Question: Suppose that in the absence of human intervention the stock of tuna (z) would change according to the following equation: dz/dt = 10z - 0.02z2. Furthermore, suppose E units of fishing effort will produce a harvest of tuna (x) given by x = 0.02zE. Finally, suppose the cost of E units of effort is $4E, where $4 is the wage rate, and that the price of tuna is constant at $1.5 dollar per unit of x.
A. Find the profit-maximizing sustainable equilibrium for this model when the tuna are not common property (that is, when the level of effort can be controlled). Solve for the levels of Z, E, x and profit.