Economics of Renewable Natural Resources

1. Economics of Renewable Natural Resources Bioeconomics of Marine Fisheries Ashir Mehta • Source : The Economics of Marine Capture Fisheries, Steven C. Hackett, Professor of Economics, Humboldt State University

2. Fisheries What is a fishery? The interaction of fish populations and human harvest activity The economically valuable portion of a fish population is a renewable but potentially exhaustible natural resource.

3. The Bioeconomics of a Fishery • Background information on the biological mechanics of a fishery • Identification of a steady-state bioeconomic equilibrium • Harvesting under open access • Socially optimal harvest Bioeconomics combines the biological mechanics of a fish population with the economic activity of harvesting fish.

4. Biological Mechanics Imagine a rich marine habitat for a certain species of fish. There’s lots of food and shelter and few predators and parasites. If the number of reproductive mature fish in this habitat is low, but there is mating success, will the habitat generally allow for reproductive success? Suppose that a breeding pair is able to produce 10 young that reach adulthood. Then from an initial stock of 2 fish (male and female), the stock grows by 10 fish.

5. Biological Mechanics Rate of Growth . 10 Number of Adult Fish 0 2

6. Biological Mechanics Next breeding season we have 12 reproductively mature fish (assume the original 2 are still alive). Suppose there is still plenty of habitat, so that again each pair produces 10 young that reach adulthood. How many new adult fish are produced this season? 6 breeding pairs x 10 = 60 new adults

7. Biological Mechanics Rate of Growth . 60 . 10 Number of Adult Fish 0 2 12

8. Biological Mechanics Next breeding season we have 50 mature fish (assume mortality of 10 adult fish due to old age or predation). Suppose that the habitat now only allows each pair to produce 4 young that reach adulthood. Why might this be happening? How many new adult fish are produced this season? 25 breeding pairs x 4 = 100 new adults

9. Biological Mechanics Rate of Growth . 100 . 60 . 10 Number of Adult Fish 0 50 2 12

10. Biological Mechanics Next breeding season we have 126 mature fish (assume 24 old adults die). Suppose that the habitat only allows each pair to produce, on average, 2.3 young that reach adulthood. Why might this be happening? How many new adult fish are produced this season? 63 breeding pairs x 2.3 = 145 new adults

11. Biological Mechanics Rate of Growth . 145 . 100 . 60 . 10 Number of Adult Fish 0 50 126 2 12

12. Biological Mechanics Next breeding season we have 224 mature fish (assume 47 old adults die). Suppose that now the habitat only allows each pair to produce, on average, 0.5 young that reach adulthood. Why might this be happening? How many new adult fish are produced this season? 112 breeding pairs x 0.5 = 56 new adults

13. Biological Mechanics Rate of Growth . 145 . 100 . . 60 . 56 10 Number of Adult Fish 0 50 126 224 2 12

14. Biological Mechanics Eventually, the population or stock of fish will reach a biological maximum for the available habitat. At this maximum, the birth rate equals the death rate. If conditions do not change, the population will remain at this maximum, making it an equilibrium.

15. Biological Mechanics Rate of Growth Population growth rate curve: Describes population growth for different populations of fish . 145 . 100 . . 60 . 56 10 Number of Adult Fish 0 50 126 224 2 12

16. Biological Mechanics • Let’s suppose that X stands for the stock (population) of economically valuable fish. • Moreover, suppose that F(X) is the population growth rate for the fishery (birth rates – death rates). • F(X) reflects the rate of net recruitment (number of new fish enter a fishery, net of fish removed from the fishery). • Note that if the fish stock is described by the usual logistic function (smoothly increasing at a decreasing rate), then the stock growth rate can be given as follows: F(X) = aX – bX2

17. Biological Mechanics F(X) = aX – bX2 Note that the maximum value for the fish population X equals (a/b), which we will define as k (carrying capacity) for a given habitat. When X = k, stock growth rate F(X) = 0.

18. Biological Mechanics Rate of Growth Note that one can have the same fishery stock growth rate F(X) at two different sizes of the stock (X1 and X2) Rate of Fishery Stock Growth F(X) Fishery Stock X X1 X2 k 0

19. Introduction to Bioeconomics Basic Principles: Begin with an unexploited fishery in biological equilibrium (where X = k): 1. Suppose that the harvest rate H exceeds even the highest possible population growth rate for the fishery. Then population X eventually falls to zero. Fishers are “mining” the fishery.

20. Mining the Fishery (H > F(X)) Rate Harvest rate H Fishery stock growth rate F(X) Fishery Stock X k 0

21. Example of Mining the Fishery Rate Harvest rate H 2,000 Year 1: Harvest 2,000 fish  8,000 left for next year. Fishery Stock X 0 k = 10,000

22. Example of Mining the Fishery Rate Harvest rate H 2,000 Year 2: Harvest 2,000 fish, popul. grows by 700  6,700 left for next year. 700 Fishery Stock X 0 X = 8,000 k

23. Example of Mining the Fishery Rate Harvest rate H 2,000 Year 3: Harvest 2,000 fish, popul. grows by 1,200  5,900 left for next year. 1,200 Fishery Stock X 0 X = 6,700 k

24. Example of Mining the Fishery Rate Harvest rate H 2,000 Year 4: Harvest 2,000 fish, popul. grows by 1,400  5,300 left for next year. 1,400 Fishery Stock X 0 X = 5,900 k

25. Example of Mining the Fishery Rate Harvest rate H 2,000 Year 5: Harvest 2,000 fish, popul. grows by 1,450  4,750 left for next year. 1,450 Fishery Stock X 0 X = 5,300 k

26. Example of Mining the Fishery Rate Harvest rate H 2,000 Year 6: Harvest 2,000 fish, popul. grows by 1,400  4,150 left for next year. 1,400 Fishery Stock X 0 X = 4,750 k

