Suppose we are analyzing the intertemporal allocation of oil. Assume a generation is 35 years, and we are concerned with only two generations. The demand and supply functions for oil in the present generation are given by:

Demand: Q_d = 200-5P_d

Supply: Q_s = 5P_s

where Q is expressed in millions of barrels and P is the price per barrel.

a) Solve for the equilibrium price and quantity algebraically.

b) Solve the marginal net benefit function algebraically.

c) Suppose that the marginal benefit function is expected to be the same for the next generation. But there is a discount rate of 4% per year, which for 35 years works out to be approximately equal to 4 = (1.04)³⁵. The total oil supply for both generations is limited to 100 million barrels.

Calculate the efficient allocation of resources between the two generations.

(Hint: Draw a graph, similar to Figure 5.4 on page 115. Set the marginal net benefit equal for the two periods, remembering to include the discount rate.)

d) Calculate the appropriate depletion tax per barrel in the current generation?

e) Calculate the new market price of oil in the current generation after imposing the tax.