amenity services attributable uniquely to the existing stand must be greater than the net value of immediate harvests. On the other hand amenity values that decline with stand age lead to a harvest solution that is less than the Faustmann rotation age. If amenity values are completely insensitive to stand age then the rotation age of the standing timber will not be affected. Introducing multiple use values into the Faustmann model can increase the average supply of timber (Bowes and Krutilla, 1989). If the value from amenity services of a standing stock is an increasing function of stand age, the optimal harvest rotation will be longer than the Faustmann rotation (Bowes and Krutilla, 1989). This will most likely drive the optimum rotation age closer to the age of maximum sustained yield. This higher level of stocking required to support the amenity services results in a higher average timber harvest. Multiple use may also justify management expenditures on lands that are uneconomic from the perspective of timber alone; this could also lead to an expansion of the timber supply. 3.4 The Present Value Production Possibility Curve This section describes an extension to the familiar production possibility curve often used in the multiple use economics literature (e.g. Gregory, 1955; Pearse, 1969; Saastamoinen, 1982). Customarily, such curves define the frontier of joint production possibilities for two products. The curve illustrated in Quadrant I of Figure 3, in contrast, defines the frontier of the combined present values of two products — timber and recreational hunting — produced jointly on a tract of forest land. Each point on the curve indicates the maximum combined present values of hunting and timber that can be generated on the tract of land for a particular rotation 21 F I G U R E 3 22 age (Bowes and Krutilla, 1989). Different points along the curve correspond to different rotation ages. Any output combination within the confines of the curve, such as at point C, represents inefficient combinations of outputs because it is possible to increase the output of both the value of timber and hunting simultaneously. This present value production possibilities curve is concave to the origin implying that, given fixed prices for the two products, the marginal rate of transformation is increasing. This is consistent with the customary theory of joint production, though there may be cases of incompatibility which would result in curves of a different shape. Figure 3 describes the relationship between the present value function and the rotation age. Quadrant II describes the timber present value function X(T) (with a reversal of the axes). The rotation period (T) increases to the left. T F is the Faustmann rotation age, the point at which the net present value of timber is maximized. Quadrant IV describes the present value of hunting as a funciton of the rotation age. A critical assumption is that both timber and hunting unit values are held constant and management costs are zero. To understand the diagram, suppose a Faustmann rotation T F were chosen. There would be a value X* (T) for timber (read from Quadrant II). With this same rotation period there would be a value B(T F ) for hunting (read from Quadrant IV). Point K on the value possibility curve in Quadrant I is the result of selecting the Faustmann rotation age. The objective is to identify the point of maximum combined value along the present value production possibility curve. That point is where the slope of the curve is 45 degrees, indicating that a marginal change in the combination of products will generate benefits of one kind just equal to a sacrifice in the value of the other. At any other point on the curve, the benefits generated from an increase in one product will exceed the loss in value of the other. The point of this diagram is that it illustrates the relationship between a possibility 23 frontier and the timing of outputs. This diagram is only valid with the assumption that both timber and hunting values are constant and all management costs are zero. As it is drawn, Figure 3 is a useful conceptual framework for structuring F O R P L A N problems because it links the multiple use trade-off problem to the harvest schedule, which is exactly what a F O R P L A N model does. 3.5 Impact of Non-Timber Values in Practice Non-timber forest values may represent a varied mix of services. This makes it difficult to determine the impact that including multiple use values will have on the rotation age. While aesthetic values may increase with stand age, other services such as wildlife habitat quality may decrease. The combined effect of several multiple use services may offset any advantage gained from altering the timber rotation (Bowes and Krutilla, 1989). In fact, it is debatable just how sensitive the optimal rotation is when multiple use values are included in the calculation. Calish et al. (1978) concluded that the rotation period changed very little when stock amenity values were introduced into the Faustmann problem. The relative costs of foregoing timber harvests was far greater than the gain in amenity services from preserving the standing stock. Timber values in this study region were much higher, on a relative basis, than all of the amenity values combined. There are exceptions to the results of the study where, implicitly at least, amenity values surpass those of the timber and provide means for justifying preservation of the forest (e.g. many provincial and national parks). Moreover, there are reasons why one should treat the results of Calish et al. (1978) with caution. First, some forest lands have very low timber productivity and multiple use values may dominate the management approach taken on these lands. Second, very little is known about multiple use values of a single stand of timber. Usually they depend upon the condition of adjacent stands in the forest. A meaningful definition of the 24 values of one particular stand are the incremental values due to management of this one stand, given that management of adjacent stands is somehow already determined (Bowes and Krutilla, 1989). Each management alternative will likely lead to different patterns of amenity values over time. Third, the rate of change in amenity value is of significance to the harvest age decision. Even very low absolute levels of stock amenity value can have a tremendous effect on the rotation age solutions if these values suddenly increase. On the other hand, high amenity values will not necessarily affect the harvesting decision if these values are not too dependent on stand age. Lastly, focus on the rotation age as a measure of the impact of multiple use values can be misleading because a small change in the rotation age can drastically change the value of multiple use services. In summary, the model is an elegant but simplistic description of the multiple use forest management problem. The assumptions about constant prices, costs, and productivity will rarely hold. These conditions only hold for the steady state forest for which conditions are constant over time. Hartman's model is perhaps overly simplistic because it focuses only on the single stand and because it assumes constant real prices over time. The focus on a single stand means that the impacts of interrelated management and the resulting net benefits are not captured. The assumption of constant prices is simplistic because relative values are bound to change, such that subsequent rotations might find amenities, for example, taking on different values in the future. While it is important to recognize these weaknesses, Hartman (1976) is still a useful model. In a simplified form, with a focus on the harvest timingfor even-aged stands, F O R P L A N 25 is an analogue to the Hartman model. But F O R P L A N has features which include the ability to incorporate the management of spatially interrelated stands and to allow for changes in the real prices of competing land uses. Thus, F O R P L A N is much more than just a stand level model, and the discussion of F O R P L A N is the focus of the next chapter. 26 C H A P T E R 4 T H E F O R P L A N M O D E L 4.1 Introduction F O R P L A N was developed from the Timber Resource Allocation Model (Timber R A M ) (Navon, 1971) and the Multiple Use Sustained Yield Calculator (MUSYC) (Johnson and Jones, 1979). Both of these models were linear programming timber harvest scheduling models used to decide when, where and how much timber to cut. A documented history of land management planning and the development of these planning tools is provided by Iverson and Aston (1986). There are two versions of F O R P L A N . F O R P L A N Version 2 was used in this thesis so for the remainder of this discussion F O R P L A N means F O R P L A N Version 2. F O R P L A N can be further classified into a Model I and Model II formulation (after Johnson and Scheurmann, 1977). These labels denote two fundamentally different ways to define decision variables in a timber harvest scheduling problem. Model I defines decision variables that follow the life history of a hectare over all planning periods. Model II defines decision variables that follow the history of a hectare over the life of a stand growing on the hectare, from regeneration to final harvest. In other words, Model II hectares may pass through a number of decision variables before reaching the end of the planning horizon. Model I formulations are sensitive to the number of choices for the regenerated timber, such as management intensities, rotation ages, or thinning regimes, while the size of Model II formulations is relatively insensitive to these choices. Model II formulations, on the other hand, are sensitive to the number of regenerated groupings specified because these have to be tracked throughout the life of the problem. Model I problems are completely insensitive to this aspect of problem formulation. The features that make either Model I or Model II attractive to the user 27 will depend on the particular problem that needs to be analyzed. One is not necessarily better than the other. F O R P L A N - Version 2 has the flexibility to use both. A Model I version of F O R P L A N is used in this thesis. Refer to Johnson and Scheurmann (1977) or Davis and Johnson (1987) for further discussion of this issue. Figure 4 presents the system structure of F O R P L A N . As mentioned, F O R P L A N is a linear programming-based system that represents a forest management problem as a set of choices for a particular land grouping and then allows an objective to be maximized or minimized, subject to a set of user specified constraints. The three components of F O R P L A N are a matrix generator, a linear program, and a report writer. Appendix 2 describes the assumptions of a linear programming model. The matrix generator reads the problem data, checks for logical and typographical errors, summarizes and prints the data in readable form, and creates the columns and rows required by the linear program. The linear programming system reads both rows and columns, and then solves the problem or declares it unsolvable. This is accomplished by maximizing or minimizing the objective function, subject to the set of constraints specified in the model. The report writer interprets the solution and then writes a series of reports that describe how the solution has allocated the forest among the management choices and scheduled activities over the planning period. All of the outputs, and their financial and environmental effects, as initially defined, are included in the report writer. F O R P L A N has two specific functions (Johnson et a]., 1986). It is both an accounting and an analytical tool. The accounting system provides a link between the analysis and the U.S. Forest Service's management information system. This function will not be discussed here. Refer to Johnson et a]. (1986, p.2-10) for a brief discussion of FORPLAN's accounting function. 