Luxottica produces Ray-Ban sunglasses in Italy and sells them in the US market. Let's assume that in the US the inverse demand for Ray-Ban glasses is =2000.01, and that Luxottica's total cost of producing Ray-Bans in Italy for the US market is 1 =1000+201 +0.0112. The marginal cost is 1 =20+0.021. a. If the US market for Ray-Bans was perfectly competitive, what would be the equilibrium number of Ray-Bans sold in the US? What would be the equilibrium price of a pair of Ray- Bans? What would be the consumer surplus and the producer surplus in this case? [Hint: recall that MC is the supply curve in perfect competition] b. In fact, Luxottica is a monopolist in the market for Ray-Bans (and most other brands of sunglasses). If Luxottica cannot price discriminate, how many pairs of Ray-Bans does it sell in the US market? At what price per pair? What is the consumer surplus and the producer surplus in this case? What is the deadweight loss caused by the monopoly (compared to the perfectly competitive market in "a")? Calculate the Lerner index, and interpret it. c. Recently, Luxottica opened in China a new plant for producing Ray-Bans to be sold in the US market. In China, Luxottica's total cost of producing Ray-Bans for the US market is 2(2)=1000+802, and the 2(2)=80. If Luxottica uses only the plant in China, how many pairs of Ray-Bans would it sell in the US (as a monopolist)? At what price per pair? d. Luxottica considers using both plants to produce Ray-Bans for the US market. In this case, how many pairs of Ray-Bans does Luxottica sell in the US? At what price? How many pairs of Ray-Bans are produced in Italy, and how many pairs are produced in China? e. Now assume that Luxottica can produce Ray-Bans only in the Chinese plant. But it can sell the sunglasses as the sole seller, in both the US and the Chinese markets. The inverse demand for Ray-Bans in China is: C = 100 - 0.01QDC. E1. If Luxottica cannot prevent re-sales across the two markets and must charge the same price in the US as in China, would Luxottica sell any pair of Ray Bans in China? How many pairs are sold in each country, and what is the price per pair? E2. If Luxottica can charge different prices in the American and the Chinese markets (that is, 3rd-degree price discrimination), what would be the price in each market, and how many pairs of Ray Bans would be sold in each market?