A manufacturer of automobile tires produces tires at a cost of $10 per tire. It sells units to a retailer who in turn sells the tires to consumers. Suppose that the retailer faces the inverse demand curve p= 200- 9 100 That is, if the retailer brings q tires to the market, then these tires will be sold at a price of p = 200-100- The retailer has no cost of production, other than whatever it must pay to the manufacturer for the tires. 1. Suppose that the manufacturer and retailer interact as follows. First, the manufacturer sets a price a that the retailer must pay for each tire. Then, the retailer decides how many tires q to purchase from whereas the retailer's profit is the manufacturer and sell to consumers. The manufacturer's payoff (profit) is q(x - 10), q 9 (200- -)q- xq 200g - - xq 100 100 Calculate the subgame perfect equilibrium of this game. 2. Suppose that the manufacturer sells its tires directly to consumers, bypassing the retailer. Thus, the manufacturer can sell q tires at price p = 200-100 Calculate the manufacturer's profit-maximizing choice of q in this case. 3. Compare the joint profit of the manufacturer and retailer in part (a) with the manufacturers profit in part (b). Explain why there is a difference. This is called the double-marginalization problem.