Reference no: EM132410788

Consider a resource stock that grows according to dx/dt = rx(1-x/k) where r is called the intrinsic growth rate of the stock and k is the carrying capacity. Harvest is given by h = ex where e is the fishing effort and x is the resource stock. The net growth of the fish stock is its growth minus the harvest.

• Derive the yield or harvest - effort relationship using the steady state condition that the net growth of the resource stock is zero.
• What is the steady state open access harvesting effort given a unit cost of effort c and a price of fish equal to p?
• Consider the marginal yield (harvest) - effort relationship dh/de = k (1- 2e/r). What is the efficient level of effort (the effort that maximizes the steady state profits) given a unit cost of effort c and a price of fish equal to p?
• Which effort level is larger: the effort level that maximizes profits or the open access effort level? How much larger is one than the other?
• Which fish stock is larger, the open access fish stock or the fish stock that maximizes economic profits.