Scenario

Consider an aluminum mine that is operating for two periods and wants to maximize extraction profits.

Period 1's demand for aluminum is given by the equation: P = 210 1.5Q

In Period 2, the population is greater but there are also different uses for aluminum that affect demand. They have a different demand function:

P = 190 - Q

The marginal cost of extraction is constant and equal in both periods: MC = 30

The resource endowment of aluminum to be allocated across both periods is 200 units and the future is discounted at rate r = 5% per period

1. Suppose that users in Period 1 are selfish, and do not account for the welfare of users in Period 2.

(a) How much aluminum will be consumed in Period 1?

(b) How much aluminum will be consumed in Period 2?

(c) What is the marginal user cost in each period?