ENTRY AND EXIT OF LABOR AND CAPITAL IN A FISHERY

ABSTRACT. Exit and entry of fishermen, as well as vessels, is modeled explicitly. If the speed of exit and entry of fishermen is less than instantaneous the wage rate varies with the fortunes of the fishing firms and affects the endogenous labor supply creating a second transmission mechanism from profits to effort. There are realistic cases where this mechanism has important effects on the stability of the dynamic system and on the effects of taxes (subsisdies) on the size of the fish stock. If labor supply depends negatively on the wage rate, the immediate effect of an increase in the tax rate is to increase effort and harvest. This condition makes it also more probable that the dynamic system is unstable. In those cases where the dynamic system is unstable the increase in the tax rate increases overexploitation not only in the short‐term but also in the long‐term.     

Some irreducibility and indecomposability results for truncated binomial polynomials of small degree

In this paper, we show that the truncated binomial polynomials defined by \(P_{n,k}(x)={\sum }_{j=0}^{k} {n \choose j} x^{j}\) are irreducible for each k≤6 and every n≥k+2. Under the same assumption n≥k+2, we also show that the polynomial P _n,k cannot be expressed as a composition P _n,k (x) = g(h(x)) with \(g \in \mathbb {Q}[x]\) of degree at least 2 and a quadratic polynomial \(h \in \mathbb {Q}[x]\). Finally, we show that for k≥2 and m,n≥k+1 the roots of the polynomial P _m,k cannot be obtained from the roots of P _n,k , where m≠n, by a linear map.