1.Consider a static model of the fishery.Suppose the biological mechanics for the fishery are given by the equation F(X) = 120X - 20X², where X is the biomass.Also suppose the harvesting function for this fishery is H(E,X) = EX, and that the fishery is in perfect competition with the constant price of output p=40 and constant marginal and average costs per unit of effort c=10.

a)Calculate the maximum sustainable yield biomass (X_MSY) and the biological carrying capacity (K).

b)Write down the conditions that define the bionomic open-access equilibrium and derive the associated level of effort and stock.

c)Write down the conditions that define the economically efficient equilibrium (MEY) and derive the associated level of effort and stock.

d)Derive the optimal ad valorem (percentage) tax on output that would be required to get this fishery from the bionomic equilibrium to the socially optimal one.