II. Suppose the marginal benefit of a unit of a certain non-renewable resource is given by MB=80-2Q. (Q is the total extracted amount at a certain period) The marginal cost of extracting a unit of this resource is 20. The risk-free interest rate is 10%.

To answer questions 1) to 3): Assume that there are two periods.

1) When will the marginal user cost be zero on an socially efficient extraction path? Give a range of quantity of reserves.

2) Assume there are 50 units of this resource. How much of this resource will be extracted in period 1 and period 2 in a competitive market? What will be the price of this resource in each period?

3) Suppose instead, the resource is owned and sold by one single company. How much would this company extract in each period? What will be the price of this resource in each period? (Suppose there are still 50 units of resources.)

Now suppose that there are 3 periods. Answer 4) and 5)

4) When will the resource never be exhausted on a socially optimal extraction path? Give a range of the quantity of reserves.

5) When will the resources be exhausted in less than 3 periods on a socially optimal extraction path? Give a range of the quantity of reserves.