The Baldonian shoe market is served by a monopoly firm. The demand for shoes in Baldonia is given by Q = 10 - P, where Q is millions of pairs of shoes (a right shoe and left shoe) per year, and P is the price of a pair of shoes. The marginal cost of making shoes is constant and equal to $2 per pair.
a) At what price would the Baldonian monopolist sell shoes? How many shoes are purchased?
b) Baldonian authorities have concluded that the shoe seller's monopoly power is not a good thing. Inspired by the U.S. government's attempt several years ago to break Microsoft into two pieces, Baldonia creates two firms: one that sells right shoes and the other that sells left shoes. Let P1 be the price charged by the right-shoe producer and P2 be the price charged by the left-shoe producer. Of course, consumers still want to buy a pair of shoes (a right one and a left one), so the demand for pairs of shoes continues to be 10 - P1 - P2. If you think about it, this means that the right-shoe producer sells 10 - P1 - P2 right shoes, while the left-shoe producer sells 10 - P1 - P2 left shoes. Since the marginal cost of a pair of shoes is $2 per pair, the marginal cost of the right-shoe producer is $1 per shoe, and the marginal cost of the left-shoe producer is $1 per shoe.
i) Derive the reaction function of the right-shoe producer (P1 in terms of P2). Do the same for the left-shoe producer.
ii) What is the Bertrand equilibrium price of shoes? How many pairs of shoes are purchased?
iii) Has the breakup of the shoe monopolist improved consumer welfare?
Note: To see the potential relevance of this problem to the Microsoft antitrust case, you might be interested in reading Paul Krugman, "The Parable of Baron von Gates," New York Times (April 26, 2000).