ANDERSON: OPTIMUM ECONOMIC YIELD 



U2 



M 



FIE 



Pj, dMIdE 



(6) 



Conditions for the maximization of social welfare, 

 however, are: 





M 



dFldE ^ dF_ 

 dMIdE " dU 



(7) 



dF 



An expression for — — - is given in (3) and 



dM 



{FIE)l{dMldE) can be expressed as: 



The ratio 



{FIE)l(dMldE) = -ia 

 FIE 



m^ 



(8) 



will increase in absolute size as 



dMIdE 



M increases, and because of the assumption that 

 the maximum E is less than alb, it will always be 

 negative, even when the slope of the PP curve is 

 positive. It can be seen that when they are both 

 negative, this ratio will be larger in absolute size 

 than the slope of the PP curve at that point; i.e. it 

 will have a steeper slope. The small lines on the PP 



FIE 

 dMIdE 



at 



curve in Figure 1 represent the ratio 

 that point. 



In terms of Figure 1, open-access equilibrium 

 will occur at point B where the slope of the indif- 

 ference curve as it intersects the PP curve is equal 



to the ratio of 



FIE 



at that point.^ The social 



dMIdE 



optimum is at point D where the indifference 

 curve is just tangent to the PP curve. The common 

 property or open-access equilibrium will always 

 be to the left of the optimal point; therefore with 

 open access, too many resources will be allocated 

 to F under the market system. It is even possible 

 that the market equilibrium will occur in the posi- 

 tive sloped segment of the PP curve. 



By way of comparing the present analysis with 

 the standard one, point H on Figure 1 is the point 

 of maximum sustained yield for a fishery and 

 point D is the MEY. The latter point has less fish 

 but more manufactured goods than the former 

 (and may even have less fish than the point where 

 the unregulated fishery wall operate). At MEY, 



■•As Scott and Southey (1970) point out, if there are increasing 

 returns to scale and if the social utility function is not linearly 

 homogeneous, it is possible that there may be multiple equilib- 

 ria. I have ignored that complication for purposes of this paper. 



however, no fish is produced unless its value is 

 greater than its opportunity cost. Although MEY 

 in the traditional literature refers to a specified 

 amount of fish production, it assumes that the 

 resources not in fishing are used efficiently in the 

 production of other goods. Describing the model in 

 terms of a PP curve makes this explicit. 



Through proper regulation, the country can 

 move to MEY. This could involve a ceiling on the 

 amount of fishing effort allowed or the granting of 

 property rights to the fishery to certain individu- 

 als. The former has been tried but usually by 

 means of decreasing efficiency rather than by 

 shifting resources to other types of production, and 

 the latter can lead to monopoly or oligopoly unless 

 the property rights are distributed widely or there 

 are other fish stocks that can provide the neces- 

 sary competition. 



If the government only allows a units of effort, 

 where a is less than the open-access amount of 

 effort, and then distributes the rights to this 

 number of units among a large enough group such 

 that there is still pure competition in the market 

 for both effort and fish, these people will be earn- 

 ing a rent per period, R, of PpF(a) - P^a where 

 Fia) is the amount of fish caught by a units of 

 effort. Unless reductions in effort have perverse 

 effects on price, average catch, or cost of effort, this 

 rent will be positive. See Anderson (1973:513). 



The optimal amount of effort is where the total 

 amount of rent is a maximum (Christy and Scott 

 1965:8). By using the standard mathematical pro- 

 cedure it can be shown that the first order condi- 

 tion for 7? to be a maximum is: 



p dF _p 



Under the above assumptions, the open-access 

 problem of the fishery has been solved in a way 

 that keeps pure competition in the production of M 

 and £. Therefore -P^^IP^ is equal to dEldM and so 

 maximization of the rent of the fishery will 

 guarantee that 



M 



dFldE dF 



Pp dMIdE dM ^^^ 



This will mean that the conditions for the maximi- 

 zation of social welfare, expressed in (7) above, 

 will hold. Therefore a policy that maximizes the 

 rent from the fishery also maximizes social wel- 

 fare. 



In summary, a country with exclusive rights to 

 an open-access fishery wall operate inefficiently as 



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