22-BioEcon1

22-BioEcon1 - BIOECONOMIC MODEL OF A FISHERY Now we are...

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BIOECONOMIC MODEL OF A FISHERY Now we are going to develop and analyze a model for the economics of fishing. Anderson (1986), on the Recommended Reading list, provides a brief overview of basic economic theory and terminology and covers much of the material shown below. For simplicity we will use the Graham-Schaefer model for the biological dynamics, but any of the surplus-production models could be used instead. Start with the logistic model for latent productivity (natural biomass growth) and examine a fishery at equilibrium. G B ( ) r B 1 B K - = At equilibrium removals by the fishery are just balanced by the latent productivity of the stock. G B ( ) Y B ( ) = q f B = B and f represent equilibrium values. r B 1 B K - q f B = ==> Y f ( ) K q f 1 q r f - = We derived this relationship in an earlier lecture. Biomass, B dB/dt B e Equil. Effort, f Equil. Yield, Y f e You may recall that the growth curve G(B) has slope r at the origin. The equilibrium yield is zero if (q·f) is greater than r. To proceed with our economic analysis we need to transform yield in biomass to yield in money. If, for simplicity, we assume that the price for one unit of fish biomass is constant p, then the long-run equilibrium relationship between the total revenue from the fishery and the size of the fishing fleet f is a parabola, reflecting the shape of the growth curve. TR f ( ) p Y f ( ) = TR f ( ) p K q f 1 q r f - = The TR(f) curve is identical to the Y(f) curve but with a different vertical scale. FW431/531 Copyright 2008 by David B. Sampson BioEcon1 - Page 141
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Total Revenue versus Effort Effort Revenue The average revenue (averaged with respect to fishing effort) is AR f ( ) TR f ( ) f = p K q 1 q r f - = The AR(f) curve represents the gross earnings per unit of effort. The marginal revenue (marginal with respect to fishing effort) is Effort Revenue per Unit Effort MR f ( ) f TR f ( ) d d = MR f ( ) p K q 1 2 q r f - = The maximum total revenue occurs where the marginal revenue is zero (where the slope of TR(f) is zero). If the marginal revenue is negative, it means that adding another unit (here, a unit of effort) reduces the total revenue. Now we will add costs to the model. Assume that the fishing fleet consists of f identical vessels and that each one incurs costs c to operate per unit time period. The total cost of maintaining and operating the fleet is TC c f = . FW431/531 Copyright 2008 by David B. Sampson BioEcon1 - Page 142
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Effort f oae The average cost is AC TC f ( ) f = c = . And the
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22-BioEcon1 - BIOECONOMIC MODEL OF A FISHERY Now we are...

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