Two firms compete by setting prices in a differentiated goods market. The quantity sold by each firm depends on the two prices, as given by the following demand functions:

q1 = 60 4p1 + 2p2

q2 = 60 4p2 + 2p1

where q1, q2 and p1, p2 are the quantities sold and prices set by each of the two firms.

Suppose both firms have zero marginal cost of production.

1. Solve for the Bertrand equilibrium

2. Are the goods complements or substitutes? Explain.

3. Suppose one firm were to take over the other firm so that the merger chooses now both prices. What prices would it choose? How much would profits increase? Are consumers worse or better off?

4. Would consumers gain from the merger if instead q1 = 60 4p1 2p2; q2 = 60 4p2 2p1.