ABSTRACT Optimum Allocation of a Renewable Resource A Bioeconomic Model of the Great Lakes Whitefish Fishery by M. Reza Ghanbari Lack of specific knowledge about the socio-economic values required to improve upon the utilization of fishery resources is a major problem for decision makers in the Great Lakes. This study a) documents some of the economic values of the Great Lakes Whitefish fishery, and b) evaluates some of the alternative uses of the Great Lakes resources. Using a bioeconomic model of the Whitefish fishery of the northern half of Green Bay in Lake Michigan (MM-1), sustainable yield (OSY) was estimated to be 800,000 kg., at an effort of 12,700 units, resulting in a producers' sur- plus of $520,000 in 1973. For the same year (1973), actual yield was 590,000 kg., actual effort was 26,000 units, and actual producers' surplus was $17,000. According to this model, the fishery in the district is apparently over- exploited. Since the district produces almost 25 percent of Michigan's Whitefish, producers' surplus at OSY for the M. Reza Ghanbari entire state would be about $2,080,000. that: An econometric model of U.S. whitefish fishery showed a) b) C) The a) b) c) 6) under normal, competitive conditions, Michigan's share of the net all-or-none value (social sur- plus) of the whitefish fishery was estimated to be $750,000, the portion of social surplus that a monopolist could collect would be about $500,000, under very optimistic conditions, assuming near record catch levels for all possible species, at 1973 price levels, the estimated net all-or-none value (social surplus) of Michigan's commercial fishery would be between $14 and $25 million (1977 dollars) per year. This is much lower than the equivalent sport fishing value of $250 mil- lion (Talhelm, 1977). Under the same conditions, the monopoly rent would be about $10 million per year. elasticities for U.S. whitefish were: price elasticity of demand of between -2 and -4, income elasticity of demand of about 2.2, cross-price elasticity of demand with the price of choice beef of about 2.3, cross-price elasticity of demand with the price of lake trout of about 2, M. Reza Ghanbari e) price elasticity of supply of .25, f) cross elasticity of supply with the price of lake trout of about .18. The models indicate that removing lake trout from the market (because pesticide levels are too high) would increase the retail price of lake trout from 49 cents per pound to about 100 cents per pound. Assuming the produc- tion of whitefish could not be easily increased, the retail price of whitefish would increase from 47 to about 70 cents per pound. If production of whitefish could easily be increased, the production of whitefish would increase from 4.2 million to about 10 million pounds and the retail price of whitefish.would slightly decrease from 47 to 39 cents per pound. Fishing gear limitations may reduce the efficiency of labor and capital by imposing some unnecessary costs on the fishermen. Relaxing the limitations could make fishing more profitable for some fishermen and probably increase the supply of whitefish, but would probably decrease employment in the industry. A linearization of the surplus production equations proved to be the best technique for estimating the bioeco- nomic model. The results of a graphical technique also seemed acceptable. Among the different econometric models used in esti- mating supply and demand equations for U.S. whitefish, a M. Reza Ghanbari system of four equations for supply and demand of lake trout and whitefish, using II and III stage least squares gave the most reasonable results. Single and double equa- tion models all resulted in negatively sloped supply curves, which were not acceptable. This study was limited by inaccurate and unavailable data. More accurate data on catch, effort, and economic factors is needed. At the same time, more sophis- ticated and more suitable models for the Great Lakes are required, to take into account technological and environ- mental changes, and some of the relationships between species and other ecological factors, such as water temper- ature and fertility. OPTIMUM ALLOCATION OF A RENEWABLE RESOURCE A BIOECONOMIC MODEL OF THE GREAT LAKES WHITEFISH FISHERY by M. Reza Ghanbari A Dissertation Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Agricultural Economics 1977 (gzcnofi exf‘. Ck" Dedicated to my parents ACKNOWLEDGMENTS I wish to express my appreciation to my government for financially supporting my graduate studies at Michigan State University. I am particularly grateful to Dr. D. R. Talhelm, the principal investigator of this Michigan Sea Grant study and my research supervisor who made this research possible. My gratitude to professor Warren Vincent, my major professor, is difficult to express adequately; however, I wish to thank him for his direction of my studies and for his confidence in me. I wish to thank Drs. Robert Stevens, Stan Thomson, for their help as members of my thesis committee. I also want to thank professors Gustafson, Park, Shapiro and Suits for serving on my guidance committee. I am thankful to Mrs. Ellen Vander Lugt and Cathy Lemonds for typing the earlier drafts of the thesis. iii TABLE OF CONTENTS List of Tables . . . . . . . . . . . . List of Figures . . . . . . . . . . . Glossary . . . . . . . . . . . . . . . Chapter I II III IV Introduction . . . . . . . . . Background . . . . . . . . . . Definition of the Problem . . . Objectives . . . . . . . . . . Plan of the Study . . . . . . . Origins of the Conflict Between Sport mercial Fisheries: A Historical Review . . . Rise of the First Significant Sport Interests . . . . . . . . . . . The Sea Lamprey Invasion . . . Discovery of DDT . . . . . . . Discovery of PCB . . . . . . . Restocking Programs . . . . . . Fisheries Economics Literature Gordon's Model . . . . . . . . Schaefer's Model . . . . . . . Turvey's Model . . . . . . . . Fullenbaum's Model . . . . . Fullenbaum and Dow et a1. (Main Herfindahl and Kneese Model . . Jensen's Study . . . . . . . . Patriarche's Study . . . . . . The Bio-Economic Model . . . . Assumptions of the Model . . . The Model . . . . . . . . . . . Biological Equations . lMaximum Sustainable Yield iv Pi and Com- shing Page vii xii |-‘ QUINN 10 ll 14 15 20 20 22 23 24 26 28 32 34 34 35 37 37 VI Page Bioeconomic Equations . . . . . . . 40 Optimum Sustainable Yield (OSY) . . . . 40 Estimating the Parameters and Outputs of the Bioeconomic Model Using Fixed Prices . . . . . 48 Methodology . . . . . . . . . . . . . . . . . 49 Long-Run vs Short-Run Models . . . . . . . 49 Data Base . . . . . . . . . . . . . . . . . 54 The Period of Study . . . . . . . . . . . . 61 Criteria for Selecting Results . . . . . . 67 Results of the Short-Run Biological Models . . 68 Linear Relationships Between Catch and Effort . . . . . . . . . . . . . . . . . 68 Quadratic Relationships Between Catch and Effort . . . . . . . . . . . . . . . 71 Fishing Cost per Unit of Effort . . . . . . . . 74 The Whitefish Fishery in 1973 . . . . . . . . 75 Results of the Long-Run Biological Models . . . 77 Linearization Approach . . . . . . . . . 77 Results With and Without Sea Lamprey (1967- 76) . . . . . . 80 Results Without Sea Lamprey (1929- 1950) 85 Results With Sea Lamprey (1929- 1950) . 88 Numerical Analysis Approach (A Search Routine . . . . . . . . . . . . . . . 91 Results Without Sea Lamprey (1963-1975) 95 Graphical Method . . . . . . . . . . . . 97 Results Without Sea Lamprey (1963-1976) 101 Sensitivity Analysis . . . . . . . . . . . 102 Summary . . . . . . . . . . . . . . . . . . . . 107 Estimating the Supply and Demand of Whitefish . 110 The Whitefish Fishing Industry . . . . . . . . lll Methodology . . . . . . . . . . . . . . 112 The Period of Study . . . . . . . . . . . 112 Data Base . . . . . . . . . . . . . 113 Criteria for Selecting the Results . . . . 117 Demand Estimations Using OLS . . . . . . . 122 Supply Estimations with Distributed Lag, Using OLS . . . . . . . . . . . . . . . . . . . . . . 124 Simultaneous Equations . . . . . . . . . . . . 125 Reduced Form . . . . . . . . . . . . 125 II and III Stage Least Square (A System of Two Equations) . . . . . . . . . . . . . 128 II and III Stage Least Square (A System of Four Equations) . . . . . . . . . . . . . . 129 Elasticities . . . . . . . . . . . . .'. . . . 138 Page 'VII Management and Policy Exploration of Alterna- tive Conditions . . . . . . . . . . . . . . . . 144 The Impact on the Supply and Demand for White- fish Because of Eliminating Lake Trout Fishing 144 The Whitefish Fishery Under Alternative Market and Production Conditions . . . . . . . . . . 149 The Whitefish Fishery in 1973 . . . . . . . 149 Optimum Production and Producer Surplus Under Competition . . . . . . . . . . 149 Net All- -Or-None Evaluations of the Fishery Under Competition . . . . . . . . . . . . . 151 Commercial Fishery Under Perfect Monopoly . 154 Maximum Potential Value of Commercial Fishery . 156 Producer, Consumer, and Social Surplus . . 159 The Impact of Gear Limitations on Gear Effi- ciency . . . . . . . . . . . . . . . . . . . . 160 Welfare Effects on Relaxing the Gear Limitations . . . . . . . . . . . . . . . . 161 VIII Summary, Conclusions, and Recommendations for Future Research . . . . . . . . . . . . . . . . 164 Summary and Conclusions . . . . . . . . . . . . 164 Recommendations for Future Research . . . . . . 169 Bibliography . . . . . . . . . . . . . . . . . . . . . 176 Appendix . . . . . . . . . . . . . . . . . . . . . . . 180 vi LIST OF TABLES TABLE Page II-l. Change in the Percentage Composition by Weight of Harvest on Michigan Waters of the Great Lakes 0 O O O O I O O O O O O O O O O O O O 0 l3 II-2. Beginning Dates of Modern Stocking Program in the Great Lakes . . . . . . . . . . . . . . . 16 V-1. Data Used in the Analysis (1929-1950) and (1963-1976) 0 o o o o o o o o o o o o o o o o 56 V-2. Catch and Effort and Catch-per-Unit-of-Effort (CPE) for Different Types of Gear for Lake Whitefish in District MM-l . . . . . . . . . . 57 V-3. Total Catch in Pounds and Total Effort for. Lake Michigan in District MM-l (Using 4-1/2 Inch Gill Net as Standard Gear) . . . . . . . 59 V-4. Deflated Prices, Catch, and Total Value Pro- duct (TVP), 1963-75 . . . . . . . . . . . . . 63 V-5. Sea Lamprey Abundance Index . . . . . . . . . 65 V-6. Abbreviations Used Throughout this Study . . . 69 V-7. Current (1973) State of the Fishery in Dis- triCt MM-l o o o o o o o o o o o o o o o o o o 78 V-8. Results of the Analysis Using Linearization Technique, 1967-76; LAFC = 21.38 . . . . . . . 81 V-9. Results of the Analysis Using Linearization . Technique, 1967-1976, AVFC = $12.82 . . . . . 84 V-10. Results of the Analysis Using Linearization Technique, 1929-1950, SAVFC = $12.82 . . . . . 87 V-ll. Results of the Analysis Using Linearization Technique, 1929-1950, SAVFC = $12.82 . . . . . 90 vii TABLE V-12. V-13. V-14. V-15. V-16. V-l7. v-18 O V-19. V-20. VI-l. VI-2. VI-3. VI-4. VI-6. VI-7. VII-l. Symbol, Definition, Inital Guesses, and Mathe- matical Formulae for some Variable in Pella and Tomlinson Model . . . . . . . . . . . . . Results of the Analysis Using Search Routine 1963-1976, LAFC = $21.38 . . . . . . . . . . . Results of the Analysis Using Search Routine 1963-1976, SAFC = $12.82 . . . . Results Using Graphical Technique . . . . . . Results Using Graphical Technique . . . . . . Graphical tor Cost, Analysis with Long Run Average Fac- LAFC = $23.5 . . . . . . . . . . . . Graphical Analysis with Average Variable Fac- tor Cost, AVFC = $14.1 . . . . . . . . . . . . Summary of the Estimated Parameters Using Dif— ferent‘Approaches . . . . . . . . . . . . . . Summary of the Bioeconomic Values Using Dif- ferent Estimations Methods . . . . . . . . . . Data Used in the Supply and Demand Analysis of U.S. Whitefish (1950-1973) . . . . . . . . . . Variables Used in Estimating Demand Via OLS . Variables Used in Estimating Supply Via OLS Distributed Lag O O O O I O O O O O I O O O 0 Variables Involved in the Simultaneous System (Whitefish Demand Equation) . . . . . . . . . Variables Involved in the Simultaneous System (Whitefish Supply Equations) . . . . . . . . . Actual and Predicted Data Using Equations VI- 13 and V1-14 O C O I O O O O O O O O O O O O 0 Demand and Supply Elasticities for U.S. White- fiSh O O O O C O .0 O O O O O O O I I O O O O O Elasticities Over the Period of Study, Equa- tion V1-13 O O I I O O O O O O O O O O O O O 0 Analysis of the Michigan's Commercial Fishing viii Page 93 98 99 103 104 105 106 108 109 114 123 124 131 132 136 140 142 158 TABLE VII-2. VIII-1. Page Maximum Potential Values of the Great Lakes Commercial Fishery . . . . . . . . . . . . . . 159 Economic Values of Michigan's Commercial Fishery . . . . . . . . . . . . . . . . . . . 168 ix FIGURE 1.1. III-lo IV-1. IV-2. IV-3. LIST OF FIGURES Lake Michigan . . . . . . . . . . . . . . . . An Example of an Overexploitation Situation The Sustainable Yield Curve . . . . . . . . . Yield-Effort Curve, a Long Run Harvest Func- tion 0 O I O O O O O O O O O O O O C O O O I 0 Comparison of OSY, MSY, and the Open Access Equilibrium (Long Run) . . . . . . . . . . . . Equilibrium and Non-equilibrium Conditions of the Fishery. . . . . . . . . . . . . . . . . . Trend of Catch (pounds), Effort, and CPE for MM-l, 1929-1976, for 4 1/2 Inch Gill Net Fish- ing Only . . . . . . . . . . . . . . . . . . . Trend of Total Catch for District MM-l, 1963- 1976 O O O O O O O O I O O O O O O O O O O C Total Value of the Catch Using Deflated 1973 and Yearly Prices with Total Effort for Dis- triCt MM-l O I O I O O O O O O O O O O O O O 0 Trends of Total Whitefish Catch (kg) at MM-l and Index of Sea Lamprey Abundance with Four and Five Year Lag . . . . . . . . . . . . . . Actual and-Predicted Catch and Effort (a Linear Relationship) . . . . . . . . . . . . Actual and Estimated Catch and Effort (a Qua- dratic M0661) o o o o o o o o o o o o o o o 0 Total, Average, and Marginal Costs in Short and Long Run 0 O O O O O O O O O O O O O I O O Linearlization Technique, 1967-1976, with 1973 Deflated Price . . . . . . . . . . . . . . . . Page 31 38 39 44 53 60 62 64 66 70 72 76 82 FIGURE V-10. V-ll. V-12. V-l3. VI-l. VI-Z. VI-5. VI-6. VI-7. VI-8. VII-l o VII-2 o VII-3. Page Analysis Without Sea Lamprey, 1929-50 . . . . 86 Analysis With Sea Lamprey, 1929-50 . . . . . . 89 Results of the Analysis Using Search Routine, 1963-1976 . . . . . . . . . . . . . . . . . . 96 Results of a Graphical Technique 1963-76 . . . 100 Annual Catch, Nominal, and Deflated Ex-vessel Price for U.S. Whitefish . . . . . . . . . . . 115 Annual Nominal Ex-vessel Price and Total Quan- tity of Whitefish . . . . . . . . . . . . . . 116 Deflated Price and Quantity of Whitefish per 1000 People of U.S. . . . . . . . . . . . . . 118 Nominal Ex-vessel Prices and Quantity per 1000 People of U.S. Whitefish . . . . . . . . . . . 119 Monthly Nominal Ex-vessel Prices and Total Quantity of Whitefish for 1973 Only . . . . . 120 Actual and Predicted Equilibrium Points for Whitefish, 1961-75 . . . . . . . . . . . . . . 133 Actual and Predicted Trends of Equilibrium Quantity (per capita) Whitefish, 1963-75, Us- ing Equations V1-13, V1-14 o o o o o o o o o o 134 Actual and Predicted Equilibrium Prices (Deflated) for Whitefish, 1963-75, Equations V1-13, V1-14 o o o o o o o o o o o o o o o o o 135 Estimated Demand and Supply Equation for White- fish Before and After Eliminating Lake Trout PrOduction O O O O O O O 0 O O O O I O O O O O 148 Estimated Supply and Demand Curves in 1973 . . 152 Hypothetical Demand and Supply Curves to Show the Welfare Effects of Relaxing the Gear Limitation O O O O O O O I C O O O O O O O O O 162 xi Biomass Depletion Ex-vessel price Fishery Fishing effort I Gear Landings, commercial Maximum sustainable yield Mesh GLOSSARY The total mass or amount of living or- ganisms in a particular area or volume Reduction of stock size due to over- fishing or any other cause induced by man or a natural cause, resulting in substantially reduced yield and requir- ing a reduction of fishing to enable replenishment of the stock. Price received by fishermen for fish, shellfish, and other aquatic plants and animals landed at the dock. The act of or place for commercial and recreational fishing, often with refer- ence to a particular season, species, or group of species. The activity of catching or harvesting fish, usually measured as a combination of the amount of gear and time used while fishing. Fishing equipment of various types, such as nets, lines, and traps. Quantities of fish, shellfish, and other equatic plants and animals brought to shore and sold. The scientific term describing the balance between catching a certain num- ‘ ber of fish of-a particular species and leaving the necessary number to allow propagation. One of the openings between the cords of a fishing net. xii Optimum sustainable yield Overfishing Recreational fishing The amount of fish which will provide the greatest overall benefit to the Nation, with particular reference to food production and recreational oppor- tunities, and which is prescribed as such on the basis of the maximum sus- tainable yield, as modified by any relevant economic, social, or ecologi- cal factor. Harvesting fish or shellfish in an amount greater than the maximum sus- tainable yield. Fishing for pleasure, amusement, relax- ation, or home consumption. If part or all of the catch is sold, the mone- tary returns constitute an insignifi- cant part of the person's income. xiii CHAPTER I Introduction The "best" use of natural resources--using them where they are needed the most and can provide the greatest return to society with respect to economic, political, and environ- mental standards--is a basic question facing our society. It is a question that has received more and more attention in recent years, as an acute awareness of ecological prob- lems has developed in the industrialized portion of the world. The problem has also become more complex as more and more natural resources are subjected to more intensive multiple uses. Conflicts arise between the users of such resources when the actions of one user encroach upon the use of the resource by another. Usually such conflicts can only be resolved by limiting one or more uses. In the case of renewable natural resources, such as fiSheries, forests, or pOpulations of other wild animals, assuming there is more than one user, the primary problems are, first, what is the Optimum annual yield and how do we harvest only that amount, and second, how to divide the annual yield or harvest of the resource among the alterna- tive users. In the Great Lakes,1 there is a general recognition by fisheries managers that there is some optimum combination of commercial and sport fishing that would best utilize the productive capacity of the resource (Talhelm, 1975). How- ever, at present no one can precisely document the social values, the ecological constraints and the management tech- nology needed to precisely determine Optimal management of Great Lakes fisheries. The overall purpose of the MSU Sea Grant fisheries economics research project (of which this study is one com- ponent) is: ". . . to assist individuals and organizations in making better use of the Great Lakes and fish culture resources by applying the social science of economics to that task. Overall project goals are as follows: 1. Provide information needed for selecting optimal utilization of Great Lakes fisheries by document- ing the benefits, costs and other impacts of potential management strategies. 2. Assist private and public planning efforts by documenting economic impacts incidental to commer- cial and sport fishing for Great Lakes fish. 3. Promote better utilization of the commercial and recreation resources of the Great Lakes through 1The Great Lakes form the largest body of fresh water in the world, with 95,000 square miles in area. Although the upper three lakes are cold and infertile, because of their size and location, they have a tremendous potential for both sport and commercial fishing. economic and business statistics, direct assis- tance to small firms, and studies of related aspects of recreational behavior." (Talhelm, 1975) The first goal is of primary importance here. It is divided into three sub-goals: a) determination of sport fishing values, b) determination of commercial fishing values, and c) formulate and apply an optimum harvest model. The purpose of this study is to examine part b) in the con- text of a particular, renewable resources: the whitefish2 fishery of Michigan's Great Lakes. Until recently, Great Lakes fishing was dominated by commercial fishing.3 Since the mid-1960's however, sport fishing increased tremendously, becoming one of the most important sport fisheries in the world (Talhelm,1975). The Great Lakes commercial fishing industry, on the other hand, has become increasingly depressed for several reasons. Currently, management agencies are greatly restricting the species, location and methods of commercial fishing, and sharply reducing the number of commercial fishing licenses4 with the objective of maintaining a more limited but econo- mically viable industry. 2Common and scientific names for the Great Lakes fish are given in Appendix A. 3Some parts of this section paraphrase or quote Tal- helm (1975). 4The number of licensed commercial fishermen in Mich- igan has declined from about 1100 in 1950 to around 150 at present. Reasons for the present condition include: overfish- ing for certain species, ecological disruptions by sea 5 6 populations, DDT7 and PCB8 contamina- lamprey and alewife tion and other pollution. However, one of the most impor- tant reasons is recognition by the Departments of Natural Resources of the Great Lakes states that our present society finds sport fishing for fish produced in the Great Lakes, including salmon, to be more valuable than commercial fish- ing. Studies show that in 1971 over 184,000 sport fishing license holders fished about two million days for Great Lakes salmon and steelhead in Michigan (Jamsen, 1973). Talhelm (1973) and Ellefson (1973) estimated the net econo- mic value of Michigan's 1970 salmon and steelhead sport fishing including and not including non-residents of Michi- gan to be $30 million and $23.8 million respectively. On the other hand, comparable economic values of commercial fishery (the social surplus) have not been docu- mented. Apparently, however, the Michigan Department of Natural Resources (MDNR) assumes that the social value of commercial fishing is much.1ower than that of sport fishing. See Chapter II, History of Whitefish Fishery. Ibid. Ibid. ”\IO‘UI Ibid. Commercial fishing for sporting species including perch, lake trout, other species of trout, bass and walleye is prohibited or nearly so in most areas. Also, gillnetting with large mesh gill nets, which has been predominant in Michigan, is now being prohibited in favor of trap netting because the gill nets reportedly kill too many lake trout. Objectives The objectives of this study are the following: 1) to construct a general bio-economic optimization model of whitefish fishery in northern Lake Mich- igan (MMl)(Figure I-l) for the following purposes: a) to determine and compare the optimum level of harvest (Optimum sustainable yield--OSY)9 and maximum level of harvest (maximum sustaina- ble yield--MSY)10 of the whitefish fishery; b) to determine the Optimum level of effort and producers' surplus,11 to be compared with the same values under present (1973) conditions; 2) to estimate the U.S. supply and demand of white- fish in order to: a) determine the consumers',12 producers', and social surplus13 (the net all-or-none value) for the U.S. and Michigan portion of the Great Lakes whitefish fishery, 9See Chapter IV. loIbid. 11Producers' surplus is the area above the supply curve and below the equilibrium price. 12Consumers' surplus is the area below the demand curve and above the equilibrium price. 13Social surplus (net all-or-none value) is the sum of consumer and producer surplus. FIGURE I-l. Lake Michigan -- - —- Iniersia'h- Bomamy ...”