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: Qd = 200 − 5P or P = 40 − 0.2Qd Supply: Qs = 5P or P = 0.2Qs where Q is expressed in millions of barrels and P is the price per barrel.

a) Draw a supply-and-demand graph showing the equilibrium price and quantity consumed in this generation in the absence of any consideration of the future. Solve for the equilibrium price and quantity algebraically.

b) Next, draw a graph showing the marginal net benefits from consumption in this period at all levels of consumption up to the equilibrium level. Express the marginal net benefit function (benefit minus cost) algebraically.

c) Suppose that the marginal net benefit function is expected to be the same for the next generation. But there is a discount rate (interest rate) of 4 percent per year, which for 35 years works out to be approximately equal to 4, or (1.04)35. Total oil supply for both generations is limited to 100 million barrels. Calculate the efficient allocation of resources between the two generations and show this graphically, similar to Figure . (Hint: Set marginal net benefits equal for the two periods, remembering to include the discount rate.)

d) What is the appropriate resource depletion tax in the current generation? Include a curve showing the marginal user costs and the resource depletion tax in the market graph for the current generation. You can either draw a new graph or just add these two lines to your graph from part (a). Finally, calculate the new price, with the resource depletion tax, in the current generation.

e) Briefly describe how your answers would differ if we used a higher or lower discount rate (without solving numerically or drawing new graphs)?