Assume that Toyota has a factory in Coventry that produces small-size cars. The (monthly) demand for small-size Toyotas in London is given by P = 1,000 - 0.1Q, where P is the price per car and Q is the number of cars demanded. Assume that Toyota has already produced a large number of cars and now it has to decide how many of them to sell in London.
a) Assume that Toyota transports the cars to London by itself at a cost of $120 per car. What price should Toyota set in London in order to maximize its profit? What will its profit in London be in this case?
b) Suppose that instead of transporting the cars by itself, Toyota is considering using a transportation firm called Movers Inc. to transport the cars from Coventry to London. Movers' marginal cost is $40 per car. Suppose that Movers charges Toyota $100 per car. Should Toyota use Movers' service in this case? What will be Movers' profit and what will be Toyota's profit, in this case?
c) Suppose that instead of paying $100 per ton, Toyota offers to pay Movers the exact amount it paid in part (b) above but as a lump sum. Should Movers accept Toyota's offer?
d) (5%) Suppose that instead of the offer considered in part (c) above, Toyota is considering offering Movers a two-part tariff contract (F,w), where F is a lump sum payment and w is a price per ton that Toyota will pay Movers for transporting its product. Suppose that Movers will accept this contract only if its profit under this contract is at least as high as its profit in part (b) above (i.e., the profit it could make if it was paid a single-part tariff of $100 per car). What is the price per car, w, and the lump sum, F, that maximizes Toyota's profit in this case? e) (5%) Suppose that instead of the offer considered in part (d) above, Toyota is considering offering Movers a profit-sharing contract (S,w), where S is the share of Toyota's profit that it will transfer to Movers, and w is a price per car that Toyota will pay Movers for transporting her product. Suppose that Movers will accept this contract only if its profit under this contract is at least as high as its profit in part (b) above (i.e., the profit it could make if it was paid a single-part tariff of $100 per car). What is the price per car w, and the share of profit S, that Toyota pays Movers that maximizes Toyota's profit in this case?