....nrga Eynhxéary 0Q" / / / I I t. . I 3 ’s b) analyze the fishery under hypothetical mono- poly conditions to calculate potential "mono- poly rent," c) determine the maximum potential monOpoly rent, and maximum potential net all-or-none value under very optimistic conditions, for Michigan's commercial fishery, comparable to the maximum potential net all-or-none value of the sport fishery mentioned earlier, d) analyze the impacts of potential alternatives for commercial fishing, including alternative levels of harvest and kinds of fish to be caught. Plan of Study Chapter II briefly describes the history of Great Lakes fisheries and the origins of the conflicts between sport and commercial fisheries. Chapter III reviews the literature dealing with the economics of commercial fisher- ies. Chapter IV introduces the bioeconomic optimization model, including an explanation of the concepts of maximum sustainable yield (MSY), optimum sustainable yield (OSY), and the equilibrium under an unregulated fishery. Chapter V estimates the parameters of the model and examines the results with a fixed price for whitefish. Chapter VI estimates the parameters of the U.S. supply and demand of whitefish. Chapter VII looks at the management and policy implications of the results. Chapter VIII summarizes the study and presents the conclusions and recommendations for future research. l4Talhelm (1973, 1975, 1977), has used "economic rent" for the maximum potential net all-or-none value of the sport fishery, to compare with "economic impact" of the sport fishery. - CHAPTER II Origins of the Conflict Between Sport and Commercial Fisheries: A Historical Review1 Since the earliest years of Michigan's settlement, the abundance of fish in the rivers and lakes has greatly impressed residents and visitors alike. Most of Michigan's first inhabitants depended very heavily upon the plentiful whitefish, herring, and lake trout for food. At Sault Ste. Marie, it was a common practice to net large quantities of whitefish in the rapids of the 18t. Mary's River during the fall spawning run in order to have a large winter supply. The most well-known fishing grounds were the Detroit, St. Clair and St. Mary's Rivers, the Straits of Mackinac, Sagi- naw Bay and the extreme Southeastern end of Lake Superior (Oosten, 1938). *Until about 1830 fishing had been confined exclusive- ly to Indians and employees of several fur companies, who kept most of the catch for their own consumption (Bessel, 1887). During the period 1830-1850, some of Michigan's first commercial fishermen chose to live along the rivers and near shallow water, and some chose to occupy the islands of Lake Michigan and Superior. 1For a more detailed story of the Great Lake Fishery see Moore (1975). At this time two major groups of fishermen evolved. The first group consisted mainly of Indians and other fish— ermen with small operations. For fishing they used hook and line, the gill-net, and the haul siene. Because this equipment is inexpensive many peOple were attracted to the fishing business. The second group consisted of groups of fishermen or companies, rather than individual operators. This group utilized the pound net. The pound net required a relatively large amount of capital investment, discourag- ing many individuals from adopting it. Beginning about 1870, the large steam tugs which gradually replaced the small sailboats and schooners became another means of dif- ferentiating the two groups. The primary species harvested at this time were white- fish sturgeon. Overfishing apparently caused a drastic decline in their respective populations, from which the sturgeon never recovered. When that happened, the intensive competition for fish meant that many fishermen were forced to find employment in other occupations. By 1889, total number of persons employed in the Great Lakes commercial fishery went down from 11,300 to 9,760 (Townsend, 1902). In 1907, 2,100 boats and 47,000 nets were being Operated by about 6,500 people. By 1919 the number of licensed boats had dropped another 40 percent to 1,300. In 1921 the sea lamprey made its way into the Great Lakes via the Welland Canal but was not very important at the time. 10 The period of 1929 to 1942 has been considered by some as a period of normalcy for commercial fisheries. The industry's fishing efforts stabilized somewhat, averaging about 68,000 nets and 1,100 boats in operation annually. An average yearly harvest of about 27 million pounds of fish was sustained as well. In other respects, however, the industry drastically changed, greatly increasing fishing efficiency. In early 1940's the large steam tug and the smaller gasoline powered boats were displaced by the more efficient diesel engine; cotton and linen nets were quickly replaced by the more expensive, yet more productive and longer lasting nylon and later (late 1950's) monofilament netting; hand driven stake pounding Operations were con- verted to mechanical means. Ice, which was originally cut in the winter with hand saws and stored for summer was later cut with power saws and eventually not cut at all as automatic ice makers appeared. During the 1930's a very important event concerning commercial fishermen was the rise of the first significant sport fishing interests on the Great Lakes. Sport trolling for lake trout became popular, especially in Lake Michigan, and soon conflicts arose between the two types of fisher- men. During this decade frequent appeals were made to the state legislature by sports fishing interests to have cer- tain areas closed to commercial fishing. As a result, after a great deal of verbal and sometimes physical hostility, some areas, including Grand Traverse Bay in Lake Michigan 11 and Potagannissing Bay in Northern Lake Huron, were desig- nated as "sport fishing only" areas (Fishermen Magazine, 1935). With the coming of World War II, probably as a result of the increased need for food, fishing effort increased tremendously. From 1942 to 1943 the number of nets being used in Michigan almost doubled, from 70,000 to 130,000 (Scott, 1974). S. H. Smith (1968) believes that for Lake Michigan, such an increase in fishing pressure may have been suffi- cient to initiate the decline of fish stock (lake trout in particular). Especially when the increased fishing effort combined with the deadly effect of the invading sea lamprey it started a drastic decline in the fisheries of the Great Lakes. By the 1940's the numbers of sea lamprey in Lakes Michigan and Huron had increased enough to cause signifi- cant damage, first to the lake trout population, and later to the whitefish and other large fish pOpulations. Lake Superior was not affected by sea lamprey until early 1950's. The sea lamprey is an eel-shaped parasite with aver- age length of 17 inches and average weight of six ounces (Eschmeyer, 1955). In the Great Lakes it is primarily a predator of the Salmonid family, specially the lake trout. It attaches itself to live fish and rasps a hold in the flesh. With the aid of an anti-coagulant which it injects into its prey, it feeds on the fish's blood and body fluids for several days. After feeding, it detaches itself and 12 swims off. Some fish are killed by one attack, some after several and some weakened fish are killed by secondary causes. The side effect of the lamprey was the creation of an ecological unbalance in the Great Lakes. The absence of large predators such as lake trout and whitefish gave the invading alewife population an opportunity to increase, and compete for the food supply of the small ciscos and chubs, already under heavy pressure by fishermen. The alewife is a small fish that also invaded the Great Lakes from its normal Atlantic Ocean habitat via the Welland Canal. By 1950, the alewife had practically displaced a wide variety of fishes and become overwhelmingly predominant in Lakes Michigan, Huron, and Erie. Its pOpulation seems to still be increasing slowly. Lamprey control programs were initiated in a joint effort by Canada and the U.S. through the Great Lakes Fish- eries Commission, but had no appreciable effect upon the lamprey's numbers until the early 1960's.2 Lampreys spawn and spend their larval phase in streams and only emerge into the lakes when they become adults. Electric wires in streams were not effective in reducing lamprey predation, although they are still maintained to monitor the size of the lamprey pOpulation in the streams. In 1958, the Commission began treating the streams with a 2For a more detailed historical and biological treat- ment of the sea lamprey problem, see Smith (1968). 13 poison, TFM, which selectively killed the lamprey larvae. By 1962, the lamprey spawning runs in Lakes Michigan and Huron were reduced by 80 to 85 percent from the levels of the 1950's. Since 1962 the program has kept lamprey levels to that of a minor nuisance. With the lake trout populations almost extinct in Lakes Michigan and Huron and whitefish stocks also at a low level, most of Michigan's commercial fishermen were in bad shape financially. Some managed to make a living by fishing less desirable species such as carp, suckers, alewife and catfish. But many simply went out of business. According to Scott (1974), from 1963 to 1967 the number of commercial fishing license holders dropped from about 900 to 660. Among those who remained in business, eighty-one percent reported gross sales of less than $5000. Table II-l shows how the Species composition of the fisheries harvest changed over time (Shapiro, 1971). TABLE II-l. Change in the Percentage Composition by Weight of Harvest on Michigan Waters of the Great Lakes Valuable;native fish ‘ Exotics and others Years (Lake Trout, Lake Herring, (Carp, Alewife, Chubs, Whitefish, Yellow Perch, Smelt, Sheephead, Sturgeon) Others) 1855 90 10 1922 81 19 1965 40 60 1967 28 72 14 It is important to note that three of the species in the list, carp, alewife, and smelt, are not native to the Great Lakes but are among the most abundant today. In the late 1960's a high level of DDT was discovered in some stocks of Great Lakes fish. DDT, dichloro- diphenyle-trichloro-ethane, is a colorless, odorless water insoluble crystalline insecticide. It is used mainly against agricultural pests. Irrigation and rain wash some of the chemical away from the agricultural lands and take it to the lakes. Fresh water sport fish become contaminated by storing the chemical in their bodies. In 1968, sales of most Salmonids caught in Michigan were prohibited by the U.S. Food and Drug Agency and several states because they exceeded the tolerance limits of five parts per million. Fortunately, this contaminant seems to be diminishing and is now generally below the maximum tolerance limit. However, in the early 1970's dangerous levels of PCB (polychlorinated biphenyls), a contaminant similar to DDT, were discovered in Great Lakes fish. This chemical, a highly stable, heat-resistant compound, which has been very useful in almost everybody's life, is still a big problem. Snowfall in the area contains the dangerous molecules. So do fish swimming in the Great Lakes and many American rivers, in levels so high, in fact, that Michigan residents have been warned not to eat more than one Great Lakes fish meal a week. The PCB applications form a long list. It is used mainly in the production of electrical transformers 15 and capacitors, but the chemical is found in a wide array of products that the average consumer comes in contact with as well. It is used in paints, inks, some plastic and rubber products, some envelope glues, washable wall cover- ings, copying machine toners, some toilet soaps, etc. Some of these uses have now been voluntarily stopped. However, the ban on the sale and manufacture of PCB and also indus- trial discharge have not yet taken effect (State News, 1977). It was first recognized as a problem by scientists in Sweden in 1966, in Japan in 1968, and in the United States in 1971. On September 23, 1971, Governor William Milliken of Michigan banned the commercial sale of Lake Michigan coho salmon because of high levels of PCBs. Wis- consin Governor Patrick Lucey followed suit on October 1, 1971 by restricting the sale of fish, primarily coho and chinook salmon and lake trout, from Lake Michigan and the Upper Mississippi River. In the 1960's, the overall situation encouraged the Federal and State fishery officials to restockfthe lakes with large predator species, primarily the native lake trout and the exotic pacific coho and chinook salmon. It was hoped that this restocking program would improve the ecological balance and provide better quality fish for com- mercial and sport fishermen. The lake trout stocking pro- gram began first on Lake Superior in 1953, as part of the battle against the Lamprey. Lakes Michigan and Huron were 16 stocked in the 1960's. Table II-2 shows the order in which these stocking programs were begun. TABLE II-2. Beginning Dates of Modern Stocking Program in the Great Lakes . Lake Lake Lake Spec1es Superior Michigan Huron Lake Trout 1953 1960 1970 Coho 1966 1966 1966 Chinook 1967 1967 1966 In conjunction with.the restocking effort, the Michi- gan Department of Natural Resources (MDNR) began to acquire the regulatory power and formulate the management policies necessary for controlling the commercial fishery loosely regulated commercial fishing industry, officials reasoned, could easily thwart the purpose of the restocking program by catching newly stocked fish before their popula- tions had built up to acceptable levels. In 1973, regula- tions to ban gill netting with large mesh gill nets in favor of trap netting were initiated but little effect of the regulation was felt until 1976. Gill netting has been predominant in Lake Michigan. The main reason for its prohibition is that gill nets reportedly killed too many lake trout. Other regulations restricted commercial fish- ermen to certain species, locations and fishing effort. Those who fished less than a given minimum number of days annually were eliminated from the fishery. It was hoped 17 that by eliminating some of the part time and marginal fish- ermen the others would remain viable. Bishop (1973) argues that these kinds of programs can have a short run deterior- ating effect on the income of those excluded from the fish- ery, because fishermen represent immobile labor and special- ized equipment with a low opportunity cost. Those commercial fishermen who were eliminated from the fishery complained that their livelihood had been destroyed through no fault of their own, and claimed that they had a legitimate right to the fish in the lakes. They also questioned the MDNR's decision in putting higher prior- ities on stocking sport fish (salmon) instead of commercial fish like chubs and whitefish. The sportsmen (with their numbers increasing tremendously in the mid-1960's, on the other hand, again found themselves in competition with the commercial fishermen. They feared that the commercial fishery would deplete the stock of lake trout, ruining their sport. Most of the sport fish in the lake were hatchery reared, and the state hatcheries were financed by the revenue from sport fishing license fees and taxes on fishing equipment. Therefore, the sportsmen argued, they had more right to the fish than the commercial fishermen. Commercial fishermen argued that other programs for stocking commercial fish could have been financed by commercial fishing fees or taxes. In addition to the conflict between these two parties, there is another major interest group (the Indians) who 18 claim the right to unrestricted fishing in about half of Michigan's Great Lakes waters. For the purpose of simpli- fying the theoretical analysis, this study will leave out this third group. At the present time, the lake trout pOpulation in Lakes Michigan and Huron is being maintained artificially. Officials hope that natural reproduction will begin again in order to help sustain the stock. Of course, it is impor- tant to note that it takes eight to ten years for lake trout and three to four years for whitefish to mature, and the lamprey has been under effective control only since 1962 (Watt, 1968). Now, that the fish stocks have improved and fish populations have reached an acceptable level for fishing, management of the Great Lakes becomes the sole guarantee to the survival of the industry. The fact that commercial fishing has declined sharply and is declining even more, and sports fishing, on the other hand,is growing and gaining more and more power, requires a better utiliza- tion of the resource approaching the optimum sustainable yield), continuation of the restocking programs, continua- tion of the lamprey control, and better allocation of fish species. In Chapter III, the fisheries literature dealing with the economics of commercial fisheries is discussed. From the examination of the relevant literature, it will become clear how the previous writers have dealt with this complex problem, "the management of the fishery." 19 Unfortunately, regulations of the Great Lakes fisher- ies as a whole have been quite lax and irregular at times in the past, mainly because of lack of unification over the whole region. Commercial fishing regulation for the five lakes has been hampered by the fact that eight states and one Canadian province have legal jurisdiction over different sections of the lakes.‘ Even though many conferences have taken place in different regions over the years, regulations among these often conflicting jurisdictions has not been uniform. As a consequence, complaints have arisen due to situations such as one state allowing fishermen to use larger mesh nets than other states to catch the same fish in the same lake. Regulation of the Great Lakes by an inter- national commission has been proposed on several occasions but the states have successfully blocked such a move. The only exception, however, is the Great Lakes Fisheries Com- mission, established in 1955 to implement the sea lamprey control program. CHAPTER III Fisheries Economics Literature One of the first published articles on fishery econo- mics in economics literature is that of Gordon (1954). He _emphasized the importance of the common prOperty nature of the fishery, and defined the Optimum degree of utilization of any particular fishing ground as that which maximizes the net economic yield, the difference between total cost, on the one hand, and total receipts (or total value of produc- tion), on the other. He was one of the first to point out that biologists in their treatment of the principles of fisheries management have overlooked essential elements of the problem by taking maximum physical landings as the objective of management, thereby neglecting the economic factor of input cost. He expressed total cost and total production as a function of the degree of fishing intensity ("fishing effort"), so that a simple maximization solution is possible. The model is expressed in terms of four var- iables and four equations: III-l. B = B(TR) III-2. TR Pf(B,E) III-3. TC h(E) III-4. H = TR-TC 20 21 Where, B (biomass) represents the pOpulation of the particular fish species on a particular isolated fishing bank; TR (total revenue) the value of the total quantity landed by man; E (effect) the intensity of fishing or the quantity of "fishing effort" expended; and TC the total cost of making such effort. He applied the model in examining two different equi- libria: a) as it occurs in the state of uncontrolled or un- managed exploitation of a common prOperty resource, where TR - TC (equation III-4). b) as it occurs in the state of a socially optimum manner of exploitation, where TR - TC is being maximized. The conclusion of this comparison was that common property natural resources, which are free goods for the individual and scarce goods for society, can yield no rent under unregulated private exploitation. In the long run, rent can be obtained only by methods which make the resource private property or public (government) property, in either case subject to a unified directing power. He also concluded that competition among fishermen eliminates the rent and is the main reason for fishermen not being wealthy. The question of sole ownership versus competitive exploitation was further examined by Scott (1955). He Showed that in the long run sole ownership of such a 22 resource is much superior to competition. In the short run, however, because of the diminishing returns to fishing, there is little difference between the efficiency of the two. Schaefer (1957) developed the following biological model: III-5. s = 3% = f(B) III-6. Y = Y(B,E) III-7. B = B(E) III-8. f(B) = tlB-(M-B) III-9. Y = q EB where M is maximum biomass (carrying capacity), t is time, B is growth of biomass and t1 and q are constants. The constant, q, representstjmz"catchability" of the fish. The difference between this model and that of Gordon's is in equations III-1 and III-7. In the first model bio- mass is a function of yield while in the second it is a function of effort. Also equation III-5 is a new feature in this model which estimates growth, or the change in population over time. Equations III-8 and III-9 specify the approximate form of B and Y. In equilibrium, yield (catch) equals the rate of natural increase (growth) in biomass, equation III-10. III-10. Y = qEB = t1 B'(M-B) = f(B) Equation III-ll which is now known as "Schaefer's yield function" is derived from equation III-10. III-ll. Y = qE (M-g—E) 1 23 The catch (yield) and effort curve (See Chapter IV) can be drawn from this equation. In 1969 Crutchfield converted Schaefer's biological model to a bioeconomic model by multiplying both physical yield and fishing effort by relevant prices in order to get dollars revenue and cost. He then applied the model to the Pacific Salmon Fisheries to analyze the three cases of pro- duction, MSY, OSY, and competitive exploitation. Turvey in his 1964 article tried to compromise between economists and biologists by emphasizing the biolo- gical factors such as the impact of net mesh size on the age distribution, weight and size of the fish stock. Although he emphasizes the relationship of fisheries regu- lations to optimum resource allocation, he believed that if overall optimization is impossible then suboptimization is still desirable. Some of the relationships of his static model are as follows: III-12. Fishing Mortality f(E) III-13. Natural Mortality - g(age distribution) III-l4. B(biomass) = h(age distribution) III-15. TR = £(weight, size of fish, freshness) He believed that the optimum marketable size of fish should determine the mesh size. He stated that in the short run the use of a larger mesh size may cause losses to the individual fishermen (by increasing the number of hauls necessary to achieve any given weight of catch), yet, in the long run, this may lower the costs of all fishermen 24 together (by increasing the number of large fish to be caught later). He also stated that an increase in demand for fish generally causes an increase in the competitive equilibrium catch. However, if fishing effort has been carried beyond the point of maximum yield, a greater employment of resources in the industry leads to a smaller total product. Finally, he concluded that with the existence of these external diseconomies in both level of fishing effort and in the choice of mesh size, to achieve the optimum resource allocation, regulation of both these variables is required. As alternatives, he also considered subOpti- mum conditions in which only one of the two is regulated. Turvey's model differs from the others in addressing the biological and mechanical factors in more detail. This can be considered a positive step towards further clarifi- cation of the relationships between economic and biological factors. In 1971 Fullenbaum et al., developed the following model: III-16. AB = f(B,Y) III-17. g = g(B,E") III-18. Y = E"g = E"g(B,E") where 39: as 91>° 25 111-19. TC = E"V III-20. n = PY - TC = PE"g (B,E") - E"V III-21. E" H 0') :1 ~ :1 V O III-22. E" = 6 H, H < 0 Where AB is stock growth under exploitation; E" is effort (number of homogOEOus Operating units or vessels); 9 is yield per vessel; Eg=Y is total quantity landed; V is total annual cost per vessel (in constant dollars), includ- ing opportunity costl; n is industry profit in excess of opportunity cost (economic rent); P is the real ex-vessel price; and 61 and 62 represent the rates of entry and exit of vessels, respectively. One important improvement in this model over the pre- vious models is that this model looks at both individual firms and the industry as a whole while the previous ones look only at the aggregate. The biological part of Fullen- baum's model differs from Schaefer's model in that equation III-16 is growth under fishing exploitation including total landings. Equation III-18 and III-6 are basically the same. One the economic side, Fullenbaum's cost equation III-19 is more explicit than Gordon's III-3. Equation III-20 des- cribing economic equilibrium in Fullenbaum, is also more explicit than in Gordon's model. Equations III-21 and III- 22 are very important since they indicate that vessels will lOpportunity cost is defined as the necessary payment to fishermen and owners of capital to keep them employed in the fishery, rather than finding alternative employment or uses of capital. 26 enter the industry when excess industrial profits are greater than zero (i.e., greater than that rate of return necessary to hold vessels in the fishery, or the opportunity cost), and will leave the fishery when excess industrial profits are less than zero (i.e., below opportunity cost). The equilibrium condition for the industry (H=o) may be formulated as shown below: III-23. PE"g (B,E") - E"V = 0 ___EL__. 