(lbs. per Unit Time) 



Fi^re 5. — Comparison of equilibria: competitive output lower 

 than regulated output. (If, with demand as given, output 

 is restricted to MSY, the welfare loss is area HJKL plus 

 the shaded area above the demand curve and to the right 



of LRMS curve.) 



use. In Figures 4 and 5, a rent loss (PiAGCi) 

 is also included. In Figure 4, the entire loss 

 consists of rent. That is, output under decentral- 

 ization and optimal regulation are identical. 

 However, that output would be produced with 

 a much larger stock of fish, and hence lower 

 costs, under optimal regulation than under a 

 regime of decentralization. Thus, all the extra 

 units of effort used to produce output X„ are 

 "wasted," and could better have been used in 

 other industires. 



A MEASUREMENT MODEL 



The derivation of marginal congestion and 

 growth costs can be expressed mathematically. 

 This will permit estimation of the production 

 function, once specific growth and catch func- 

 tions are determined. With the addition of 

 costs and demand, estimation of the welfare 

 losses discussed above may be achieved. 



Summarizing all inputs under the umbrella 

 term "effort" (£■), catch (X) is a function of 

 effort and the stock of fish ( W) : 



(1) X = f(E. W). 



Effort, catch, and stock can all be expressed in 

 terms of the long run equilibrium catch, A', 

 which will give us an expression in terms of 

 long run equilibrium catch alone: 



(2) E{X) = g{X, W(X)), 



where E(X) is the effort associated with a long 

 i-un equilibrium catch of A', and W(X) is the 

 stock of fish consistent with a sustainable catch 

 of X — i.e., one such that dWIdt = X. Since 

 cost is a function of effort, we have, for long 

 run equilibrium, 



(3) C = C(X, W(X)). 



From (3), we can obtain marginal congestion 

 cost, marginal growth cost, and long run 

 marginal cost: 



(4) MCC = dc/dx = Cx 



(5) MGC = 'dc/dw ' ^ "^ Cw ~- 



(6) LRMC = MCC + MGC = Cx+ Cw ■ 



dw 

 dx 



69 