28 FIGURE 4 System Structure of FORPLAN STAGE7USER INPUT COMPUTER PROGRAMS COMPUTER PRINTOUT Matrix Generation Phase USER'S FORPLAN INPUT DATA MATRIX GENERATOR 3 MATRIX (DATA) PRINTOUT II LP Solution Phase CONTROL STATEMENTS LINEAR PROGRAMMING SYSTEM III Report Writing Phase LP ITERATION LOG + SOLUTION REPORT WRITER ALLOCATION AND SCHEDULING REPORT Source: Kent, Kelly and King (1985) The primary analysis function of F O R P L A N involves four key steps that develop a forest plan, usually involving an interdisciplinary team of resource managers. They include: 1. analysis of the forest management problem 2. development of a set of forest management alternatives 3. estimation of the effects of each management alternative 4. comparison and evaluation of each management alternative. These steps follow from directives laid out in regulations of the National Forest Management Act (NFMA). The process brings resource managers and other experts together at the beginning of the F O R P L A N analysis, such that the whole process is a funnel for data collection, analysis, and consensus building, especially if data are lacking. A description of this process is presented in Figure 5. 4.2 Problem Specification We begin with the assumption that the owner's objective is to maximize the net public benefits from the combined production of timber and amenity services for black-tailed deer hunting over a 100 year planning horizon. This multiple use optimization problem is formulated for the Tsitika River watershed on northern Vancouver Island. The intent is to build on existing work and available data. The analysis is on a "stand-alone basis". The focus is the values of these two products which could be realized from the Tsitika, considered in isolation. That is, in the case of benefits attributed to hunting services, no attempt is made to account for the fact that some of the hunting activity of the Tsitika may simply be redirected from other areas of British Columbia. Similarly, in dealing with timber, it is assumed that the drainage has an allowable annual cut (AAC) in its own right, even though in reality it is part of a much larger sustained yield unit. 30 FIGURE 5 Flow Chart of the FORPLAN Analysis System Analysis Stage User Input Computer Programs Reports Problem identification Conceptualizing goals and constraints II Data Yield tables, costs prices, constraint levels, inventory, land classification HI IV Control Statements FORPLAN Matrix generator Defines decision variables, rows, column data i *3 j L O C A L LINEAR P R O G R A M M I N G SOFTWARE Report writer Interprets solution to problem for easy anderstanding FORPLAN (Lists of goals and constraints) Matrix report Tabular feedback of matrix to check problem L P . iteration log & L P . solution Allocation and scheduling report Harvest schedule, activity and economic reports: tables, charts, graphs I Source: Davis and Johnson (1987, p. 6S4) 31 The scale of the problem is limited to this drainage, which is roughly 21,000 hectares, but this was a practical decision to keep the project manageable within the constraints of the thesis. This limitation is not necessary. F O R P L A N is a strategic planning tool designed to be used on large tracts of land, the size of tree farm licences (T.F.L.'s) or timber supply areas (T.S.A.'s). However, a tract of land this size will not deter the explanatory or illustrative power of the model. It simply limits the data set to a size fitting for this thesis. A strata-based approach to land organization is adopted, after Johnson and Stuart (1987). A stratum is a category of land such as western hemlock (TsugaheterophyllaRaf. Sarg.), age 80, that responds in a uniform way to a particular management action. The general form of the linear program is: (10) (11) s I K max E s = l E i = l B S l k ^ i k s.t. k E i = l E k = l X s i k = A s f o r S = 1 > X s i k >0 v i > v k where: X s i k = hectares assigned to timing choice k of prescription i of analysis area s, where analysis area s is a stratum of the forest, B s j k = contribution to objective function (per hectare) of timing choice k of prescription i on analysis area s, S = number of analysis areas (15), I s = number of prescriptions on analysis area S (2), Kj = number of timing choices for prescription i on analysis area s, A = size of analysis area s, in hectares. A copy of the F O R P L A N data and yield files developed for this problem are presented in Appendix 3. 32 The following issues are evaluated in this problem: 1. the impact of implementing a harvest policy of non-declining yield, 2. the amenity values required to reserve different amounts of old growth winter range for black-tailed deer habitat over the planning period, 3. marginal analysis of both a non-declining yield policy and preservation of old growth winter range. 4.3 Resource Data Forest inventory data for the major portion of the Tsitika River watershed, located on northeastern Vancouver Island, British Columbia was aggregated into 15 analysis areas based on suitability as winter range, species, site, and age classes. This inventory is presented in Table 1. Stand specific volume data are omitted from this table because they are confidential. Data for the mature inventory consisted of approximately 900 different stands. It was aggregated into two species groups, as determined by the major species in each one. A major species group contains at least 50 percent of the volume of that stand. Western hemlock, and amabilis fir (Abies amabilis Dougl. Forbes) stand types were aggregated into the western hemlock ( H E M ) species group. Douglas-fir (Pseudotsuga mensiezii Mirb. Franco) and Sitka spruce (Picea sitchensis Bong. Carr) stands were minor (by area) so they were added to the H E M species group, the assumption being that they would have very little impact on the analysis. All western redcedar (Thuja plicata Donn.) and yellow cedar (Chamaecvparis nootkatensis D. Don Spach) stand types were combined into the western red cedar (CED) species group. H E M covers 79 percent of the forest area while C E D covers the remaining 21 percent. Therefore, the assumption is that each species group is made up entirely of 100 percent hemlock or cedar, respectively. Aerial photographs of the Tsitika River watershed showed the predominance of western hemlock, western redcedar, and amabilis fir timber. 33 T A B L E 1 FOREST INVENTORY FOR THE TSITIKA RIVER WATERSHED Analysis Area Species h Group Site 2- Winter 3-Range (Y/N) (ha) 1 H E M G N 1129.0 2 H E M M N 141.7 3 H E M M N 3528.5 4 H E M P N 957.0 5 H E M P N 8572.1 6 C E D G N 10.9 7 C E D M N 739.7 8 C E D P N 102.7 9 C E D P N 2901.9 10 H E M G Y 278.7 11 H E M M Y 467.0 12 H E M P Y 33.3 13 H E M P Y 682.7 14 C E D M Y 36.0 15 C E D P Y 492.0 T O T A L 20973.2 Source: MacMillan Bloedel Limited, Woodland Services Division, Nanaimo, B.C. Notes: 1. H E M = Hemlock Stand Type C E D = Cedar Stand Type 2. Site Codes: G = Good M = Medium P = Poor 3. Y = Yes; N = No 3 4 Further checking of this assumption involved examination of Ministry of Forests scale and royalty records. Five years of historic records which represent a good distribution of stand types over the entire watershed showed 95 percent of the production as hemlock, amabilis fir, and redcedar, so this aggregation is reasonable. Site class represents the average height of the dominant species (in metres) at the reference age of 50 years. This is the standard forestry measure of site fertility. Three classes were used: good, medium and poor. Good sites were classified at 33.5 m or greater. Medium sites were between 27.6 and 33.5 m, while poor sites were below 27.6 m. Three age classes were defined; immature (0 to 60 years), mature (61 to 130 years), and overmature (>130 years). These broad classes helped focus on the trade-off between harvesting marginal hectares of old growth timber or holding them in reserve as winter range habitat. All timber stands were 300 years old initially. Merchantable volumes for existing mature stands are average volumes per hectare, net of decay, waste, and breakage. Yields for juvenile stands are generated from yield functions for western hemlock. They are taken from Nawitka Resource Consultants (1987). Yields are for normal, fully stocked, unmanaged stands. They are expressed as net merchantable volume per hectare as well. Winter range is assumed to be a critical requirement for deer habitat in this watershed, critical, that is, for survival of the resident deer population. This assumption is supported by the work of Harestad et a l (1982) and McNay and Doyle (1987), who describe suitable criteria for such habitat. Winter range is defined on the basis of elevation (less than 300 m above sea level), aspect (either south, east or west), proximity to spring forage, and effective crown closure of the forest canopy. These criteria are assumed to be relatively independent of timber type, so the aggregation discussed above into hemlock and cedar species groups would not affect the quality 35 of winter range. Existing winter ranges, as defined in the 1985 Development Plan for Tree Farm Licence 39, Cutting Permits 19 and 20 (MacMillan Bloedel Limited, 1985) exhibit these physical characteristics and are prescribed as winter ranges in this problem. Four other similar land units were added to this list of suitable winter ranges. A further critical assumption for this problem is that spring forage habitat is provided evenly throughout the watershed for the entire planning period, adjacent to winter range habitat, where it is thought to be most suitable. This assumption is implicit because the actual winter ranges selected for this problem are distributed throughout the entire watershed. Yield relationships for hunter days per hectare of winter range were obtained from the Ministries of Environment and Forests (1983). This study was conducted for Tree Farm Licences 37 and 39. The Tsitika comprises a portion of T .F .L . 39. It seemed reasonable to use this information in this thesis because on balance it is representative of conditions found in the Tsitika. This study used a simulation model to develop a yield curve describing deer populations as a function of the supply of winter range habitat. The study estimated an average number of 1.1 deer per hectare of winter range habitat. It further estimated an average of 1.23 hunter days per harvestable deer. No attempt was made to differentiate the hunting effort between bucks and does because the data would not support it. The study did not differentiate between different qualities of winter range. However, in the F O R P L A N model formulation, quality could and would have been addressed if other than average data were available. Given the average figures of 1.1 deer per hectare of winter range and 1.23 hunter days per harvestable deer, every hectare of winter range thus supported an average of 1.35 hunter days. This figure was used for all winter range analysis areas, across all three site indices in the problem. The assumption in the problem of 1.35 hunter days per hectare of winter range implies 36 a linear yield curve. The problem with the linear assumption of this yield curve is that it does not exhibit diminishing marginal returns to winter range. In economic theory, the law of diminishing marginal returns states that as the amount of a variable input is increased, all other factors held constant, a point is reached beyond which the marginal product of the input diminishes (Mansfield, 1979). Applying this law to this problem suggests that above a certain point, adding a marginal hectare of winter range would increase the number of hunter days to a maximum, beyond which the marginal product of winter range should decrease. The approach taken here is that over a relevant range of habitat area, returns are constant which seemed to be a reasonable assumption for an initial F O R P L A N problem formulation. As discussed in Chapter 5, the optimal solution was insensitive to this assumption of constant marginal returns to hectares of winter range. 