Suppose the demand for Pepsi-Cola is qp = 50 - 2pp + 1pc. The firm faces a constant marginal cost of m, and pc denotes the price of Coca-Cola. Assuming Bertrand behavior, derive Pepsi-Cola's best-response function and explain how the firm changes price in response to changes in its own marginal cost and changes in Coca-Cola's price
What will be an ideal response?
For Pepsi-Cola, profit maximization means ??/?pp = 50 + 2m - 4pp + pc = 0. Solving for pp yields Pepsi-Cola's best-response function: pp = 12.5 + (1/2)m + (1/4)pc. A $1 increase in marginal cost yields a $0.50 increase in price. A $1 increase in Coca-Cola's price yields a $0.25 increase in price.
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