Ashley (Brand A) and Lino (Brand L) are the leading brand names of fitness shoes. The direct demand functions facing each producer are given by
qA(pA; pB) = 180 2pA + pB and qB(pA; pB) = 120 2pB + pA
Note: The demand functions are not symmetric (i.e., they have different intercepts). Assume zero production cost (cA = cB = 0) and solve the following problems:
(a) Solve for the Nash-Bertrand equilibrium prices. Then, compute the equilibrium output levels, the equilibrium profits and aggregate industry problems:
(b) Suppose now that the two firms merge. However, they decide to keep selling the two brands separately and charge, possibly, different prices. Compute the prices pA and pB which maximize joint industry profit. Then, compute aggregate industry profit and compare it to the aggregate industry profit made under Bertrand competition which you have already computed under separate ownership.