Pear Inc. is a monopolist producing the iWatch, a wristwatch mobile communication device. The iWatch is a device that will last for exactly two periods, after everyone will switch to Boogle Glass, a eyeglass mobile communication device that is not yet available. Demand for the use of the iWatch is R = 144 - 3Q in both periods. Pear can produce the iWatch at a marginal cost of zero.
1. Suppose that Pear is able to commit to a production plan for the iWatch in both periods. Write down Pear's maximization problem under commitment.
2. If Pear is able to commit, what is its optimal production plan?
3. What is the price of an iWatch in each period?
4. Now suppose that Pear chooses how much to produce in each period, with no commitment. Given that it produces Q1 in period 1, how much should Pear produce in Period 2?
5. Without commitment, what should consumers expect the period 2 price to be once they observe Q1?
6. Given this, what is the price of an iWatch in Period 1 as a function of Q1?
7. What is the optimal quantity Pear produces in Period 1?
8. Does Pear make more profit with or without commitment? Explain your answer by either calculating profit or using your knowledge of durable goods models from class.