Exercise 3 (Multi-Country Regulation) Consider two countries, s = 1, 2. In each one there is a unique firm (a local monopolist) which produces a homogeneous good and a national regulation authority that supervises its activities. The demand for this good is identical in the two countries and is given by Ds(ps) = 1 ps,

where ps is the price paid in country s. The two monopolists have identical costs and technology, given by

Cs(qs) = cqs + F,

with F > 0. The regulator chooses the quantity that the firm should produce, qs, and transfers resources to the firm. Let Ts denote the transfer. The cost of public funds is > 0. Answer the following questions.

1. Assume the countries are isolated (that is, there is no trade). For each country s = 1, 2, find the quantity qs that maximizes social welfare. Assume, for the remaining of the exercise, that both countries are connected. That is, the goods can be traded and consumers can buy from either country. As a result, the equilibrium price must be the same in both countries. 2. Suppose that there is a supranational regulator that chooses how much the firm in each country should produce in order to maximize aggregate welfare. Argue why at the optimum, consumers in both countries consume the same amounts. Compute

aggregate and country-level production. Is there any gain from integration? Inter- pret. [Hint: Think of the problem of the supranational regulator as if it faced the

sum of the demand of both countries, D(p) = 2(1 p), and the total costs were C(q) = cq + 2F. That is, assume that both firms produce.] 3. Consider now the case in which there is no supranational regulator and, instead, national regulators choose simultaneously how much the local firm should produce. Characterize the equilibrium quantities. Show that integration reduces aggregate welfare. Why? [Hint: Start by setting up the social welfare function that each regulator maximizes. Recall that when markets are integrated there is a unique equilibrium price that depends on the quantity produced in both countries.]