9 BE") Equation III-24 merely stipulates that ex-vessel price III-24. P = is equal to average cost per pound of fish landed (i.e., no excess profits). Some important properties of the Fullenbaum model are as follows. First, the optimum size of the firm is given and may be indexed by V. Second, the long-run catch rate per vessel per unit of time (9) is beyond the individual firm's control. It is, in effect, determined by stock or technological externalities. Finally, it is assumed that the number of homogeneous vessels is a good proxy for fish- ing effort. Alternatively, Fullenbaum et al. suggest that we may employ fishing effort directly in the system by determining the number of equivalent units of fishing effort applied to the resource per vessel. In 1974 the Fullenbaum model was applied to the Maine Lobster Industry by Dow et a1. (1974). One of the unique characteristics of this research is bringing together and discussing the fisheries biology and pOpulation dynamics, 27 as well as economic relationships. Also, before explaining the bioeconomic simulation model they discuss some of the most important behavioral factors of the fisheries over some period of time, such as ex-vessel prices, fishing effort, earnings, and catch under conditions of free access to fishery resource. Herfindahl and Kneese (1973) had a different way of looking at the fisheries, involving the services of capital, K, in their model. They assumed a constant returns Cobb- Douglas production function with two inputs, the services of the stock of fish, measured by biomass (g), and the ser- vices of capital (K). They also assumed unitary operation of a fishery and freedom to choose any output and popula- tion, but required a steady state (equilibrium) solution. The Herfindahl model is as follows: III-25. g = f(B), f' §.o, f" < o III-26. Y = g(BIK) III-27. s = Bf(B) = F(B) III-28. AB = F(B) - Y = F(B) - g(B,K) Equation III-25 defines the relative rate of growth of the fish population. This aspect differs from the pre- vious models. Equation III-25 is assumed to have one maxi- mum not at B=o. Equation III-26 is a production function with capital as one of the two inputs. Equations III-27 and III-28 define natural growth and net change in biomass over time. 28 Since the steady state is assumed, the problem is to maximize n (profit) in equation III-29, subject to III-30. III-29. n = TR - TC = Pg(B,K) - wK III-30. AB = F(B) - g(B,K) = 0 Here P is the constant price of the product and w is the price of one unit of capital services. Herfindahl used the Lagrange Multiplier technique to find the maximum: III-31. L = Pg(B,K) - wK + l (F(B) - g(B,K)) - 1E.= 39.- _ _g _ _ _ 33 _ III 32. BK PaK w ,1 K — w (A P)3K _ 0 III 33. as Pas + 1(33 3B) o III-34. %% = F(B) - g(B,K) = o The A can be interpreted as the implicit or shadow price of one unit of fish in stock (i.e., remaining in the water after fishing). This model has the advantage of looking at the fish- ery from a different angle, involving a new variable (K) in the production function. All the bioeconomic models so far have been applied to various parts of the U.S. fish industry. Unfortunately, there have been no known bioeconomic analyses of Great Lakes commercial fisheries. In the biological side, however, there have been some recent studies. In 1976, Jensen applied the logistic surplus produc- tion model2 to the commercial whitefish yield and effort 2"Surplus production” is the amount of biomass that can be removed by a fishery without changing the size of the stock. 29 data of selected districts of the Michigan waters of Lake Superior, Lake Huron, and Lake Michigan. He investigated a set of biological goals such as carrying capacity (M), biomass levels (B), maximum sustainable yield (MSY), fishing effort that produces the maximum sustainable yield, and the relative importance of commercial fishing and sea lamprey 3 predation. The equation of the surplus production model based on the logistic equations are: dB _ _ 5 2 III 35. 3E — kB M B III-36. Y = qEB k 2 III-37. AB = kB -'— B - qEB M In the steady state, AB=O, and annual equilibrium yield is 2 III-38. Ye = kB - = qEB 3hr m where: k is a pOpulation growth constant; %% is the natur- al growth of the biomass, and AB is the growth under fishing exploitation. The only difference between this model and Schaefer's is that of notation. By setting k=t M, this model can be 1 converted to that of Schaefer's. By "linearizing" equation III-35 and applying least squares, Jensen was able to estimate three of the parame- ters, k, M, and q for three districts: MM-l (district one of Michigan's Lake Michigan), MS-4 (District four.of Michi- gan's Lake Superior), and MH-l (district one of Michigan's 3The logistic surplus production model was developed by Hjort et a1. (1933) and by Graham (1935). 30 Lake Huron). The calculations were adjusted to assume 4 1/2 inch gill nets as the standard gear, with and without lam- prey predation. In all districts the observations were greatly scat- tered about the equilibrium stock production curve. How- ever, most observations for Lake Michigan (MM-l) were scattered at low level of biomass. This indicates that over the years too much effort has been applied to the fishery, forcing the biomass to stay below its optimum level. This condition is considered overexploitation. An example of overexploitation is shown in Figure III-l.4 In studying the sea lamprey, Jensen plotted the biomass removed by fishermen and the biomass estimated to have been removed by sea lamprey predation. The result shows a tremendous impact of the sea lamprey on the whitefish population as compared to the small impact of commercial fishing. ”These estimates of sea lamprey predation are accur- ate enough to conclude that although the whitefish stock in this district has been consistently over- exploited, the decline in whitefish biomass during the 1950's was caused by the sea lamprey and not by overfishing."4 The results for Lake Superior (MS-4) were considera- bly different. For this district observations appear to be available for all stages of the fishery, which indicates the absence of overexploitation. 4Jensen (1976), page 754 and 756. Yield FIGURE III-1. 31 An Example of an Overexploitation Situation 1'” ‘4} $44 Biomass 32 In Lake Huron (MH-l) the whitefish stock appeared overeXploited when poundnets were used as the standard gear, but underexploited when using gillnets. Another biological study of the Great Lakes is that of M. H. Patriarche in 1976. The object of the research was to establish quotas for whitefish in order to assure a stabilized population and fishery. In the study Patriarche modified Ricker's dynamic pool model, and applied it to statistical districts, MM-l and MM-3 in northern Lake Michigan. He recommended a quOta based~on the premise that the annual harvest of a population should be confined to the weight gained each year by the harvestable proportion of the population (surplus production). He claimed that this would maintain the population at status quo. He stated that one of the keys to successful manage- ment of a fishery, among the biological factors, is infor- mation on the size of the pOpulation being managed. Since direct counts were impossible for populations in a lake as large as Lake Michigan, Patriarche developed an indirect means of estimating the biomass. "With estimates of either exploitation rates or mor- tality and survival rates at hand, along with total catches by age group, it is possible to compute the numbers of whitefish of different age groups." The results of Jensen's study (using the logistic surplus production model) agree closely with computed biomass in A; 5Patriarche (1976) page 17. 33 this study.6 The method developed in this study can be used for stabilizing the fishery at the current population level by matching yield with production. This strategy should be satisfactory for obtaining sustained yield but there is no provision for building up a depleted stock. The study does not address itself to explain how one can move to Optimum sustained yield. He suggests two ways to increase the current level of pOpulation, by a) arbitrarily cutting the equilibrium quota and permitting more spawners to survive for additional egg production, and b) changing the minimum size limit in order to allow greater escapement of immature fish, thereby build- ing up the number of spawning fish. However, the study did not address the question of whether the number of spawning fish has any effect on the recruitment of fish into an age class. 6For the breakdown of the pOpulation in terms of the different ages see Patriarche (1976) table 7, page 30. CHAPTER IV The Bio-Economic Model This chapter introduces the bio-economic model deve- loped in this study. Based upon this model, a detailed dis- cussion is presented of: l) the point of maximum sustainable yield (MSY), 2) the point of optimum sustainable yield (OSY), and 3) the competitive equilibrium point. The remainder of the dissertation is based upon this model. Chapter V will estimate the actual parameters of the model and examine its predictions, assuming a fixed price of whitefish. Chapter VI will estimate the U.S. supply and demand for whitefish to find the price of whitefish under competitive as well as monopoly conditions. Chapter VII will analyze the management and policy implications of the results. Some of the simplifying assumptions of the model are: 1) it is long run and static, 2) it is concerned with a single fishing ground con- taining only one species of fish (whitefish), 3) all the fishing (production) units are to be homo- geneous, 4) all factors of production are to be in prefectly elastic supply, 34 35 5) perfect mobility of assets, 6) real ex-vessel price (p) is given, 7) effort and output can be controlled in order to reach Optimum sustainable yield (OSY), 8) Cobb-Douglas production function. These assumptions may make the model rather unrealis- tic, but are important for the model to be operational at this point. In latter stages of develOpment some of these assumptions will be released. For the purpose of this study, however, these assumptions seem to be apprOpriate. The Model In this study a surplus production model (Hjort et al., 1933) and Graham (1935) is used to develop the follow- ing bioeconomic static optimization model. 3B(t) _ ' _ _ k. m at ’ B ‘ k Bt M Bt In this model parameter, m, is assumed to be equal to IV-l. two (m=2) which is a parabola. Iv—2. Y = qEBt kB - EBZ - qEB IV-4. TFC CE IV-5. TVP = PY = PqEBt IV-6. n = TVP - TFC where: . dB B W = growth in biomass without fishing exploita- vtion, D; t B = biomass of the fish population, k = population growth constant, M = carrying capacitYp (Maximum sustainable biomass), 36 I-< II dockside quantity of fish landed, q = "catchability" coefficient, E = fishing effort (e.g., as used in this study, a list of 1,000 linear feet (almost 300 meters) of 4 1/2 inch gill net), Em = effort at MSY, Bm = biomass at MSY, AB growth in biomass with fishing exploitation, TFC = total factor cost, C = cost per unit of effort, TVP = total value product or value of the total product (yield times price), P = average ex-vessel price, n = producers' surplus.1 The model consists of two parts: biological and bio- economic. On the biological side, the logistic surplus production model (equations IV-1, IV-2, IV-3) has been adapted from the models found in the fisheries literature (e.g., Hjort et al., 1933 and Graham, 1935). This model was applied to the Great Lakes whitefish population by Jensen (1976). On the economic side the physical yield and fishing effort are multiplied by relevant price of white- fish and cost per unit of effort in order to get dollars revenue and cost. The Lagrangian multiplier technique is then used to determine the optimum levels of yield, fishing effort and "economic rent" at this point. 1For the definition of "producers' surplus" see footnote I-ll. 37 Biological equations Equation IV-l relates the natural rate of growth to the size of the biomass. It describes the growth of the biomass under no fishing exploitation and can be shown by Figure IV-I. Equation IV-2 relates the yield of the fishery to the level of effort and the size of the biomass at any period of time. In the steady state, AB = 0 (equation IV-3), and the equilibrium yield, Ye, as a function of biomass is: IV-7. Ye = kB - £132 Solving equation IV-3 for B, where AB = o, and substituting that into equation IV-7, gives the equilibrium yield, Ye, as a function of effort, equation IV-8; 2 IV-8. Ye = qME - ”351— E2 k Given equations IV-l, and IV-2, the "surplus, produc- tion" is the amount of biomass that can be removed by a fishery without changing the size of the biomass. There- fore, the fishery will be in long run biological equilibrium when harvest equals natural growth as in equation IV-3. Equation IV-7 further illustrates this concept. The sus- tainable yield curve is defined as the locus of all the combinations of yield and biomass for which equation IV-7 is satisfied, as in Figure IV-I. Maximum sustainable yield (MSY) is the maximum point of the curve, where the slope is equal to zero. To obtain MSY, equation IV-7 is differen- tiated with respect to B; the result is set equal to zero and solved for B max (equation IV-9), where B max is 38 FIGURE IV—l. The Sustainable Yield Curve. Equation (1) where m = 2 (parabola) B max = Y max (MSY) j..---'-----——-- = Yield 0‘13 A B max Biomass 39 biomass at MSY. Substituting B max into equation IV-7 gives equation IV-lO. IV-9. B max = 1;- IV-10. MSY = kB max - 1%- B2 max = 9% The fishing effort at MSY is IV-ll. E max = Bfigiq = g5 Since yield is a function of both biomass and fishing effort (equation IV-2), a similar relationship is derived between sustainable yield and fishing effort (equation IV-8) and Figure IV-2. FIGURE IV-2. Yield-Effort Curve, a Long Run Harvest Func- tion Yield MSY Ym —---—*--------- Em E The above figures (IV-1, IV-2), however, do not show yield/effort production functions in the normal sense of the term Y = f(E,B), where B is biomass fixed at a certain 40 level, because each point on the curve relates to a differ- ent size of the biomass. The éurve is rather a locus of long—run equilibrium pointsz, because we have specified that Y=B, and in order to change B, B must change (see equation IV-l). Bioeconomic Equations Surplus production models are usually applied to determine the maximum sustainable yield (MSY) and the level of fishing effort that will produce the MSY. This informa- tion has been considered important in the management of a fishery. The bioeconomic model developed in this study, however, is applied to determine the maximum economic yield (MEY), also called the Optimum sustainable yield (OSY). The OSY is the yield at which sustainable economic rent is maximum. Equation IV-4 computes the total factor cost. In the fisheries economics literature this equation is usually called total cost. Parameter C is cost per unit of effort. IV-4. TFC = CE Equation IV-5 is the value equation. Since price is held constant in the value equation; PY is the total value product, or the value of the total product. 2Starting with a given level of biomass, B , and a -fixed level of effort, E , equilibrium levels of yield and biomass are obtained. NOW, if effort is increased to E , over a period of time another equilibrium is reached fog biomass and yield. Therefore, in Figure IV-2 every change in effort causes a change in yield and a change in biomass, which does not satisfy the production function Y = f(E,B). 41 IV-5. TVP = PY = P qEB Equation IV-6 gives H as the difference between the value of the total product and the total factor cost. IV-6. H = TVP - TFC Total factor cost includes all costs: variable, fixed, and Opportunity costs of labor, management, and investment. Variable H is called "producers' surplus" and is earned because the fish stock is unique, there is a limited number of fishing areas, there are limited market substi- tutes, and the fact that not all the fishing areas are equally productive.3 Management and policy implications of producers' surplus will be discussed in more detail in Chapter VII. Equation IV-6 is the objective function of this study, which is being maximized subject to equation IV-3, a biolo- gical constraint, to find the Optimum sustainable yield (OSY), Optimum level of effort, and economic rent at OSY. IV-3. ABt = Bt - Y = o = kBt - EB: t Equation IV-3 specifies that the rate of change in biomass - qEB under fishing exploitation is equal to zero. 3 The assumption of fixed rice of out the monopoly question. p put rules out 42 In equations IV-12 and IV-l3 the Lagrange multiplier technique is used to find the maximum possible rent (n), subject to the biological constraint (AB)=o.4 IV-12. H = TVP - TFC + A(AB = o) PqEB - CE + A(kB-§ 32 - qEB) IV-13. A Where A is the coefficient of the constraint. It is the change in economic rent when the constraint changes by one unit of fish, or the shadow price of the constraint. The values of biomass (B), effort (E) and A, can be found by differentiating equation IV-12 with respect to B, E and A, setting all three equations equal to zero, and solving the system. IV-l4. %%-= PqB - c - AqB = 0 an- -2_k_ _ IV-lS. 3g — PqE + A(k M B qE) — 0 an _ _ k 2 _ _ IV-16. 3A - kB M B qEB — o The results are, _“M C IV-17. B* — 7 + 755 k C ._ *-_—___ -— IV 18. E 2q (1 qPM) _ __C_ IV-l9. A — P qB* where B* is biomass at OSY, and E* is effort at OSY. To obtain the Optimum sustainable yield (OSY) the values of B* and E* are substituted in equations IV-2 or IV-4, giving equation IV-20. . 'This study concerns only with the static case, dyna- m1c maximization, however, is possible by integrating the rent over time and discounting it by the interest rate. _rt n = &)(TVP-TFC+A(AB=0))e dt 43 IV-20. OSY = qE*B* = kB* - 1712' (3*2) In Figure IV-3 the MSY (point G) and OSY (point F) and the open access equilibrium (point H) can be compared. The total value product curve (TVP), and the total factor cost curve (TFC) are shown in Figure IV-3a. The factor-product relationship, Figure IV-3b shows the average value product (AVP), marginal value product (MVP) curves, and the marginal and average factor cost curves (MFC, AFC). Point G corresponds to the value of maximum sustaina- ble yield (MSY) which was explained in Figures IV-l and IV-Z. At this point the slope of the long run marginal revenue function is equal to zero, and total physical yield is being maximized. At point F (OSY), fisheries economic rent is maximized, at this point the value of the marginal product (VMP)5 of the input is equal to the price of the input, Equation IV-Zl. IV-21. VMP = P E E where P is the price of the input E (effort). To maintain E production at point F, however, restrictions on the number of vessels and vessel outputs are necessary. Under free entry, the existence of greater than normal profits would encourage entry of new vessels until average industry reve- nue is equal to the average factor cost. At this point the average industry profit is zero and marginal value product 5In this analysis VMP=MVP, because the product price is assumed to be fixed. 44 Comparison of OSY, MSY, and the Open Access Equilibrium (Long Run) FIGURE IV-3. a) TFC r Input E (effort) 45 (MVP) is less than the price of the resource used (the cost of the effort). It is obvious that point H cannot be an optimal point for production because the same harvest and revenue could be earned with far less effort (E2), at a much lower cost. Point H is called "over-exploitation," because too much resource (effort) is expended and the fish stocks are pursued too intensively. Biologists have in the past argued that if the fish- ery resources were controlled such that entry and effort were restricted, the rational choice for total harvest would be at point G with Em effort, Figure IV-3a, which would maximize total physical product or total value product. This point is MSY, calculated in equation IV-9. Economists, on the other hand, argued that the maxi- mization of sustainable yield can be only a sub-Optimal and the optimum depends on the position of the total value pro- duct and total factor cost curves, Figure IV-3a. To econo- mists, the Optimum allocation of the resource is obtained only when equation IV-21 is satisfied. In equation IV-21, the optimum point of allocation changes as P (price of the E input, or cost per unit of effort) varies. Most past fisheries treaties of the U.S. have been written in terms of MSY, but biologists and managers have recently come to accept the concept of OSY. In fact, the 6 U.S. Senate committee on commerce, in S 1988 in 1974, defined OSY as ”. . . the largest net economic return 6Report No. 93-1079, August 8, 1974. 46 consistent with one biological capabilities of the stock, as determined on the basis of all relevant economic, biologi- cal, political, and environmental factors." Equations IV-9 and IV-ll calculate two points related to MSY, and equations IV-l7 and IV-18 are their equivalents for OSY. The main difference between equations IV-9 and IV-l7 is the addition of the term in equation IV-l7. _9_ 2qP This term introduces the economic factors of input cost and output price. Optimum biomass, B*, is directly related to fishing cost and inversely related to output price. This relationship shows that if cost per unit of effort (C) increases, ceteris paribus, fishermen cut back in produc- tion (effort) and in the long run the equilibrium biomass moves upward. Also, as average price of fish increases, ceteris paribus, fishing becomes more profitable and produc- tion increases, which in the long-run forces the equilibrium biomass to decline. Egfiations IV-ll and IV-l8 can also be compared. The difference is the term (1 - agfi biOmass, B*, is inversely related to fishing cost and ). Optimum directly related to output price which is exactly the Oppo- site of that with biomass (B*). In Chapter V, coefficients of the bioeconomic model will be estimated and the model will be tested with a fixed price. Chapter VI estimates the aggregate supply and demand relationships for U.S. whitefish to compute economic rent. Chapter VII discusses the bioeconomic model under 47 different pricing systems such as a monopoly or a perfectly discriminating monopoly. CHAPTER V Estimating the Parameters and Outputs of the Bioeconomic Model Using Fixed Prices Introduction The main goals of this chapter are to: 1) Estimate the parameters of the bioeconomic model using alternative methods of estimation. 2) Compute and compare the optimum effort, optimum sustainable yield (OSY), maximum sustainable yield, and "surplus values" for each alternative method. 3) Select the most "reasonable" set of parameters and results for the bioeconomic model. In the next chapter (VI), aggregate supply and demand of whitefish will be estimated, and the results will be compared with those of this chapter. To estimate the model coefficients, the following pro- cedures are: l) a simple linear relationship between yield and effort, 2) a quadratic relationship between yield and effort, 3) the method developed by Schaefer (1957) using the two point approximation formula to linearize the deri- vative of equation VI-l, 4) the method developed by Pella and Tomlinson (1969) using numerical integration instead of approximation of the derivative, and 5) a simple graphical 48 49 technique as the final procedure. The state of the fishery in 1973 is also analyzed and compared with those predicted by the above procedures. A curve fitting to the data using the graphical technique seems to fit the data (1963-1976) well, as a reasonable compromise solution. Among the other procedures the linearization technique using data from 1967 to 1976 gave a reasonable result, but seems to be a bit too high. In general, results from applying different procedures for the period 1963 to 1976 seem to be too high and procedures applied for the period 1929 to 1950 seem to be too low. These methods, however, provide us with a range of estimates of optimum effort, Optimum sustainable yield (OSY), maximum sustainable yield (MSY), and "producers' surplus." The author believes that the Optimum points for the fishery fall somewhere within these ranges. These procedures and conclusions are explained in detail in this chapter. Methodology A. The Methods: Both short-run and long-run biological models have been estimated in this chapter. Short-run models explain the fishery condition at a time period too short to permit changes in biological aspects of the fishery, such as the stock size. Equations V-l, V-2 are short-run models of. yield as a function of effort. v—1. Yt = th CBt dt = b Et 50 _ 2 total yield or catch during year (t) where: Y t Et = total effort during year (t) q = catchability coefficient St Btdt biomass in year (t) ob,c,d = constants Equation V-l is a linear non-equilibrium relationship between catch and effort, and equation V-2 is a quadratic non-equilibrium relationship between catch and effort. These short-run models are not able to explain or predict the long-run behavior of the fishery because they are too simple and do not take into account the biological side of the models. Long-run models, such as the surplus production model, on the other hand, can explain the equilibrium relationships I between catch, effort, and stock level (equations IV-l, a. 3 , IV-5, IV-6, and I967, develOped in Chapter IV). dB . t _ _ _ k m V-3. .3? — Bt - kBt M(Bt) Equation V-3 models growth (B) without exploitation, and usually assumes m = 2. In equation V-3, k is a constant and M is carrying capacity. V-4. Y = E B q t This equation shows the relationship between yield (Y) per period of time as a function of catchability (q), effort (E), and level of biomass (Bt). Yield is usually measured in kilograms. By subtracting equation V-4 from equation V-3, net change in stock (AB), or growth under fishing 51 exploitation, is obtained, equation V-5. One of the assump- tions of the surplus production model is that in equili- brium, the net change in stock equals zero. '*_ -£m_ By taking into account the effect of the sea lamprey, equation V-6 is obtained. V-6. ABt = k Bt - - q E Bt - s 3 st where s is a constant and S is the sea lamprey abundance B 3|?