Consider the pricing problem of Alcoa's cookware division. Suppose that the world last for only two periods, period 1 and period 2. A saucepan last two periods, so that a saucepan that is bought in period 1 can also be used in period 2. Consumers values of using a saucepan for one period are distributed uniformly between 0 and 100. So for example, someone who values the saucepan at 30 will get utility of 60 if they use it for two periods. There is no discounting. Marginal cost of making saucepans is zero.
(a) Suppose that the firm announces that it will set prices of 80 in period 1 and 45 in period 2. How many consumers will buy in each period?
(b) Suppose that the firm announces that it will set prices of 80 in period 1 and 35 in period 2.How many consumers will buy in each period?
(c) Suppose that all consumers with per-period valuations above 40 buy in period 1. If the firm is free to sets it price in period 2, what price will it set given the consumers who are left in the market?
(d) Suppose that the firm instead rents saucepans every period. What rental price should it set?