Suppose a firm has become a monopolist in the market for DVD players (remember those?). The market that lasts for exactly two periods (after 2 periods everyone switches to a newer technology). A DVD player is a durable good, so if it is sold in period 1 it can be used in period 2. Demand for the use of a DVD player for 1 period is described by P(Q) = 400 - Q (demand is the same in both periods). Consumers who purchase a DVD player in period one may either use the DVD player again in period 2 or resell it to another consumer. The firm can produce DVD players in either period at a marginal cost of zero. To simplify the math, assume the firm does not discount future profits (δ = 1) and that used DVD players are just as good as new ones.
1. Suppose the firm decides only to rent DVD players with single period contracts. If the firm is behaving optimally how many DVD players does it decide to rent in each period?
2. What is the price of DVD player rental in each period, and what is the firms total profits.
3. Now suppose the firm sells DVD players rather than rents. Also assume that the firm can commit in period 1 to how many DVD players it will sell in both periods. What is the optimal strategy for the firm. How many DVD players does it sell in each period?
4. What are its total profits from this strategy?
5. Compare profits from the rental market to profits from selling with commitment. Why are they similar or different?
6. Compare the price of rental in period 1 to the price of DVD's in period 1 when the firm can commit. How are they similar or different?