Consider two firms i and j producing goods at marginal costs ci and cj , respectively, with ci , cj 0. Consumers consider the two goods to be perfect complements; that is, consumers have demand for bundles consisting of one of each good. Assume that aggregate demand for bundles is given by

q = a (pi + pj) with a > ci + cj 0.

Denote the amounts demanded of the good by qi and qj and note that qi = qj = q.

Q: Suppose the two firms merge and set prices in order to maximize joint profits. Write down the merged firm's maximization problem and derive the equilibrium price, quantity, and profits.

Does the merger increase social welfare?