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1- Alpha (Brand A) and Beta (Brand B) are leading brand names of clothes. The direct...

1- Alpha (Brand A) and Beta (Brand B) are leading brand names of clothes. The direct demand functions facing each producer are given by qA = 180 – 2 PA + PB and qB = 120 – 2PB + PA Assume zero production cost (cA = cB = 0), and solve the following problems: (i) Derive the price best-response function of firm A as a function of the price set by firm B. Show your derivations, and draw the graph associated with this function. (ii) Derive the price best-response function of firm B as a function of the price set by firm A. Show your derivations, and draw the graph associated with this function. (iii) Solve for the Nash-Bertrand equilibrium prices. Then, compute the equilibrium output levels, the equilibrium profits, and aggregate industry profit. (iv) Suppose now that the two producers hold secret meetings in which they discuss fixing the price of clothes to a uniform (brand-independent) level of p = PA = PB. Compute the price p which maximizes joint industry profit, ?A + ?B. Then, compute aggregate industry profit and compare it to the aggregate industry profit made under Bertrand competition which you computed in part (iii). (v) 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, ?A + ?B. 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.

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