4.4 Marginal Values Monthly average log price data for each species and grade from 1981 to 1987 inclusive, as listed on the Vancouver Log Market were used to generate weighted average selling prices for both western hemlock and western redcedar species groups. Prices were corrected for inflation using the Industrial Product Price Index for B.C. softwood lumber (Stats. Canada, 1986) and are expressed in constant 1987 Canadian dollars. Weighted average selling prices for both species groups were calculated using log grade data representing the Tsitika River drain-age. Western hemlock is priced at $51.52/m3 while western redcedar is priced at $80.34/m3. A n average logging cost was calculated using inventory and road cost data representative of the Tsitika River drainage. The 1987 Coastal Appraisal Manual (MOF, 1986) was used to estimate a delivered wood cost to the Vancouver Log Market at Howe Sound, British Columbia. It was estimated to be $45.80/ m 3 , expressed in 1987 Canadian dollars. Corrections for inflation were also made using the Industrial Product Price Index. This cost estimate does not include a logging profit. 37 Prices and costs are held constant throughout the 100 year planning period. No adjustment is made for the shadow price of labour. The timber industry is assumed to be perfectly competitive. The long run equilibrium condition holds such that the long-run average total cost equals log price. The marginal net value or conversion return for western hemlock and western redcedar are $5.72/m3 and $34.54/m3, respectively. Consumer's surplus, expressed in dollar terms, is the conceptually correct measure of an individual's satisfaction or value of a good. This is defined as the difference between the maximum a consumer would be willing to pay for his current consumption of a good and the amount he actually pays for it (Layard and Walters, 1978, p. 149). There are four measures of consumer surplus accepted in the literature of which two are important to this decision. A recreationist's willingness-to-pay to use a resource over and above his costs is one. This is known as the compensating variation. It is the maximum amount of money one would be prepared to pay for access to the recreation rather than be excluded (Pearse, 1968, p.88). The second approach is called willingness to sell, which is the minimum amount a consumer would have to be paid (bribed) to willingly abstain from participating in a recreational activity. This is called the equivalent variation. To see the difference between the two measures, consider, as Varian (1984) does, status quo and current prices. Equivalent variation uses the status quo prices as the base and asks what income change at the current prices would be equivalent to the proposed change. Compensat-ing variation, on the other hand, uses the new prices as the base and asks what income change would be necessary to compensate the consumer for the price change. The choice between these two measures usually depends on the activity being analyzed, and the question trying to be answered but agreement on the proper choice between each 38 measure is not clear, as pointed out by Krutilla and Fisher (1975, p.30-36). If one is considering trying to arrange for some compensation scheme at the new prices, then the compensating variation seems reasonable. On the other hand, if one is simply trying to get a reasonable measure of "willingness-to-pay", the equivalent variation is probably better. The reasons are first, the equivalent variation measures the income change at current prices and it is much easier for decision makers to judge the value of a dollar at current prices than at some hypothetical price. And, more generally, if more than one proposed policy change is being compared, the compensating variation keeps changing the base prices while the equivalent variation keeps the base prices fixed at the status quo. Thus the equivalent variation is more suitable for comparisons among a variety of projects. In this thesis estimates of consumer surplus are estimates of willingness-to-pay. Willingness-to-pay for a resource, and the resulting consumer surplus, can be described in terms of a demand curve. For black-tailed deer hunting, a hunter is willing to pay a maximum amount over and above his necessary costs in order to pursue hunting activities. In addition, this hunter would be willing to "buy" a certain number of units of that activity at different prices below the maximum. The verb "buy" is used figuratively here because a hunter day is not purchased, as are other commodities. Nevertheless, a price and quantity relationship should exist forming an individual demand curve for each hunter. The sum of individual demand curves constitutes the aggregate or market demand curve for this recreational activity. Different recreational areas would each have their own demand curve and the area under the demand curve, over and above existing costs incurred using the site is an estimate of the consumer surplus. Demand curves are affected by consumers' tastes, substitute areas and their prices, disposable income, leisure time, access and expectations of a successful hunt (McDaniels 39 Research Limited, 1980). Increasing the number of animals, or managing a herd of deer for "prize bucks" in one hunting area, while holding all other variables constant, would certainly increase demand for those hunting services. When considering the effects of forest management with regard to trade-offs between recreational deer hunting and timber production, it is marginal, rather than average willingness-to-pay that is required. Moreover, instead of focussing on the average value of recreational activities (which is influenced by other factors such as scenery and climate, as well as number of animals), what is required is to isolate how an increase (decrease) in the stock of black-tailed deer affects hunter numbers and satisfaction, with all other variables held constant (McDaniels Research Limited, 1980, p.18). This isolates the marginal value of consumer surplus that is attributed to an adjustment in the game stock, and it is this value that is required, rather than the marginal consumer surplus per recreation day. A few investigators (i.e. Hammock and Brown, 1974 and Langford and Cocheba, 1978) have attempted to measure marginal values per animal. Neither case supplied estimates regarding the change in marginal values as increasingly larger quantities of animals were provided in a given area. Only one point was estimated on the "total consumer's surplus" curve. Moreover, both studies analyzed recreation values over large geographic areas, rather than in more localized areas with substitutes nearby. In practice the marginal values attributed to an adjustment in the stock of deer are unavailable. Instead, an estimate of average willingness-to-pay for a deer hunter-day for northern Vancouver Island is used. It was calculated by Reid et a]. (1985) and is presented in Table 2 along with estimates from other authors. It is $31.57 per hunter-day, expressed in 1987 dollars. This figure is the average consumer's surplus per hunter per day, across the range of hunting opportunities in wildlife Management Unit 1-10, located on northern Vancouver Island (see Figure 6). It is assumed to remain constant over the 100 year planning period. Reid et al.'s 40 TABLE2 PUBLISHED ESTIMATES OF THE VALUE OF HUNTING BLACK-TAILED DEER Value of a Description Source Hunter-Day (1987 $Cdn) 63.40 .44.51 41.52 34.85 31.57 30.10 Deer in Arizona Deer in Utah, Idaho, Wyoming, Nevada Deer in Utah Deer and elk in Oregon Deer on north-eastern Vancouver Island Deer - B.C. Provincial Martin et al., 1974 Hansen, 1977 Wennegren et al., 1973 Brown et al., 1973 Reid et a]., 1985 Reid etal., 1985 1. As reported in Pope (1986), adjusted from 1983 to 1987 $Cdn. 41 FIGURE 6 B.C. Wildlife Management Unit 1 -10 42 1985 estimate applies to hunters currently using Management Unit 1-10, which includes the Tsitika River. These hunters are the referent group for his study. Reid et al. (1985) used the contingent valuation method to estimate this figure. Non-user existence and option values are not included in this study, as explained below. This value is used to estimate the imputed willingness-to-pay of hunters for days of hunting in the Tsitika River watershed because it is the most recent estimate of consumer surplus published and it pertains to the study area. The assumption is that marginal and average consumer surplus values are equal, and this implies that the demand curve for black-tailed deer hunting is perfectly elastic. The Tsitika River watershed represents a perfect substitute for surrounding watersheds in Management Unit 1-10. McDaniels (1980) assumed that the marginal net benefits of deer hunting in the Sayward Forest after enhancement were 80 percent of the provincial average figure, or $25.26 per day. Therefore, the average figure used in the example of the Tsitika may overestimate the marginal value of a hunter day. Conversely, the use of the average value may be reasonable when other non-hunting values of deer are considered. For example, it is possible for individuals to derive satisfaction simply from knowing that black-tailed deer exist, even though they never expect to see them, let alone hunt them. This type of satisfaction is known as existence value (McDaniels, 1980, p.17). Another example of a non-hunting value of deer is option value. It occurs when an individual places value on having the option, either for himself or for others, to participate in some form of wildlife activity in the future (McDaniels, 1980, p.17). Option value can occur separately from consumer surplus, especially in situations where environmental change means irreversible loss of wildlife populations or scenery. 43 Marginal additions or reductions in relatively common animal species, such as black-tailed deer, means consideration of these non-user values is of little consequence because there is no major loss of animal populations (McDaniels, 1980). This is why Reid et al.(1985) did not include these values in his figures. Since major animal population losses are not at issue in this thesis, these values do not matter, and no attempt is made to include them. Even if these values are small, they may account for some of the difference between mean and marginal values. Thus the use of average values may be reasonable at least in terms of an initial problem formulation. This notion that the non-hunting values of deer are not trivial was in part addressed by Bishop etal. (1984). The objective of this study was to see how the actual and contingent values compared and to test different bidding or auction methods for eliciting the contingent value estimates. The study found that the different bidding methods all gave about the same numerical results but the highest hypothetical bids for deer hunting licences were 60-80 percent higher than actual bids. This result suggests that McDaniels (1980) figure of $25.26 per hunter day may be too low. 4.5 Other Relationships Management costs for black-tailed deer, other than opportunity costs of foregone timber, are assumed to be zero. Silviculture costs for regenerated stands are also zero. This assumption is reasonable because the Tsitika watershed is dominated by mature timber. In other words, within the 100 year planning horizon, the scheduling of old growth harvests dominates the problem. For these costs to become a factor, the planning horizon would have to be extended considerably. Al l prices and costs are expressed in real 1987 dollars. Selecting the correct discount rate for forestry investments is especially important, because of the long time for forest crops to reach maturity. In this thesis, a real discount rate 44 of 4 percent is adopted on the strength of the analysis of Heaps (1985) who reasoned that investments should reflect the risks inherent in forestry, which are considered to be relatively low. Heaps accepts the reasoning of Row et al. (1981), who determined the appropriate real rate of return to be 4 percent, which was the relatively risk free rate for Aaa corporate bonds. Central to the purpose of discounting is the concept of intertemporal efficiency such that resources are allocated efficiently between present and future generations. A high rate of discount tends to shift consumption away from the future towards the present, because earlier periods of consumption are relatively more valuable. In Chapter 3, the claim was made that F O R P L A N , in its simplest form, is a linear programming analogue of Hartman's (1976) model. Hartman assumed amenity services as well as timber values to be related to stand age and focused on the timing of harvests for even-aged stands. In F O R P L A N , different land units can be defined as stands of a particular age class and thus optimize on a stand by stand basis. However, a more realistic formulation optimizes over the whole forest (and not just individual stands). As a forest level model F O R P L A N can address a variety of policy or other technical constraints that apply to the entire forest or specified portions of it, but not just to a single stand. For example, a policy constraint of non-declining yield on the forest does not necessarily imply that this constraint would apply to particular stands of timber. Moreover, a variety of management regimes may be considered for different stands, including management for non-timber products. These capabilities embody Hartman's model at the stand level but extend it with application to the whole forest. The main weakness of a strata-based multiple use F O R P L A N problem is that the linear programming structure provides no attention to the production linkage between individual stands. But, as a general rule, management of one stand will affect the amenity services provided by adjacent stands. 