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 2

6. Biological Mechanics 6 breeding pairs x 10 = 60 new adults
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 22 12

8. Biological Mechanics 25 breeding pairs x 4 = 100 new adults
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 2 12 50

10. Biological Mechanics 63 breeding pairs x 2.3 = 145 new adults
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 2 12 50
126

12. Biological Mechanics 112 breeding pairs x 0.5 = 56 new adults
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 2 12 50
126
224

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 2 12 50
126
224

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

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

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
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
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
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
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
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
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
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
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
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
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 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
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
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
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

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

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 [
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 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. }H(X1) }H(X0) 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 X1

51. Introduction to Bioeconomics
Basic Principles:
Without harvest activity, recall that the unexploited steady-state biological equilibrium occurs where X = k. Fishery stock growth equals zero.
With human harvest activity, the net stock growth rate equals the stock growth rate minus the harvest rate (F(X) – H(t)).
Thus a steady-state bioeconomic equilibrium occurs when the net stock growth rate equals zero F(X) – H(t) = 0  thus, when F(X) = H(t)

52. Steady-State Equilibrium Harvest
Rate
Steady-state equilibrium harvest occurs where harvest rate H = biomass growth rate F(X). H
F(X*) = H
F(X)
Fishery Stock X X*

53. Introduction to Bioeconomics
Basic Principles:
Note that there is a higher level of effort E that will yield the same harvest rate. This corresponds to the low biomass vs. high biomass equilibria.

54. Steady-State Equilibrium Harvest
Due to low fishery stocks (Xlow), it takes a higher level of effort (E2) to generate the same harvest rate.
Rate
With high fishery stocks (Xhigh), it takes a lower level of effort (E1) to generate the same harvest rate.
H = G(E2,X)
H = G(E1,X)
Fishery Stock X
Xlow
Xhigh

55. Introduction to Bioeconomics
Basic Principles:
Since effort costs money in a fishery (fuel, bait, labor (opportunity) costs), the low biomass equilibrium is bioeconomically inefficient for the fishing industry as a whole. It generates the same harvest rate (i.e., tons per day) as the high biomass equilibrium, but involves higher effort costs.

56. Harvesting Under Open Access
Derivation of the open-access equilibrium
Assume that no private/common/govt. property rights are asserted over the fishery. Thus anyone can fish and catch as much as they want (“open access”).
Assume (for simplicity) that a unit of effort costs “c” dollars, and a unit of harvested fish generates “p” dollars.
Total revenue equals price per ton multiplied by total landings of fish  TR = P x H.
Recall that in equilibrium the harvest rate H equals stock growth rate F(X). Thus the total revenue curve looks like the F(X) curve.

57. Steady-State Equilibrium Effort$
Open access means that equilibrium effort (Ehigh) is found where fishing industry profit = 0, which occurs where total revenue equals total cost.
TC = cE
TR = pH(E)
Effort E
Ehigh

58. Steady-State Equilibrium
Zero profit under open access results in high levels of effort, which makes the harvest curve steeper and pushes the bioeconomic equilibrium fishery stock [found where F(X) = H(t)] below MSY.
Rate
H = G(Ehigh,X)
Fishery Stock X
Xlow
Xmsy

59. Harvesting Under Open Access
Efficiency of the Open Access Equilibrium:
Under open access, equilibrium can only occur when profit is zero (no incentive to enter or exit).
Economic efficiency occurs at the profit-maximizing level of effort where MR = MC. Yet under open access, the equilibrium level of effort is selected where profit equals zero and MC > MR.
Thus the open-access equilibrium always features an inefficiently large amount of effort being deployed in the fishery.

60. Group Optimum Harvest
Group optimum harvest (or “socially optimal” harvest) takes into account the stock effect, and occurs where industry-wide profits are maximized, which occurs where marginal revenue equals marginal cost.