“ rt 8 index. Under equilibrium conditions, when catch (Y)equals instantaneous population growth (Bt), and net change in stock (ABt) equals zero, then equation V-3 is equal to equation V-4, as equation V-7. -Laigz t k t Taking into account the sea lamprey predation, equation V-8 is obtained, v-8 Ye- M _rvisi32_s_£_mg ' q t k t k t where the third term represents mortality caused by the sea lamprey. A more general form of the equation is equa- tion V-9. 2 v-9. Ye = (q M - E'EEE‘Q) Et - EES— E: The derivation of these equations from equations V-3, V-4, V-5, and V-6 are given in Chapter IV. 1 The following example of the surplus production model illustrates the relationship between a hypothetical long-run 1This example is paraphrased from that given by Jen- sen (1976). 52 equilibrium and hypothetical short-run non-equilibrium yield curves for an exploited fishery. In the non-equilibrium condition the relationship between annual yield, Y and effort at each level of bio- t' mass is only a straight line (equation V-é and Figure V—l). The slope of the line (b) increases as biomass increases. In this non-equilibrium situation the stock size increases as effort decreases, but at the same time an increase in the stock size will tend to increase the amount of effort applied to the fishery because the higher the stock density the greater the yield (and revenue) per unit of effort. For example, three short-run yield curves and an equilibrium yield curve for a hypothetical population are drawn in Figure V-l. Suppose that the stock size is B2 and the effort is E0, so catch is Y1. If at this non-equilibrium point revenue exceeds cost, effort will increase, assuming E is allowed to increase. Biomass also will increase until effort exceeds the equilibrium level. Assume that effort reaches E1. Initially the biomass will be greater than B1, but as effort continues at E1, the biomass will approach B1 as the stock is depleted. At this point the fishery is being overexploited. For the fishery to reach an equilibrium at stock size B1 and effort level E1, costs must equal revenue at this point,2 assuming free entry and 2In the classical case of unregulated fisheries, pro- duction would expand to the point where total value product (TVP) equals total factor cost (TFC). 53 FIGURE V-l. Equilibrium and Non-equilibrium Conditions of the Fishery. The x's Represent Possible Observation Points of Effort and Yield. 0‘) Yield 5\ 54 competition. If costs are greater than revenue, fishermen will begin to reduce their effort before the biomass decreases to B1; as effort decreases, catch decreases and the biomass will begin to increase. The SIOpe of the short- run yield curve (b = CPE) will gradually increase. From this point fishery may or may not follow the long-run curve (the parabola). The reason that the parabola may not go back through all the previous points is that population level and CPE change. At some point, however, revenue will again exceed cost, effort will increase and the cycle begins again. Of course the major reason for the existence of the cycles is the fact that catch and effort tend to fluctuate because occasionally environmental conditions are suitable for production of one or more large or small year-classes. When these year-classes enter the fishery, catch changes and effort responds. This results in large but fairly regular fluctuations inthe observed catch and effort. The x's in Figure V-l are hypothetical catch and effort data belonging to a series of increasing population levels which are all lower than the population at point f. This mechanism determines the shape of the long-run equili- brium curve. This point becomes very important when we estimate the long-run models later in this chapter. B. Data Base: Short-run and long-run biological models were esti- mated using annual data. A complete listing of all data 55 used in this analysis is provided in Table V-l, including the symbolic names, definitions, and sources of all varia- bles used. Annual data for catch and effort of whitefish by fishing gear type in Michigan District One of Lake Michigan (MM-l) are given in Table V-2. Total catch (in pounds), total effort and CPE using 4 1/2 inch gill net as standard gear from 1963 to 1976 are given in Table V-3. The 4 1/2 inch gill net was the major gear used in MM-l until 1973. The formula (Jensen, 1976) which has been used to convert catch and effort to a standard gear is: Total Effort = (ES) (Yt) / YS where: E s effort with standard gear Yt Y8 = yield with the standard gear total yield In Figure V-2 catch, effort, and catch-per-unit-of-effort (CPE) for 4 1/2 inch gill net (only) are plotted over time.3 There are three major peaks for catch: in the 19203, late 1940s, and early 19703. The decline in the 1930s may be due to overexploitation, but the pOpulation apparently did not readily rebuild itself. The decline in the 503 may be partly due to overexploitation, but the major factor at the time apparently was sea lamprey predation. Another reason for these fluctuations as was explained before, can be the occasional large year classes entering the fishery. 3Note that this is only for 4 1/2 inch gill nets, but total catch has fluctuated in a similar manner. 56 Table V-l. Data Used in the Analysis (1929-1950) and (1963-1976) Symbol Definition-Description Source E Total effort for trap, National Marine Fishery pound, and gill net, Service, 1977 using gill net as stan- dard gear. Y Catch from different National Marine Fishery types of gear in Service, 1977 pounds and kilograms S Sea lamprey index of Walter and Hogman, 1971 abundance C Cost per unit of Research in progress, effort Fisheries and Wildlife Dept., Sea Grant Project, Michigan State University Over the period, catch has ranged from few pounds in 1959 to more than two million pounds in 1948. Over the period CPE has also changed drastically from a low of .55 pound per unit of effort4 in 1957 to a high of 48.89 pounds per unit of effort in 1973. This fluctuation in CPE apparently has both biologi- cal and technological origins. The biological origin is the fact that CPE fluctuates as the fish stock fluctuates. Technological causes on the other hand, are things like improved gear efficiency and improved weather information. The peak in CPE in 1948 may be partly a result of the intro- duction of nylon nets in the late 1940s. 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Total Catch in Pounds and Total Effort for Lake Michigan in District MM-l (Using 4 1/2 Inch Gill Net as Standard Gear) Year Total Catch Total Effort Catch/Effort (CPE) 1963 73,636.00 9,359.27 7.87 1964 81,478.00 7,911.35 10.30 1965 117,560.00 11,526.92 10.20 1966 85,800.00 7,392.63 11.61 1967 114,578.00 9,394.13 12.20 1968 111,779.00 8,992.14 12.43 1969 210,011.00 11,691.43 17.96 1970 352,309.00 15,524.61 22.69 1971 975,571.00 23,789.14 41.01 1972 1,093,352.00 23,449.78 46.63 1973 1,300,850.00 26,606.03 48.89 1974 1,044,098.00 29,578.83 35.30 1975 926,764.00 25,004.90 37.06 1976 1,287,705.00 33,085.95 38.92 very possible that this peak and those in 1929 and 1973 Yvere caused instead by temporary increase in carrying capa- C=ity (M), which these models assume to be fixed. Nylon neets are stronger than cotton nets which were previously u=sed. Nylon nets are handled easier and can be set in deeper water. In the late 1950s and early 19603, monophy- laxnent net was introduced. MonOphylament net is even more 60 \ .< 6) O V o\ .a \k .f\ om ONH omH . com Ammov uHOMHM\£oumo 1.1.1.1.1 pHOMMm 111111111 noumo ovm mace massage umz Hana nocH mxa 6 you .msma1mmma .Huzz mom mmo can .uuommm .Amncsomo guano mo ncmma ow O 00 O N H Catch/Effort .ooH com ova .m1> mmoon 61 efficient than nylon. This has made it possible for the commerical fishermen to fish in even deeper water. Figure V-3 shows total annual whitefish catch (in pounds) from 1963 to 1976 in district MM-l. Table V-4 shows various catch (in kilograms), effort, and price sta- tistics from 1963 to 1976. Figure V-4 also shows total value product using 1973 deflated price and total value product using yearly deflated prices from 1963 to 1976 as compared to total effort. In Figure V-4, the points in the 19603 and those in the 19705 seem to form two different groups. The pOpulation level has apparently changed over this period of time. This change in population from one level to another could change the harvest function and as a result, optimum catch and effort, assuming the cost per unit of effort remains unchanged. In Table V-5, the index of sea lamprey abundance is presented. In Figure V-5 level of catch and sea lamprey abundance are compared. This figure will be discussed in Part C of the methodology sec- tion. C. The Period of Study: Data from 1963 to 1976 are used in this study.5 Year 1963 is used as starting point because of the biological disruptions caused by the sea lamprey predation in the 19508. It is believed that by 1963 the stock had built up to a stable level, so the period of 1963-1976 seemed to be 51n some cases 1963-1966 were left out because of producing unsatisfactory results. 62 How» wh m5 vb mm Nb an on mm mm 5m mw mm we mm 4 H \ l). 11 N m v .3 .0 m 1 x m s .a . m m n .1 m h m oa a C Ha NH m4 ma mhmaummma .Huzz nonuumfla now soumo Hmuoa mo ocmua .m1> mmoon 63 mm.ba oo.mmo.mm ov.omv.omm vm.mmm.mom om.hmv.mhm om.omm.mmm hm. h¢.H ;. whoa mm.oa om.voo.m~ mm.mbo.mmm mv.amo.mmv om.mvo.hav mm.mm~.amw No.a mo.a mbma mo.mH mm.mnm.mm oo.oma.mvm oe.~¢¢.mvm oa.vmm.mow oo.omm.vhv om.H oo.~ vuma mm.mm mo.ooo.wm mm.mom.omh om.mmm.mmm om.mmm.mmm mv.mmm.amm mm. mm.H mnma o~.HN mh.mvv.mm h¢.vov.amm ab.mma.mmv ov.moo.~mv ma.whm.mmv mm. 5H.H tha ¢Q.ma va.mm>.mm hm.mam.mhw Hm.mom.vmm mm.moo.mmv mm.H¢v.mv¢ mm. mo.H Ahma Hm.oa Hm.v~m.ma mm.mha.oom .mo.amm.~ha mo.mmm.mma mv.ova.ooa mo.H mm.a onma mH.m mv.Hmm.aH om.mam.hma mm.omv.oaa mm.vom.wm mm.mmv.mm -.H vm.H mood mw.m va.mmm.w mm.mmo.mm mH.mvm.mmu mm.oom.om vm.mom.om mm.a vm.~ mama mm.m ma.vmm.m om.mwm.mo mm.mmm.mo oa.owm.am Hm.omo.mm m~.H mm.H hood mm.m No.mmm.h oo.oom.mv oo.ono.vv oo.oaw.mm oo.ooo.mm nH.H oa.a coma om.¢ mm.omm.HH oo.omh.mm ma.mmm.am oo.~om.mm mm.mmv.mm 0H.H 0H.H mmma mm.v mm.aam.h mh.omm.mv vm.omm.mm oa.mwo.wm m¢.mmo.hm Nv.a Nm.H voma mm.m hm.mmm.m om.mma.mm vm.mmm.av o~.mma.mm am.on¢.mm mN.H vH.H mmma mowum umow >Hm>m pruMwaov Acmuwamwav msmnmoawx .mM Mom .mx Mom uuommm vacuum woumammo1coz moowum mango» mofium mnma a“ guano mofium ouaum .Hmow \noumo scum: m>a magma ass magma m>a H6069 cmumammo oommwmmo mhumoma .Am>ac posooum msam> Hopes can .coumo .mwoaum omumammo .v1> manna 64 1oa x uuommm mo muficanuuomwm m cm cm on om 0H i $.35 1.. . H i or. N .w 0 m 1. x Q h ._w m £31. m MW w; . ? flri e m h t 9.; «.1 6 f 6. 0 ¢ m m a m V 1 ca m mowum pmumHmmv maummm moans m>B 0 HA T 5mm.» 0 mo . moaum Umumammp mhma mcwms m>B x NH . 4 H122 uOflHumflo HON uhommm annoy nuns mmoflmm sauna» can mnma vmumamma mafia: guano 0:» mo msam> H6009 .vl> fimeHm 65 Table V-S. Sea Lamprey Abundance Index Year Index of Abundance 1945 1 1946 3 1947 16 1948 27 1949 43 1950 148 1951 345 1952 90 1953 252 1954 199 1955 164 1956 155 1957 165 1958 80 1959 68 1960 52 1961 101 1962 63 1963 59 1964 36 1965 29 1966 9 1967 0 1968 0 1969 0 1970 0 1971 0 1972 0 1973 O 1974 0 1975 0 the most reasonable period for this analysis. Figure V-S presents the trend of whitefish catch at MM-l and the sea lamprey abundance index. The index has four and five year lags in order to show the correlation between the index and the whitefish catch. In 1957-58 the lamprey index drops and in 1962-63 whitefish catch increases. This comparison shows that lamprey (T-S) has a higher correlation with 66 N H6 cs 5 6 o m 6 m N am om 6m mm an op m m m m 6 m m as om 6 mm mm m m 6 m an on m m a m m 6 Ho om mx ;.7 11 1&§. III \J Lu . /. / /I . I :4 /: \ux s» ,< 1. ,% x ,\ (x 1 and mung» m>flm can unom naw: mocmccsnd mounfimq mom mo xwch can H122 um Amxv conmu cmflwmuflnz kuoa mo mesons OH 0N om ov on 00 on cm «18 mlB noumo om 00H omH CON .ml> mMDUHm 67 catch than (Th4), and must be used as a variable in the estimation procedures. The 1963-76 data have been used to estimate the para- meters of the biological model by applying different esti- mation procedures. A separate study (Jensen, 1976) estimated the same parameters using a different period of time, 1929 to 1950. Jensen applied only one estimation procedure (the linearization technique) to estimate the parameters. The bioeconomic model developed in this study will make use of parameters estimated in this study by different pro- cedures and over different periods of time in order to com- pute and compare the various computations of Optimum effort, yield, and Optimum consumers' surplus. D. Criteria for Selecting the "Best" Results: Many different types of equations using different combinations of the variables in Table V—l were estimated. However, this chapter will not describe all of the results. Instead the "best" estimates of each procedure will be presented. Criteria for selecting "best" results in their approx- imate order of importance were as follows: 1) Coefficients estimated for independent (exogenous or.1agged dependent) variables should have the expected sign. 2) R2 (coefficient of determination) should be as high as possible. 3) Coefficients should be significant at or below the 10% level. This criterion was waived if the overall 68 equation met this criterion and other criteria were satisfied. 4) The standard error of the estimate should be mini- mized. 5) The residuals should show no pattern of consistent over or under estimation over the time period ana- lyzed based on the Durbin Watson test. The results of the analysis are presented in the fol- lowing four parts. 1) Analysis of the state of the fishery in 1973. 2) Short-run biological models. 3) Long-run biological models. 4) Computing variables via graphical techniques. Except for the short-run estimates, the results are pre- sented within two frameworks: First, using long-run aver- age cost per unit of effort (C = LAC), and second, using short-run average variable cost per unit of effort (C SAVC). In each case, the following results are presented, (a) effort at optimum level of harvest (E*), (b) optimum sustainable yield (OSY), (c) Optimum total value product (TVP*), (d) rent at OSY (Rent*), (e) effort at MSY (Emax), (f) maximum sustainable yield (MSY), (g) maximum total value product (Tvpmax)’ and (h) rent at MSY (Rentmax). A list of all the abbreviations used throughout this study is presented in Table V-6. Results of the Short-Run Biological Models A. A Linear Relationship Between Catch and Effort: To find the linear relationship between catch and effort, equation V-é was estimated using 1963-76 data and 69 Table V-6. Abbreviations Used Throughout this Study Symbols Definitions E* Effort at the Optimum sustainable yield (OSY) OSY Optimum sustainable yield TVP* Optimum Total Value Product = OSY x P LAFC Long-run average factor cost TVFC Total variable factor cost AVFC Average variable factor cost STFC Short-run total factor cost AFFC Average fixed factor cost LTFC Long-run total factor cost SAFC Short-run average factor cost LMFC Long-run marginal factor cost SMFC Short-run marginal factor cost Rent* Rent at the optimum sustainable yield E max Effort at maximum sustainable yield MSY Maximum sustainable yield TVP max Total value product at MSY Rent max Rent at MSY CPE Catch per unit of effort (catch/effort) plotted in Figure V-6. V-lO. Yt = 16.2 Et Equation V-lO is the relation between annual yield, Yt' and effort for a given level of biomass and is called a short-run yield equation. The estimated coefficient was significant at 1% level, using the t-test. The equation was forced to have a zero constant term (i.e., to go through the origin). Jensen (1976) estimated the same relation 70 2‘1. mloa x unommw mo mufics ca uuommm om om ow om om oH ewv .t .1. A: Q? AmwsmGOwumamm HOOOHA my uuommm ocm.noumo Umuoacmum can Hmzuod cw -5 0") kg x 10 q in Total catch .wl> HMDUHm 71 using data from 1929 to 1950. His coefficient was 12.5 and R2 = .56. The difference in the magnitude of the coeffi- cient, which represents CPE, can be partly explained by the new technology, such as improved nets and vessels, since CPE would be affected by new technology. The difference in R2 values shows that effort explains more of the variations in yield over the more recent period. B. A Quadratic Relationship Between Catch and Effort: 2 In this section equation V—} was estimated using data from 1963 to 1976, and plotted in Figure V-7. _ _ 2 V-ll. Yt — .16 Et + .0007 Et R2 - .96 The only difference between equations V-lO and V-ll is the quadratic term. The quadratic term was significant at the 1% level, while the linear term was not significant even at the 10% level. The R2 indicates that 96 percent of the variation in yield is explained by effort. Figure V-7 compares actual and predicted catch and effort. Fishing Cost per Unit of Effort Since cost function is a major component of the econo- mic side of the bioeconomic model, it is appropriate at this point to identify different costs and sources of data used in this study. To find the cost per unit of effort, some data on costs and returns for "typical" commercial fishermen in the Great Lakes were collected as a separate component of the 72 cm ammo 10H x uuomum m cm ow cm on CA 31>. “H0602 oaumuumso 6o uuommm can noumo omumsaumm can Humane -5 Total catch in kg x 10 OH 4 .hl> HMDOHE 73 overall project.6 The survey consisted of a combination of mail questionnaire (to organize the meetings and verify some of the answers in later stages), and a one time personal interview. Telephone was also used in organizing the group meetings and verifying the answers. The author participated in the various discussions of the results of the survey and in one occasion participated in interviewing the commercial fishermen. Different opportunity costs of management, labor, and investment were calculated based on the following criteria: a) ten percent of the gross income for Operator's manage- ment, b) a wage rate of $3.25 per hour used by Telfarm in 1973 (Telfarm is a cooperative extension service project which provides management information based on the data supplied by the participating farmers), eight hours a day and forty hours a week was assumed for operator's labor for an average commercial fisherman, c) an eight percent (8%) interest rate was assumed for investment. Investment items were mainly the value of the net and boat. Crew Share (which is the amount of money or catch given to the crew members) is a component of the variable cost. It represents all the labor related costs and includes hired and family labor except for the primary operator. Crew share was as high as one third of the gross income in some C3868 . 6Research in progress, Fisheries and Wildlife Depart- ment, Sea Grant Project, Michigan State University. 74 From the results of the survey, two types of costs were identified which have been used in this study, (a) long-run cost, and (b) short-run cost. According to econo- mic theory, the time framework for long-run analysis is defined to be long enough so that the industry can adjust itself to different changes (i.e., such as switching from gill nets to trap nets). In other words, in the long-run every input is variable. This added flexibility means that the long-run cost of harvesting any amount of fish will be as low as, or lower than, the cost of harvesting that level in the short-run. Long-run total factor cost (LTFC) is the sum of all the costs. Long-run average factor cost (LAFC) is computed by dividing LTFC by total effort. Since costs per unit of effort are assumed to be constant, LAFC = LMFC. LTFC Total Effort On the other hand, in the short-run, the industry can C = LAFC = LMFC = not adjust itself to many different changes. There are variable as well as fixed costs. The number of firms is fixed. There are opportunity costs of labor and management which can be considered as either fixed or variable costs. In this study, however, those opportunity costs are treated as short-run fixed costs. In the short-run the total fac- tor cost is the sum of all three costs, equation V-12. V-12. TSFC = Fixed Cost (FC) + Opportunity Cost (CC) + Variable Cost (VC) The short-run average variable factor cost is calculated as, 75 Short-run Average Variable Factor Cost (AVFC) = Total Variable Factor Cost (TVFC) Total Effort where the denominator is the total effort in district MM-l. Since AVFC is assumed to be constant in this model, short-run variable factor cost is equal to short-run margi- nal factor cost (SMFC). Average fixed factor cost (AFFC) is calculated as follows: Fixed Cost + Opportunity Cost Total Effort Since both long-run and short-run factor costs are AFFC = assumed to be constant in this study, long-run average factor cost (LAFC) equals AVFC + AFFC. In Figure V-8 total, average, and marginal factor costs in both short and long-run are illustrated. The following cost data are used throughout this chapter. C1 = LAFC = LMFC = 21.38 C5 = AVFC = SMFC = 12.82 Average fixed factor cost (AFFC) = 8.56 These costs have been deflated by the 1973 Consumer Price Index (CPI) (1967 = 100). This study also makes use of the 1973 price per kilo- gram of whitefish deflated by the CPI (8.99). Current (1973) State of the Fishery in District MM-l The 1973 catch and effort data were used to compute some important values of the commercial fishery. The results of this analysis using 1973 price of $.99 per 76 FIGURE V-8. Total, Average, and Marginal Costs in Short and Long Run 5 1 I v 65 C; , Y 65’ C' «VF O at Effort 1 $ 21.38 LAFC = SAFC = LMFC Fixed Cost 12.82 AVFC = SMFC 0 Effort 77 kilogram and deflated long-run cost (1973) per unit of effort equal to $21.38 are presented in Table V-7. Results of the Long-Run Biological Models The long-run biological equation models are given by equations V-4, V-5, and V-6. The coefficients of these equations have been estimated using two different proce- dures; a) a linearization approach, and b) a numerical analysis approach (a search routine). The linearization approach has been applied over two different periods, 1929-50 (Jensen, 1976), and 1967-76. Both periods were tried with and without the sea lamprey abundance index. The numerical approach, however, has been applied only to the 1963-76 period and without the sea lamprey index of abundance, because the numerical technique utilized does not allow for the sea lamprey abundance index. A. Linearization Approach This technique starts by finding the average biomass during year (t) from equation V-5, as in equation V-13. _ _Y(t) __1_ Y(t) _; V 13. Bt — q E1; — q (—Et ) - q (U(t)) Where Yt is annual yield, Ut is yield per unit of effort, and q is the "catchability" coefficient. The derivative in equation V-5 or V-6 has been approximated by using _ B(t+l);;B(t-l) ‘ 2 Substituting equation V-l3 into V-l4, V-15 is obtained, V-14. AB(t) v—15. AB(t) = AU(t) uQIH 78 mumaaoo. ooowa . msamudm. A122 afi_msamusm .mumoscoum mumaaoo ooommm onus umoo,uopomm :smumcoq Hopes mumaaon ooommm m>a uoscoum msflm> Hmuoa amumoafix oooamm .» noumo Hmuoa 00:13.19: m) 6 no 003 83. oomom m £83m H32. ...._._ .A.. ..._. ..1. ............1. ......._._... . pass mmpnuwcmms mc0flumw>munn¢.. . mOsHm> anocoomoflm H122 unauumho ca mumcmam mg» no mumum Amemao acmuuso .au> manna 79 where AU(t) = (U(t+1) 3 U(t-1)). Substituting equations V-13 and V-15 into equations V—S and V-6 gives equations V-16 and V-17. V-16. AU(t) = k U(t) - fig U2(t) — q Y(t) v-17. AU(t) = k U(t) - fig U2(t) - q Y(t) - s s u (t) where s S U(t) represents the effects of sea lamprey preda- tion. These equations can be rewritten as the following linear equations. V-18. Z(t) V-l9. Z(t) = a where: Z(t) = AU(t) X1 = U(t) x2 = U2(t) X3 = Y(t) x4 = s U(t) a1 = k a2 = — 3E a3 = - q a4 = - s From the description of the model it becomes obvious that the expected sign for a1 is positive, and those for a2, a3, and a4, negative. Given estimates of a1, a2, a3, and a4, the corresponding estimates of M, k, and q in equa- tions V-4, V-5, and V-6 can be found. 80 Results With and Without the Sea Lamprey, 1963-1976 and 1967-1976 In this section the period 1967-1976 gave more reason-- able estimates. The results using data from 1963-1976 were too high and the estimated curve did not give a good fit. The estimated parameters (1967-76) had the correct signs only when the index of sea lamprey abundance was used with a lag of three years or more. According to Figure V-S and based on the abundance lagged five years (T-S) was used. The estimated parameters of equations V—7 and V—9, using (T-S) and 1967-1976 data are as follows: k = 2.1 q = .66 x 10'4 M = 1,591,000 s = .025 These parameters are used in the following analyses. 