ANDERSON: OPTIMUM ECONOMIC YIELD 



Note however, that in country X, average catch 

 (F^ lE^ ) is a function of both Ex and Ey . Therefore 

 an equilibrium in country X can be reached only 

 for a given level o^Ey, (i.e. for a given PP curve). 

 Similarly an equilibrium in country Y is possible 

 only for a given level of £'y . Therefore an interna- 

 tional equilibrium is possible only at that 

 combination(s) of E^ and Ey where Equations 

 (11a) and (lib) both hold simultaneously. 



If free international trade between these coun- 

 tries is possible, the price ratios in both countries 

 will be equalized, and so at the equilibrium, the 



marginal rates of substitution^ — ijwill also be 



equal. Therefore the following condition will hold: 



m Uo 



^xl^x 



Uf Uj dM^ldEx 



dMv/dE. 



(12) 



Graphically the international trade case can be 

 interpreted as follows. For a given level of E 

 produced in the other country, each country will 

 produce at that point on the PP curve where the 



trade price ratio is equal to ^ '^ . It will then 



dM/dE 



trade along the price ratio line until welfare is 

 maximized. Consider a country that would oper- 

 ate under autarky at point B in Figure 1. Under 

 our assumptions the location of the PP curve is 



related to the amount of E being produced in the 



p 

 other country. If trade opens up with a lower _M , 



the production point will move to A, but the con- 

 sumption point will be at C because of imports of 

 M and exports of F. From this it can be concluded 

 that for each level of E produced in the other 



p 



country, a decrease in -^, i.e. a relative increase 



"f 

 in Pp, will increase the amount of E produced 

 locally. 



p 

 As a sidelight notice that the decrease in -^ 



actually decreased the welfare of the fish export- 

 ing country described in Figure 1. Trade allowed 

 for a further misallocation of resources due to an 

 expanding market for fish to such an extent that 

 welfare fell. Of course, if the price line through A 

 intersected the indifference curve through B, then 

 welfare would have been increased in spite of the 

 harmful effects. To be precise it should be noted 



that in the general equilibrium analysis, the 

 amount of E produced by the other country will 

 fall in most cases which will shift the PP curve out 

 and may cause welfare to increase enough to over- 

 come the initial loss. On the other hand, increases 



p 

 in p^ brought about by trade will improve the 



F 



allocation of resources and always increase wel- 

 fare initially; however, the increase in E in the 

 other country will have the opposite effect on wel- 

 fare. So whether the country exports or imports 

 fish, changes in the terms of trade may decrease 

 welfare depending upon the direction and mag- 

 nitudes of the changes caused by these two factors. 

 Equation (7) above states the condition for the 

 maximization of social welfare (i.e. MEY) in the 

 one country case. With free international trade, if 

 both countries attempt to maximize welfare given 

 the level of effort used in the other country, the 

 condition for an international equilibrium is: 



U2 _ Ui _ dF^/dEx _ bFy/bEy 



jjx jjY dMxIdEx dMyldEy 



The last two terms can be simplified to 



9Fv 



bMx 



(13) 



and 



respectively. These will be recognized as the 



■dMy 



slopes of the PP curves of the two countries. What 

 this condition states is that for a local MEY, the 

 marginal rate of substitution between M andF in 

 each country must equal each other and they must 

 also equal the internal marginal rate of transfor- 

 mation between M and F given the level of effort 

 in the other country. In terms of Figure 1, each 

 country will be operating at a point such as D, 

 where the slope of the social indifference curve is 

 equal to the slope of the existing PP curve. Notice 



that in equation (13), -^rr^ and -r^ are both par- 



A Y 



tially determined by the level of effort in the other 

 country, so that here again the equilibrium com- 

 bination of Ex and Ey must be simultaneously 

 determined. 



One main purpose of this paper is to describe the 

 necessary condition for an international MEY. 

 It is important to note at this time that they are 

 different from Equation (13), the conditions of 

 local ME Y's given the level of effort in the other 

 country. Since the level of effort in each country 

 affects the PP curve, and hence potential welfare, 

 in both countries, the maximizing conditions 



55 



