Determine the pricing problem of Alcoa's cookware division. Assume 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. Consumer's 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.
1. Assume that the firm announces that it will set prices of 80 in period 1 and 45 in period 2. Determine the numbers of consumers will buy in each period?
2. Assume that the firm announces that it will set prices of 80 in period 1 and 35 in period 2. Determine how many consumers will buy in each period?
3. Assume 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?
4. Assume that the firm instead rents saucepans every period. What rental price should it set?