FISHERY BULLETIN: VOL. 73, NO. 1 



long as there is no regulation of fishing effort. This 

 will be because as long as the average returns to 

 fishing are greater than the price of effort, private 

 decision makers will continue to demand E. Also 

 since E andF are directly related, there is always 

 a direct relationship between Pg and Pp . 



II 



Now to turn to the case of more than one country 

 exploiting the same fish stock, analysis of this is 

 made very difficult by a variety of intriguing prob- 

 lems. For instance, technology may be so different 

 in the two countries that it is very hard to find a 

 common measure of fishing effort, tastes may be 

 such that one country prefers small fish while the 

 other prefers large ones and yet the sustained 

 yield curve is dependent on the size of catch, each 

 country may be using other criteria for harvesting 

 the fish; for example, one may look at it as a place 

 to put unemployed labor, or as a source of earning 

 foreign exchange. For purposes of discussion these 

 intricacies will not be considered. 



Assume that two countries, country X and coun- 

 try Y, both with specified production capacities 

 (G^ (Ex, M^) = and G^ {Ey, My) = 0) and lin- 

 early homogeneous community welfare functions 

 (U^ = U^ (Fx, Mx) and U^ = U^ (Fy, My) ,are 

 the exclusive users of a fish stock with the sus- 

 tainable yield curve (2) above. Since a unit of 

 effort in country X, (Ex), is identical to one in Y, 

 (Ey), the sustained yield curve can be expressed 

 as: 



F(Ey,Ex) - aiEx + Ey) - h{Ex + Eyf- 



As before the total catch from the fishery will 



reach a maximum when E^ plus Ey is equal to hx 



and will fall to zero if total effort gets as large 



a 

 asr- 

 o 



The catch of one country v^ll be in proportion to 

 its effort in relation to total effort, therefore: 



[• 



F^ (E^ ,E^) 



E, 



Ex + E-\ 



aiEx +Ey) - biEx + Ey) 

 This can be simplified to: 



F^ wdll reach a maximum when Ex equals 

 and will fall to zero if it gets as large as 



a 



bE, 



26 

 a -bE, 



The equation for Fy is analogous. 



The amount of fish that country X can catch 

 using a specified amount ofE^ depends upon how 

 much Ey country Y is producing and using. Simi- 

 larly the catch of country Y depends upon the 

 amount of Ex used by country X. Therefore, the 

 shape and position of each country's PP curve for F 

 and M is dependent upon the amount of E the 

 other country uses. Let the two PP curves in Fig- 

 ure 1 be two possible ones for country X. The solid 

 one is for the larger level of Ey Note that the 

 lower curve gets further away from the higher one 



P\E 

 as My decreases. This is because -— ^ , the vertical 



^ dEy 



displacement of the curve due to a change in effort 

 in country Y, is equal to -bE^. Therefore, the 

 higher the level of Ex , that is the lower the level of 

 M^, the greater will be the vertical displacement. 

 The maximum amount of F-^ will be at a higher 

 amount of Mx^ (a lower amount of F^, ) because F^ 



is a maximum when Ex is equal to — ^-r — -. 



2.0 



Using this two country model let us consider the 

 implications of three types of exploitation: 1) open 

 access in both countries, 2) local MEY in both 

 countries, and 3) a true international MEY. 



From the above description, it can be seen that 

 the shape and position of the PP curve for M andF 

 in each country is dependent upon the level of 

 effort used in the other. Therefore the open-access 

 free market equilibrium in each country will de- 

 pend upon the level of effort used in the other. The 

 mathematical condition for an international 

 open-access equilibrium is the following set of 

 simultaneous equations: 



X 



Country X 





ul 



Country Y — ^ = 



dMy/dEy 



F ,E 



Yl Y 



dMy/dEy 



(11a) 



(lib) 



aEx — bEx 



bE^Ey 



(10) 



This simply states that the open-access condition 

 for each country (see Equation (6)) must hold in 

 both simultaneously. In terms of Figure 1, each 

 country must be operating at a point such as B. 



54 



