ANDERSON: OPTIMUM ECONOMIC YIELD 



follows then that any distribution of property 

 rights to the fishery represented by a point inside 

 the area delineated by PRIxi will lead to an im- 

 provement in welfare in country X over that 

 which is obtained at the international open-access 

 equilibrium. Note that because of the shape of the 

 curve, welfare in country X can actually be in- 

 creased in some cases where its allowable level of 

 effort decreases while that for the other country 

 goes up. This is possible because at the open-access 

 equilibrium, country X can gain from switching 

 some resources from producing effort to producing 

 the other good and, up to a point, these gains are 

 possible even if country Y increases effort. (Points 

 A, B, C, D, F, and G are analogous to A', B', C, D', 

 F', and G'.) The reader should be aware by now of 

 the similarity between these curves and trade in- 

 difference curves in international trade theory. 

 Before using these curves in the analysis of the 

 problem at hand, however, a few more points are 

 in order. The short line through 1 2 at F is meant to 

 represent the slope of the PP curve if Ex remains 

 constant and Ey decreases so that country X is 

 operating at F. A decrease in PRy will cause the 

 slope of X's PP curve to decrease at every level of 

 Mx-^ As pictured here it has decreased from a 

 positive to a negative. If it decreases such that it is 

 steeper than the social indifference curve at that 

 point, then the PRI curve will look like PRIx4- 

 That is, the PRI curve will not have a negatively 

 sloped segment to the left of the open-access 

 equilibrium amount of effort for country X. This 

 means that reductions in the allowable level of 

 effort in country X, with the amount in country Y 

 held constant, will always result in a reduction in 

 welfare for country X. Along the same line if coun- 



level of effort in country Y onF^ decreases asE^ increases (i.e. 

 dFx 



dKy 



= -bEx). Therefore greater reductions in PRy will be 



necessary to compensate for equal reductions in PRx as the 

 amount of Ex is reduced from the international equilibrium 

 level. For increases in PRx , the greater the increase the smaller 

 is the marginal increeise in fish caught and yet the greater must 

 be the increase in catch in order to keep welfare constant. 

 Therefore greater reductions in PRy will be necessary to 

 compensate for equal increases in PRx as the amount ofE^ is 

 increased from the international equilibrium level. 



'dMZ 



G^ 



= - (a - 2bEx - bEy) 



and so 



\dMx/ _ 



dEv 



91 



Therefore, as Ey decreases, the slope will decrease. 



try X pursues a local maximizing policy (i.e. it 

 operates at point G in Figure 4a), the interna- 

 tional equilibrium will be at point G' in Figure 4b. 

 This means that under no circumstances will 

 country X be better off if it unilaterally decreases 

 its allowable effort and it will always be worse off 

 if country Y increases its level of effort. This is not 

 the case if the international equilibrium is at 

 point A'. 



Figure 5a is similar to Figure 4b except that PRI 

 curves for country Y have been added. PRIyi has 

 the same meaning for country Y as does PRI xi for 

 country X and is constructed in an identical fash- 

 ion. 



Any distribution of property rights represented 

 by a point inside the area delineated by PRIyi 

 would result in an increase in the welfare of coun- 

 try Y. It follows then that any combination that is 

 in the area common to both PRIxi andPiJ/y^ (see 

 hatched area of Figure 5a) will increase the wel- 

 fare of both countries over that achieved by the 

 open-access "law of capture" distribution of the 

 rights to the fishery. Note again that it is possible 

 for both countries to be better off in some cases 

 where the trade involves a reduction in property 

 rights in one country and yet an increase in the 

 other. 



^(EY)^' 



PRv  



'(EY) 



PRIy 



PRI 



XI 



PRX,EX) 



Figure 5. — The area common to the initial property right indif- 

 ference (PRI) curves of both countries represents those distribu- 

 tions of the fishery where both countries will be better off than at 

 the open-access equilibrium. In some special cases, there is no 

 such area (see b). 



61 



