Suppose instead that the firms in Problem 9 compete by setting quantities rather than prices. All other facts are the same. It is possible to rewrite the original demand equations as P1 = [150 - (2/3)Q 2] - (4/3)Q1 and P2 = [150 - (2/3)Q1] - (4/3)Q 2. In words, increases in the competitor's output lowers the intercept of the firm's demand curve.
a. Set MR1 = MC to confirm that firm 1's optimal quantity depends on Q2 according to Q1 = 45 - .25Q2. Explain why an increase in one firm's output tends to deter production by the other.
b. In equilibrium, the firms set identical quantities: Q1 = Q2. Find the firms' equilibrium quantities, prices, and profits.
c. Compare the firms' profits under quantity competition and price competition. Provide an intuitive explanation for why price competition is more intense (i.e., leads to lower equilibrium profits).