FISHERY BULLETIN: VOL. 73, NO. 1 



G {E, M) = 0. 



(1) 



Assume that it is quasi-concave so that there will 

 be a concave transformation curve between E and 

 M. Let the sustained yield curve of the fish stock 

 (i.e. the production function) be expressed as:^ 



F{E) ^ aE - bE^ 



(2) 



Using this equation assumes that the fish stock 



vidll always be in a biologic equilibrium. F will 



increase until E is equal to -^ and vdll thereafter 



Zo 



decrease. F will be zero whenE = and whenE = 



^. As long as the maximum amount of £ possible is 

 greater than ^ but less than-?-, then the PP curve 



for M and F will be similar to the solid one in 

 Figure 1. (Ignore for the moment the dotted one.) 

 The slope of the curve is: 



dF dF dE 



G, 



dM dE m =-^-- 2^^) ^ 



(3) 



where Gj is the derivative of G with respect to its 

 first argument, etc. Fish output will be at a max- 

 imum when E equals ^, not when all of the re- 

 sources are used in the production of E. As long 

 as the marginal productivity of E in fishing is 

 negative, the PP curve will have a positive slope. 

 Switching resources out of effort and into manu- 

 facturing will actually increase both F and M. 

 Where E's marginal productivity in F is positive, 

 the PP curve will have its normal negative slope. 



Because both -^ and (a - 2bE) increase as M 



increases (i.e. as E decreases), the curve wall be 

 concave to the origin. Also assume that there is 

 a linearly homogeneous social utility function 

 of the form 



U = U (F, M). 



(4) 



As pointed out in the literature cited above (see 

 especially Turvey 1964 and Scott and Southey 

 1970), as long as no one regulates entry into the 

 fishing industry, profit maximizing individuals 

 will continue to produce or buy E as long as the 



'The sustained yield curve is the relationship between the 

 amount of effort expended and the amount of fish that will be 

 captured period after period. The particular expression here 

 follows Schaefer (1957). Although other expressions have been 

 discussed recently (see the papers by Southey and Gould cited 

 above), Expression ( 1) is descriptive enough to capture the essen- 

 tials of the argument. 



OM 



Figure 1. — The solid concave curve is the production possibility 

 curve and the set of convex curves are the community indiffer- 

 ence curves. Open-access equilibrium will occur at B, maximum 

 sustainable yield at H, and maximum economic yield at D. In the 

 two country model, a decrease in fishing effort in the other 

 country will shift the production possibility curve to the dotted 

 one. 



value of the average catch per unit of £^ is greater 

 than the price of effort. The effects of this are as 

 follows. If £■ and M are produced in pure competi- 



tion,then- ^ = % 

 t^E dM 



Equilibrium will occur in 



the open-access fishery when P^-^ equals P^ ; that 



is when the average return to effort equals its cost. 

 [Smith (1969) has shown that vmder certain cir- 

 cumstances, the fishery wdll not reach an equilib- 

 rium. For the moment let us ignore this possibility 

 although its effects will be discussed briefly 

 below.] It can be shown therefore that with an 

 open-access fishery and pure competition in the 

 production of E and M, producers will arrange 

 their production such that for any given price ratio 

 the following condition will hold: 



M 



FIE 

 dMIdE 



(5) 



Maximum consumer welfare occurs where the 

 slope of the social indifference curve is equal to the 

 price ratio. That is where 





M 



Therefore a general equilibrium in the production 

 and the consumption sectors of the economy will 

 occur when 



52 