1. Analysis with LAFC = $21.38 (long-run) The results of the analysis using the estimated parameters and the long-run average factor cost are pre- sented in Table V—8. Figure V-9 shows the total harvest function and different cost functions. In Figure V-9 the total value product function (TVP) is found by substituting the estimated parameters in equation V-7, giving equation V-20. v—20. TVP = 104 E - .003 E2 In equation V-20 the sea lamprey abundance index (S) 2 equals uero because the analysis is done for 1973. However, 81 mumaaop ood.0m¢ .xmfi msamusm NOE m an msamusm .mumospoum mumaaoo ooo.ovm omqe xme um umoo Houomm :5H1mcoH Hmuoa mumaaom ooo.omm x65 m>e pogo 10Hm Osam> annoy EOwamz Emumoafix ooo.mmm um: vamflm manmcwmumam EOwamz Doc 430 :05... «\H v m0 umwm oooa oamfia mg m um: um uuommm mumaaoo oom.mHm msflmusm «m um msamusm .mumoscoum mumHHoo oom.anm owns am pm umoo Houomm asunmcoa Hmuoa mHmHHOO ooo.omh «m>B Donn 1oum OOHO> Hmuou EOEHUQO amumoaax ooo.oom wmo unH» manmcwmumsm asswumo umc :33 nos“ «\H v m0 DOOM coca oop.ma «m uuommm EOEwumo .wuwcs ..mmpsuwcmoz acofiu0w>ok044 ,f .wuld0>iowaocoomoflm mm.a~ u omen «mauaomfl .mswaaaoma coaumuaummcaq msHmD mwmhamcfi 0:» mo muasmmm .mn> manna 82 OH x uuommm mo muwcs Ga uuommm m- cm on ow om ON a, A. 5 n7 own an. .0 1. X s m n .1 v t ‘ +r m m .m r am: ma 6. 0 e m vausv. n. M «e. a 9% Y. t + > m m v¢w¢»\ §ow .% vovTY. .+» m . .8 J$$v eF/ + v OH 1‘ mm mmoo. I m VGA 0 m>B a manna umumamma mama spa: .mamauaomfl .mswwcnoma cowumuaummqaq .ml> mmDGHh ’1' 83 to show the effect of the sea lamprey index of abundance, two indexes for 1963 (S = 59) and for 1965 (S = 29), along with other parameters are substituted in equation V-9. For 1963, equation V-Zl was obtained and for 1965, equation V-22 was obtained. 2 V-21. Y 31.00 E - .0033 E 2 V-22. Y 68.00 E - .0033 E The harvest function corresponding to each equation is presented in Figure V-9. In comparing these results (Table V—8) with the actual 1973 data (Tagle V-7), it is obvious that B*, which is almost half of E, produces a much larger catch and total revenue and generates a larger amount of rent. According to this model the fishery (MM-1 district) is being "over- exploited." In Table V-8 the producers' surpluses at OSY and MSY are also compared. The rent at OSY is larger than that at MSY. 2. Analysis with AVFC = $12.82 (short-run) In this analysis the short-run average factor cost is used. The results are presented in Table V-9. This analysis using AVFC gives a larger value per optimum effort and smaller rent at OSY. Comparing the results with Table V-7, however, the effort, B*, is still much smaller than the actual effort in 1973. This short- run analysis is also shown in Figure V-9. 84 mumaaop ooo.oam msamusm um um msamusm .mumospoum umoo mumHHOU ooo.oom Ohms Houomu asu1uuonm Hmuoa uosuoum mHmHHOO ooo.oam «m>9 Osam> amuou Esauumo mamumoaux ooo.o~m Mmo mama» manmnumumzm Esauumo um: Haum zoqu «\H v uo umwu oooa ooo.va «m vacuum Esauumo muwcs ._........wmosuusmma .wcowuuweonngc.. .m.wudam>iousoc0000um mm.NHm u Uh>m..mhmalhmma rmsvucnome Goaumnflummcwq mnuma mumwamcd on» uo muasmmm .m1> manna H 85 Results Without Sea Lamprey, 1929-1950 The following parameters were estimated for equation V-4, V-5, and V-6 by Jensen (1976) using the same lineariza- tion technique. k = .22 M = 9,160,000 q = .17 x 10'-5 By substituting these parameters in the bioeconomic model, the following equation for the total value product is obtained, equation V-23. v-23. TVP = 15.42 Et - .00012 E: The harvest function and different cost functions are plotted in Figure V-10. 1. Analysis with LAFC = $21.38 (long-run) By looking at the graph it is obvious that the opti- mum point under this analysis (LAFC = $21.38) is at the origin. 2. Analysis with SAVFC = $12.82 (short-run) Substituting the above parameters in the bioeconomic model provides us the results in Table V-lO. In Table V-10, optimum effort and OSY are lower than the previous cases. Optimum rent in this case is negative because while Optimum total value product is greater than the variable cost, it is not greater than the total cost. The results of this analysis are very much different from the previous analyses. The total value product function is 86 N OH x uuouum uo mafia: cu uuouum ME I ooavmux m m «moflau4m om om ow on on ad 4 o a 5 _ N m X m A? .m _w; r a, v t / .N C 135 1. m .w 4* a m we. P . a 1 .qu> h m ti 1.. 0 m M \C. T s» 4. ca 1+ m NHooo. I m N¢.mH u m>B ..mx HOG mm.m u mum .mm.a~ n o .omummmH .mmumemq 60m unonuuz mumsamca .0H1> mmDOHm 87 NME mumaaop ooo.nmm1 unamusm _wmz um madmusm .mnmospoum 0000000 ooo.mmm.0 xmsomma x020 00 umoo Houomm GOM1uHonm 00009 ME 0000000 ooo.mmu xmam>a x m um nonpoum OOHM> Hmuoa 50000000 ooo.oom mm: 0000» 00000000000 2080x02 000 000m 0000 ~\0 v u0 0000 ooo0 ook.0m xmem mm: 00 000uum mnmaaop oom.mhl mzamusm Mmo um msamuam .mnmoscoum 0000000 oom.mmm omma 000o Houomm csmluuonm 00009 0000000 oom.0m ommma 0moo 00000m 00800 00m10uoam 00009 0000000 ooo.0v0 om>me 0000 000000 0000000> 00m100osm 00009 0000000 coo .30 :50. 00000.00 0000> 00000 0550000 20000000 ooo.am0 wmo 0000000000000000 2020000 00: 0000 0000 «\0 0 00 0000 0000+ «no.00 40 000000 5080000 ..mHHGD._. .mmwfluHGGMZZ mGOHUMH>OHQQ4 ... ..mMDHM>.OfiEOdOO¢OHm mm.NHm u Om> OHQMB 88 a very wide parabola and its predictions tend to underesti- mate the most recent catch and effort data. Results with Sea Lamprey, 1929-1950 The following parameters were also estimated by Jen- sen (1976) using the same linearization technique including the sea lamprey variable in the equation. k = .30 M = 8,830,000 q = .17 x 10'5 By substituting these parameters in the bioeconomic model the following equation for the total value product function is obtained, equation V-24. v-24. TVP = 14.86 Et - .000084 E: The TVP curve and cost curves are plotted in Figure V-ll o 1. Analysis with LAFC = $21.38 (long-run): With the given long run average cost per unit of effort the Optimum point is at the origin, Figure V—ll. 2. Analysis with SAVFC = $12.82: Table V-ll presents the results of the analysis using short-run variable cost. Results in Table V-ll are very similar to those in Table V-lO, and tend to underestimate (see the graph) the more recent data. The results from subsections (1) and (2) of this section show that the parameters which were 89 l: N o0 0 000000 00 00000 00 000000 m1 om om 0v on em OH 1 o H .w m _m X m S. m M . ..Fv w t $w$ Aw; W d i m 0 4+. .00 m. 0 .0. Out? 0. m wFV- .u \U m t O T m 0.? Q 00 m oooooo. 1 0 00.00 1 0>0 .omuomo0 .0000200 000 0003 0000000< .HHI> HMDUHK 90 0000000 ooo.mm~001 0909000 002 00 0509050 .000090000 0000000 ooo.m~0.0 000000 0000 00 0000 000000 050100000 00008 . x08 x0e 0000000 ooo 000 0B. 000 0000000 0000> 0000.0. 000000000 ooo.000 002 00000 00000000000 0000002 . x00 000 0000 0000 «\0 0 00 0000 ooo0 ooo o0 0 000 00 000000 0000000 ooo.mm1 0500050 000 00 090muam .000090000 0000000 .ooo.mm~ 0000 0000 000000 camIHHonm 00009 0000000 ooo.mo0 o0000 0000 000000 00000 000100000 00000 0000000 ooo.0m0 o0>0e 0000 000000 0000000> 000100000 00000 0000000 ooo .20 0000. 0000000 0000> 0000.0 0000000 000000000 oo0.000 000 00000 00000000000 0000000 000 0000 0000 ~\0 0 00 0000 ooo0 000.00 «0 000000 0000000 000:3 0005000m0z 0000000>muan¢ 00500> 0080:00000m «0.000. n Uh> m0n0B 91 estimated using data from 1929 to 1950 do not predict the recent changes in the commercial fishery and therefore the model prediction for 1973 using these parameters are under- estimated. B. Numerical Analysis Approach (A Search Routine) This approach, develOped by Pella and Tomlinson in 1969, uses the same equations as those in Schaefer's. In this model equation V-S, which is a special case of Bernoul- li's differential equation, has been solved for B(t) (biomass), equation V-25. The Constant H in equation V-25 is equal to, k/M, in equation V-5.‘ H H l-m m (m 13(0) ) e- (M+q-E) (l-m) tl‘f-‘rn' V-25. B(t) = [ If a fishery of E units of effort is Operating on the population at time t, the instantaneous catch rate is 3Y(t) at By substituting equation V-25 into equation V-26 an V-26. = q E B(t) equation for yield as a function of time and effort is obtained, equation V-27. __£i__ M+ qE t l e-(M+ qE)(l-m) lI-m There is no explicit expression for the integral of [ H _ ._Xl£l - _____.- _ 1-m V 27. t — q E M+ qE B(O) ) ( this equation. Fortunately it can be integrated numerically for given values of the parameters H, M, and g. In order to estimate these parameters, the authors (Pella and Tomlin— son) have created some new parameters such as F r, Opt, q, 92 and Umax' Definitions, suggested initial values, and mathe- matical formulae for these are presented in Table V-12. These parameters and their mathematical formulas are used in order to estimate the original parameters through the following equations. -l V-28. H = ( T )( q* )m q F l m Umax opt _ m V-30. q = g In these equations m is the same as the exponent of the variable B(t) in the surplus production model (m:2). It determines the shape of the harvest curve. In Schaefer's model, m is assumed to be equal to two. Once the parameters are computed the program computes a sequence of predicted catch values (éi) by integrating the differential equation V-3. Using the predicted catch values, the sum of squares of the deviations from the estimates are computed as follows. v-31. SS(H, M, q, E, 3767): .? (01-01)2 then (fi, i, q, E, fiTfiT) is the "bestxoestimate of the model parameters provided that for all feasible values of the parameter set SS in equation V-31 is minimal at (fi, Q, q, a, 3737). To obtain the best estimate of the parameters of the model a search routine is conducted over the surface (H, M, q, m, 3(0)) by numerically approximating SS at points selected in such a manner as to lead us to the minimizing point. 93 Table v—12. Symbol, Definition, Initial Guesses, and Mathematical Formulae for some Variable in Pella and Tomlinson Model New Definition Initial Guesses Mathematical Parameters Formulae F Effort required to Mean effort over M(l-m) opt . . . . —— maintain the popu- the period of esti- mq lation at its op- mation. timum size and to harvest the maxi- mum sustainable yield. U Maximum catch per U =maximum CPE 1 max . max -- unit of effort. U _ (M/H)m-1 max q Four times maximum B =4*maximum 1 max catch max catch '63? ' (M/H) = B max q Catchability Umax/Bmax q coeff1c1ent r The ratio of the .8 B(0)/Bmax = stock size at the 1 time when the E fishery first B(O)/M/H) comes under obser- vation to the max- where B(O)=rU /q . . max imum stock Size. m The exponent of In this study m variable B(t)(m=2 in Schaefer's model). User must provide different values of m when using the search routine. values m=l.2 and m;2.0 were exa- mined. m can take a wide range of variables. It determines the shape of the harvest curve. 94 The search routine takes the initial guesses as a base q, r, U ), and begins the exploratory phase, poxnt, (F max opt' to modify the guesses and search for the best estimates of the parameters. It evaluates SSl at this point (Fo + AF, pt ) and compares it with SS at (Fopt' q, r, U ). r q: I max Umax It is important to note that the user must provide the step intervals (AF Aq, Ar, AUmax) for Fopt' q, r, U , opt' max and supply lower and upper bounds for each of the four parameters. If SS1 is less than SS, then SS1 is taken as a new base point and the routine explores in the q direction. On the other hand, if 88 is less than 581' the routine tries the poxnt 882(Fo AF, q, r, Umax), and 1f SS2 13 pt less than SS, then 582 is taken as the new base point; if not, it retains the old base point, and in either event, begins exploring in the q direction. In a similar manner each of the remaining axes of the parameter space corres- pondingter and Umax is eXplored. At the termination of this exploration a check is made to see if the base point has been changed. If the base point has changed, a pattern phase is entered; if not, the routine reenters the explora- tory phase with the step intervals for each parameter divided by 10. The routine is halted when the exploratory phase, with the step intervals divided by lOkk (kk is speci- fied by the user) fails to change the latest base point. This search technique was applied to estimate the parameter of equations V-4, V-S, V-6, without the sea lamprey abundance index. The routine does not permit using 95 this index as a variable. Data from 1963 to 1976 was used. Different values for m were tried. The best results accord- ing to the same criteria as before, were obtained when m= 1.2 and m=2.00. The results of m=l.2, however, were better than m=2.00 (having a larger value for R2), but the results of mr2.00 were chosen to calculate, B*, TVP*, OSY, Rent*, MSY, TVPm , Emax' and Rentma for the follow1ng ax x' reasons: a) All other estimation procedures in this study have assumed m=2.00. b) Using m=l.2 makes the Optimum calculations more difficult. Results without Sea Lamprey 1963-1976 The estimated parameters of equations V-4, V-S, V-6, using the numerical analysis (the search technique), for m=l.2, and m=2.00 are as follows, m=l.2 m=2.00 k=l.2 k=.24 M=47,600,000 M=33,900,000 3='12 x 10-5 3:.85 x 10-5 R =.84 R =.82 10 9 Sum of Squares=23 x 10 Sum of Squares=54 x 10 By substituting the estimated parameters where m=2.00) into the bioeconomic model the following equation V-32 is obtained for the total value product. 2 t Figure V-12 shows the total value product and total V-32. TVP = 28.51 Et - .0001 E factor cost curves. 96 n-0H x uuoumm mo mugs: cg uuouum can uuozmcm can acoH am 00 on ov on ON CA A 4 Total value product in $ x 10-5 mm Hooo. . m Hm.m~ u m>a .mhmaumomfl .mcfiusom goummm magma mwmsamcm an» no muasmom .Nau> mmome 97 1. Analysis with LAFC = 21.38 (long run) m = 2.00: Applying the above information to the bioeconomic model developed in Chapter IV, the following results were obtained, Table V-13. In Table V-13, the level of effort at the optimum is much higher than the previous cases. There is a posi- tive producers' surplus obtained at the optimum level of effort but a very large negative rent at the maximum level of effort. 2. Analysis with SAVFC = 12.82 (short run) m = 2.00: Table V-l4 presents the results using the short run average variable fixed cost. C. Graphical Method Graphical technique is a very subjective way of fitting a curve to a set of data. The results can change from one person's graph to anothers. In this study the author has followed the following criteria in plotting different curves to the data in Figure V-13. (1) It seems that there are at least two different levels of fish stock that fishery has been in equilibrium over the period studied. In the 1950's and 1960's due to sea lamprey predation, the equilibrium level is very low, and in the 1970's where fishing is almost back to its nor- mal level. Therefore, at least two curves are relevant here. ”ME mumaaoo coo.m~o.HI moamnsm um: um moamnsm .mumoscoum mumHHoc ooo.m~o.m mem an umqe mem an umou Houomm sum mcoq Hmuos ”ME ME mumaaoo ooo.mmo.~ m>a x m um uoscoum moam> kuoa msmumoahx .ooo.¢ho.~ um: came» mannaflmumsmpesshxmz XME um: Hana coca «\H e no ammo oooa ooo.¢va m um: um uuommm mumaaon ooo.mNH msamusm wmo um msHmunm .mnooscoum mumHHoo ooo.mmn «m um omqa «m um umou Houomm cam mcoq annoy mumfion ooo .2; RE. uozcoum 33> 138. suing memnmoaflx ooo.~mm .wmo chH» manuaflmumsm assuage um: Haas such ~\H w mo ammo coca «Hm.mm «m uuommm assuage .mpH:a. _____ .mmusuwcmuz maoeumm>muna< .... .mwsHm>Auflaoqoum0flm mm.HNm n ..... omen .mhmaummma .mcfiusom conmwm mcflmo mumsamca we» no muasmmm .mau> manna 99 ooo.m~o.flu «mg mumHHOU moamuom um: um moamnom .mumoswoum s s mug mumaaoc ooo muo m ohms m an “moo uouomm cam unocm Hmuoe mumafloc ooo.mm~.a ommme xmsm um umoo omth annoy mumaaoo ooo.m¢m.fl om>ma xmsm um umoo manmwum> cam uuonm Hmuoe mHMHHOU ooo.¢vl msamusm Mme um msamuam .mumosooum mumaaoo ooo.amm.a omma umoo uouomm com unonm Hmuoa mnmaaoo ooo.mom ommma umoo uouomm cmxfim cam uuonm annoy mumaaoo ooo.mmm om>ma umoo uouomm maauflum> cam unonm Hayes 98:8 ooo .Sm . H ER. 33on 33> 138. 5538 msmumoafix ooo.vmm.H demo vamwu manmcwmumam assuage uma Hana soc“ Nxa a mo ammo coca ooo.>e «m assuage um uuomum mafia: monouwcmmz mcoHDMH>oHnn< . mmus> owfiocoomowm ummm .mhmasmoma manuaom soummm mnums mammamqa mnu.momufinmwm .va-> manna 100 N OH x unomum mo muHcs :H uuommm Ml om om ov om om OH f - .H . a 4 o w l 5 .$ H .o .l. N x s m n .1 H a w . m \ ... m .. a a JR «7*. m V m 1. our . m h .u oY a» m m m. )Y ow m #0H m MHoo. - m 5.Hm u m>a .oemmomH maqunoma HmoHnmmuw a no muHsmmm .mH-> mmoon 101 (2) Once the number of curves are determined the goal is to minimize the square of the deviations from the obq served points. (3) Among different analytical procedures applied in this study, the results from linearization technique, with sea lamprey (T-S), 1967-1976, look the most reasonable, Table V-8. This method indicates that the MM-l district is being overexploited. In this section, in order to be con- sistent with the linearization technique, the overexploita- tion of the MM-l district is assumed. This means that commercial fishermen have been applying too much effort to the resource. However, to the author's view the MM-l dis- trict is not as much overexploited as that shown by the linearization technique, Figure V-9. In other words, the results of the linearization technique are a bit too high. (4) This study assumes perfect parabola, m=2 (follow- ing the assumption of the surplus production model) in order to be able to compare the results with the other methods. One of the advantages of the graphical technique is its flexibility. It can fit certain curvilinear relations more closely than the more rigid mathematical functions. Of course, it can be a disadvantage because it also reflects the subjective errors of the analyst. Results of the Analysis Using Graphical Technique without Sea Lamprey Variable, 1963-1975 There are two curves plotted to the available data. This study makes use of the curve which goes through the 102 more recent data. The results of the analysis are presented in Tables V-lS and V-16. 1. Analysis with LAFC = 21.38 (long run): The results of this analysis using the long run aver- age factor cost are presented in Table V-lS. The results in Table V-15 are similar to those in Table V—8 where the linearization technique is applied to data from 1967 to 1976. The optimum level of effort is much smaller‘ and the optimum economic rent is much larger than the observed values in Table V-7, where the state of the fishery (1973) has been analyzed. 2. Analysis with AVFC = 12.82 (short run): The results using short run average factor cost are presented in Table V-l6. Sensitivity Analysis Any changes in the opportunity costs of management, labor, and capital effect the cost unit of effort (C). To test the sensitivity of the data ten percent increase in C is assumed. This change would increase the long run cost form $21.38 to $23.5 and the short run cost from $12.82 to $14.1. These changes in cost were tried using graphical analysis. The results of the long run analysis were ten percent decrease in producers' surplus, and a ten percent decrease in the effort at optimum (B*). More specific long run and short run results are presented in Tables V-l7 and V-18. z ”ME mHMHHoc ooo.mm msamusm_ Mm: um msamusm .mnoosuoum mHMHHoc ooo.mm¢ onus xmsm um umoo uouomm Hmuoa mumHHoc ooo.omm xm5m>a amen um uoseoum msHm> Hmuoa a. msmumoHHx .ooo.mmm ems onHw mHnmchumsm snemez M” van HHHm goaH «\H e no umwm oOOH oom.o~ xmsm um: um uuommm mumHHom ooo.ohH msHmusm susHumo um msamusm .mumoocoum 82m.HHoHu oom.mmm onus umoo uouomm cam mqoq Hmuos -msmumoHHx ooo.om¢ wmo onH» memnHmumsm sseHudo mumHHoo ooo.m~¢ .m>s uoaooum maHm> Hmuoa assHumo umc HHHm nocH «\H q no ummm oooH ooo.~H .m uuommm essHumo mafia: ............. moosuwamdz, mGOHum«>munn< (mosam> owEo:0000fim osvwanoma Hmowsamuw OCHmD madammm .mHI> OHQMB 104 mHmHHOU ooo.mma. unnamudm . Mme mm msHmHsm .mumospoum mHmHH0© ooo.m~m omma umoo HODUMh com unonm Hmuoa mumaaow ooo.nmv am>B posooum mnam> Hopes EaEwumo mamumoHHx ooo . com $0 33» mHnmcHSmsm 5538 um: HHfim coca ~\H v m0 Doom coca oov.ma «m uuommm Esfiwumo muwco. moosuwcmuz mQOHumwemunnm mmswm> owsosoooofim onuwdnoma Hmownmmuu msHmD.muH9mom .mHI> «Hana 105 ”we mumaaoc omb.mv msamusm was an msamnsm .muwosvoum mumHHoo m.em~.nmv omqe mem an umoo uouomm Hmuoa mamumoHHx OH~.mHm um: onH» mHnmaHmumsm esstmz . E ME mumHHoe th.ovH.m an m>a x m UM #05GOHQ $9Hm> HMUOB . me umc HHHm nocH «\H q no ummm oooH mam mH m um: um uuommm mumaaoo Hmm.~ma «madeSm NmO um moamunm .mumoscoum mumHHoo mem.¢mm omHa wmo um umoo Houomm com mcoq Hmuoa mamumoHHx mmo.~Hv mmo chHw mHnmchumsm assHudo mMMHHoHV sea .2; RE uoscoum msHm> H38. .5530 umc HHHm socH ~\H o no ummm OOOH omm.0H «m uuommm essHumo muacs movauflcmmz msofiumw>munnm mosam>.oasoq00mon muMNW fl Uhflqnsumou HOHOMh mmMHm>4 35M mcoq nqu mHmmHma¢;Hmuwnmmuo..«nHy>.mHnme 106 mumaaoo nvmrmma ...amsamuom ....Mmo um.msamusm .mumoscoum mumHHon vmm.mmm ohms umoo Houomm com uhonm Hmuoa mHMHHoo hnn.mh¢ «m>e noncoum msHm> Hmuoa EflEHumo mamumoHHx mmm.omv wmo nHmH» mHamchumsm eaeHumo uwc HHHm nocH ~\H a mo ummm oQOH Hmv.vH .m uuommm aseHumo muHcD umcauwcmuz m:0aumw>ounn¢ mmsHm> Ofleosoomowm Hcsm uuonmv H.¢Hw u Uh>€ ~umou Houomh mannanm> wmuum>¢ nuw3 mflmhamcfl Hmownmwnw .mHI> manna 107 Summary A summary of the estimated parameters and the related bioeconomic results are presented in Table V-l9 and V-20. Table V-19 presents all the estimated parameters using different methods. Table V-20, on the other hand, presents the results of the analytical techniques and the graphical method. Except for the linearization technique, Table V-8, Figure V-9b, the rest of the procedures resulted overesti- mated values. The search routine (numerical analysis) does not seem to work well in this study. The linearization technique gives more reasonable results, except they still seem to be too high. Considering the fact that there is not very much data available for the whitefish fisheries for MM-l after sea lamprey control became effective, and the quality of those available leaves much to be desired, these results seem to be the best available up to this time. From the author's view the results obtained by using graphical technique are much more reasonable than any other. The author believes that District MM-l is being overexploited at a level very close to the MSY, as shown using the graphical technique. 108 muOH x 5H. ooo.omm.m om. swumsmq «mm uaonuHs ommHummch mica x ha. ooo.oma.m mm. houmfimq mom nuw3 ”msvfisnomu sowHMqummsflq muOH x «H. ooo.oom.hq ~.H o~.H.w.s.nqu lmhmHummmHv , . .. . . ..... .. . Hocwusom suummmv o-OH x mm. ooo.oom.mm «N. oo.~ u eunqu mHmsHmca HmoHumssz AmpmHumomHo «noH x we. ooo.Hmm.H H.~ Amuse smumemq mmm aqu ”machnomu coHumuHummcHH ...s.. .x . wuonuuz. ......... ....................... monumoummm ucmnommao mchD mumuwemumm counseumm may no wquEsm .mHu> mHnma 1139 000.N0 000.N0 000.0N0.HI 000.0N0.HI 000.50N.HI 0 000.000! 0 000.00v 000.00¢ 000.000 000.0mv 000.050.m 000.050.m 000.0N0.H 0 000.00m.H 0 000.0vm 000.0vm 000.000 000.000 000.N00.N 000.N00.N 000.000 0 . 000.00v 0 000.0N0 000.0N0 000.000 000.000 ooo.ono.m ooo.ouo.~ 000.050 0 ooo.oom o ooo.mmm ooo.mmm 000.0N 000.0N 000.vva 000.cvd 000.00 0 005.00 000.0H 000.0H fl000.0H l HmauoB 000.500 000.0Nv 000.0H0.H 000.000 000.05H 0 000.00H 0 000.0H0 000.005 ' 000.H00 guano Hmuoa 000.000 000.00v 000.VMO.H 000.000 005.H5H 0 000.50H 0 000.0N0 000.000 000.0N uuouum HMHOH 00v.0H 000.NH 005.55 000.00 000.NH 0 mm.H~nom ~0.Nauoh>H N0.