INTRODUCTION TO BIOECONOMIC MODELS FOR FISHERY - THE SCHAEFER-GORDON MODEL

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

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

3. 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

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

5. 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

6. 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

7. 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

8. 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

9. 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

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

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

12. The Basic Biological Model . . . 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)

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

14. The Basic Biological Model . . . The biological productivity curve

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

16. The Fishing Effort 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

17. The Fishing Effort ... 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

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

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

20. 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

21. Diminishing returns to population size Short-run yield with diminishing returns to population

22. This gives a short-run yield equation as Y = qPfa (8) Where 0 < a< 1

23. Diminishing Returns to Nominal Effort - upper limit to yield in the short run (9) Y = qfbP Short-run yield with diminishing returns to nominal effort

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

25. The Long-Run Equilibrium The impact of fishing on the population size 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

26. The Long-Run Equilibrium …. To find equilibrium let us set equation (10) to zero which gives P = K(1-qfb) a (11)

27. The Long-Run Equilibrium . . . 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) (11) P = K(1-qfb) a Y = qfbP (9)

28. The Long-Run Equilibrium . . . These give us (12) Ys = Kfqb (1-qfb) a If b = 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.

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

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

31. The Long-Run Equilibrium . . . MSY - Differentiate (13) with respect to effort and set it to zero (14) fmsy = (a/2q) 1/b If b= 1, MSY is half of fmax In general, fmsy = (1/2)1/bfmax (15)

32. The Economics of Fishing - Revenue Revenue as a function of fishing effort

33. Long-run total revenue function TRf = pYs Which by substitution from equation (12) gives TRf = pKqfb(1-qfb) a (16) Which is a function of f ARf = TRf f (17) MRf = d(TRf) df (18)

34. The Economics of Fishing - Cost TCf = cf ACf = MCf Cost as a function of fishing effort

35. The Bioeconomic Equilibrium The open-access equilibrium

36. Model Limitations • 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

37. Model Limitations . . . • 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.

38. Model Limitations . . . • 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.

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

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

41. THANK YOU!

42. Overview of Models Differing impacts of diminishing returns to nominal effort on sustainable yield

43. Overview of Models The impact of fishing when diminishing returns to population are present

44. Overview of Models The sustainable yield curve when diminishing returns to population are present

45. Overview of Models The effect of shifting revenue curves on the open-access equilibrium

46. Overview of Models Fundamental relationship between catch, effort and costs in a fishery

47. Overview of Models Market equilibrium of fishery sector in a supply-demand model

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

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

50. 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