must take this into account. With free inter- 

 national trade, these conditions are:^ 





(14) 



dEx 



dE, 



*This condition can be derived in the following manner. With 

 international trade, the community welfare fiinctions become 



U 



X _ 



U^ [F;f (£;f , £y ) + F^ , Afx + Mf] and 



U^ =U^' [Fy(Ey,Ey)-Fj,My -Mt] 



where Fj and Mj are the amounts of F and M respectively that 

 are traded. If we wish to maximize the welfare of country X 

 subject to a specified amount in country Y and to the productive 

 capacities, we get the following Lagrangian function. 



L =r/^ + X,([/^ - t/^) + KiG^iExMx) +X3G^(£y,My). 



The first order conditions for a maximum (using the normal 

 notation for derivatives) are: 



(a) 3L _ ,rX dFx . -v jjY ^Fy . /jX _ 



(b) 



(0 



a^y- =U^+ XaG^ - 



dL 



3Fv 



= ttX 



U 



dFx 



1 3Fv 



^if^rll; + Xgcr =0 



(d) fiT- = A,[/r + A.G,^ =0 



dsr^ 



(e) 



(f) 



dL 



dL 



dL 

 dFr 



^•^2 



■3'-'2 



f/f + XiU\ = 



U^ + XiU2 = 0. 



Note that Conditions (a) and (c) show that a change in the level of 

 effort in one country has a direct effect on the level of welfare on 

 the other. For this reason the Pareto conditions for an interna- 

 tional optimum are different than in the standard case. Solving 

 (e) for X 1 substituting that expression in (a) and then dividing (b) 

 by (a) yields 



Ul 



dFy 



dFy 



Gf 



Similarly substituting the value of Xi into (c) and (d) and then 

 dividing (d) by (c) yields 



Ul 



u^ 



dFy ^ dF^ 



dEy hEy 



G\ 



[/2 ul 



Since from (e) and (f) it can be shown that ^ = "" — , and by 



G ^ dM G ^ dM ^ ' ^ ' 



definition = ,„^ and = je^ — , it can be shown that 



gI °*'X Gi °^'^ 



Condition (12) holds. 



FISHERY BULLETIN: VOL. 73, NO. 1 



Alternatively this condition can be written as: 



f/r 



Ul 



(-) 

 dFx 



+ 



( + ) 



dFy 



(-) 

 bFy 



+ 



( + ) 



dFx 



Ul U^ dM^ dMx ^^Y ^My 



(14') 



Expression (14) is useful for comparisons with the 

 open-access free market international equilib- 

 rium conditions in (12) and with the local MEY 

 condition in (13), while Expression (14') is useful 

 for tying the analysis to the PP curve. 



In words these conditions state that the margin- 

 al rate of substitution for M and F and a special 

 type of marginal rate of transformation (MRT) in 

 both countries must equal each other. The margin- 

 al rate of transformation is special in that it con- 

 siders the effect on fish production in both coun- 

 tries, of a change in manufacturing in only one. 

 To be more precise a "socially optimal" interna- 

 tional policy should guarantee that neither coun- 

 try expand their fishing effort unless the value of 

 the extra yield, regardless of who catches it, is 

 equal to the value of the extra M that must be fore- 

 gone. That is country X should compare the oppor- 

 tunity value of producing effort with its effect on 



local catch ( J^ ) and with its effect on country 

 Y's catch (—^) . The same restriction must be 



placed on country Y's fishing industry also. 



It is important to stress at this point that these 

 international MEY conditions were derived by 

 maximizing the level of welfare in one country 

 while specifying a certain level in the other. That 

 is, an initial distribution of the fishery is essential 

 before the maximizing conditions for an interna- 

 tional MEY can be utilized. This same condition 

 will hold at many combinations of ^^^ ^^id Ey de- 

 pending upon how the wealth of fishery is distrib- 

 uted. This is one of the major differences between 

 a national MEY and an international MEY. The 

 importance of the beginning distribution will be 

 discussed in greater detail in Section EI. 



It can be shown from the equations for Fx and 



9^x , ^Fy , dFy , dFx , ,, ^ 



equals ^r^ + W^ and that 



Fy that ^^ 



+ 



X 



dEx 



dE^ 



dE, 



F^IE^ equals FylEy. Therefore in both the open- 

 access equilibrium (Condition 12) and at any true 

 international optimum point (Condition 14), 

 dM^ldEx must equal dMy /dEy. That is, the real 

 cost of producing fishing effort will be the same in 

 both countries. The difference is that only in the 



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