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

Determine the social planner's optimal allocation of aluminum across Periods 1 and 2 when users in both periods are considered jointly.

(a) What is the optimal amount for Period 1 users to extract?

(b) How much is left over for users in Period 2?

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