2. May 2000 INTRODUCTION TO BIOECONOMIC MODELS FOR FISHERY - THE SCHAEFER-GORDON MODEL INTRODUCTION TO BIOECONOMIC MODELS FOR FISHERY - THE SCHAEFER-GORDON MODEL Dr. Mahfuzuddin Ahmed International Center for Living Aquatic Resources Management Dr. Mahfuzuddin Ahmed International Center for Living Aquatic Resources Management

3. May 2000 What is a Fishery? Fishery is a stock or stocks of fish and the enterprises that have the potential of exploiting them

4. May 2000 Fish Stock and Fishery Management Influence of socioeconomic and institutional factors A complex process of integration of resource biology and ecology Behavior of fishers and policymakers

5. May 2000 Syndrome of Overexploitation Both biological and economic overexploitation Failure of market (under unrestricted access) from optimally allocating fishery resources Unclear property rights regime

6. May 2000 Syndrome of Overexploitation... Conflicting interest over rights and duties can lead to fisheries collapse Generate externalities between resource- users (Seijo et al 1998)  stock externalities  crowding externalities  technological externalities  ecologically based externalities  techno-ecological externalities

7. May 2000 Developing Country Syndrome High exclusion cost Social trap and the free rider behavior High transaction cost  information cost  enforcement cost  contractual cost Inadequate legal and institutional framework

8. May 2000 Fishery Management Decisionmaking aiming at a sustainable management of fish stocks Biological, ecological, economic, social and legal analysis Identify and quantify the objectives and goals of management Select appropriate combination of performance variables and determine the control variable

9. May 2000 Fishery Management... Determine alternative management strategies and implementation mechanism Monitor and evaluate the impacts of alternative management strategies and plans Revise and redo plans, if necessary

10. May 2000 Bioeconomic Model Assumes allocation of property rights as a way to mitigate risks of stock overexploitation Bioeconomic Model allows the evaluation of the fishery in biological, economic and ecological sense Provide an optimal allocation of efforts and output and help achieve the desired level of performance criteria

11. May 2000 The Basic Biological Model Single fish stock Stock growth over time (logistic growth) Model Assumptions G =dP = f(P) dt (1) G = growth P = initial population

12. May 2000 The growth of population is proportional to initial population, i.e., G =aP (2) a = intrinsic growth The Basic Biological Model...

13. May 2000 There must be a maximum size of population that can be supported. It is called Environmental Carrying Capacity (ECC) denoted by K. Hence, G =aP[(K-P)/k] = aP(1 - P) K (3) The Basic Biological Model...

14. May 2000 Maximum growth occurs when population size is half of ECC, i.e., G’ =a(1 - 2P) = 0 K (4) Hence, P = K/2 The Basic Biological Model...

15. May 2000 The biological productivity curve The Basic Biological Model...

16. May 2000 The Effect of Fishing: the Short-Run Y = y (P,f) (5) Y = yield f = fishing effort Once fishing is introduced yield or catch at any period will depend on  size of fish population  amount of fishing effort

17. May 2000 Economic measure »boat, gear, crew and other inputs required for fishing »called as nominal effort (f) and is calculated by using standardized measure such as vessel- ton-days The Fishing Effort

18. May 2000 Biological measure »Effective effort (F): the fraction of the average population taken by fishing » F is often calculated as the negative of natural logarithm of proportion of fish surviving fishing in a year The Fishing Effort...

19. May 2000 F = qf (6) q = catchability coefficient; = represents the state of technical efficiency The Fishing Effort... »Both nominal and effective efforts are related by

20. May 2000 Y = qfP (7) The Fishing Effort …. »Using nominal effort we can define yield equation for short-run as

21. May 2000 Yield and population size Short-run yield as a function of population size  for a given level of nominal effort, yield will vary with population size

22. May 2000 Short-run yield with diminishing returns to population Diminishing returns to population size

23. May 2000 Y = qPf  (8) This gives a short-run yield equation as Where 0 <  < 1

24. May 2000 Y = qf  P (9) Diminishing Returns to Nominal Effort Short-run yield with diminishing returns to nominal effort - upper limit to yield in the short run

25. May 2000 G = aP(1-P)-qf  P K (10) The Long-Run Equilibrium in a Fishery G = aP[(K-P)/k] = aP(1 - P) K (3) Y = qf  P We obtain Combining biological production with the yield function (9)

26. May 2000 The impact of fishing on the population size The Long-Run Equilibrium For an effort level f1, a population P2 and a yield of Y2 may be sustained into the long run, because yield from fishing, Y2 will be balanced by the growth of stock. G2

27. May 2000 The Long-Run Equilibrium …. P = K(1-qf  ) a (11) To find equilibrium let us set equation (10) to zero which gives

28. May 2000 The Long-Run Equilibrium... (11) For the chosen effort level, equation (11) tells us the sustainable population Different effort levels will produce different sustainable yield We can now derive a sustainable yield function by using equations (9) and (11) P = K(1-qf  ) a Y = qf  P(9)

29. May 2000 Y s = Kfq   qf  ) a If  = 1, sustainable yield is a simple quadratic function of effort. In this case the sustainable yield curve will simply be the mirror image of the biological productivity curve. These give us (12) The Long-Run Equilibrium...

