Consider a two-period world with this period, and next period, . The marginal benefits (demand) of crude oil consumption in each period are . Further, assume that crude oil is a nonrenewable resource with a constant marginal extraction cost (i.e., of $50. Initially there are 300 units of stock at the beginning of period . The discount rate is 5%.

a.If this was a static problem, how much of the resource would be used in each period?

b.Solve analytically for the dynamically efficient allocation in each period.

c.Graphically depict the efficient solution.

d.Use a graphical or analytical approach to show how a change in the social discount rate to 10% would change the optimal allocation. Explain the reallocation.

e.Suppose the marginal extraction cost in period 1 decreases to $20 because of technological advances in extraction. Show analytically or graphically how optimal extraction would adjust between periods 0 and 1. Explain the reallocation.

f.Suppose the oil field is open to all drillers. In this scenario, what would be the extraction levels in each period?