Question

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 1

Answer:

For Pepsi, profit maximization means    $\delta \pi /\delta p_{p} = 54 - 4p_{p} + p_{c} = 0$ For Coke, profit maximization means $\delta \pi /\delta p_{c} = 54 - 4p_{c} + p_{p} = 0$   Both firms are at equilibrium setting a price of 18. . On the off chance that Pepsi's demand curve shifts, benefit maximization for them suggests $\delta \pi /\delta p_{p} = 104 - 4p_{p} + p_{c} = 0$ . The two firms are currently at equilibrium when Pepsi charges31.33 and Coke charges 21.33.