45 This problem has been described by Bowes and Krutilla (1989) and, while they are correct for certain formulations within F O R P L A N , (i.e. strata-based analysis areas) another formulation alleviates this problem by defining geographic decision variables. As Bowes and Krutilla (1989, p.119) say, "A more appropriate treatment of multiple use, in a linear programming framework, may be accomplished if land units are defined based on geographical or demand based criteria rather than timber stand age." This is accomplished by structuring a coordinated allocation choice (C.A.C.) problem, as described by Johnson et a]. (1986). This defines two types of decision variables, strata-based and area-based. The area-based variable defines a specific geographical area or zone. A linkage system allows F O R P L A N to decide whether to harvest this zone or keep it intact for a particular set of amenity services. Relative values of these actions can be specified and by so doing capture the interrelated management implications of a multiple use problem. A more thorough discussion of this type of problem structure is left to s.7.1. In summary, one of the innovative features of F O R P L A N is its capability to model different forest products with their own yield functions, prices, and costs. Previous timber harvest scheduling models such as M U S Y C and Timber R A M could only constrain timber production, in order to provide non-timber products. A second feature is FORPLAN's capability to theme prices, costs, and yields. Theming allows different decision variables with the same prices, costs, or yields to be expressed only once without repetitive entry. In previous models, every decision variable had to have these parameters entered separately, even if they had the same value. This is a very important practical advantage, because it saves time entering data and reduces the size of yield files considerably. 46 C H A P T E R 5 APPLICATION A N D R E S U L T S 5.1 Application The F O R P L A N model was used to analyze four scenarios. The first scenario was a timber harvesting problem. The harvest schedule was divided into ten, 10-year periods, which were user defined to suit this problem. The model was unconstrained. This is the only scenario that applies the Faustmann rule. The other three scenarios discussed below do not follow the Faustmann because they impose policy constraints on the feasible set. The second scenario added a non-declining yield constraint to the previous problem. It simulates an even-flow timber harvest policy through time. Imposing this constraint and measuring the difference in objective function values between this and the previous scenario provided an estimate of the opportunity cost of the harvest constraint policy. In other words, holding a portion of the economically mature timber stock and cutting it in future periods bears a cost equal to the yield the timber capital would be earning in alternative investments. This scenario was included to simulate the current harvest policy, but, as discussed in Chapter 2, non-declining yield will, in most cases, impose a cost on society because the rotation length will be longer than economically optimal. The third scenario addressed the joint production of timber and black-tailed deer hunting services. The deer population is a function of the area of winter range available since this is the assumed critical habitat. The deer population will, in turn, support a certain number of hunter days of recreational activity. The larger the deer population, the greater the number of hunter days available and assumed to be demanded. This scenario is the Hartman model. Lastly, the fourth scenario incorporated two policy constraints. The first was a non-declining yield constraint. It provided an even-flow harvest schedule over the entire planning 4 7 horizon. This is a Hartman model with an added constraint of non-declining yield that will force the model to choose rotation lengths that are longer than economically optimal. The second was an absolute constraint on the available area of winter range. It was set at a minimum of 1,700 hectares. 5.2 Results Table 3 presents the optimal solutions for all scenarios. For scenario I, all mature timber, which totals 14.9 million m 3 , is harvested in period one. Regenerated forests are harvested in the 9th and 10th periods, resulting in 2.1 and 3.8 million m 3 of harvest, respectively. The net present value of the objective function is $135.4 million. The scheduling solution is consistent with a Faustmann net present value maximization criterion. The decision rule dictates that a timber stand be cut when the growth rate in stand value plus the land rent is less than, or equal to, the discount rate. For the mature stock of timber the growth rate G'(t)=0. Prices and costs are constant, inflation is zero and the real interest rate is 4 percent. Therefore, in the context of Equation (2), Chapter 3, V'(T), has long since fallen below the interest cost, and the stands are cut immediately. For second growth stands, higher valued red cedar timber is harvested first, in the 9th period. A mixture of redcedar and western hemlock stands on medium and poor sites is left to the last period. The Faustmann rule still carries. The growth rate in value, V'(t), which is the growth rate in value of the combined value of the land and timber stock at harvest, is greater for redcedar stands. These will be cut first, because V'(t) will grow and then fall to just equal 4 percent first. Subsequent harvests follow on a combination of western hemlock and poor site redcedar stands in period 10, because V'(t) is lower for these stands. 48 TABLE 3 FORPLAN RESULTS: OBJECTIVE FUNCTION VALUE AND HARVEST/PERIOD Objective Function (NPV -10 3 $) H I H2 H3 H4 H5 H6 H7 H8 H9 H10 L T S Y (m3/yr) Winter Range Constraint (ha) Cases I II III IV 135.4 80.3 135.4 79.2 Harvest/Period (105 m3) 14.9 1.7 14.9 1.6 1.7 1.6 1.7 1.6 1.7 1.6 1.7 1.6 1.7 1.6 1.7 1.6 1.7 1.6 2.1 1.7 2.1 1.6 3.8 1.7 3.8 1.6 0 23,034 0 21,406 > 1,700 49 This "one-time" harvest solution of the old growth timber in the first period assumes log prices are unaffected by such a rapid harvest. In reality, such quantities could have a significant downward pressure on log prices. If this turned out to be true, then net present values for the harvest would be lower than the value reported here. This scenario also assumes there is no capacity constraint on the harvest. The objective function value for scenario II falls to $80.3 million, a difference of $55.1 million, which is the opportunity cost of the harvest constraint policy. The yearly sustainable harvest calculated with this policy is 23,034 m 3 . F O R P L A N still harvests the relatively higher valued redcedar stands first, subject to the harvest constraint, and then progressively, by period, harvests stands of lower and lower value. Average revenue falls from $34.50/m3 in the first period to $23.20/m3 in the second period because the higher valued redcedar stands are taken first. The next six periods are constant at $5.72/m3 where the harvest is predominantly western hemlock. Average revenue then jumps to $8.13/m3 in the 9th period and ends at $21.80/m3 in the 10th period because redcedar stands are harvested again as a second rotation. F O R P L A N chooses the most valuable timber first. In other words, it "highgrades" the inventory, which is to be expected from a present value harvest criterion. An alternative is to constrain F O R P L A N to a non-declining net present value instead of non-declining yield, and compare the scheduling solutions. This type of constraint maintains the timber quality of the inventory, because the harvest of the higher quality timber is spread over the planning period. However, economic efficiency is sacrificed in the process. Arguments can be presented for rationalizing a non-declining yield policy. For example, risk aversion coupled with uncertainty over the size of externalities might lead some to choose a culmination age rotation over a Faustmann rotation. Another example is the notion of 50 irreversible development, after Krutilla and Fisher (1975). If the values of amenities are growing faster than timber values, then the Faustmann solution is myopic and some would prefer less development (i.e. a longer rotation age). The difference in the value of the objective functions of an unconstrained and constrained model, or between Scenarios I and LT, $56.8 million, is a measure of the collective value that some might put on the externalized amenities. A more mainstream view is that the non-declining yield constraint is a measure of the opportunity cost associated with spreading out the cut. In other words, society must pay $55.1 million for the benefit of a non-declining yield policy. Using Reid et al.'s (1985) estimate of $31.57/hunter day for the average willingness-to-pay for deer hunting, the optimal harvest schedule for scenario III is the same as scenario I. This value for a deer hunter day is so low, that the economically efficient solution is to continue managing the forest for timber production only. Sensitivity analysis was undertaken to determine how responsive the solution was to the average willingness-to-pay estimate. The objective-function coefficient for the value of a hunter day did not result in a changed optimal basis until a value of $100/hunter day was substituted. This yielded 1,974 hectares of winter range. There is nothing to be gained by allocating hectares to deer winter range allocation issue if hunting black-tailed deer is only worth $31.57 per day. The value of this amenity service must rise in real terms to $100 per day before economically efficient forest management includes management for both timber and deer. Assuming additivity, an alternative interpretation is that the sum of all public goods, over $31.57 per day must reach $100 per day on winter range sites before these old growth stands are reserved under economically efficient forest management criteria. Given that many of the externalized amenity values have public good characteristics, and thus demand curves are summed vertically, it is quite possible that the total value of $100 per day can be justified. The fact that plans exist for 5 1 other forest uses in the Tsitika supports this idea. The optimal solution was insensitive to the assumption of constant marginal returns to hectares of winter range because the relative value of deer hunting is so much lower than the value of timber. If the yield curve did, in fact, exhibit diminishing marginal returns, the optimal solution would have favoured timber that much more. Scenario IV applies two policy constraints: a non-declining yield and an absolute constraint on the available area of winter range. This latter constraint is set at a minimum of 1700 hectares. The objective function value falls to $79.2 million. This is $1.1 million less than scenario II, which was a timber model constrained by a non-declining yield policy. Therefore, the opportunity cost of reserving this winter range is $1.1 million over the entire 100 year planning period. The non-declining yield flow drops 100,000 m 3 per period. The incremental addition of constraints is a way of measuring the cost of the policy. Constraining, however does not allow measurement of the value of what is produced. 