~Huom>¢m 0m.HNuUhwumemq mmm nuwz ~0.NHuUm>¢m 0m.H~uom¢m 0m.HNuUm44 A muuvhoumada Suez _ Hmbuho. coflumufiummcflq .H unmm x08 Uh? x08 m>B Amxcamz tucflm «DEB am>9 Amxcwmo am moonuoz muonumz meowumfiwumm usmumwuwn mafia: munam> oafiocoomo«0 may no >umeasm .0NI> wanna CHAPTER VI Estimating the Supply and Demand of Whitefish Introduction The main goals of this chapter are, first, an economic analysis of the supply and demand of whitefish at the dock- side level, and second, using these equations to find dif- ferent elasticities of supply and demand. To the author's best knowledge, these are the first estimatates of supply and demand and elasticity ever calcu— lated for the Great Lakes whitefish fishery using annual data. Therefore, different analytical methods were tried, including simple ordinary least square (OLS) equations, OLS equations with distributed lags, reduced form equations reduced form equations are special case of simultaneous equations), a system of two simultaneous equations using two and three stage least squares, and a system of four simultaneous equations (for whitefish and lake trout) using two and three stage least squares. The ordinary least squares equations with and without the lagged variables and the reduced form equations did not give satisfactory results, because a negatively sloped supply and a negative sign for the income variable in the demand equation were obtained. The best results were obtained from the system 110 111 of four simultaneous equations for whitefish and lake trout. The price elasticity Of demand ranged from -l.5 in a single demand equation to -5.05 in the system of four simultaneous equations for whitefish and lake trout evaluated at mean values. From the author's view, -3.94 (evaluated by Log- Log functions in the system of four equations) is the best estimate of the average price elasticity of demand for whitefish over the period 1960-73. This seems relatively elastic, but a study in Wisconsin (Bishop, 1973) applying a very simplified equation for demand using monthly data found similar results. If this is true, it could be partly due to the possibility that a relatively large number Of other types of food are close substitutes and inexpensive. Another reason may be because whitefish is not a very impor- tant part of our diet. All the methods mentioned are dis- cussed in detail and a summary of all the elasticities computed in each method is given at the end of this chapter. The Whitefish Fishing Industry The Great Lakes whitefish fishing industry is highly fragmented. Fishermen consist, for the most part, of small independent fishing vessel Operators. Some operators Oper- ate only part time, but in the late 1960's most part-time Operators in Michigan were eliminated. Part-time Operators have not been eliminated in other states. Most of the Operators own their vessels and manage their own operations. Over the past 20 years, partially due to the declining 112 number of commercial fishermen, Michigan fish production has dr0pped. Most of the whitefish are sold by fishermen to whole- salers in nearby locations. However, some fishermen sell directly to hotels and restaurants, or to retail customers who buy at dockside. Lakeside wholesalers receive about 88.3 percent of the total Michigan whitefish catch.l In 1973 only 11.7 percent of all the sales of whitefish in Michigan were made to non-wholesalers, with 6.6 percent of that sold to fish retailers (all within.a few miles of the fishermen), 3.5 percent sold directly to consumers; and 1.6 percent sold to hotels and restaurants. Other institution- al sales (schools, hospitals) are negligible for Michigan whitefish. Only 20 to 25 percent of whitefish sales are prepared by consumers for their own consumption. The rest are pre- pared by hotels, restaurants, and other institutions. Methodology A. The period of the study: The author believes that the elasticity coefficients and demand-supply relationships derived from data for 1960 to 1973 can be more representa- tive than coefficients computed from other periods. The reason is that biological disruptions, such as sea lamprey predation in the 1950's, caused a drastic reduction in the fish stocks of the Great Lakes. Great Lakes are almost the 1Based upon the results of an unpublished study by Agricultural Economics Dept., MSU, 1976. 113 sole source of domestic whitefish for the U.S. Data for 1974, 1975 and 1976 are available but are not included in the analysis. The reason is that the price in 1974 is unusually high, and including it in the equations causes most of the signs to change. This problem may be related to the PCB problem and the "energy crisis." B. The data base: The demand and supply equations were estimated with annual data. Monthly data were used in only one case to plot ex-vessel prices against quantity, for comparison with annual data. A complete listing of all symbolic names, definitions and sources of all variables used in the study are presented in Table VI-l. The trends of landings in the U.S. waters of the Great Lakes and aver- age ex-vessel prices in the Great Lakes in actual dollars, and in dollars deflated by the consumer price index (CPI) are plotted in Figure VI-l for the period 1950-1976. Great Lakes landings varied during the 1950-1976 period from a low of .6 million in 1958 to a high of 5.4 million pounds in 1976. Annual deflated ex-vessel prices moved in an Opposite direction from a high of 72 cents per pound in 1959 to a low of 39.3 cents per pound in 1976. Annual prices were obviously responsive to the quantity of white- fish landed. The relationship between annual nominal whitefish ex-vessel prices and total quantity of whitefish landed is shown in Figure VI-2. These points actually represent temporary equilibria between supply and demand for the industry. The relationship between annual deflated 1114 Table VI-l. Data Used in the Supply a fish (1950-1973) nd Demand Analysis of U.S. White- Definition-Description Symbols Source Per capita quantity (U.S. population QWFP National Marine Fishery of whitefish landed: pounds/1000 Service, 1977 people/year Per capita quantity of lake trout QLTP " landed in the U.S.: pounds/1000 people/year ' Annual dockside price of whitefish PWFD " deflated by CPI (1967-100), cents/ pound Annual price of lake trout deflated PLTD " by CPI (1967:100) cents/pound U.S. income per capita (U.S. popula— IPD Agricultural Statistics tion), deflated by CPI (1967:100) 1949-1976 dollars/person Consumer price index, l967=100 CPI " Annual price of choice beef, deflated PCBD " by CPI (1967:100), cents/pound Index of transportation cost, deflated TRlD American Trucking by CPI, cents/intercity vehicle mile Trends, 1975 Index of transportation cost, deflated TRZD " by CPI, dollars/intercity ton Wage paid to manufacturing workers, WD Agricultural Statistics deflated by CPI, dollars/hour 1949-1976 Index of sea lamprey abundance Sealam Walter, G., and W. J. Hogman (1971) Lagged variable (T-S) for sea lamprey Sealam T—S " Per capita quantity (U.S. population QWIP National Marine Fishery of whitefish imported, pounds/1000 Service people/year Annual price of walleye, deflated by PWD " CPI, cents/pounds Annual price of pork, deflated by CPI, PPD Agricultural Statistics cents/pound 1949-1976 Total quantity of lake trout landed in QLTLM National Marine Fishery Lake Michigan, pounds/year Services, 1977 115 Nominal and deflated price in cents per pound Ham» ov 6 cm . t\\lI%//\\\ o0 . 05 cm x» cm ooa OHH oma oma ova 00H cod smemwanz .m.s you moHum Hmmmm>uxm wmumHmma can 55 05 05 05 m5 N5 H5 05 00 00 50 00 00 00 m0 N0 H0 00 00 00 mm. 00 mmlflmfmm N0 H0 00 .Hmcwsoz .noumu Hmscc< .0.” L on " m., as 00 . 00 .05 -5 L cm 1 cm gooa 0 Odd lama L OMH Yield in pounds x 10 00H 00H 400a . HIH> EDUHW 116 IOH x menace :H A.m.ov anmmanz mo muHunmsO Hmuoa mm me ow mm .. omm mm on mH OH m o k 1 on 00 . 00 S . . Nfi an m0 .9 . NV .na . m...» . ow. . W0 .70 0.0 00 05 Price in cents per pound .¢5 + nmwmmuflsz mo huwucmso Hmuoe 0cm mOfiHm Hmmmm>nxm Hmfiwsoz HMDGG< .NIH> mmauHm 117 ex-vessel price of whitefish and per capita quantity of whitefish is plotted in Figure VI-3. The nominal ex-vessel price of whitefish is plotted against per capita quantity of whitefish in Figure VI-4. In Figure VI-5 the 1973 monthly nominal price of whitefish is plotted against the total quantity of whitefish. By looking at the price- quantity relationships in Figure VI-3 it seems that the demand curve has been fairly steady, shifting in 1964, 1969 and 1973-74, whereas the supply curve has been increasing fairly steadily, except in 1967—68 and 1974, and jumping in 1971. The points, therefore, trace out something like a set of demand curves. Throughout the study two statistical computer pro— grams, STAT, and SPSS, were used. These computer programs are designed for the Michigan State University CDC 6500 computer. For each statistical procedure used, many different combinations of the variables in Table VI-l were tried. In this chapter only the "best" estimates of each procedure are described. However, the "unsatisfactory" model struc- tures (specifications) will receive comments later in the chapter. C. Criteria for selecting the results: Criteria for selecting the "best" estimation results, in their approximate order of importance, were as follows: (1) The use of a variable should be based on a priori reasoning about the role it plays, 118 OH x mccdom mufiusmso m mm om mm om ma OH 0 3 m m on r e P on m n e c . ov n J« . .1 Nw . e H .w . . o0 .c s... ...: . n M! o p . «G S . .fig . 00 a . 3.... a t 3 3 .s h 2. 4.... D om .m.D mo wamomm OOOH “mm nmflmwuwnz mo huflusmsa 0cm muwum omumdmma .MIH> mmstm 119 OH x mwcsom cw augusmso m cm 0N om 0H 0H 0 o OH om d O on o. r e D. 3 s t n e . . . om c . F . . . n "w 3 3 3 3 3 i . ...... m... m. om w 3 s s... .n P 2 1 a n . .m . m... 8 0* M cm L. nmfimmuwnz .m.D mo manomm OOOH umm wufiucwso can mmowum Hmmmm>txm Hmaafioz .vIH> HMDUHh 120 A OH x .nHV muHucmso n X. A, m om 05 00 om ow om om OH O d n u 0 P r e oe. P s t n e c om .m s e c . .n o ‘1 o "ah o P 000 . . . . . . ea o0 ...s .z .... ...w ... .... . h m. 30 n 0 cm a: o N O5 ch0 mOmH you :mHmmquz mo suHucmso Hagoe can mmoHHm Hmmmm>uxm Hmaesoz mHnuaoz .0IH> HMDUHm 121 (2) Coefficients estimated for independent (exogenous or lagged dependent) variables should have the expected signs (according to economic theory and a priori reasoning). (3) R2 value should be as high as possible. (4) Coefficients should be significant at or below the 10% level of significance (¢). This criteria was waived if the overall equation was significant and other criteria were satisfied. (5) The standard error of the estimate should be minimized (between 1/2 and 1/3 of the absolute magnitude of the corresponding coefficient would be satisfactory). (6) The residuals should show no consistent pattern over or under estimation over the time period analyzed based on the Durbin-Watson test. Results The results Of the supply and demand estimations are reported in five parts: (a) single equation OLS for demand; (b) single equation OLS with lags for supply; (c) simultan- eous equations including (1) reduced form demand and supply equations (2) two and three stage least squares in a sys- tem of two equations estimating the supply and demand Of whitefish, and (3) two and three stage least square in a system of four equations estimating the supply and demand of whitefish and lake trout. Throughout this section the following notational rules will be followed in reporting specific regression results: a single asterisk (*) indicates statistical 122 signfiicance (t test) at a=10%; two asterisks (**) indicate 5% and three (***) indicate 1%. Unless otherwise noted, all signs on reported coefficients are as expected (based upon economic theory and a priori reasoning). A. Demand estimations using OLS No distributed lag demand equations were estimated. The quantity of whitefish per capita (QWFP) was the depen- dent variable. Various combinations Of the variables in Table VI-2 were examined. Equtaion VI-l was selected as superior in this group on the basis Of the criteria dis- cussed earlier. VI-l. QWFP = .82-.30 PWFD + .32 PCBD - .12 QWFIP + Ex-vessel (**) (**) demand .002 IPD R2 = .92 Standard deviation = 1.88 pounds/1000 persons/year Time period of analysis: 1960-1973 (n=l4) Durbin-Watson = 2.28 (showing no auto correlation) Price elasticity of demand = —l.51 Income elasticity of demand = .49 Cross price elasticity of demand with beef = 2.52 All the signs of the coefficients in equation VI-l are as expected. Coefficients for price of whitefish and price of beef (substitute) are significant at 5% level of significance, but coefficients of imports and income per capita were not significant at 10%. However, the overall equation is significant at 1%. Equation VI-l is a 123 Table VI-2. Variables Used in Estimating Demand Vis OLS . . . Expected Type of Definitions Symbols Signs Variables Per capita quantity of whitefish QWFP dependent Annual price of whitefish deflated by CPI (1967:100) PWFD - Income per capita (U.S. pOp.), deflated IPD + predetermined Per capita quantity of whitefish imported QWFIP - Annual price of choice beef, deflated PCBD + Annual price of lake trout, deflated PLTD + Time T + Final equation: QWFP = .82-.30 PWFD + .32 PCBD - .12 QWFIP + .002 IPD a satisfactory estimate of ex—vessel demand for whitefish. This equation yields a fairly high price elasticity (-l.51). This means that the demand is fairly sensitive to price at the dockside. Income elasticity, on the other hand, is small (.49), meaning that as income increases by one percent only .49 percent of the increase will be spent on whitefish. Finally, a high cross price elasticity (2.62) means that at price of choice beef (substitute) increases by one percent, the ex-vessel demand for whitefish increases by 2.62 per- cent. This shows that whitefish is a good substitute for choice beef. 124 B. Estimating supply with distributed lag, using OLS The quantity of whitefish per capita (QWFP) supplied was estimated as a function of different combinations of variables (Table VI-3). Table VI-3. Variables Used in Estimating Supply Via OLS Distributed Lag Definitions and Symbols Symbols Exgigfied Variables Quantity of whitefish per capita QWFP dependent Lagged price of white- fish PWFD(T-l) + Lagged price Of lake trout PLTD(T-l) - Lagged sea lamprey index of abundance Sealam(T-l) - Sealam(T-Z) - Sealam(T-3) - Sealam(T-4) - Sealam(T-S) - independent Deflated transportation TRD - cost cents/intercity TRD(T-l) - mile Deflated wage of manu- facturing ‘WD — Workers per hour WD(T-l) - Quantity of whitefish imported per capita QRFIP - Quantity of lake trout- Lake Michigan QLTLM - Catch per unit of effort CPE + Final equation: QWFP = 43.83 - 26.00 PWFD(T-l) - .31 PLTD(T-l) - .013 Sealam(T-S) 125 Equation VI-Z was selected as an example; VI-Z. QWFP = 43.83-26.00 PWFD (t-l) - .31 PLTD (t-l) Ex-vessel (***) (**) (***) supply - .013 Sealam (t-S) R2 = .91 Standard error of the residuals = 1.947 pounds/1000 people/year Time period Of analysis: 1960-1973 (n=l4) This equation represents a negatively sloped supply curve which was not expected. A similar result was also obtained when deflated ex-vessel price of whitefish (PWFD) was used as a dependent variable. (The main reasons that the method does not work are not clear at this stage. How- ever, some possible reasons can be the error involved in measuring the price data, the sea lamprey predation, the PCB or DDT affecting the demand for the product, and differ- ent state regulations imposed on the fishery. Another factor is probably the fact that the supply and demand equations are likely to be interdependent. The interdepen- dence of the supply and demand usually requires a simultan- eous estimation of the system. C. Simultaneous equations (1) Reduced form: There are two forms of simultaneous equations; 1) Primary form - original structural equations 2) Reduced form, achieved by solving the model so 126 that each current endogenous variable is a func- tion of predetermined variables only. Assume, for example, the following "just identified"2 system of supply and demand of whitefish, VI-3. QWFP = a PWFD + 812 IPD + ut 1+311 VI-4. PWFD = a2.+ 821 QWFP + 822 PLTD + ut There are four variables; P or Q are endogenous and IPD and PLTD are predetermined. Unlike the conventional supply and demand models, in this study the author believes that the ex-vessel price of whitefish is determined by the quantity of whitefish landed (supplied), rather than the quantity supplied being a function of ex-vessel price of whitefish. This is due to the fact that government regulations, weather conditions, and water temperature prevent the supply from reacting to the market price. Fishermen seem to operate at various levels primarily as a function of the availability of fish, rather than price. The assumptions of conventional demand and supply theory are that quantity supplied is a function of the price of the commodity, and that either the quantity demanded is a function Of the price of the commodity, or price is a function of the quantity demanded. Equations VI—3 and VI-4 are the structural form equa- tions of the system. By substituting for price and The equation is "just identified" if H+F-1=k where, number of endogenous variables in the equations, number of predetermined variables in the equation, number Of predetermined variables in the system. wru=::o "II" and 127 quantity, two reduced form equations are Obtained: equa- tions VI-S, VI-6. VI-5. QWFP VI-6. PWFD Once equati method, the origi lowing formulae: H11 + 012 IPD + H13 PLTD + wi = H21 + H22 IPD + H23 PLTD + Wi ons VI-5 and VI-6 are estimated by the OLS nal coefficients can be found by the fol- B = II12 11 n22 B =:I_Z_3_ 21 n12 812 = II13 (1'811 521) 811 = II22 (1’811 321) _ II11 ' 811 II22 “1 ‘ 1 - a 8 11 21 II22 ’ B21 1111 “2 = 1 - B B 11 21 The results independently, us VI-7. QWFP VI-8. PWFD R2 = .30 Time period These estim equations: VI-9. QWFP VI-lO. PWFD of estimating equations VI-S and VI-6 ing OLS are: = 6.03 + .79 IPD - .27 PLTD = 73.96 -.13IPD + .24 PLTD of analysis = 1960-1973 (n=l4) ates result in the following primary form -lO3.39 - 6.07 PWFD + 1.2 IPD -18.17 - .9 QWFP + .57 PLTD 128 In the reduced form estimates, in order to obtain negatively sloped demand and positively sloped supply equations in the original form, H12 and H22 must have Oppositesigns and 023 and n13 must have alike signs. Therefore, these two estimates do not meet the above expec- tations, because n and H13 have Oppositesigns, giving a 23 negatively sloped supply curve, equations VI-lO. In the results presented here, the predetermined var- iables are deflated price of lake trout and deflated per capita income. Other combinations were also tried including wage and income, transportation and income, sea lamprey index of abundance and income, etc. None of the combinations gave satisfactory signs. (2) Two and three stage least squares (TSLS, BSLS). (a system of two equations for whitefish) Adding more variables to equations VI-3 and VI-4 causes an overidentification3 problem, which can be largely overcome by using two stage least squares (TSLS), although this is not the only possible technique. Two of the results of estimating the two equations simultaneously are as follows: VI-ll QWFP = 27.394.5 PWFD + .25 PCBD - .11 QWFIP - demand .0018 IPD PWFD = 80.00 - 1.2 QWFP + .002 SealamT-S - .5 SUPply TRD + .36 Time 3The equation is overidentified, when k>H+F-1, See Footnote,l. 129 VI-12. QWFP = 21.6 - .6 PWFD + .2 PCBD + .0021 IPD demand PWFD = 98.5 - .7 QWFP + .01 Sealam T-S - supply .5 Time R2 = not meaningful in TSLS. Period of analysis: 1960-1973 (n=l4) All the estimates gave negatively sloped supply curves which were not expected. The demand equations, on the other hand were satisfactory. In the system VI-12, all the signs in the demand equation were as expected, but in the system VI-ll the demand equation has a wrong sign for the per capita income variable. (3) Two and three stage least squares (TSLS, BSLS) (A system of four equations) It is believed that lake trout and whitefish are closely related because they are usually caught, sold (at dockside) and processed (by wholesalers) together, and Offered as substitutes in the final markets. Therefore, two equations estimating supply and demand Of lake trout, were added to the system. The estimates for this four equation system are as follows: VI-13. QWFP = -4.92 - .99 PWFD + .37 PLTD + .0045 Demand IPD + .41 PCBD VI-14. PWFD = 14.29 + 1.28 QWFP + .99 PLTD + .04 Supply T-S Sealam - .52 Time VI-15. QLTP = 5.4 - .21 PLTD + 0.28 PWFD - .0004 Demand IPD + .064 PCBD 130 VI-16. PLTD = 107.6 - 25.8 QLPT + .42 PWFD + .11 SUPPIY T-S . Sealam - .67 Time R2 = not meaningful for TSLS and BSLS. Period of analysis = 1960-1973 (n=l4) In estimating these equations, a number of different combinations of the variables in Tables VI-4 and VI-4a were examined. Most of the results for whitefish were satisfac- tory (based on the criteria explained before). Almost all the variables estimated in the system, equations VI-l3, VI-14, VI-15, VI-l6, were not significant at the 10% level. All the signs for the supply and demand equations for whitefish are as expected. Lake trout produc- tion is apparently a substitute for whitefish production, because as the price of lake trout increases fishermen apparently switch to lake trout production and whitefish production declines. Therefore, the positive sign for PLTD in supply equation VI-l4 is as expected. It is important to note, however, that since the discovery of DDT in 1967 and later ban on lake trout production and tighter regula- tions, this substitution has not been so possible. In this analysis, the coefficients estimated by two stage least squares were exactly the same as those estimated by three stage least squares. In two and three stage least squares, the R2 is biased and cannot be used to evaluate the results. Many computerized statistical programs deisnged for econometric analysis do not even calculate the value of R2. The most reasonable way to evaluate the 131 Table VI-4. Variables Involved in the Simultaneous System (Whitefish Demand Equation) Definition Symbols Exgigfied Variables Deflated price Of white- fish in cents per pound PWFD - Endogenous Quantity of whitefish (U.S.) in pounds per 1000 Dependent people QWFP .variable Deflated price of lake trout in cents per pound PLTD + Endogenous U.S. income per capita, deflated (1967 = 100) IPD + Predetermined Deflated price of choice beef, cents per pound PCBD + Predetermined results, however, is to compare the actual and the pre- dicted values of the variables. Equations VI-13 and VI-l4, which are chosen as the best estimates of supply and demand for whitefish, are plotted along with the actual data used in this study. Figure VI-6 shows the actual and predicted equilibrium points. Figures VI-7 and VI-8 show the trends of actual and predicted equilibrium quantity and equili- brium prices. To find the predicted equilibrium points, first the actual values of the independent variables for each year were substituted into the equations, providing two equations and two unknowns, and then the two equations were solved simultaneously. Table VI-5 shows the actual values of price and quantity of whitefish, value of the 132 Table VI-4a. Variables Involved in the Simultaneous System (Whitefish Supply Equations) Definitions Symbols Exgected Variables igns Deflated price of white- Dependent fish,cents per pound PWFD Variable Per capita quantity of whitefish, pound per 1000 people QWFP + Endogenous Deflated price of lake trout,cents per pound PLTD + Endogenous Total catch of lake trout from Lake Michigan in pounds QLTLM - Predetermined Sea lamprey abundance index (t-l)r (t-2)I (t-3)I (t'4)r (t-S) Sealam + Predetermined Transportation cost in cents per intercity vehi- cle mile TRD + Predetermined Wage Of the manufacturing workers in cents per hour WD + Predetermined Time T - Predetermined Dummy, to show the change in technology in the 1950's Dummy l - Predetermined predetermined variables, and the predicted prices and quan- tities of whitefish. The two equations predict price and quantity fairly well except for 1966, 1974 and 1975. In 1966 the lagged sea lamprey index of abundance increased from 52 to 102, and dr0pped to 63 in 1967. This unusual change caused the poor predictions in this year. For 1974 and 1975, the predicted 133 Hoooa x monsomv muwuamsv muflmmo Hmm NN Hm 0N 0H 0H 5H 0H 0H 0H 0H NH HA 0H 0 m 5 0 0 v m N .H \ \\\ A." [III Ow ¢H|H> .mH|H> mcowuwsvm .mwmaHmcm O a 0 map Eouu muflmmo H00 0 wmumammo 0 II II mOuHOOH .amHmmanz How mucHom asHunHHHsvm umuoHcmum can Hmsuoa 00 « ll . \ ‘Q I I! A. I wl|l 4 “WV 0‘.qu §3 a» 3 omuowvoum III IIIIIII 1 Hmsuoa 00 00 00 pound Deflated price in cents per .0IH> mmDUHh 134 .(L Hum» 05 05 m5 N5 H5 05 00 00 50 00 00 00 m0 N0 OHuH> .mHuH> mcoHumsOm mnHmo .mOumOOH .amHmmuHsz imuHmmo nmmo muHucmsO ssHunHHHsvm mo mucmua OmuoHcmum cam Hmsuoa .5IH> 3) Per capita quantity of whitefish (pounds x 10 HMDUHh 135 00 00 00 00 N0 H0 15 \N w. . 0 Ar «HIH> .MH1H> mcowumsvm .meumOOH .amHmmanz How HuoumHmmaO mmoHum esHunHHsOm OmuoHemum can H05000 00 00 00 Price in cents .0IH> HMDUHM 136 OO.HOH 0.0H~ me mm.mH O0.0m O. mo.mm O0.0mHm «0.0m mm.mv mv.H~ OH.OOH O.mO~ we N0.0H me.mv O. Hm.mm vo.mmHm O0.0m om.HO O0.0N OH.mmH m.OO~ mp OH.O~ mm.Ov O. OH.~OH O0.0mmm OO.~¢ mO.mv mm.H~ Om.m~H m.mOm up mm.OH mn.ve O. OO.OO «o.emom Om.~v Om.me h0.H~ Om.HmH O.mOm HO OO.vH O0.00 O.m Oh.mm OO.HOO~ O0.0v ov.Ov mv.mH Om.OHH 0.00~ OO OH.mH O0.00 0.0~ NH.mO vm.~om~ O0.00 H0.00 ¢~.HH O0.00H «.mmH OO mH.~H mO.mm o.em m0.0m vo.ommm mO.mm Om.mm ~>.HH O~.OOH m.OmH OO N0.0 mH.vm O.mm OO.mm m.O~m~ mm.Om vm.mm O0.0 O0.00H 0.00H Om O0.0 mm.mm O.mO OO.mO O0.000~ OO.~O OO.mm m~.m O~.Om O.mOH OO mm.m O¢.~O O.HOH mm.Om HO.OOO~ mm.mm OO.Hm m0.0H Om.vm m.OOH mm mm.m OO.HO O.mm OO.vm mm.OOOm O0.00 Hm.~m Hm.m OO.~O H.OOH Om HH.O Om.mO 0.00 Hm.Hm mv.em0~ «O.HO Om.vm Om.O OO.HO «.mOH no O0.0 mm.HO 0.0m OO.mm «O.Hmmm H0.00 H0.0m vO.v O0.00 m.