61. Open Access v. Group Optimum Harvest
Open access means that equilibrium effort (E0) is found where fishing industry profit = 0 (TR=TC). Note that the group optimum level of effort (E*) is smaller than E0, generates a higher steady state level of harvest H, and results in maximum profit as indicated below: $ }
TR(H*)
TC = cE
TR(H0)
Maximum Profit
TR = pH(E)
Effort E E* E0

62. Open Access v. Group Optimum Harvest
The group optimum equilibrium results in a stock X* that exceeds that of the open access equilibrium X0 and maximum sustainable yield (Xmsy).
Rate
H = G(E0,X)
H = G(E*,X)
H(X*)
H(X0)
Fishery stock X X0
Xmsy X*

63. TC’ (c*Eopen) TC (c*Esocial) MSY H0 max. profit zero profit H1 Eopen
Rate (H)
TC’ (c*Eopen) TC (c*Esocial)
MSY
H max. profit zero profit
H Eopen
Esocial
TR(P*H)
stock (X)
group/social optimum E = 450 (max. profit) ; open access E = 900 (zero profit)
stock size = 700 (> MSY ; H rate = H0) stock size = 300 (< MSY ; H rate = H1)

64. Extinction
Why is extinction more likely to occur under open access than under group-optimum harvest?
Biologically, a key characteristic of fisheries susceptible to extinction is that there is a threshold population > 0 that must exist in order to sustain the species. If the population falls below this threshold, the population declines to extinction.

65. Extinction
Threshold effects are more likely to occur in fish species with few births per fertile female.
From a marine mammal point of view, this is the case with blue whales.
Economically, extinction can occur under open access when the price of the fish rises sufficiently that the zero-profit level of effort only occurs at the origin.

66. II. Approaches to Fisheries Management
Restricting Access – Territorial Rights – sedentary v/s migratory
Regulating Fishing Practices – make fishing more costly – economically inefficient
TAC – rivalry – no ind. Quotas
ITQs - tradeable

67. Approaches to Fisheries Management (contd……..)
Individual Quotas and Other Alternative Management Systems for Marine Capture Fisheries
A key problem with both open-access fisheries and traditional fishery management tools is that fishermen do not have any property rights to a share of the available fishery stock prior to capture.
Because fishermen do not have a property right to fish until capture, the harvest by one vessel imposes a rule of capture externality on all others by reducing the remaining stock of fish.

68. Individual Quotas and Other Alternative Management Systems for Marine Capture Fisheries
The rule of capture is old common law. It states that withdrawals from a common-property or open-access resource become private property upon “capture”. Ex: Fish in a fishery are government property (public trust resource) until legally landed by a fisherman, at which point they become private property.
When the rule of capture externality is operating, fishermen have an incentive to overcapitalize in vessel, crew, and gear.
The rule of capture externality promotes a race for fish that leads to diminished product quality and increased fishing hazards.

69. Individual Quotas and Other Alternative Management Systems for Marine Capture Fisheries
Individual quotas (IQs) have been implemented in an increasing number of fisheries around the world. IQs assign a share of the TAC to individual fishermen (IFQs), vessels (IVQs), or communities (CFQs). Those who hold quota shares own a share of the TAC. Therefore the fishing season does not end until all quota shares are filled, subject to biological constraints.
By assigning withdrawal rights to a quota share prior to capture, IQs eliminate the rule of capture externality.

70. Individual Quotas and Other Alternative Management Systems for Marine Capture Fisheries
By eliminating the rule of capture externality, IQ’s can reduce or eliminate derby (race for fish) conditions and the incentive for overcapitalization.
Reducing overcapitalization increases the economic efficiency of the fishing industry by reducing the total cost of harvesting a given quantity of fish.

71. Individual Quotas and Other Alternative Management Systems for Marine Capture Fisheries
issues that can make IQs difficult to implement?
Establishing a TAC on the fishery may be difficult.
Must monitor landings to prevent cheating on quota shares.
Quota shares must be allocated to individuals, vessels, or communities, and the initial quota allocation can be contentious. Processors? Crew members? Allocation based on historical landings?

72. Individual Quotas and Other Alternative Management Systems for Marine Capture Fisheries
issues that can make IQs difficult to implement (continued)?
A decision must be made about whether IQs are to be tradable. If IQs are to be tradable, then a determination must be made regarding who is allowed to purchase quota shares, and whether there is to be an upper limit on quota holdings by an individual, vessel, or community.
Some see IQ systems as a giveaway of public resources to private individuals, and so a decision must be made over whether some sort of auction or tax should be used to fund monitoring and enforcement.