Assume that two companies (C and D) are duopolists that produce identical products. Demand for the products is given by the following linear demand function:

P = 600 – Q_{C} – Q_{D}

where Q_{C} and Q_{D} are the quantities sold by the respective firms and P is the selling price. Total cost functions for the two companies are

TC_{C} = 25000 + 100Q_{C}

TC_{D} = 20000 + 125Q_{D}

Assume that the firms act independently as in the Cournot model (i.e., each firm assumes that the other firm’s output will not change).

a. Determine the long-run equilibrium output and selling price for each firm.

b. Determine the total profits for each firm at the equilibrium output found in Part (a).