~mH NO Hm.m HO.HO O.mOH Hm.OO ON.OO- mm.OO O0.0m mv.m O0.00 0.05H HO O.» v.0O O.mmH mO.OO Om.va~_ mO.mO mH.mm mm.O On.mm 0.0NH Om 0.0 Om.mm 0.00H OH.OO OO.mmHm O~.vO ~m.mo «v.0 mzo muHmmo,umm mam noumHmmo smocH. .mwo.m000 . .moo; . .. Ops. mquno ~00 H00 .000 msHe swumEMH moHum muHmmo umm oeqm mo moHum mso O O m sanaHHHsvm OOHOHemum mmm . msoocH . ¢H|H> 0cm mHIH> mOOHumsvm 0sHmD mama Umuowcmum 0am Hmsuom .0|H> GHQMB 137 price is not very satisfactory, although the predicted quantities are fairly close. These two years should not affect the results of this study because the 1973 prices and quantities have been used in all the computations. The following elasticities were computed based on equations VI-13, the demand equations, using mean values: price elasticity of demand = -S.00, income elasticity of demand = 1.15, cross price elasticity (with beef) = 3.36. In comparing these results with those obtained by using equation VI-l, we find that this price elasticity is much larger, demand in this case is even more sensitive to the price of whitefish than that of equation VI-l. Income elasticity which was less than one (inelastic) before, is greater than one (elastic) using equation VI-13. Cross price elasticity is also larger in VI-l3. A very similar system, but with the per capita quan- tity of lake trout (QLTP) instead of the deflated price of lake trout (PLTD) in the supply equation for whitefish and QWFP (quantity of whitefish per capita) instead of PWFD (price of whitefish deflated) in the supply equation for lake trout gave very similar results. 8 Including the quantity of whitefish imported per capita (QWFIP) in either supply or demand equations of the system, VI-13 or VI-l4, gave a negatively sloped supply curve for whitefish. 138 Two periods were tried, 1960 to 1973, and 1960 to 1975. The results using 1960 to 1975 were entirely different from 1960 to 1973. The following are the results using the per- iod 1960-1975: VI-17. QWFP = 54.98 - .55 PWFD - .33 PLTD + .14 PCBD Demand - .0025 IPD VI-18. PWFD = 165.75 - .89 QWFP - .51 PLTD + .01 Supply T-S , Sealam - 1.1 Time VI—19. QLTD Demand 19.67 - .054 PLTD + .3 PWFD - .0095 PCBD + .0031 IPD VI-20. PLTD Supply 265.32 - 25.5 QLTP + 2.67 PWFD + .16 Sealam + 2.96 Time Most of the signs were "incorrect" (using 1960-1975) and the whitefish and lake trout supply equations had negative slopes. This might be due to the unusually high magnitude Of the 1974 price of whitefish (see Figure VI-6). Elasticities4 In order to directly estimate the elasticities over the period of study, it is very common to estimate a system of Log-Log equations. Log-Log procedure refers to a case where all the dependent and predetermined variables are converted into logarithm dependent and predetermined varia- bles are converted into logarithm forms, then the system is estimated. The results are as follows: 4Elasticities are measures of responsiveness and com- pare the percentage change in one variable to a percentage change in another. 139 VI-21. Log QWFP = -7.7 - 3.94 Log PWFD + 1.97 Demand Log PLTD + 2.2 Log IPD + 2.3 Log PCBD VI-22. Log PWFD 37.13 + 3.76 Log QWFP - .66 Supply T-S Log PLTD + .49 Log Sealam - 21.2 Log Time VI-23. Log QLTP = 12.7 - 8.5 Log PLTD + 8.8 Log PWFD Demand - 1.8 Log IPD - 3.5 Log PCBD VI-24. Log PLTD = 2.08 - .18 Log QLTP + .58 Log PWFD Supply T-5 + .029 Log Sealam - .75 Log Time R2 = not meaningful Period of analysis = 1960-1973 (n=l4) The coefficients in these demand equations are elas- ticities and those in the supply equations are flexibili- ties. Under certain conditions, where there are no predetermined variables, so elasticities may not be the same as the inverses of the flexibilities. None of the coefficients of this system were significant, based on the t test. In Table VI-6 the price, income, and cross-price elasticities of demand and the price elasticity (inverse of flexibility) and price flexibility of supply for the most satisfactory supply and demand models are summarized. All elasticities are calculated at the mean values, as well as at the 1973 values, except the constant elasticies. Very little of significance can be drawn from the elasticities and flexibilities calculated in Table VI-6. Almost all of these estimates are statistically insignifi- cant (not different from zero) at the 10% level of 140 05.m 5m. H0. v0.a 0m. 00.m In II II II II In I: II II NHIH> II In I: II It In m.m m.m Om.m 00.H 00. 00.n1 0m.m 0H.H 00.01 HHIH> mecoz cowueawm msowcmuHOEHm >uouomwmwumm no: NIH> II II II II 1| 1| In I: In m0.H on. m0. I m0.~ mv. H0.HI H1H> H0002 mcoHunowm OH0COm . a 8 u m u m u m m a m m m i... m m I a m m a p a p a p p d a e I p d p d a e I p d p d a p I p d x s x s x s s 1 I. s u s 1 s 1 I. s u s 1 s 1 3 s u s 1 I. 3 I. 3 I. 3 3 I 3 O 1 I. 3 I. 3 m 1 I 3 I. 3 O 3 I a. I. a. I. a. I. I. o D I. o I. O I. O 3 I. I. O I. O D I. o I. O I. O I. O I. O O a 1 O m O a O a 1 O m O a O a 1 O m O a I .. .. .. ... ..... ..... m ...... ..... ..... H... ..... ..... ..... O u. .... n. .M H. .M n K .A s .A .A A s .A .A K s .A A A A A cowumsvm mmOHO> m50~ mmsam> c002 sawuocsm moaumoq mmOHm> M50H mmOHO> cam: 53 vmusam>m um cwumsam>m um pwumsam>m :mHmmemm3 00 500000 mmHmMBHmz mom 020200 :mflmmuwnz .m.D mom mmfluwowummam >Hmmsm 0:0 OsmeQ .0IH> mande 141 significance, except the price elasticity in equation VI-l. The elasticity values differ widely between single equation models and simultaneous models. In general, single equa-' tions tend to have smaller elasticities than the simultan- eous models. It is also important to note that elasticities have declined over the years (Table VI-7. The reason for the decline of price elasticity may be due to the fact that over the years supply and demand for whitefish have increased with supply increasing faster. This has shifted the equilibrium point to the less elastic part of the demand curve (Figure VI-3). The 1973 cross price, price, and income elasticities (Table VI-7) are much smaller than those computed by Log-Log equations. Few satisfactory results were Obtained for the supply for whitefish. Supply price flexibility was 3.76. Flexi- bility in this case means that there is a 3.76 percent price response to a one percent quantity change. If we assume the supply price elasticity is equal to the recipro- cal of the corresponding price flexibility, then supply price elasticity is equal to .27, fairly inelastic. This low elasticity means that commercial supply are not very responsive to market price changes. This apparently veri- fies our supposition that commercial fishermen Operate pri- marily as a function of the availability of fish, rather than the prices. Demand price elasticity on the other hand is relatively high, averaging around -4. In other words, the quantity demanded declines by four percent as price 142 Table VI-7. Elasticiteis Over the Period of Study, Equation VI-13 Y PCBD P PWFD IPD gross Price Income ear Q Ela::::ity Elasticity Elasticity Mean value 87.25 10.64 54.27 2667 3.36 -5.05 1.13 1960 .90 4.42 .66 2184 8.6 -l4.l 2.22 1961 .87 6.85 .59 2214 5.5 — 8.3 1.45 1962 .91 5.49 .60 2279 6.4 -10.4 1.87 1963 .85 4.74 .52 2332 7.3 -12.2 2.21 1964 .82 7.37 .65 2457 4.3 - 8.2 1.50 1965 .85 8.51 .53 2578 4.5 - 6.3 1.36 1966 .84 10.05 .51 2679 3.4 - 5.8 1.20 1967 .83 8.22 .58 2749 4.7 - 7.5 1.50 1968 .83 8.68 .58 2826 4.3 - 6.3 1.47 1969 .87 11.72 .56 2851 3.6 - 5.2 1.09 1970 .85 11.74 .49 2903 3.4 - 4.2 1.11 1971 .86 18.42 .40 2972 2.3 - 2.2 0.73 1972 .91 21.47 .42 3067 2.3 - 2.1 0.64 1973 1.02 21.33 .45 3227 2.1 - 2.1 0.68 increases by one percent. Therefore, price and total reve- nue vary in a reverse order as the quantity supplied varies. This indicates that if commercial fishermen try to raise the price of whitefish by reducing supply, it could reduce their total revenue. Some of the model specifications which were tried have been discussed throughout this chapter. The following list briefly describes those variables, specifications, and per- iods which were tried but not deemed satisfactory: (1) Nominal prices with and without consumer price index (CPI) as an independent variable, did not give satis- factory results. 143 (2) Per capita quantities gave better results than total quantities, with and without population as a separate explanatory variable. (3) Two periods Of time were tried, 1960 to 1973, and 1960 to 1975. The second period did not give satisfactory results. The period 1950 to 1973 was also tried without any successful results. (4) The quantity of lake trout caught in Lake Michigan was used as an index of abundance of sea lamprey and of different regulations, but did not give satisfactory results. (5) The quantity of whitefish imported per capita (QWFIP) was used in both supply and demand equatiqfs at different times, but did not give satisfactory results. (6) Dummy variables were used in both supply and demand equations in order to simulate the effects of new technology and other changes. None were effective. (7) Deflated prices of pork and walleye were used as predetermined variables in the demand equations (as substi- tutes), but did not produce satisfactory results. (8) Deflated hourly wages of manufacturing workers and deflated transportation costs (Table VI-l) were not significant and were unsatisfactory. (9) Catch per unit of effort for whitefish in dis- trict one of Lake Michigan (MM-l) was used as a predeter- mined variable to show the technological change in the Great Lakes, but was not significant and was unsatisfactory. CHAPTER VII Management and Policy Exploration of Alternative Conditions For the purpose of this chapter, the author has chosen a few current issues of the commercial fishery. This chapter: (1) examines the impact on the whitefish fishery of proposed new regulations (lowering PCB standards from SPPM to 2PPM) which may eliminate commercial lake trout production; (2) examines the producer surplus, yield and effort under monopoly and net all-or-none conditions; (3) computes the net all-or-none value (social surplus) for the commercial fishery under the most optimis- tic conditions, based upon historical harvest levels for various species; (4) examines the fishery with and without the gear restrictions in force in 1973. l. The Impact on the_§gpply and Demand for Whitefish of EliminatingLake Trout Fishing The U.S. Food and Drug Administration (FDA) has recently tightened its regulations by proposing a 2PPM (parts per million) allowable PCB (Polychlorinated 144 145 biphenyle) in lake trout instead of 5 PPM currently in effect. Most of the lake trout caught in the U.S. Great Lakes contain more than 2PPM PCB, so the new regulation may eliminate the market for Michigan lake trout. This section estimates the impact of this action on whitefish demand and supply. A. The procedure followed was: to delete the lake trout price from the supply equation for whitefish, equation VI-l4 because the price of lake trout would no longer be rele- vant (as a substitute) in the production Of whitefish, to set the quantity of lake trout in equation VI-lS, to zero, because we have assumed that lake trout is no longer being harvested (new supply curve is the vertical axis), to substitute the 1973 values1 for independent variables in equations VI-13, VI-l4, and VI-lS, (equation VI-16, the supply of lake trout, is no longer relevant). Then solve the system of three equations for three unknowns. The following equations are the demand for whitefish VII-l, supply Of whitefish VII-2, and demand for lake trout VII-3, resulting from applying the above three steps to equations VI-13, VI-14, and VI-15. 11h this chapter prices are deflated by the consumer price index (CPI), where 1967 = 100, unless otherwise noted. 146 VII-1. QWFP -4.92 - .99 PWFD + .37 PLTD + .0045 IPD + .41 PCBD ”14.29 + 1.28 QWFP + .04 Sealant-5 - VII-2. PWFD .52 Time VII-3. 0 5.4 - .21 PLTD + .28 PWFD - .0004 IPD - .064 PCBD Substituting the 1973 values for the independent variables, the following system of three equations and three unknowns is obtained: VII-4. QWFP 51.42 - .99 PWFD + .37 PLTD VII-5. PWFD = -23.67 + 1.28 QWFP VII-6. PLTD = ~11.52 + 1.33 PWFD Solving this system of equations simultaneously, the equilibrium prices and quantity were 35.97 pounds of white- fish per 1000 people, 22.38 cents per pound of whitefish, and 18.25 cents per pound of lake trout. These predicted equilibrium prices are not satisfactory, because after stopping the lake trout production, the price of lake trout is expected to be much larger than its 1973 price, 49 cents per pound. For instance, in 1964, when a very small quantity of lake trout was supplied, the price of lake trout increased to 71 cents per pound. It is, therefore reasona- ble to assume that price could very well reach at least 100 cents per pound, if the U.S. production of lake trout were reduced to zero. The following computations are based on the above assumption. Substituting 100 for PLTD in equation VII-4 and eliminating equation VII-6 reduces the 147 system to two equations and two unknowns. These equations predict 49.27 pounds of whitefish at a price of 39.4 cents per pound at the new equilibrium. Figure VII-l. Assuming that lake trout were still in the market, the equilibrium values are Obtained by substituting the 1973 values for all the independent variables in equations VI-l3 and VI-l4, giving VII-7 and VII-8 respectively. VII-7. QWFP 67.07 - .99 PWFD VII-8. PWFD = 21.47 + 1.28 QWFD Solving equations VII-7 and VII-8 simultaneously, we have estimates Of 20.18 pounds and 47.35 cents per pound of whitefish at equilibrium. Comparing the two results, we see that whitefish production increases from 20.18 pounds (with lake trout) to 49.27 pounds (without lake trout), and the price of whitefish decreases from 47.35 (with lake trout) to 39.4 cents per pound (without lake trout). In Figure VII-1, point a is the equilibrium point with lake trout and point b is the equilibrium point without lake trout. Apparently, if lake trout production is stopped, fishermen would concentrate their efforts on whitefish or other species which require similar types of gear. This switch would increase the whitefish production by a large amount if production were not otherwise limited. Eliminate ing the domestic supply of lake trout from the market place would cause the price of lake trout to increase (as we have assumed), so consumers would switch to other species such as whitefish, increasing the demand for those species. 148 muHamo 000 AOOOH x .OHO mancmsO OO On OO Om OO Om .Om OH All J u q q q ul N d o ., . .8 . _ ... .‘ . . 0 . d . OH m. G Oom r . . m... .0. OO m n a . 0v % .m . on e .m . O0 r nu P . o. d O OO m a 8 .1. 0 n w _ m. . OO .anmmpan 000 umm>umn OOHHEHH 0:0 0:00» 0x0H usospHs EOHHOHHHOOO Ho 300000023 00 umw>umn cmuHEchO :uw3 .uOOHu mxma psonuw3 Edwnnflaflswm An noon» 0HOH OOH; EOHHOHHHOOO Hm . .mIHH> .OIHH> 0:0 OHIH> .mHuH> mcoHumOOm :0 cmmmm .coHuosooum Ozone 0x0H OcHumc tweflam H0900 0cm maommm nmwmmuflsz How coaumowm mammsm 0:0 ocmamo omumEHumm .HIHH> WMDGHW 149 These changes could establish a new equilibrium with a larg- er quantity and a slightly lower price of whitefish (point a, Figure VII-l). However, if whitefish production were limited to 20.18 pounds per 1000 peOple, the new equilibrium price of whitefish would be 68.24 cents per pound, point c in Figure VII-l. 2. The Whitefish Fishery Under Alternative Market and Production Conditions A. The Whitefish Fishery in 1973: In Chapter V we found that total revenue (in 1973 prices and 1967 dollars) for district MM-l was $585,000, and producers' surplus was $17,000. The ratio of producers' surplus to total revenue was three percent. These results will be projected to the entire fishery later in this chapter. B. Optimum Sustainable Yield and Producer Surplus Under Competition: Among the procedures to estimate the production func- tion in Chapter V, two methods are of most interest, a) the linearization technique with sea lamprey over the period 1967 to 1976 (Table V-8), and b) the graphical method, using the most recent data from 1970 to 1976 (Table V-l4). The results of the linearization technique, although believed to be too high, appear to be the most reasonable analytical (Objective) results found for MM-l. The graphical method, on the other hand, is more subjective, but reflects the personal judgement of the author. These results are also 150 believed to be very reasonable. Total revenue at the point of Optimum sustainable yield using the linearization technique for district MM-l is $790,000, (in 1973 prices and 1967 dollars) and Optimum producers' surplus $518,500, giving the ratio of Optimum producers' surplus to Optimum total revenue of 66 percent. The graphical method, on the other hand, predicts on opti- mum total revenue of $429,000 (in 1973 prices), optimum economic rent of $170,000, and a ratio of optimum producers' surplus to optimum total revenue of 40 percent. The opti- mum producers' surplus Obtained by using the linearization technique is 89 percent of the actual total revenue earned in 1973. The optimum producers' surplus predicted by the graphical technique was about 29 percent of the actual 1973 total revenue. It is important to note that these ratios and rents are only for district MM-l and only for whitefish. It is also important to note that district MM-l is apparent- ly one of the most productive districts in Lake Michigan. The MM-l district produces almost 25 percent of Michigan's total whitefish catch and has been heavily fished at dif- ferent times. In order to find the Optimum economic’rent and the ratios for the entire Great Lakes, similar models should be constructed for other species and other districts as well. However, if we assume that all the other districts and species are as productive as whitefish in MM-l, then the ratio of economic rent to total revenue computed in this 151 district will be the same for the entire Great Lakes. Later in the chapter we will use this assumption and these ratios to compute some Of the economic values of the commercial fishery. C. Net all-or-none evaluations of the fishery under compe- tition: The purpose of this section is to evaluate the net all-or-none value (social surplus) for the commercial -fishery for comparison with the equivalent value from sport fishery. The "social surplus" (net all-or-none) value is the amount of producers' surplus that a perfectly discrimi- nating monopolist can Obtain by selling the same commodity at different prices. Area f'b'P in Figure VII-2 is the social surplus which is the sum of consumer's surplus, area P,b'P, and producer's surplus, area P,b'f. These values can be estimated either geometrically or analytically. In this study, calculus is used to estimate these values by inte- grating the areas above the supply curve and under the demand curve, equations VII-7 and VII-8, over the relevant ranges: 67.74 VII—9. Consumers' Surplus = I (67.07 - .99P)dP 47.35 = 207.88 cents per 1000 people 47.35 VII-10. Producers' Surplus = I (-16.75 + .78P)dP 21.47 = 261.13 cents per 1000 people. VII-11. Social Surplus = 207.88 + 261.13 = 469.00 cents per 1000 peOple 152 muHOmo 000 HOOOH x .OHO suHucmso @ 00 05 00 00 00 00 0N +. 0H 0 S A! d d J u 4 d 4 t . V , . _ n e e: . c q¢ . L OH 6 . C . .1 . m. iOm . I .N m . h 4cm “m N¢.0m 0 0‘ r—LOCQ far?“ *— HvH1H> can MHIH> msoOumzvm so momma .M5mH cw mm>uso confimo 0cm hammsm cmuMEfiumm .NIHH> mmDUHh 153 These values are in cents per one thousand people, or thousandths of cents per capita. To find the total value in terms of 1967 dollars per capita, these values should be divided by 100 (to convert to dollars) and multiplied by 207,300 (the 1973 population divided by 1000). This is equivalent to multiplying by 2073, as in VII-12, VII-12. Social Surplus = 469.01 x 2073 = $973,000.00 Following the same procedure, the total value of con- sumers' surplus is $431,000, and total producers' surplus is $541,000. The actual deflated total revenue from white- fish in 1973 was $1,990,000. Given the above values, the ratio of Social Surplus to actual total revenue in 1973 is 49 percent and the ratios of producers' surplus and consu- mers' surplus to actual 1973 total revenue are 27 and 22 percent respectively. These ratios and values are for the entire U.S. whitefish fishery. Since 75 percent of the U.S. whitefish are caught in Michigan’s Great Lakes (MNRC, 1976), Michigan's share of the deflated social surplus from the whitefish fishery is: VII—13. $973,000 x .75 = $730,000 In 1973 the Michigan's Great Lakes whitefish fishery contributed slightly less than half of the value of Michi- gan's total Great Lakes commercial fishery (MNRC, 1976). Interpolating from the whitefish results, the total social surplus (consumers' and producers' surplus, or net all-or- none value) of Michigan's Great Lakes commercial fishery in 1973 was about $1.5 million (in 1967 dollars). Taking 154 into account the 75 percent inflation since 1967, but assum- ing the 1973 levels of production and relative prices, the 1976 net all—or-none value of the Michigan's Great Lakes commercial fishery, is more than $2.6 million. This repre- setns the maximum net willingness of the Michigan commercial fishermen (as representatives of consumers) to contribute (beyond their present costs) either to prevent the total loss Of the fishery, or, conversely to promote the gain of the existing fishery if one did not already exist. The equivalent net all-or-none value for this sport fishery is roughly $250 million (Talhelm, 1977). D. Commercial Fishery Under a Perfect Monopoly This section estimates the potential monopoly rent and the optimum level of production under monOpoly condi- tions. These conditions could conceivably arise from either a government "take over" and control of fishery production, or under a situation where commercial fishermen collude and control the output. The aggregate supply VI-14 and demand VI-13 equations are used in this analysis. According to economic theory, the aggregate demand function represents the industry's average revenue (AR) function and the aggre- gate supply function is equivalent to the industry's margi- nal cost (MC) function, Figure VII-2. 4 Assume that the industry has the following profit equation, VII-l4. n(Q) = TR (Q) - TC (Q) 155 where H is the profit, TR is total revenue, and TC is the total cost. These variables can be Obtained from the demand and supply equations, VII-7 and VII-8. Total reve- nue (TR) equals price multiplied by quantity demanded, equation VII-15. VII-15. TR(Q) = P. Q From equation VII-7, P = 67.74 - 1.01 Q, so VII-16. TR(Q) = 67.74 Q - 1.01 02 Total cost (TC), on the other hand, is Obtained from equation VII-7: the supply and marginal cost equation. Equation VII-7 can be written as P = 21.47 + 1.28 Q. By integrating this equation, total cost (TC) is Obtained, equation VII-17. VII-17. TC(Q) = 1': MC dQ = 21.47 Q + .64 Q2 Substituting equation VII-16 and VII—l7 into equation VII-l4, gives equation VII-18, VII-18. 0(0) = TR(Q) - TC(Q) = 46.27 Q - 1.64 02 To maximize profits, differentiate equation VII-18 with respect to Q and equate the result with zero: VII-l9. §%-= 46.27 - 3.3 Q = 0 Q = 14.02 pounds per thousand people Equation VII-19 is a necessary condition for the mono- poly firm to maximize profits. A sufficient condition for maximizing profits is that the second derivative of profits equation VII-18 with respect to output be negative. 156 2 VII-20. 2_1%91 = -3.3 < o 30 The monOpolist's Optimum selling price, P, is then found by substituting Q for Q in the demand equation VII-7. VII-21. F = AR(Q)= 53.58 cents Now we can calculate the Optimum profit of the monOpo- list, the shaded area in Figure VII-1: VII-22. II = TR - TC VII-23 TR = 14.02 x 53.58 = 751.19 cents per thousand people VII—24. TC = 21.47 x 14.02 = .64 x (14.02)2 = 426.8 cents per 1000 people Multiplying the values of TR by 2070 (U.S. population divided by 100,000) we have an estimate of total revenue for the U.S. of $1,555,000. Similarly for TC, we have $883,500. profit is $672,000, equation VII-25, VII-25. H = 1,555,000 - 883,500 = $672,000 The ratio of the U.S. monopoly rent from whitefish, $672,000, to the actual 1973 total revenue, $1,990,000, is 34 percent. This represents about 3/4 of the net all-or- none value. 3. Maximum Potential Values of Commercial Fishery This section estimates the maximum potential consum- er', producers', and social surplus as well as monopoly rent for the Great Lakes commercial fishery, under the most favorable conditions. To find these values the following procedure was followed; 1. 157 a list of all the major fish species historically caught in the Great Lakes along with their har- vest level were presented (Table VII-l). The harvest data for each species has been chosen in a subjective basis under very Optimistic condi- tions. These catches are slightly below the peak year harvest for different species over the per- iod 1930 to 1975. Prices in Table VII-l are found by dividing the 1973 nominal total value of each species by its total catch. the grand total revenue from Table VII-1 was cal- culated using 1973 nominal dockside prices. the grand total was multiplied by the different ratios presented in Table VII-2 (these ratios were computed in the previous sections.), to estimate the maximum potential surplus values for Michigan's Great Lakes. It is assumed that these ratios, either for MM-l or for the entire U.S., are the same for the Michigan Great Lakes. The maximum potential gross revenue (the grand total) producers' from the Great Lakes commercial fishery equals $21,000,000, as shown in Table VII-1, using 1973 nominal prices. The results of multiplying each surplus/revenue ratio by the grand total revenue computed in Table VII-1 are presented in Table VII-2. Social surplus is about $10 million, but it could be over $20 million, judging by the estimates of surplus. Table VII-l. 158 Analysis of the Michigan's Commercial Fishery 3:28.330? ...... P823821? 