Summary 387b. Explain why a lower price by its competitor should cause the firm to
lower its own price.
c. In equilibrium, the firms set identical prices: P 1 P 2. Find the firms’
equilibrium prices, quantities, and profits.- 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 P 1 [150 (2/3)Q 2 ]
(4/3)Q 1 and P 2 [150 (2/3)Q 1 ] (4/3)Q 2. In words, increases in
the competitor’s output lowers the intercept of the firm’s demand
curve.
a. Set MR 1 MC to confirm that firm 1’s optimal quantity depends on
Q 2 according to Q 1 45 .25Q 2. Explain why an increase in one
firm’s output tends to deter production by the other.
b. In equilibrium, the firms set identical quantities: Q 1 Q 2. 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 four firms engage in price competition in a Bertrand setting
where the lowest-price firm will capture the entire market. The firms
differ with respect to their costs. Firm A’s marginal cost per unit is $8,
firm B’s is $7, firm C’s is $9, and firm D’s is $7.50.
a. Which firm will serve the market? What price (approximately) will it
charge?
b. Would your answer change if firms A and B had somewhat greater
fixed costs of production than firms C and D? - In Problem 9, suppose that firm 2 acts as a price leader and can commit
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, P 1 52.5 .25P 2. In committing to a price, firm 2 is contemplat-
ing either a price increase to P 2 $73 or a price cut to P 2 $67. Which
price constitutes firm 2’s optimal commitment strategy? Justify your
answer and explain whyit makes sense. - Firm Z faces the price equation P 50 A.5Q, and the cost function
C 20Q A, where A denotes advertising spending.
a. Other things (price) held constant, does an increase in advertising
spending lead to greater sales? Does advertising spending represent a
fixed cost or a variable cost?
b. Find the firm’s profit-maximizing quantity as a function of A. (Hint:
Treating A as fixed, we have MR 50 A.52Q.) Do the same for
the firm’s price. Explain these results.
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