5.3 Sensitivity Analysis of RHS Coefficients Systematic variation of a constraint within a linear programming model, holding all other coefficients or parameters constant, is parametric right hand side (RHS) analysis (Dykstra, 1984). Paredes and Brodie (1988) refer to this procedure as post-optimality analysis. Dykstra (1984) and Paredes and Brodie (1988) illustrate the utility of parametric analysis of forest planning problems. Both Paredes and Brodie (1988) and Hof (1987) argue that it has not been used enough in U.S. forest planning efforts. The purpose of this section is to demonstrate parametric programming of right hand side variables (or parametric RHS), discuss the economic interpretation of the results, and describe the usefulness of the results for policy analysis. Dykstra (1984) describes parametric analysis of RHS in the following way. The RHS 52 parameter LI is replaced by the expression B ; + . The general parametric RHS linear programming problem is then stated as: maxZ(X) = E C X . (12) j=i J J s.t. E A . X. <B,+m for i = l , n (13) j=i 1 1 > X.>0 j = l , . . . ,N where X is a parameter to be varied over a specific range and /Jj is the relative rate at which RHS value Bj is to be changed as the parameter varies. The parametric RHS technique systematically shifts through the feasible region by successively incrementing the value of B ; by X/S;. As Bj increases, the right hand side increases and eventually cuts off a portion of the feasible region. If the optimal solution to the linear programming problem with an initial objective function Z l had previously fallen within that portion of the feasible region that is now cut off, then the optimal basis will change, and so, of course will Z l . One continues to do this over a wide range of possible values of the RHS parameter. In this F O R P L A N example, as in many forest planning problems, some constraints describe resource availability, while others describe policies that represent society's desires on output production and factor utilization. A resource constraint is the number of hectares of each analysis area, while a non-declining even flow constraint represents an even-flow timber production policy. Recall that the problem formulated here assumes profit maximizing behavior for the production process, and that a Pareto optimal solution requires price to equal marginal cost of producing the good or service. For many public goods, demand curves are unavailable, or, as in the case here, there is a high level of uncertainty around the estimate. Nevertheless, the 53 decision process is enhanced by deriving the marginal cost curve of each good, and these curves are derived easily by parametric variation of RHS variables (Paredes and Brodie, 1988). Figures 7 (a) to (c) describe the marginal curves for parametric variations of analysis area 15, minimum deer winter range area, and the nondeclining yield constraint. Figure 7 (d) estimates the production possibility frontier for timber and deer winter range. The timber problem defined in scenario III was used to develop the demand curve for land in analysis area 15, which is drawn in Figure 7(a). Analysis area 15 is defined as a redcedar stand type on a poor site class. The curve is derived by plotting the parametric variation of the RHS value of this constraint (land in analysis area 15) as a function of its dual or shadow price. The dual measures the opportunity cost to the land owner of adding an extra hectare to the total number in this analysis area. In this curve, the present value declines, causing the quantity demanded to increase. Since the relative change in quantity demanded is much greater than the relative change in present value, the demand for this analysis area is said to be elastic with respect to price (Layard and Walters, 1978). The policy implication is obvious. Goods with many substitutes have relatively higher elasticities. Goods with fewer substitutes tend to have lower elasticities. Similarly the greater the number of possible uses of a commodity, the greater its elasticity. Therefore, in the application here analysis areas with relatively higher elasticities will be effective substitutes for other analysis areas, as winter range habitat. Figure 7(b) describes the discounted cost per hectare for different levels of winter range habitat provided. This is a supply curve for winter range habitat, derived from applying a minimum winter range constraint to scenario III. This is useful information for public planning purposes, where analysis of the public's demand for alternative levels of habitat can be compared to the estimated cost of supplying various levels. Figure 7(c) is useful for evaluating a policy that constrains the flow of harvests over time 54 FIGURE 7 Parametric Variation of Dual Variables of Constraints (o) (b) 1000 2000 3000 4000 5O00 LAND IN ANALYSIS AREA 15 (Ho.) o c N 30 Z 2.0 a. 1.0 0 500 600 1700 2200 MIN. WINTER RANGE (Ho.) 55 to a non-declining yield (NDY). The N D Y "produces" a flow of timber that does not decrease by more than a specified amount from one period to the next. By systematically departing from the N D Y constraint, and measuring the dual price of the departure, a measure of the marginal cost of maintaining N D Y policy is obtained. In this example, the marginal cost curve is derived from parametric testing of the non-declining yield constraint at periods 8 and 9 of the model described in scenario III. No other constraints are included in the model for this test. This curve measures the marginal cost of departing from a non-declining yield (NDY) policy. The objective function, on the other hand, increases because the constraint has been relaxed. For the Tsitika River watershed, the marginal cost curve is relatively elastic for small departure levels. Therefore, over a wide range, departures from N D Y would have a significant impact on the value of the objective function, as was shown by comparing scenario I with II. Analysis regarding timber receipts versus community instability can be approached with this technique. The greater the departure, the less the foregone opportunity revenues, but the greater the harvesting variability. Taken to the extreme, the N D Y constraint is relaxed completely and the planning problem collapses to a Faustmann solution, similar to that described in scenario I. A practical application relevant to British Columbia is to imagine an economically depressed community where restrictions on the log export policy are relaxed. Departing from N D Y to take advantage of the relaxed policy and measuring the foregone opportunity revenue would be useful information concerning the community instability that the increased economic activity might cause. Figure 7(d) is a diagram of the production possibilities curve that describes the physical trade-off between timber production and winter range area. This curve is obtained from a parametric test of a minimum winter range constraint added to the model in scenario III. As 56 different levels of winter range are preserved, the non-declining yield for timber declines. The line is virtually straight because the per unit volume for all winter ranges have similar values. For all practical purposes, for most prices, the production possibilities curve implies that the watershed should specialize in timber production. 57 C H A P T E R 6 DISCUSSION The theory of economic multiple use forestry offers no conceptual problems, assuming economic efficiency is accepted as an adequate guide for forest management decisions. The enormous problem is the difficulty applying the theory. Still, there is value in attempting applications. This is because developments in computer hardware and software (i.e. FORPLAN) make routine application of neoclassical economic theory possible, albeit within a linear programming framework. The results of the previous chapter, taken together, provide some quantitative informa-tion on which to base an economic judgement as to whether to manage for timber alone, or for the joint production of timber and black-tailed deer. A paucity of data exists for some variables used in computing the results for this analysis, namely deer yields and values. Nevertheless, the emphasis here has been to use readily available information, and, where necessary, make some assumptions about how to apply the data. At the outset of this analysis, an examination of the economic tradeoffs between deer hunting and timber production was not considered trivial. While joint management for both deer hunting and timber was a priori considered to be the best solution, the results show, with reasonable assumptions and estimates of existing prices and costs, an overwhelming case for managing the timber resources only. Managing for both timber and black-tailed deer is not even close to being the most economically viable forest management option. This result is illustrated in Scenario III, and explained by the economic model formulated by Hartman (1976). In terms of equation (7), as the stock amenity value, B(T) increased; everything else being equal, management would shift from timber production to provision of deer winter range habitat. B(T) in this case is the average total consumer surplus attributed to 58 a hunting day, which is a function of winter range supply. In Hartman's words, timber stands allocated to winter range would have an infinitely long rotation period, because the marginal increase in value on winter range sites would be greater than the opportunity cost of delaying the harvest. But B(T) in this example had to increase to a value well over $100 per hectare before winter range was preserved. Hartman's results are applied to a single forest stand and they extend to this F O R P L A N application, because winter range analysis areas represent particular stands. When their relative price is high enough, they are preserved for winter range. Otherwise, winter range is included in the harvest schedule and logged. F O R P L A N is a forest level model that has the capability to define and model the behaviour of individual stands within the entire forest. An added feature of F O R P L A N , although not included in this analysis, is its capability to examine trends in product prices and costs. This also extends F O R P L A N beyond Hartman's paradigm. In summary, two points are drawn here. The first is that the results of this empirical example are consistent with those of Hartman (1976), obtained within a forest-wide setting. The second is that this F O R P L A N application is consistent with the study done by the Ministries of Environment and Forests (1983), in that both studies showed that the most economically efficient forest management option was timber management. These results are dependent in part on the definition of consumer surplus estimates used in this study. As noted earlier estimates of consumer surplus will differ. The Tsitika River watershed is a relatively isolated drainage. If a watershed much closer to a large urban centre had been used as the illustrative example instead, the results might be significantly different. First, the conversion return for timber would shift, either higher or lower, depending on the relative changes in logging costs (which would decrease because the timber would be closer to 59 market), and timber selling prices which might increase or decrease, depending on log quality. More importantly, consumer surplus estimates for deer hunting activities would increase, because the relative distance that many hunters need travel to reach this hunting area would be reduced, with everything else held constant. The potential hunter distribution would be modified according to other factors, the most important one being hunting quality. The point here is that a relative shift in consumer surplus for deer hunting could significantly impact on the F O R P L A N results illustrated here, making deer management a much more viable alternative. In addition, the results are also sensitive to the marginal values chosen for the problem formulation