1. Suppose a monopolist faces demand Q=100-P. The marginal cost of production is 20.
a. Calculate the price P the monopolist will set, the corresponding Q, and the monopolist's profits.
b. Suppose there is a technology the monopolist can adopt, for a fixed cost C, that reduces the marginal cost to 10. For what values of C will the monopolist adopt the technology? Calculate P, Q, and the monopolist's profits when the technology is adopted.
c. Could the government ever increase total surplus by providing a subsidy to the monopolist to adopt the technology?
2. Suppose there is a firm consisting of two divisions: an upstream division that manufactures yarn and a downstream division that manufactures sweaters. Yarn can also be purchased for a price of 40 per unit on the outside market (1 unit of yarn is the amount needed to make 1 sweater). Suppose the upstream division cannot sell its yarn on the outside market. The total cost for the upstream division to make Q units of yarn is 4*Q2. The total cost for the downstream division to make Q sweaters is Q2, plus the price of yarn. The demand for sweaters faced by the firm is: P=100-Q.
a. Suppose the firm sets a transfer price for yarn of 100. How many sweaters will be produced? How much yarn will the upstream division produce? How much yarn will be obtained from the outside market? What will the profits of each division be, and what will total profits be?
b. Suppose the firm sets a transfer price for yarn of 0. What will the outcome look like now?
c. What is the optimal transfer price? What will the outcome look like if the transfer price is set optimally?
3. A firm produces for two periods. It must decide how much to produce in each period: q1 and q2. The firm faces a price in period t of 320-qt. The marginal cost of production in period 1 is 200. The marginal cost of production in period 2 is 200-q1. Assume no discounting takes place.
a. Assume no production takes place in period 2. How much should the firm produce in period 1?
b. Assume the firm produces in period 1 the amount you calculated in part (a). How much should the firm produce in period 2? Calculate the firm's profits in each period, as well as total profits.
c. Now assume the firm jointly chooses how much to produce in each period. Calculate per-period profits of the firm, as well as total profits. How do your answers compare to part (b)? Explain the difference.