13.26. Two firms, Alpha and Bravo, compete in the European chewing gum industry. The products of the two firms are differentiated, and each month the two firms set their prices. The demand functions facing each firm are:

where the subscript A denotes the firm Alpha and the subscript B denotes the firm Bravo. Each firm has a constant marginal cost of $7 per unit.

a) Find the equation of the reaction function of each firm.

b) Find the Bertrand equilibrium price of each firm.

c) Sketch how each firm’s reaction function is affected by each of the following changes:

i) Alpha’s marginal cost goes down (with Bravo’s marginal cost remaining the same).

ii) Alpha and Bravo’s marginal cost goes down by the same amount.

iii) Demand conditions change so that the “150” term in the demand function now becomes larger than 150.

iv) The “10” and “9” terms in each demand function now become larger (e.g., they become “50” and “49,”

respectively).

d) Explain in words how the Bertrand equilibrium price of each firm is affected by each of the following changes:

i) Alpha’s marginal cost goes down (with Bravo’s marginal cost remaining the same).

ii) Alpha and Bravo’s marginal cost goes down by the same amount.

iii) Demand conditions change so that the “150” term in the demand function for each firm now becomes larger than 150.

iv) The “10” and “9” terms in each demand function now become larger (e.g., they become “50” and “49,”

respectively).