and in particular to those values assumed to be zero. F O R P L A N has the capability to allow for this type of analysis. Note also that only deer hunting values were included in this study, unlike McDaniel's (1980) and Ministries of Environment and Forests (1983), who used both deer and Roosevelt elk values. Nevertheless, F O R P L A N is a generic model and is able to handle an analysis involving many different forest products. The example used here was chosen for its simplicity. Had elk been added to the analysis here, total consumer surplus estimates for hunting values and option value would have been significantly higher. The further addition of non-consumptive (or non-hunting) values attributed to the many forms of diverse recreation adds a further dimension to the results of this study. Arguably, the benefits derived from these forms of recreation are public goods, as defined in Chapter 2. Watching a deer while hiking in the forest does not preclude others from deriving the same benefit at the same time or in the future, assuming no congestion problems. Shooting a deer on the other hand, precludes others from deriving the same benefit, thereby giving hunting a private good dimension. To complicate the problem though, hunting has a public good dimension too. Sighting a sought after animal before shooting it is a public good (Langford and 60 Cocheba, 1978). The valuation problem therefore exhibits elements of both public and private goods. Relatively small public good values can result in very large aggregate values (Langford and Cocheba, 1978). This is simply the case of adding up these small values over a large number of individuals who define the referent group and who demand this recreational service. Vertical summation, even over a relatively small number of people (e.g. in a town or municipality) would more than likely reach the $100 required to alter the optimal land allocation in favour of some non-timber uses. Procedures for aggregating demand curves for private and public goods are well defined (e.g. Varian, 1984, p.255). Because most wildlife valuation problems do not fit neatly into a public or private good category, the ability to aggregate values depends on the ability to distinguish between the two types of benefits. In this study, non-consumptive values were excluded. Even so, Foster (1989) states that very few people come to the Tsitika River watershed to watch black-tailed deer or carry out other non-consumptive activities, leading one to infer that these values are relatively insignifi-cant anyway. The point here is that the relative magnitude of public and private goods is of considerable importance. Depending on the particular F O R P L A N problem, these considera-tions could easily be formulated into the model. Nevertheless, of equal concern here is not just current values, as the previous discussion presupposes, but the relative rate of change in values over time. Even if amenity resources have relatively low values currently, they could change at a relatively faster rate. If they change to the point where they are equal to or greater than corresponding timber values, then management emphasis will shift from straight timber management to management of the amenities as well. Casual observation of the land use controversy in British Columbia suggests this is happening. 61 Amenity service values are relatively low compared with timber values, but the expected or potential values could increase faster, and shift the emphasis of forest management towards recreation and away from timber production. The point is that irrespective of amenity resource values (for many estimates have a high degree of uncertainty and others are unknown), F O R P L A N has the capacity to analyze forest management scenarios that assume different price trends and this is a very important feature for forest management planning. 62 C H A P T E R 7 C O N C L U S I O N 7.1 Strengths and Weaknesses of F O R P L A N This study developed an economic multiple use forestry problem using F O R P L A N , and provided an economic interpretation of the results. The inherent strengths of the model can be summarized as follows. First, F O R P L A N has the technical capability to be an effective tool for analyzing strategic multiple use plans under economic efficiency criteria. No longer is there an inherent bias towards timber in problem formulations, as was the case with Timber R A M and M U S Y C . F O R P L A N is generic. Economic and yield data for any number of forest products can be structured into a F O R P L A N problem without relating them to the timber stock and harvest schedule. Second, the level of spatial resolution in F O R P L A N is much superior to that of earlier planning models. The combination of strata and area-based decision variables into a "co-ordinated allocation choice" problem permits recognition of landscape heterogeneity and makes it possible to treat land areas with particular attention to wildlife habitat capability. The importance of this feature is illustrated in Figure 8. This figure shows the timber blocks defined as winter range sites in the Tsitika River drainage. Different parts of each winter range are aggregated into strata based analysis areas, but physically each analysis area exists in parcels spread throughout various winter ranges. The red areas in Figure 8 illustrate one analysis area. A n alternative formulation introduces a second overlapping land category into the problem. In addition to the strata-based analysis areas already defined, the planning model is structured to include geographically defined sub-divisions of the forest, called area-based 63 FIGURES Winter Range in the Tsitika River Watershed 64 analysis areas. Combining the two types of decision variables into one problem produces a coordinated allocation choice data set. Zones are user defined, but often based on natural land features or administrative boundaries. They range in size, usually between 2,500 and 25,000 hectares. Within each allocation zone are portions of strata-based analysis areas because, by definition, the zones are heterogeneous, contiguous land units. The zone allocation choice and the harvest schedule decision for analysis areas make up two distinct parts of the linear programming structure. For every geographical zone there is a discrete choice of management emphasis. The choices are very general, such as wildlife habitat or timber management. Analysis areas continue to be chosen from the array of user specified prescriptions for harvest scheduling. Constraints link the two types of decision variables together by forcing the harvest scheduling program to be compatible with the zones allocated to multiple use. For example, the choice of management emphasis for an allocation zone sets constraints that ensure compatibility when management emphases are assigned to adjust allocation zones, which presents two or more totally incompatible products prescribed side by side. The advantage of this mathematical structure lies in the fact that specific multiple use outputs can be identified with specific geographic areas, thereby alleviating the problem of a strata-based structure discussed earlier (Bowes and Krutilla, 1989). Outputs and their respec-tive costs can be modelled as products of the overall zone. Moreover, a specific timber management prescription may represent the marginal benefit of a non-timber product and this would be defined by the management emphasis of the allocation zone, thereby providing marginal analysis of amenities by parametric testing, much as has been presented in the previous section. Spatial definition has been lacking in the example provided by this thesis, but this is not 65 a significant problem because the land base is small, relatively homogeneous and there are only two prescriptions, timber or deer management. Selecting winter range allocated by scenario III becomes a practical mapping problem of choosing those hectares of winter range that best reflect the analysis areas chosen by F O R P L A N . The solution targets the amount allocated and the planner transcribes this to suitable areas defined generically as winter range. For much larger problems (i.e. many analysis areas and prescriptions spread over a huge land base) this becomes intractable. A research effort which is beyond the scope of this thesis is to define the Tsitika watershed as one area specific decision variable, within an entire tree farm licence. Economic analysis of management alternatives for the Tsitika would provide area specific marginal benefits of these activities. For these reasons, mixed area - strata-based problem structures have proven very successful for multiple use planning (Bowes and Krutilla, 1989; Mealey, 1987; Vella, 1988). A generalized mathematical structure for this type of F O R P L A N problem is presented in Appendix 4. The capability of F O R P L A N to theme problem data sets is another technological im-provement of the model. This means that entry of yield and economic information need only be done once. If the same information applies to more than one type of analysis area, it maybe coded to it in the data file. This avoids repetitive re-entry, customary of earlier models, and creates smaller, more efficient files. The main weakness of F O R P L A N is inherent in the structure of linear programming problems. The objective function and constraints are linear functions of the decision variables. This means that the coefficients of the objective function and constraints can be computed even if the underlying predictive model describing the ecological system is nonlinear. Nonlinear relationships can be represented with linear approximations. 66 The assumption of linearity is adequate for some applications, but for many it is not. Many ecological systems are characterized by large jumps in parameter values (e.g. population levels) at threshold levels, rather than continuous behaviour. Therefore, when criteria such as the maintenance of certain wildlife populations are required, linear models may be unreliable. Constraint inequalities, such as the minimum amount of winter range available, may be used to circumvent this problem, but still this requires the use of detailed population models as input to F O R P L A N to estimate what the constraints must be to maintain species populations (DeAngelis, 1987). 7.2 Opportunities for Improvement F O R P L A N applications on U.S. National Forests have been large, complex, and expensive. Sedjo (1987, p. 162) summarizes this point by saying, "... the criticism was that in trying to be comprehensive and include everything, the model lost its ability to be a useful, flexible and perceptive analytical tool." Modelers had the problem of a technological capability to include "everything", a legal mandate to do so, but in many cases, would only use poor, inaccurate data at a level that far surpassed its capability. Judgments and "best guesses" were substituted, to the extent the planning problem became intractable. This left National Forest plans wide open to public criticism and litigation. One opportunity for improving F O R P L A N applications is the "Max-Loss" procedure developed by Navon et a]. (1986). In their study rows and columns of the F O R P L A N matrix were aggregated and a boundary on the loss of efficiency was calculated. In their sample problems these authors achieved small losses in efficiency with large reductions in problem size (e.g. 20 - 56 percent reduction in either column or row size). This further suggests that the net 67 present value surface is very flat near the optimum, and that many different forest management plans have similar economic outcomes. Therefore, one lesson learned is to keep F O R P L A N problems relatively simple, because the utility of incremental analysis presumably, falls off very quickly. The following recommendations were offered by Sedjo (1987, p.162) for future F O R P L A N work: "(1) F O R P L A N could be useful as a 'strategic' model to provide a broad overview. (2) The model should be kept small and of minimum complexity. (3) Other tools and models ought to be used at the tactical and implementation levels to complement and supplement F O R P L A N . " Sedjo (1987) concludes that F O R P L A N has polential to be a very useful decision making tool if applications are kept within these bounds. Another improvement is to replace yield tables with yield functions in the F O R P L A N model. There are two benefits of this modification. First, yield data entry would be much easier. Entering yield equations is shorter and, therefore, easier than using a long list of numbers from a yield table. Second, the yield data could be more precise. Yield table records are often inter-polations, discrete numbers on a continuous curve. Substituting the curves for the tables eliminates the need to interpolate. This presupposes that the yield functions themselves will exhibit statistical precision. 