The oil industry in Utopia is a duopoly. Both firms draw oil from a single (and practically inexhaustible) pool. Oil can be sold on the world market at a stable price of $10 per barrel. The cost of operating a well for one year is $1000. Total output per year (Q) of the oil field is a function of the number of wells operating in the field: Q = 500*N - N^2, where N = N1 + N2 is the sum of the wells operated by firm 1 (N1) and firm 2 (N2), respectively. The output per well is given by: q = Q/N = 500 - N.
a) What is the total number of wells that maximizes the sum of the profits of both firms?
b) Suppose now that the two firms behave non - cooperatively. Solve for the Nash equilibrium of the game between the two firms. Is the total number of wells in equilibrium efficient? Why or why not?