Suppose instead that the firms in Problem 9 (photo) 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)Q2] -(4/3)Q1] and P2 = [150 - (2/3)Q1]-(4/3)Q2. 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 (Problem 9). Provide an intuitive explanation for why price competition is more intense (i.e., leads to lower equilibrium profits).
Suppose instead that the firms in Problem 9 (photo) 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)Q2] -(4/3)Q1] and P2 = [150 - (2/3)Q1]-(4/3)Q2. 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’
c. Compare the firms’ profits under quantity competition and
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In Problem 9, suppose that firm 2 acts as a
in advance to setting its price once and for all. In turn, firm 1 will react
to firm 2’s price, according to the profit-maximizing response found
earlier, P1 =52.5+0.25P2. In committing to a price, firm 2 is contemplating
either a price increase to P2 = $73 or a price cut to P2= $67. Which
price constitutes firm 2’s optimal commitment strategy? Justify your
answer and explain why it makes sense.
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