Cournot quantity

Two identical fishermen, Jill and Kevin, fish from the same lake. Since they are only two small producers, they cannot effect the price paid for their fish (P = 100), but they do influence each other’s costs. As the stock is completed, more time and sophisticated equipment is necessary to catch additional fish. We place the following structure on costs: CJ (qJ , Q) = Q ∗ qJ and CK(qK, Q) = Q ∗ qK.

(a) Write down the profit function for each fisherman in terms of qJ and qK only. (b) Derive each fisherman’s best response function. (c) Find the Cournot Equilibrium. (d) What are Kevin and Jill’s profits?