FISHERY BULLETIN: VOL. 73, NO. 1 



is just equal to the value of the resultant decrease 

 in the production of M. 



As a sidelight it is interesting to note that if one 

 country unilaterally adopts a local optimum regu- 

 lation policy given the level of effort in the other 

 country, at the new equilibrium it will be using 

 less effort and in most cases the other country v^ll 

 react to this by increasing their level of effort. 

 Therefore, while the decrease in effort will in- 

 crease its level of welfare (it vn\l move from point 

 B to point D in Figure 1), the increase in effort by 

 the other country will shift the PP curve toward 

 the origin, and this vdll reduce the gains. It is even 

 possible that the shift of the PP curve could be 

 large enough that at the new equilibrium the 

 country actually loses welfare. 



This has interesting implications for cases 

 where international cooperation in fisheries man- 

 agement does not exist. National regulation 

 policies must be derived taking into account the 

 reaction of other countries to specific actions. Each 

 country wdll have to know how the other will react 

 to a change in its level of effort. Taking this into 

 account, it should only reduce its own effort (i.e. 

 transfer resources from producing effort into the 

 production of M) as long as the resultant increase 

 in welfare is greater than the decline due to any 

 possible increase in foreign fishing.^ If these reac- 

 tions are not known, the determination of the 

 proper regulation program will require some sort 

 of game theory approach. 



In conclusion it should be pointed out that sim- 

 ply because it is possible to list the conditions that 

 are necessary for a certain type of equilibrium to 

 exist does not mean that it will in fact exist. As 

 Smith (1969) has pointed out, a fishery will reach a 

 bionomic equilibrium only if certain relationships 

 exist between the growth rate of the fish stock and 

 the rate at which effort enters and leaves the 



*In formal mathematical terms the country must maximize 

 welfare subject to its production constraint knowing that the 

 equilibrium level of effort in the other country is a function of its 

 own effort. The proper Lagrangian for country X and its first 

 order conditions are: 



The first order condition with respect to Ex takes into account 

 the total effect on the amount offish caught by a change in effort. 

 There is the direct change in catch and the indirect effect caused 

 by a change in the level of effort in country Y. 



fishery (either because of market forces or reg- 

 ulatory decree). As pointed out earlier, however, 

 the present analysis is static and will ignore these 

 complications. 



Ill 



It will prove useful to view the problem from a 

 different angle. There are two countries each with 

 its own productive capacity and preference func- 

 tion, and between them they share an open-access 

 fishery. Given this information, it is possible to 

 construct a welfare possibility curve for the two 

 countries (Figure 3). Any point on the curve is the 

 mgiximum amount of welfare that can be obtained 

 for one country at the level of welfare specified for 

 the other country given the productive capacities 

 of both countries and the sustained yield curve of 

 the fishery. At any point on the curve. Condition 

 (14) holds. Therefore, at each point there is an 

 international MEY from the fishery since in all 

 cases the value of the last fish caught vdll be worth 

 its opportunity cost. As is well known, there is no 

 way of choosing one point on the curve from 

 another. 



To digress a moment, if there were no open- 

 access resources or other market imperfections, 

 the two countries through market-directed pro- 

 duction and trade will end up at a point on that 

 possibility curve. If they each operated indepen- 

 dently, they could obtain a certain amount of wel- 

 fare, say the amounts represented by point A. 

 Under free market conditions, each would be 

 motivated to change its output combination and 

 then trade such that both would be better off at a 

 point such as B. Point B is not inherently superior 

 to any other point on the curve. It is merely the 

 point where given the productive capacities and 

 the preferences of the two countries, they will op- 

 erate under the conditions of a free international 

 market. At that point no country can be made 

 better off v^thout making the other one worse off. 

 If for some reason there was a redistribution of 

 productive capacity, the final equilibrium would 

 still be on the curve but at a different point than B. 



Now to turn back to the case of the open-access 

 fishery, if neither country exploits the fishery and 

 they do not engage in trade, then operating inde- 

 pendently, each would be able to obtain a certain 

 amount of welfare. Again let this point be rep- 

 resented by A in Figure 3. If free trade is intro- 

 duced and if both countries begin to exploit the 

 fishery taking into account the effect of their effort 



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