27. Example of Mining the Fishery Rate Harvest rate H 2,000 Year 7: Harvest 2,000 fish, popul. grows by 1,200  3,350 left for next year. 1,200 Fishery Stock X 0 X = 4,150 k

28. Example of Mining the Fishery Rate Harvest rate H 2,000 Year 8: Harvest 2,000 fish, popul. grows by 900  2,250 left for next year. 900 Fishery Stock X 0 X = 3,350 k

29. Example of Mining the Fishery Rate Harvest rate H 2,000 Year 9: Harvest 2,000 fish, popul. grows by 700  950 left for next year. 700 Fishery Stock X 0 X = 2,250 k

30. Example of Mining the Fishery Rate Harvest rate H Year 10: Try to harvest 2,000 fish, but only 950 left. Even with 400 new fish produced, stock is destroyed. 2,000 400 Fishery Stock X 0 X = 950 k

31. Introduction to Bioeconomics Basic Principles: 2. The highest rate of harvest H that can be sustained by the fishery occurs where the growth rate of the fishery stock is at its maximum. This point is called maximum sustainable yield (MSY).

32. Example of Mining the Fishery Rate Why is a harvest of 1,450 fish/year in this example equal to maximum sustainable yield? 1,450 Fishery Stock X 0 k

33. Introduction to Bioeconomics Basic Principles: MSY A. If we start with the stock at X = k (the unexploited biological equilibrium), and set harvest equal to MSY, then what happens? Hmsy > F(X), which causes X to decline. This process continues until X = Xmsy, at which point the harvest rate H equals the stock growth rate F(X) and no further reduction in biomass occurs. This is an equilibrium.

34. Biological Mechanics Rate End here Hmsy Start here Stock Dynamic A Fishery Stock X k 0 Xmsy

35. Introduction to Bioeconomics Basic Principles: MSY B. In contrast, suppose that the fishery had been over-harvested in the past and the stock is at X < Xmsy. If we start at a relatively low stock and set harvest equal to MSY, then what happens? The population is extinguished.

36. Biological Mechanics Rate Hmsy Start here Stock Dynamic B End here Fishery Stock X k 0 Xmsy

37. Introduction to Bioeconomics Basic Principles: C. For harvest rates H < Hmsy there are usually two biomass equilibria – “low biomass” and “high biomass”.

38. Biological Mechanics Rate Fishery stock growth rate F(X) H Fishery Stock X 0 Low biomass equilibrium X1 High biomass equilibrium X2

39. Introduction to Bioeconomics Basic Principles: H < Hmsy To see this, suppose that the population is at X = k (the unexploited biological equilibrium). If H > F(X), what will happen? The stock X will decline until it reaches the high biomass equilibrium where F(X) = H.

40. Biological Mechanics Rate End here Start here H Fishery Stock X Xhigh k 0

41. Introduction to Bioeconomics Basic Principles: H < Hmsy Suppose now the stock X is less than the high biomass equilibrium, but is large enough that F(X) > H. What will happen? The stock X will grow to the high biomass equilibrium where F(X) = H.

42. Biological Mechanics Rate Net growth rate F(X) - H F(X) H Start here End here Fishery Stock X Xhigh k 0

43. Introduction to Bioeconomics Basic Principles: H < Hmsy Thus the high biomass equilibrium is sustainable and is locally stable (it holds “locally” for X somewhat larger or smaller).

44. Introduction to Bioeconomics Rate Fishery stock growth rate F(X) H Fishery Stock X 0 [ ] Range of initial stock values that will result in the high biomass equilibrium X2

45. Introduction to Bioeconomics Basic Principles: H < Hmsy If the stock X is at the low biomass equilibrium, then F(X) = H. This equilibrium is also sustainable. But … if the stock X is even slightly less than the low biomass equilibrium, then F(X) < H, and X falls to zero – the population is extinguished. If X is even slightly greater than the low biomass equilibrium, then F(X) > H and X rises to the high biomass equilibrium. Thus the low biomass equilibrium is not stable.

46. Biological Mechanics Rate The low biomass equilibrium is not stable Fishery stock growth rate F(X) H Fishery Stock X 0 X1

47. Introduction to Bioeconomics Basic Principles: Assume that the fishing industry is competitive, and fishermen take ex-vessel price as well as input prices (e.g., fuel, bait, labor cost) as fixed parameters. In other words, individual fishers are too small to control price, and cannot form a cartel (like OPEC).

48. What Determines Harvest Rate? What factors would determine how many tons of fish per day will be harvested from a fishery? Total effort E (number of vessels, gear, deckhands, etc). Stock of fish X available to be caught. The harvest function H(t) defines fishing industry output at time “t”. It is a production function : H(t) = G[E(t), X(t)] E(t) is effort, and defines the quantity of inputs (e.g., labor, capital, bait, fuel) applied to the task of fishing at time “t”.

49. Introduction to Bioeconomics Basic Principles: assume that there is diminishing marginal productivity to effort, which means that each unit of additional fishing effort (e.g., a day of fishing) results in smaller and smaller landings of fish. Effort can be measured in units that aggregate the inputs into “vessel-hours”, or “person-hours per vessel”, which are indices of inputs applied to fishing. The other factor affecting harvest at time “t” is the existing stock of fish X(t). Note that effort E(t) and stock X(t) interact. For example, the marginal productivity of effort is higher when X is larger. (Why?)

50. Harvest Function Harvest Rate If the stock X is larger, then for given (fixed) amount of effort E, the harvest rate will be larger. Why? (More nos. added with a larger base) H = G(E,X) }H(X1) }H(X0) Fishery Stock X X0 0 X1