Question

An Oyster Fishery in the San Francisco Bay has population growth given by the logistic function F(X) rX(1-X/k), where X is the biomass of the fishery, r is the intrinsic growth rate and k is the carrying capacity of this fishery. The harvest function(Ht) is given by a simple linear equation Ht = E*X, the total cost function (TC) is given by TC cE, and the total revenue function (TR) is given by TR- p*Ht, where E is the level of effort, c is the unit cost of effort, and p is the price of oyster a) At the bionomic equilibrium Ht F(X), find the stock (X) in terms of effort (E), or X(E). b) Use X(E) to find the Harvest function in terms of E, or H(E) d) What is the level of Effort (E) in the equilibrium under Open Access regime, EOA? (the result should be in terms of r, k,c and p) d) What is the level of Effort (E) if this fishery was privately owned, EPP? (the result should be in terms of r, k, c and p)