Question 1:
Assume an industry with two firms facing an inverse market demand of P = 100 - Q. The product is homogeneous, and each firm has a cost function of 600 + 10q + 0.25q2. Assume firms agree to equally share the market.
a. Derive each firm's demand curve.
b. Find each firm's preferred price when it faces the demand curve in part a. Now assume that firm 1's cost function is instead 25q + 0.5q2 while firm 2's is as before.
c. Find each firm's preferred price when it faces the demand curve in part a.
d. Compute each firm's profit when firm 1's preferred price is chosen. Do the same for firm 2's preferred price. Which price do you think firms would be more likely to agree upon? Why? e. Show that neither price maximizes joint profits.
f. Find the price that maximizes joint profits. Hint: It is where marginal revenue equals both firms' marginal cost.
g. Would firm 1 find the solution in part f attractive? If not, would a side payment from firm 2 to firm 1 of $500 make it attractive?
Question 2:
What is the law toward parallel business behavior? Assume, for example, that three firms charge identical prices for a product and it is agreed by all observers that the price is unusually high compared to cost. Would this alone constitute a Sherman Act offense? Cite a relevant case to support your answer.