5. 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: 91 = 40 - 2p1 + P2 92 = 40 - 2p2 + P1 where q1, 92 and p1, p2 are the quantities sold and prices set by each of the two firms. Suppose both firms have marginal cost c = 10. (a) Solve for the Bertrand equilibrium. (b) Are the goods complements or substitutes? Explain.. (c) 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? (d) By how much should marginal cost decrease with the merger so consumers are not worse off