7.3 Policy Implications of F O R P L A N In this section, broad policy issues considered to be impediments to multiple use forest management are discussed. They are implied by this study simply because more changes and innovations than improved computer tools are required to employ multiple use as a manage-ment principle. 68 The first issue recognizes the institutional barriers that hinder multiple use forestry. There is a strong divergence between the Federal Fisheries Act (1970) and the provincial Wildlife (1979) and Park (1980) Acts, which all have a single-use orientation, and the provincial Forest Act (1979), which requires management of non-timber resources such as range and recreation. Different resources are regulated by these various Acts, and administered by separate agencies. Trade-offs are determined politically and they tend to be arbitrary (Pearse, 1988). Obviously, for multiple use to develop as a management principle, legislation must be revised to recognize and provide management for all forest products. One approach, that would streamline the administration of multiple use management, is to create (or resurrect) the Environment and Land Use Secretariat and place the design and execution of strategic plans within the responsibility of this neutral agency. F O R P L A N is one analytical tool such an agency could use to analyze the costs, benefits, and production levels of different forest products. Second, there is a need to strike a new balance between property rights and regulation for various forest resources. Within British Columbia's current forest tenure system, there is a growing opportunity to capture and internalize benefits accruing to resources other than timber. Pearse (1988) notes that interdependent resources such as timber, fish, and wildlife are regulated under separate arrangements and administered by separate agencies. Since markets for fish and wildlife, at least, do not exist, managers attempt to minimize conflicts with arbitrary trade-offs. To correct this problem, property rights for competing resource uses and users need to be provided with equal means of vesting their interests. All resource rights need not be held by the same party, only held by someone who can bargain with other holders to achieve, if need be, the optimum balance of resource use. Picture the watershed with a famous salmon run that generates tremendous recreational 69 activity. The surrounding timber rights are owned by a timber company. If the timber company relied on incentives created through property rights to manage both the fishery and the timber, then, potentially, better management and utilization of both resources would result and the public interest would be served at the same time. Therefore, amendments to existing tenures, or additions of new tenures would be one avenue of opportunity. This scheme has tremendous potential for those public goods that can, in effect, be privatized. But certain forest resources will always remain public goods, subject to the free rider problem, and therefore in need of regulation. This is where the balance between innovations in property rights for some resources and regulation for others must focus. The third issue is implied by Demsetz' (1967) theory of property rights, cited in Pearse (1988). Briefly, Demsetz argues that individual rights emerge from a state where common property, or no property rights existed, only when resources become scarce and valuable. In the absence of rights, the production of one resource begins to interfere with another. Eventually the gains from eliminating this interference outweigh the cost of organizing property rights. Demsetz' idea has implications for the planning techniques advocated in this thesis. Where forest resources are scarce and valuable, and provide the potential, at least, for greatest conflict, planning efforts should be concentrated. Moreover, if these planning efforts include making innovative changes to tenure arrangements, then they should be given priority to the tenures awarded in these areas. From another viewpoint, this suggests planning efforts should be concentrated in those TSA's/TFL's where they are expected to provide the greatest gains, and avoid a "poverty of analysis" that would result with equal planning effort applied to all areas. Fourthly, how do you measure the success of F O R P L A N ? Experience in the United States suggests two criteria: (1) the amount of political conflict, and (2) improvements in decision making ability. Political conflicts persist but they are probably no more, and con-70 ceivably less, than without the F O R P L A N planning process (Sedjo, 1987). Although conflict has not been eliminated, and perhaps never will, the planning process has provided an invaluable point of focus, for consensus building of many divergent views with regard to data and management objectives. Sedjo (1987) states that it is too early to conclude whether conflict has been reduced, rechanneled or only postponed. Nevertheless, the preliminary assessment is that it has been reduced. Has F O R P L A N led to better decision making? It is difficult to answer this question with clear reference to F O R P L A N as a model versus F O R P L A N as the whole planning process. The problem is that a preferred F O R P L A N run on most national forests has been the actual decision prescribed rather than simply being an aid in the decision-making process. Mealey (1987) says F O R P L A N has been successful. His experience deals with a model formulation similar to that advocated in s.7.1. He gauges his success on FORPLAN's ability to clearly define the multiple use issues, and, within accepted ranges for value and yield parame-ters, measure the net benefits of different management actions. While Mealey feels F O R P L A N has been successful from this viewpoint, Binkley (1987) feels that F O R P L A N is only partly successful meeting its theoretical objective of economically efficient forest plans for the national forests. The reason is that F O R P L A N is effective in eliminating prescriptions which are not cost effective. But overall economic efficiency is not always achieved because the most efficient F O R P L A N solution is unlikely to be selected as the preferred alternative for the national forest under anlysis. This is not so much a fault of F O R P L A N , the model, as it is the reality of the politics of planning. Binkley apparently accepts the view that a preferred F O R P L A N run should be the basis for the plan. However, eliminating inefficient management plans is a success in its own right. Cortner and Schweitzer (1984) discuss the relationship between the politics of planning 71 and quantitative models such as F O R P L A N . They dismiss the idea that a preferred F O R P L A N run will be central to the "decision process". Even the best results, they say, will not define the chosen plan. Instead, model results will always be combined with "outside-the-model" informa-tion and a decision will be made through political negotiation and accommodation of special interest groups. They feel that analytical procedures provide a useful starting point for the decision process. This is hardly the point. Models such as F O R P L A N are designed and intended to help make better land use decisions. A preferred F O R P L A N run will rarely make the best forest plan and land use decisions will (almost) always be decided politically, but a rational approach to the problem through a F O R P L A N analysis will make politicians accountable for the decision they ultimately make. The analysis will serve as a useful benchmark. This simply reasserts the utility of F O R P L A N and, at the same time, defines its limits. Nevertheless, there has been substantial criticism of large comprehensive F O R P L A N models (Barber, 1986). These large models, which are the norm for most national forests have helped push planning costs to the order of several hundred million dollars (Binkley, 1987). An optimal, smaller level of analysis would reduce F O R P L A N costs substantially, and the "Max-Loss" procedure referred to earlier is one possibility. Issue number five is data. Any forest management analysis, with or without a model such as F O R P L A N , is heavily dependent on the quality of data available. Yet the paucity of data available is well documented (B.C. Forest Research Council, 1983). The B.C. provincial inventory of old growth timber for TSA's dates, on average, to 1966. In many parts of the province, it is inaccurate. The growth characteristics of second growth timber, especially in response to manage-ment treatments, are poorly understood. The work of Mitchell and Cameron (1985), among 72 others is acknowledged, but much more work is required in this area. The stock inventory of other forest resources is either non-existent or poorly understood as well. Of perhaps more significance is the impact of extracting one resource on yields of others. In other words, what is the shape of production possibility frontiers? Rezende (1982) claims accurate determination of frontiers will never happen, and he is correct. Nevertheless, cooperative research between the Ministries of Environment and Forests are providing insight in this area with regard to timber, deer, and elk ( M O F & E , 1986), fish and timber (Chamberlin, 1987), and grizzly bears and timber (Archibald and Hamilton, 1982). This information will be useful to at least "ball park" the impacts of timber production on populations of these animals. While efforts should be made to enhance our knowledge of the supply of non-marketed forest resources supply, as stated above, of equal if not more significance is knowledge of demand. Reid et al. (1985) provide the latest set of information but these are broad regional averages. More localized measurement of consumer surplus values would provide better information for analysis of trade-offs at the economic margin. Our forest policies must recognize the uncertainty of present knowledge of resource stocks and their future prices and costs and the need to recognize these uncertainties by designing flexible forest policies. Policies must recognize the irreversible nature of some resource development issues. Krutilla and Fisher (1975) discuss this issue in the context of intertemporal implications of resource development. For example, harvesting a grove of old-growth timber is irreversible in the obvious sense that the amenity value associated with unique characteristics of that grove are gone forever when it is logged. But as Bishop (1982) and Freeman III (1984) point out, the sign and size of option values are, potentially, very volatile. More importantly, because of this, the relative value of timber and other forest resources might shift, such that in the long run, the optimal solution might be to preserve the grove rather than 73 cut it down. Hartman (1976) calls this an infinitely long rotation age. The practical implications of the idea have been recognized by Pearse (1976) when he recommended a portion of the allowable annual cut (AAC) be held in abeyance and not allocated to timber companies. On the B.C. Coast, at least, this recommendation has been ignored, and the consequences observed with the creation of the South Moresby National Park. The timber company lost approximately 300,000 m3/year in quota, which is a significant loss. Had Pearse's suggestion been adhered to, the cost of withdrawing this timber would be much less. Lastly, F O R P L A N is a model based on economic