Suppose that there are two producers of prokrypton-B, a rare mineral capable of incapacitating aliens from distant planets. Governments across the globe are interested in purchasing defensive stores of the rare mineral. The market demand for prokrypton-B is given by P = 200 - 0.2Q, where Q is the collective output of the industry, in tons; q A is the output of Firm A; and q B is the output of Firm B. Assume that each firm produces prokrypton-B at a marginal cost of $10 per ton.
a. Derive each firm's reaction function.
b. Solve for the equilibrium quantity of each firm, as well as industry output.
c. Solve for the market price of prokrypton-B.
d. Solve for the profit earned by each firm.
e. Suppose that a labor dispute drives Firm B's cost to $12 per ton.
i. What happens to the output of each firm as a result?
ii. What happens to the market price of prokrypton-B?
iii. What happens to the profit of each firm?