A General Equilibrium Demand Model for Living Marine Resources: An Application of General Equilibrium and Common Property Resource Theory to the U.S. Seafood Sector

The purpose of this study is to extend the traditional model of common property resouce exploitation to a more general equilibrium frame of reference, and to examine policy implications in the light of the extended analysis. The most pronounced modification consists of the specification of cross partial price derivatives of demand between the major species of seafood consumed in the United States. The estimation procedure integrates both time series and cross-sectional results in deriving all relevant price and income parameters. The time series analysis employs a technique originated by Powell (26), in which a series of linear expenditure functions--based upon the assumption of the existence of a continuously differentiable additive utility function--is estimated. Seafood is treated as a separate commodity in the budget constraint, and an implicit test of the additivity assumption in this context is devised. The method of estimation involves an iterative technique in which prior restrictions on the system give maximuj likelihood estimators and the same estimates as would be obtained using two-stage least squares. The major purpose of the time series component is to provide a forecasting equation for expenditures on all seafood commodities, which takes into account anticipated budget contraints and expenditures on all other commodities. The major parameters that are derived include b F - the expenditure A coefficient for all seafood, and 1, is equal ;to the following: (1) 3y 5. where X is the marginal utility of income, and y is income. Another related purpose of the time series analysis is to provide a control total for the sum of consumer expenditures for individual species. The aggregate seafood expenditure parameter b I" is 'distributed' across species on the basis of cross sectional income coefficients for individual species which are constrained such that their sum is equal to I;F. The major purpose of the cross-sectional component of the study--in addition to the estimation of individual species income coefficients--is to select a set of twenty-eight independently estimated reliable own and cross price derivatives, from which sixty-four price derivatives are obtained (i.e., eight species, 8x8=64 price derivatives). In order to derive A these demand parameters, the time series parameter y is utilized. The estimates follow directly from tenets of utility maximization. This completes the demand as.pect of the study. On the supply side, species are broken down according to proximity to their universal constraints at maximum sustainable yield. Those species which are at or near MSY are classified as constrained species; those *which are not close to MSY or for which artificial techniques of cultivation have been. developed are classified as unconstrained species. Forecasts of consumption are made under the assumption of perfect elasticity of supply for ail species. Then, as a result of forecasting far enough into the future such that market clea'rance• at MSY is a reasonable assumption for the constrained species, quantity adjustments--equal to the difference between quantity consumed under conditions of perfect elasticity and quantity consumed at MSY--are calculated. Given these quantity adjustments, relative price changes -for the constrained species may be obtained. The conclusion reached is that, within a general equilibrium framework, the rate of price increase due to the imposition of supply constraints is considerably dampened. Furthermore, only slight modifications of the market mechanism are needed in order to prevent excessive entry of capital and labor into fisheries which are being *exploited at maximum sustainable yield : In other words, since the rate of entry of excessive inputs is tied to the rate of change in relative prices, a policy such as a quota, when evaluated within a .general equilibrium framework, will yield .an input combination such that the level of redundant capital and labor is negligible.