Optimal Capital Accumulation in a Fishery: A Nonlinear Irreversible Investment Model

A nonlinear two-state variable, two-control variable model of a fishery with irreversible investment and harvest capacity constraints is examined. The model relaxes assumptions of linearity in investment costs and variable harvest profits in an earlier model by C. W. Clark, F. H. Clarke, and G. R. Munro (Econometrica, 47, 25-47, 1979. In both the linear and nonlinear models, the optimal capital accumulation paths in new fisheries is characterized by a period in which the physical capital stock level exceeds its long-run sustainable equilibrium. However, unlike the linear model, periods of positive net (but declining gross) investment are optimal in the nonlinear model. This accords with observed capital accumulation paths from a number of fisheries. The paper also finds different effects in optimal harvest policy depending upon whether the linearity appears in the variable profits function or the investment cost function.