30. May 2000 The Long-Run Equilibrium... Sustainable yield curves The greater are diminishing returns (lower  ) the longer it takes to reach a maximum The relationship between biological productivity curve and sustainable yield curve for various values of  (0 <  < 1) is shown by

31. May 2000 Setting equation (12) to zero and solving for f gives f max = (a/q) 1/  (13) - can be referred to as the effort that reduces sustainable yield to zero (extinction of stock) The Long-Run Equilibrium...

32. May 2000 f msy = (a/2q) 1/  (14) If  = 1, MSY is half of f max MSY - Differentiate (13) with respect to effort and set it to zero In general, f msy = (1/2) 1/  f max (15) The Long-Run Equilibrium...

33. May 2000 Revenue as a function of fishing effort The Economics of Fishing - Revenue

34. May 2000 Long-run total revenue function TR f = pY s TR f = pKqf  (1-qf  ) a Which is a function of f (18) Which by substitution from equation (12) gives AR f = TR f f MR f = d(TR f ) df (17) (16)

35. May 2000 Cost as a function of fishing effort The Economics of Fishing - Cost TC f = cf AC f = MC f

36. May 2000 The Bioeconomic Equilibrium The open-access equilibrium

37. May 2000 1. All processes affecting stock productivity (e.g. growth, mortality and recruitment) are subsumed in the effective relationship between effort and catch. 2. The catchability coefficient q is not always constant, and may differ due to e.g. different aggregation behavior of pelagic and sedentary resources. - factors related to differential gear selectivity by age/lengths are not taken into account Model Limitations

38. May 2000 3. CPUE is not always an unbiased index of abundance. - relevant to sedentary resources with patchy distribution and without the capacity of redistribution in the fishing ground once fishing effort is exerted - sequential depletion of patches also determines a patchy distribution of resource users, precluding model applicability 4. Variations in spatial distribution of the stock are usually ignored, as well as the biological processes that generate biomass, the intra/interspecific interactions, and stochastic fluctuations in the environment and in population abundance. Model Limitations...

39. May 2000 5. Ecological and technological interdependencies and differential allocation of fishing effort in the short term are not usually taken into account. 6. Improvement in technology and fishing power determines that q often varies through time. 7. It becomes difficult to distinguish whether population fluctuations are due to fishing pressure or natural processes. - in some fisheries, fishing effort could be exerted at levels greater than twice the optimum. Model Limitations...

40. May 2000 Other Models 1. Dynamic Bioeconomic Model (Smith) 2. Yield-Mortality Models - exponential - precautionary 3. Age Structured Bioeconomic Model 4. Intertemporal Analysis

41. May 2000 Other considerations for extension of bioeconomic models 1. Ecological and technological interdependence 2. Social and institutional factors

42. May 2000 THANK THANK YOU! THANK THANK YOU!

43. May 2000 Overview of Models Differing impacts of diminishing returns to nominal effort on sustainable yield

44. May 2000 Overview of Models The impact of fishing when diminishing returns to population are present

45. May 2000 Overview of Models The sustainable yield curve when diminishing returns to population are present

46. May 2000 Overview of Models The effect of shifting revenue curves on the open-access equilibrium

47. May 2000 Overview of Models Fundamental relationship between catch, effort and costs in a fishery

48. May 2000 Overview of Models Market equilibrium of fishery sector in a supply-demand model

49. May 2000 Overview of Models Gordon-Schaefer Model Sustainable a) biomass, b) yield and c) total sustainable revenues (TSR) and costs (TC).

50. May 2000 Overview of Models Population logistic growth model for K = 3.5 million tonnes and r = 0.36

51. May 2000 Overview of Models Open access regime. A) Sustainable average and marginal yields; b) average and marginal costs and revenues, as a function of effort under open access conditions

52. May 2000 Gulf of Thailand Market equilibrium of fishery sector in a supply-demand model

53. May 2000 Gulf of Thailand

54. May 2000 Gulf of Thailand

55. May 2000 Gulf of Thailand