Suppose the demand for Pepsi is qp = 54 – 2pp + 1p. The demand for Cok

Suppose the demand for Pepsi is qp = 54 – 2pp + 1p. The demand for Coke is qc = 54 – 2pc + 1pp. Each firm faces a constant marginal cost of zero. Determine the Bertrand equilibrium prices.

What happens to the Bertrand equilibrium prices and profits if increased differentiation causes the demand for Pepsi to become qp = 104 – 2pp + 1pc while the demand for Coke remains unchanged?

ANSWER

For Pepsi, profit maximization means δπ/δpp = 54 – 4pp + pc = 0. For Coke, profit maximization means δπ/δpc = 54 – 4pc + pp = 0. Both firms are at equilibrium setting a price of 18. If Pepsi’s demand curve shifts, profit maximization for them implies δπ/δpp = 104 – 4pp + pc = 0. Both firms are now at equilibrium when Pepsi charges 31.33 and Coke charges 21.33.