efficiency. Choose the forest management option that maximizes net public benefits, and leave the gainers in a position to at least be able to compensate the losers and still be better off, as a Pareto optimum solution would suggest. F O R P L A N problems are modelled after this paradigm. However, in reality distributional issues become paramount (MOF, 1985). This is not to say economic analysis is not required. At the very least, it provides the necessary framework for identifying arguments to be advanced as part of the broader analysis of regional policy issues that include the impact on macro-economic variables. Page (1977) reconciles these two ideas by defining and analyzing the characteristics of economic efficiency and conservation criteria. Briefly, the distinguishing and salient point of Page's argument is that efficiency criteria work well when markets work well and when issues of intertemporal fairness do not arise. The difficulty arises when utility functions between present and future generations become inseparable because of the presence of intertemporal externalities. The old growth timber issue described above is one example. Conversely, the conservation criterion attempts to provide a fair use of the resource base intertemporally by keeping it intact and thus preserving a world of equals among generations. Page (1977) argues that the efficiency of the present value criterion operates at a micro-74 economic level. That is, for one macro-economic context, partly specified by the intra- and intertemporal distributions of income and resource control, the present value criterion leads to one solution. For another context with a different income distribution and resource control, the present value criterion leads to yet another solution. The point is that FORPLAN shows how to maximize the net present value of a given forest management scenario, thereby providing a basis for understanding the (opportunity) costs of diverging from its prescriptions in order to pursue other social objectives. 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Utah Agricultural Experiment Station. Bulletin 448. Utah State University. Logan, Utah. 24p. Wilderness Advisory Committee. 1986. The Wilderness Mosaic. The report of the Wilderness Advisory Committee. Vancouver, B.C. 132p. + App. Zivnuska, J.A. 1961. The multiple problems of multiple-use. Journal of Forestry 59:555-60. 82 APPENDIX 1 ASSUMPTIONS OF THE FAUSTMANN MODEL The basic assumptions of the Faustmann formula are the following: 1. Even-aged management, starting with bare land, of a single stand of trees, of unchang-ing growth potential and capable of reproducing (at some fixed cost) instantaneously after harvest. This assumption is not essential as Faustmann himself showed that it made no difference if a regulated forest or a single stand was examined, the per hectare results would not change. 2. There is perfect certainty regarding the growth function of the site, future market prices, interest rates and costs. They are constant. 3. Access to capital markets is unlimited and money can be borrowed or lent at the market interest rate, i. 4. Net stumpage price (P) is not a function of tree quality, it is constant per unit volume of wood produced. This assumption is not completely necessary but it avoids the potential problem of multiple optimum rotation arguments that can arise when management ob-jectives favor different end products. 5. Regeneration costs (C r) are the only expenses and they occur immediately after harvest-ing. Intermediate costs and returns could be included. 6. The growth function describes total merchantable volume (G) as a function of timber only such that: G = G(t) where G'(T) > 0 and G"(T) < 0 The primes denote first and second partial derivatives of the growth function. Each of these six assumptions is restrictive; that is, real world conditions are either ignored or simplified a great deal. This can and presumably does cast doubt on the results of any analysis for decision making. 83 APPENDIX 2 ASSUMPTIONS O F A L I N E A R P R O G R A M M I N G M O D E L 1. Linearity - functions representing the objectives and constraints are linear. This implies resource utilization is proportional, additive, and exhibits constant returns to scale. 2. Divisibility - the decision variables take on continuous values. 3. Non-negativity - decision variables must have non-negative values. 4. Certainty - all constraints are assumed to be known with certainty. 5. Quantification - all values must be quantified. 6. Optimality - the problem being modelled must be capable of being structured such that the optimal solution is found. Source: Hillier and Lieberman (1980) 84 APPENDIX 3 FORPLAN Data and Yield Files PRINT OUT DATA AND GENERATE MATRIX TITLE DATA SET ASSEMBLED BY JIM HACKETT § FEPA VANCOUVER, B .C . OCTOBER 13, 1988 • • t FIRST DATA SET - STRATA BASED; BASE RUN;NOT A CAC DATA SET YEAR GROUP LENGTH, IN YEARS, FOR YIELD FILE IDENTIFIER AGGREGATES TREATMENT TYPES TRENDS FOR ACTIVITY COMMON COSTS TREATMENT TYPES AND QUALIFIERS USED IN COMMON RETURNS FOR OUTPUTS THEMING USE OF YIELD FILE RXS WITH A. YIELDS BROUGHT IN FROM YIELD FILE TIME *YEARS1988 10 10 10 10 10 10 10 10 10 10 *YEAR GROUP 10 IDENTIFIERS *LEVEL1 WINTERRANGE NW NOWNTR NOT WINTER RANGE WR WRANGE WINTER RANGE *LEVEL2 SPP GROUP HE HEMLOC W.HEMLOCK SPECIES GROUP;6-0,7 ;7-0,6 CE CEDAR W. RED CEDAR SPECIES GROUPS- 0 , 6 , 7 ; 6 * LEVEL3 SITE CLASS GO GOOD GOOD SITE - > 33.5M § 50 YRS. ME MED. MEDIUM SITE - 27.6 - 33.5M @ 50 YRS. PO POOR POOR SITE - < 27.5 M Q 50 YRS • * LEVEL4 AGE CLASS IM IMMAT IMMATURE TIMBER MA MAT-80 MATURE TIMBER - 80 YRS.OLD OM OM OVERMATURE TIMBER - > 80 YRS. OLD * LEVEL5 NOT USED *LEVEL6 NOT USED * LEVEL7 MGMT EMP TM TIMMAN REGULAR TIMBER MANAGEMENT DE DEER DEER MANAGEMENT •AGGREGATE LEVEL7 RT REGTIM MAN.- ALL TIMBER STANDS TM DE 85 "LEVEL8 MGMT INTEN FF FH FH CUR.STAND-FINAL HARVEST:REGEN STAND-FINAL HARVEST DEER MANAGEMENT DM DEER TREATMENT TYPES C CLEAR CT(EX) D CLEAR CT(RG) AT AGGREGATE TREATMENT TYPES G CLEAR CUT C D ACTIVITIES T100 T100: T101 T101 HAR1 HARl HAR2 HAR2 PLANT JUV. SPACE HEM HARVEST CED HARVEST *AGGREGATE NAMES FOR ACTIVITIES SIVC SIVC:SILVICULTURE COSTS HARV HARV:HARVEST COSTS HA HA M3 M3 N N N N N N N N N N N N Y N N Y N N Y N N Y N N T100 T101 HARl HAR2 *TRENDS FOR ACTIVITY COMMON COSTS 1# SIVC * 1.16 * * 1.36 2# HARV 1.00 * * 1.00 *COMMON COSTS FOR ACTIVITIES HI H 2 S + P JS CE HE HARl HAR2 T100 T101 OUTPUTS AND ENVIRONMENTAL EFFECTS TMB TIMBER VOLUME M3 OLDG OLDG:OLD GR WIN RAN. HA LTSY LTSY:LONG TERM SUS. YLD M3 SAV SAV:STAND AVE. INV INV INV:FINAL INV VOLUME FHAR FHAR:FINAL HARV VOL * COMMON RETURNS ON OUTPUTS TM1 CE TMB M3 M3 HA TM3 OG1 HE WR TMB OLDG 1.00 1.20 1.00 1.00 45.8 45.8 500. 250. 34.54 5.72 0.0 YIELD COMPOSITE NAMES FOR OUTPUTS/ACTIVITIES 86 1.04 1.24 1.00 1.00 1.08 1.28 1.00 1.00 1.12 1.32 1.00 1.00 N C P Y N N C Y Y N N c Y N N N c Y N N N C Y N N N C P N N #1TIMBY A/0 RELATED TO TMB #2 TMB #2LTSY W TMB G TI T #2SAV W TMB TI T #2INV W TMB TI T tlWRANN A/0 RELATED TO OLDG #2 OLDG OBJECTIVE PNB 10 Y .04 N Y FOREST CONSTRAINTS TIMBER HARVEST TMB *NONDECLINING YIELD 1 10 *LTSYC LTSY *VOLUME SAV * INVENTORY INV * PERPETUAL TIMBER HARVEST CONSTRAINT PRINT DETAIL 104326. 150. AP PRESCRIPTION SOURCE INFORMATION #1 NW #2 TM TM #1 WR #2 DE DE #1 WR #2 TM TM SOURCE OF ACTIVITIES/OUTPUTS #1TIMB #2 #1WRAN #2 HARVEST SOURCE # 1TMB •EXIST #2 *REGEN #2 YIELDS AA 001 NWHEGOOM AA 002 NWHEMEIM AA 003 NWHEMEOM AA 004 NWHEPOIM AA 005 NWHEPOOM AA 006 NWCEGOOM AA 007 NWCEMEOM AA 008 NWCEPOIM TM DE 1129.09 141.67 3528.54 956.96 8572.14 10.89 739.66 102.74 TMB AND OLDG COSTS/OUTPUTS 0.0 13 23 5 10 NOT WR HEM GO SITE OVERMAT. NOT WR HEM ME SITE IMMAT. NOT WR HEM ME SITE OVERMAT. NOT WR HEM PO SITE IMMAT. NOT WR HEM PO SITE OVERMAT. NOT WR CED GO SITE OVERMAT. NOT WR CED ME SITE OVERMAT. NOT WR CED PO SITE IMMAT. 87 AA 009 NWCEPOOM 2901.89 AA 010 WRHEGOOM 278.73 AA O i l WRHEMEOM 467.01 AA 012 WRHEPOIM 33.32 AA 013 WRHEPOOM 682.67 AA 014 WRCEMEOM 36.03 AA 015 WRCEPOOM 492.03 END OF DATA USE OF YIELD FILE USE NOT WR CED PO SITE OVERMAT. WNTR RAN HE GO SITE OVERMAT. WNTR RAN HE ME SITE OVERMAT. WNTR RAN HE PO SITE IMMAT. WNTR RAN HE PO SITE OVERMAT. WNTR RAN CE ME SITE OVERMAT. WNTR RAN CE PO SITE OVERMAT. OF YIELD FILE 88 ANALYSIS AREA YIELD INFORMATION CODE TMB *I HEGO •A EXIST 13 HEMLOCK MATURE GOOD SITE TIMBER CA13 901 901 901 901 901 901 901 901 *A REGEN HEM-BAL 2ND GO SITE NAT.STANDS-NO TREAT. GROSS DW2B D A 0 5 2 110 213 322 419 700 827 9 3 1 *I HEME * A EXIST 13 HEMLOCK MATURE MEDIUM SITE TIMBER CA13 897 897 897 897 897 897 897 897 * A REGEN HEM-BAL 2 N D ME SITE NAT.STANDS-NO TREAT. GROSS DW2B DA05 0 14 183 325 464 569 6 9 6 748 794 *I HEPO * A EXIST 13 HEMLOCK MATURE POOR SITE TIMBER C A 1 3 7 0 5 7 0 5 7 0 5 7 0 5 7 0 5 7 0 5 7 0 5 7 0 5 * A REGEN HEM 2ND LO SITE (MB ) NAT. STAND YLD. TABLE- GROSS DW2B DA05 0 0 48 156 275 3 6 0 431 494 5 5 0 600 *I CEGO *A EXIST 13 CEDAR MATURE GOOD SITE TIMBER CA13 829 829 829 829 829 829 829 829 *A REGEN CEDAR 2ND GROWTH-GOOD-SAME TABLES AS HEMLOCK DA05 2 110 213 322 419 700 827 931 *I CEME *A EXIST 13 CEDAR MATURE MEDIUM SITE TIMBER CA13 829 829 829 829 829 829 829 829 *A REGEN CEDAR 2ND GROWTH-MED-SAME TABLES AS HEMLOCK DA05 0 14 183 325 464 569 696 748 7 9 4 *I CEPO *A EXIST 13 CEDAR MATURE POOR SITE TIMBER CA13 581 581 581 581 581 581 581 581 *A REGEN CEDAR 2ND LO SITE (MB)NAT.STAND YLD. TABLE-GROSS DW2B DA05 0 0 48 156 275 360 431 494 550 600 89 CODE OLDG * I WR GO *T WINTER RANGE - GOOD SITES A 1 . 3 5 1 . 3 5 1 . 3 5 1 . 3 5 1 . 3 5 1 . 3 5 1 . 3 5 * I WR ME *T WINTER RANGE - MEDIUM SITES A 1 . 3 5 1 . 3 5 1 . 3 5 1 . 3 5 1 . 3 5 1 . 3 5 1 . 3 5 * I WR PO *T WINTER RANGE - POOR SITES A 1 . 3 5 1 . 3 5 1 . 3 5 1 . 3 5 1 . 3 5 1 . 3 5 1 . 3 5 END OF DATA 1 . 3 5 1 . 3 5 1 . 3 5 1 . 3 5 1 . 3 5 1 . 3 5 1 . 3 5 1 . 3 5 1 . 3 5 90 A P P E N D I X 4 Linear Progranuriirig Specification of a Mixed Area - Strata Based Problem Z M 2 N m Z = E E E A 7 m Y m n + zmn zmn max z=l m=l n=l S Ps Ip K, E E S E B X s=l p=l i=l k=l s-t- E E Y z m n = Area z m=l n=l z = l , Z Z M z N m E E E P . Y + zmnjsp zmn z=l m=l n=l E E E X . . - W . + W . = 0 spik spcj spjq p=l i=l k=l for p=l , P s s=l, S j = l , N U M P s p l < c < j l < j < q Y > 0 v v v lzmn — u v z ' v m ' v n X > 0 V V V V ^spik — u v s ' v p ' v i ' v k W .. > 0 V , V , V , V. spij s' p' V j where: Y z m n = hectares assigned to timing choice n of A L S C m on zone z A^ = contribution to objective function (per hectare) from timing choice n A L S C m on zone z X s p i k = hectares assigned to timing choice k of prescription i in prescription group p on analysis area s 91 B s p j k = contribution to objective function (per hectare) from timing choice k of prescription i of prescription group p on analysis area s A R E A ^ = size of zone z (in hectares) P z m n j s p = proportion of a hectare made available to prescription group p of analysis area s in period j through assignment of a hectare to timing choice n of A L S C m on zone z W s p i . = hectares made available in period i to prescription group p of analysis area s that were not assigned to any timing choice in that prescription group in period i and were, therefore, made available to prescription group p of analysis area s in period j (i < j) Z = number of zones N m = number of timing choices for A L S C choice m M z = number of A L S C choices on zone z S = number of analysis areas P s = number of prescription groups for analysis area s I = number of prescriptions in prescription group p of analysis area s Kj = number of timing choices in prescription i NUMTjjj, = number of timing choices in prescription i that have their first action occurring between periods j and j', where j ' is the first period beyond j in which a land accounting link between zones and analysis areas (transfer row) occurs between the zones and a prescription group that contains prescription i. If no more transfer rows occur for this prescription during the planning periods, then j ' = (the last planning period -1) N U M P s p = number of periods in which hectares can be transferred to prescription group p of analysis area s Source: Johnson and Stuart (1987, p.5-18). 92 


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