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Economics of Renewable Natural Resources

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Bioeconomics of Marine Fisheries

Ashir Mehta

- Source : The Economics of Marine Capture Fisheries, Steven C. Hackett, Professor of
Economics, Humboldt State University

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.

- 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.

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.

Rate of Growth

.

10

Number of Adult Fish

0

2

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

Rate of Growth

.

60

.

10

Number of Adult Fish

0

2

12

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

Rate of Growth

.

100

.

60

.

10

Number of Adult Fish

0

50

2

12

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

Rate of Growth

.

145

.

100

.

60

.

10

Number of Adult Fish

0

50

126

2

12

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

Rate of Growth

.

145

.

100

.

.

60

.

56

10

Number of Adult Fish

0

50

126

224

2

12

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.

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

- 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

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.

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

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.

Rate

Harvest rate H

Fishery stock growth rate F(X)

Fishery Stock X

k

0

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

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

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

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

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

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

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

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

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

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

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).

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

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.

Rate

End here

Hmsy

Start here

Stock Dynamic A

Fishery Stock X

k

0

Xmsy

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.

Rate

Hmsy

Start here

Stock Dynamic B

End here

Fishery Stock X

k

0

Xmsy

Basic Principles:

C. For harvest rates H < Hmsy there are

usually two biomass equilibria – “low

biomass” and “high biomass”.

Rate

Fishery stock growth rate F(X)

H

Fishery Stock X

0

Low biomass equilibrium X1

High biomass equilibrium X2

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.

Rate

End here

Start here

H

Fishery Stock X

Xhigh

k

0

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.

Rate

Net growth rate F(X) - H

F(X)

H

Start here

End here

Fishery Stock X

Xhigh

k

0

Basic Principles: H < Hmsy

Thus the high biomass equilibrium is sustainable and is locally stable (it holds “locally” for X somewhat larger or smaller).

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

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.

Rate

The low biomass equilibrium is not stable

Fishery stock growth rate F(X)

H

Fishery Stock X

0

X1

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).

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”.

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?)

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

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 zeroF(X) – H(t) = 0 thus, when F(X) = H(t)

Rate

Steady-state equilibrium harvest occurs where harvest rate H = biomass growth rate F(X).

H

F(X*) = H

F(X)

Fishery Stock X

0

X*

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.

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

0

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.

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.

$

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

0

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

0

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.

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.

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

0

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*

0

Rate (H)

TC’ (c*Eopen) TC (c*Esocial)

MSY

H0max. profit zero profit

H1 Eopen

Esocial

TR(P*H)

300 450 500 700 900stock (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)

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.

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.

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

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.

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.

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.

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.

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?

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.