332.1121? Lake trout 16,502,000 (1973).. .49 3,186,000 Salmon 13,004,000 .49 { 6,372,000 Steelhead & other ' ' trout 500,000 .50 250,000 Lake round white- ‘ fish ‘5,081,000 (1948) .59 . 2,998,000 Suckers V3,712,ooo (1933) .03 ’ 111,000 Carp '2,543,000 (1953) .07 178,000 Walleye 71,482,000 (1948) .40 593,000 Perch 12,233,000 (1961) .38 849,000 Alewives l5,254,000 (1973) .01 53,000 Bowfin 1,000 (1960) —- -- Buffalofish 20,000 (1973) .30 6,000 Bullheads 54,000 (1971) .16 9,000 Burbot 117,000 (1972) .01 1,000 Catfish 336,000 (1973) .37 124,000 Crappie 48,000 (1971) .53 28,000 Quilback 10,000 (1962) .18 2,000 (Rockbass 10,000 (1960) .30 3,000 Sheephead 125,000 (1973) .07 9,000 Smelt 2,297,000 (1960) .02 46,000 Whitebass 171,000 (1961) .18 31,000 Menomenee 251,000 (1972) .26 A 65,000 Whitefish 3,362,000 .60 £6,372,000 Maximium potentiiy commercial fishe dockside value '(1973 dollars) (73) 21,283,000 Maximum potential commercial fishery dockside value (1976 dollars) (76) 28,004,000 159 Table VII-2. Maximum Potential Values of the Great Lakes Commercial Fishery Surplus/ Maximum Potential Type of Value Source Revenue Value in millions Ratio % of 1973 dollars Producers' Surplus Using Linear- 89 $19 ization technique (Chapter V) Producers' Surplus Using demand 27 $ 6 and supply equations (Chapter VII) Monopoly rent 34 $ 7 Social Surplus ’49 $10 The maximum potential producers' surplus ranges from 6 to 19 million dollars (Table VII-2). The reason for such a large difference is the fact that two different techniques have been used in computing the ratios: a) the ratio of producers' surplus under perfect com- petition, using the linearization technique, to the 1973 actual total revenue (89%), and b) the ratio of producers' surplus, using the U.S. supply and demand equations estimated in this study to the 1973 actual total revenue (27%). Table VII-2 also presents the social surplus, and monOpoly rent, where monopoly rent is about 3/4 Of the social surplus. 160 4. The Impact of Gear Limitations on Fishing Efficiengy Since the late 1960's the Department of Natural Resources (DNR) has limited the amount of gill nets used in Michigan. The purpose Of the restriction is to control the harvest of whitefish. The limitation is that each fisher- man cannot have more than a certain amount (ranging up to 24,000 linear feet) of 4 1/2 inch gill net in the water (fishing) at any particular time. Fishermen claim that they have the capacity to use up to 60,000 linear feet at a time with little increase in cost. They also claim that the marginal cost of this much additional net is much less than its marginal revenue. This means that the fishermen under these restrictions arelapparently not able to utilize their resources at the fullest, which can become a source of inefficiency. In attempting to overcome this ineffi- ciency, fishermen have increased the width of their gill nets from 20 to 50 "mesh," an increase Of 2.5 times the former width. This is permitted because limitation is based on linear feet of net. This change probably does not increase the catch per unit of effort in prOportion, because fish Often swim in a certain narrow depth range, so the 20 mesh width can often catch most of the catchable fish. Without the gear limitation it is obvious that the cost per unit Of effort (a unit of effort is 1000 linear feet net) would decrease, increasing the Optimum level Of production, and making fishing more profitable for some fishermen. Doubling the allowable net length, for instance, may not 161 double the catch, but the catch should increase enough to outweigh the additional costs, leaving some profit for some of the commercial fishermen and increasing the social surplus. Welfare effects of relaxing the gear limitation are shown by hypothetical shifts in the supply curve, Figure VII-3. Suppose that prior to relaxing the gear limitation, the equilibrium price and quantity is Po and Q0. The fol- lowing are the possible changes in social welfare, a) if supply surve were perfectly elastic (horizontal line), the gain to society (change in social surplus) from relaxing the gear limitation, which lowers the supply curve to S} would be the gain in consumers' surplus (A + B + C), b) if the initial supply curve were perfectly inelastic, a shift in the supply curve from QO 8 to Q, Si would result 2 in both a change in producers' surplus (F + G - (A + B)), and a change in consumers' surplus (A + B + C), and c) if the supply curve is positively sloped, a shift in the supply curve from S to 8' would result in a change in pro- ducers' surplus (E + F - A), a gain in consumers' surplus (A + B + C), and a net gain of (B + C + E + F). Since there is only a limited amount of fish to be harvested from the lakes, increasing the harvest by doubling the allowable amount of net may force some fishermen out of business, while the others enjoying a high profit. The trade off then is between unemployment and efficiency, and the MDNR (Michigan Department of Natural Resources) has 162 HOHSSOOO 1k meowumuflEHA Home 0:» mafixmamm mo muommmm mumwamz may 3030 on mm>HOU hammsm 0cm UGOEmo Hoowumnuomwm Price .MIHH> QMDUHh 163 apparently chosen to sacrifice some efficiency to keep more fishermen in business. CHAPTER VIII Summary, Conclusions and Recommendations for Future Research Summaryand Conclusions The Great Lakes as a whole are a unique place for both sport and commercial fishing. Commercial fishing has changed drastically in the past century. Apparently over- exploitation in the 1930's in Lake Michigan, and the sea lamprey which invaded Lakes Erie, and Ontario in the 1930's, Lakes Michigan and Huron in late 1940's and 1950's and Lake Superior in late 1950's, reduced some fish stocks drastically, forcing some fishermen out of business. Technological advances in the 1950's and 1960's, on the other hand, improved fishermen's productivity, so even less fishermen were required to harvest the available fish. The number of licensed fishermen dropped from about 1100 in early 1950's to about 150 at present. In the early 1960's the sea lamprey was controlled and some of the fish stocks started rebuilding. The discovery of toxic chemicals such as DDT and PCB in late 1960's and early 1970's affected the supply and consumer demand for all Great Lakes fish, parti- cularly lake trout. The overall situation has not been in favor of the commercial fishermen for a long time, changing 164 165 the profitable and dominant commercial fishing industry to a small, generally poor, and over-capitalized industry. Sport fishing, on the other hand, became significant in the early 1930's, and has since increased greatly. There are now between ten and fifteen million angler days per year in the Michigan Waters of the Great Lakes and major tributaries (Talhelm, 1977). This increasing demand for sport fishing, the Department Of Natural Resources believes that the value of sport fishing greatly outweights the value Of commercial fishing, and the chemical pollution and biolo- gical disruptions are the main reasons for the upward trend of sport fishing and the downward trend of the commercial fishing industry. This lack of balance in improving the sport and com- mercial fisheries, has created many conflicts between the two groups, with each one claiming to use the resource more efficiently, and demanding more. There is a general recog- nition, however, that the social welfare could be maximized by some Optimum allocation of the resource between the po- tention users. The problem is that the relative values needed to determine the Optimum allocation of the resource have not been documented for various reasons. First, because Of insufficient and inaccurate economic data and biological relations, and second due to lack of appropriate biological and economic models to utilize the "best" available data. 166 The main Objective of this study was to document some of the economic values such as Optimum sustainable yield (OSY), maximum sustainable yield (MSY), effort at OSY and MSY, and producers' surplus at OSY nad MSY for the white- fish fishery of the Great Lakes. To Obtain this objective, a bio-economic model was developed and demand and supply equations were estimated for the U.S. whitefish fishery. These models were also applied to examine the fishery under different market conditions, and to find the maximum poten- tial net all-or-none value under most favorable conditions. These values can then be compared with the equivalent values computed for the sport fishing. For the biological side of the bio-economic model, several different procedures were tried in estimating the harvest function for whitefish in district MM-l. The lin- earization technique produced better estimates of the parameters than other procedures used in this study. The results were 800,000 kg for OSY, 835,000 kg for MSY, 12,700 units for effort at OSY, 15,900 units for effort at MSY, $520,000 for rent at OSY, and $480,000 for rent at MSY. For the same harvest year (1973), actual yield was 590,000 kg, actual effort was 26,000 units, and actual rent was $17,000. Comparing the actual values with the predicted Optimum values, it appears that the present fishery Operates inefficiently by using a larger amount of effort, almost twice as much as that at OSY, but harvesting less than OSY and generating a much smaller amount of producers' surplus. 167 The U.S. aggregate demand and supply of whitefish from 1963 to 1973 were estimated using several different proce- dures. The "best" results were Obtained when a system of four equations for demand and supply of whitefish and lake trout were estimated using two and three stage least squares. These equations showed: 1. a relatively high price elasticity of demand for whitefish (from -2 to -4), indicating the avail- ability of a large number of good substitutes. an income elasticity of demand of about 2.2, in- dicating that whitefish is a normal good. Since whitefish is only a very small portion of our diet, the magnitude is not exceptionally high. a cross-price elasticity of demand with the price of choice beef of about 2.3. a cross-price elasticity of demand with the price of lake trout of about 2, indicating that lake trout is a good substitute in consumption. a very low price elasticity of supply of white- fish (.25), and a very low cross elasticity of supply is not responsive to its own and substi- tute prices. The demand and supply analysis shows that stopping lake trout production (because of health regulations) will tend to increase the whitefish supply because fishermen may attempt to utilize their equipment in fishing for alterna- tive species such as whitefish, increasing supplies of 168 these species. Limited supply of lake trout in the market, on the other hand, results in a very high price of lake trout which may force some of the lake trout consumers to switch to consuming whitefish. The new equilibrium produc- tion Of whitefish would increase from 20 to almost 50 pounds per thousand people, and new price Of whitefish would decrease slightly from 47 to 39 cents per pound. These demand and supply equations were also utilized in estimating three kinds Of values under very optimistic conditions, a) the maximum potential producers' surplus, b) the maximum potential net all-or-none value (social surplus), and c) the maximum potential monOpoly rent for Michigan's commercial fishery. These values are presented in Table VIII-l. Table VIII-l. Economic Values of Michigan's Commercial Fishery Surplus or rent Potential maximum Potential maximum Type of Value as a % of value in millions value in millions TR in 1973 of 1973 dollars of 1977 dollars Producers' surplus 27-89 $6 - $19 $ 9 - $25 Social Surplus (net all-or-none value) 49 $10 $14 Monopoly rent 34 $ 7 $10 - $ 5 169 The estimated net all-or-none value (social surplus) is about $14 million, but it could be over $25 million, judging by the estimate of producers' surplus. This is much lower than the equivalent sport fishing value of $250 million (Talhelm, 1977). Maximum potential monopoly rent was about 3/4 of the social surplus ($10.5 million). Under more normal conditions, Michigan's 1973 share of the net all-or-none value for the whitefish fishery was $750,000 (in 1967 dollars), or about half as much as gross revenue. It was found that fishermen could collect- up to 2/3 of the net all-or-none value as monOpoly rent or about $500,000, if they could collude to form a perfect monopoly. Gear limitations in the fishery may lead to ineffi- cient use Of resources by imposing some unnecessary costs on the fishermen, and by affecting the Optimum level of production. Relaxing the limitations, on the other hand, makes fishing more profitable for some fishermen, and increases consumer surplus. At the same time it may decrease the employment in the industry if whitefish is overharvested. Recommendations for Future Research A. Expand Present Efforts The main problem that we have been dealing with in the Great Lakes is the lack of Specific knowledge about the socio-economic values required for better management of the fishery resources. An avenue for future research is to 170 start from where this study stOps, by a) expanding the bio- economic model developed in this study to other species and to other districts and other lakes, and b) expanding the U.S. supply and demand analysis, as developed in this. study, over other species, districts, and lakes. There are advantages as well as disadvantages associated with this approach. Advantages are a) we can make use of the availa- ble data and available models, and b) these results can be a good basis for evaluating future results. The disad- vantages, on the other hand, are a) the present data is not suitable for economic analysis, and b) the available data is not very accurate. Therefore, more data with better qua— lity for the purpose of economic analysis is required in order to improve the results. The new data, however, may or may not improve the results, because the available bio- logical models are standard models which are not constructed to fit the special characteristics of the Great Lakes, as far as the technological, and environmental changes are concerned. Therefore, there is a need for constructing more SOphisticated or more suitable models for the Great Lakes. Once the new models are constructed, they may require an entirely new set of data which should ideally be collected HOW . B. Improve Data The main data used to estimate the coefficients of the biological model were effort (E), and yield (Y). The data used to estimate the coefficients of the demand and 171 supply equations were mainly ex-vessel prices and the total U.S. quantity. The author believes that, even though the best available data has been utilized in this study, there is till a great deal of room for improvement. Some of the problems with the available data are as follows; a) Effort: The main problem with the effort data is that the nature of effort has changed over time without adjustments in the .data. For instance, one unit of effort is defined as one "lift" of one thousand linear feet of 4 1/2 inch gill net. Four major problems with this definition are, first, effort is measured in linear feet and leaves out the importance of width entirely. When recently fishermen changed the width of gill nets from 20 to 50 mesh, increasing the area of net by a factor of 2.5, the definition of effort remained unchanged. Second, the amount of time that the net remains in the water is not specified. Thirdly, the type of mater- ial used in making the gill nets such as linen, nylon and monophylament, is not identified. Finally, the Species sought are not necessarily the same as species caught. Fishermen usually report their total effort spent and the amount of different species caught. These factors can alter the efficiency in terms of catch per unit of effort. As long as these definitions remain unclear, the relation— ship between catch and effort cannot be identified satis- factorily. b) Yield: The amount of catch reported by the fishermen usually differs from the amount caught, because they catch illegal fish and return them to the lakes, and 172 they catch unpopular species without reporting them. Also, the species they report are often not the Species they were looking for. Again the problem is the true relationship between effort spent on any particular species, and the catch of that species. c) Ex-vessel price was found in this study by dividing the total ex-vessel value by catch. Since the reported catch and values are apparently not very accur- ate, the price data is also probably inaccurate. To improve the situation, more accurate reporting would be helpful. d) Cost and returns: Cost and returns used in this study were estimated for an average fisherman. The questions were asked from a group of fishermen. These groups can easily be dominated by few people, resulting in biased information (statistically invalid). To Overcome the prob- lem, more information should be collected on an individual basis. C. Improve Biological Models Some of the problems with the biological models are related to the assumptions behind the model. a) The logis- tic surplus production model used in this study has little to Offer concerning the stochastic nature of the pOpulation under exploitation. Instead, equation IV-3 could be shown as equation VIII-l. VIII-l. AB = nl(t) [kBt - § 8:] - n2(t) q E Bt Where nl(t) and n2(t) are time-varying random varia- bles. The variable n1 represents random variation in the 173 rate of production from the stock due to change in recruit- ment, growth, and natural mortality caused by the environ- ment. The variable n2 represents random variation in the catch rate due to changes in availability and catchability of fish. b) The model assumes that at each level of fish- ing effort there is an associated equilibrium pOpulation size with a corresponding stable age distribution. If the changes in the fishery are gradual, the transient age dis- tribution at any moment should not differ greatly from the associated stable age distribution so that equation IV-l will give a good approximation to the actual rate of change. In the Great Lakes, with such rapid changes in population size in the post-sea-lamprey period, the actual age distribution will lag the stable age distribution in time as the pOpulation size changes. Therefore, IV-l will not exactly describe the rate of changes in effort, which can result in even a poorer representation of the actual rate of pOpulation change. Species with relatively short generation times should most closely meet these conditions concerning population size and age structure. For white— fish with a relatively long maturation time of 3-4 years, the actual age distribution will lag the stable age distri- bution and this may change the results. c) The logistic surplus production model usually assumes that the stock production curve is a perfect parabola (where m=2). The shape of the catch-effort curves for the Great Lakes fish have not been identified. This in itself opens another line 174 of research; to identify the shape. Perhaps it might be necessary to use more accurate data to determine the shape for each population. d) In this study, the population in each district was treated as a separate unit stock. In future research the relationship between these populations should be identified. e) Present biological models have apparently utilized only the information about either catch and effort (surplus production model), or growth and morta- lity rates (dynamic pool model), ignoring the importance of other environmental factors. To improve the situation, some of the relationships between species and other ecolo- gical factors, such as water temperature and fertility, should be brought to the models. D. Other Efforts Once the problems of data and biological models are solved, then the economic tools and information can be used to identify some Of the socio-eéhomic values. The author believes that with the available data and the biological model, and given the fact that this is apparently the first complete bioeconomic model ever built for the Great Lakes, these assumptions seem to be apprOpriate. However, there si still some room for improvement: a) the study assumes a static model which may be appropriate at this stage, but a dynamic model, equation VIII-2, is also desirable. °° t VIII-2. n = f (TVP - TFC + l(AB=0))e'r dt 0 175 b) This study assumes perfect mobility of economic assets in the long run. However, it is Obvious that not all the assets are mobile (see Bishop, 1973). Therefore, in the future more attention should be devoted to this area. c) This study assumes homogeneity among fishing units. The fact is that not all the fishing units are homogenious, and more data on individual fishing units are needed to identi- fy representative fishing units. d) This study has concen- trated on long run analysis. In the future, some more attention should also be devoted to the short run analysis. BIBLIOGRAPHY BIBLIOGRAPHY Bessell, J. H. 1887. "Fish and Fish Culture in Michigan." Seventh‘ Biennial Report of the State Board of Fish Commissioners, Lansing, Michigan, p. 95. 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"Michigan's Commerical Fisheries of the Great Lakes." Michigan History Magazine, XXII. Michigan Historical Commission, Lansing, MiChigan, p. 107. Patriarche, M. H. 1976. "Biological Basis for Management of Lake Whitefish in the Michigan Waters of Northern Lake Michigan." Michigan Department Natural Resources Fisheries Division, Report NO. 1838, August 2. Pella, J. J., and P. K. Tomlinson. 1969. "A Generalized Stock Production Model. Inter Am. Trop. Tuna Comm. Bull. 13: 421-496. Ricker, W. E. 1975. "Computation and Interpretation of Biological Statistics of Fish Populations." Fish. Res. Board Can. Bull. No. 191, 382 pp. Schaefer, M. B. 1957. "Some Considerations of Population Dynamics and Economics in Relation to the Management of the Commercial Marine Fisheries," Journal of the Fisheries Research Board of Canada, XIV, No. 5, pp. 669-681. Scott, A. 1955. "The Objectives of Sole Ownership." J. Pol. Econ. 63, pp. 116-124. Scott, J. A. 1974. "A Historical Review of the Productivi- ty and Regulation Of Michigan's Commercial Fisheries, 1870-1970." Michigan Fisheries Centennial Report 1873-1973. Michigan Department of Natural Resources, Lansing, Michigan, pp. 77-79. 178 Shapiro, S. 1971. "Our Changing Fisheries." U.S. Govern- ment Printing Office, Washington, D.C., p. 332. Smith, S. 1968. "Species Succession and Fishery Exploita- tion in the Great Lakes." J. Fish. Res. Ed. Canada 25(4): 667-693. State News,l977. Wed. Jan 26, E. Lansing, Michigan. Talhelm, D. R. 1973. "Evaluation of the Demands for the Salmon and Steelhead Sport Fishery of 1970, Michi- gan's Great Lakes Trout and Salmon Fishery," 1969- 1972. Fisheries Management Report No. 5, pp. 62-70. . 1975. "1975-76 Sea Grant Program in Fisheries Economics and Marketing," July 21, Michigan State University Sea Grant, East Lansing, Michigan. . 1977. "Fisheries Economics of the Great Lakes." A paper presented at the Great Lakes Commission Meet- ing, June 13, 1977, Erie, PA. Department of Fisher- ies and Wildlife, Michigan State University, East Lansing, Michigan. Talhelm, D. R. and P. V. Ellefson. 1973. "Economic Apprai- sal of the Resident Salmon and Steelhead Sport Fish- ery of 1970, Michigan's Great Lakes Trout and Salmon Fishery," 1969-1972, Fisheries Management Report No. 5, pp. 48—67. Townsend, C. H. 1902. "Statistics of the Fisheries of the Great Lakes," Report of the Commissioner of the U.S. Commission of Fish and Fisheries, Government Printing Office, Washington, D.C., p. 581. Turvey, R. 1964. "Optimization and Sub-Optimization in Fishery Regulation." AER, pp. 64-66. Walter, G., and W. J. Hogman. 1971. "Mathematical Models for Estimating Changes in Fish Populations with Applications to Green_Bay," Int. Assoc. Great Lakes Res. 14: 170-184. Watt, K. 1968. "Ecology and Resource Management." McGraw Hill, New York. General Sources Cohen, K. J. and R. M. Cyert. 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APPENDIX APPENDIX Common and Scientific Fish Names Common Name Yellow perch Walleye Largemouth bass Small mouth bass White bass Bluegill Pumpkinseed Black crappie Rock bass Muskellunge Northern pike Suckers Rainbow smelt Lake trout Rainbow trout (steelhead) Brown trout Brook trout Coho salmon Chinook salmon Pink salmon Lake sturgeon Carp Lake whitefish Sea lamprey Alewife Chub Sticklebacks Sculpins Scientific Name Perca flavescens Stizostendion vitreum Micropterus salmoides Micropterus dolomieui Roccus chrysops Lepomis macrochirus Lepomis gibbosus Pomoxis nigromaclatus Ambloplites rupestris Esox masquinongy Esox lucius Catostomidae Osmerus mordax Salvelinus namaycush Salmo gairdneri Salmo trutta Salvelinus fontinalis Oncorhynchus kisutch Oncorhynchus tshowytscha Oncorhynchus gorbuscha Acipenser fulvescers Cyprinus carpio Coregonus clupeaformis Petromyzon marinus Alosa pseudoharengus Coregonus spp. Gasterosteidae Cottidae 180 HICH G B QRIES IlflfllfififljflifllfllyflfllyiflfiyluM 85