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 sellers 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?