2. How could the principle of allocation of resource over time be applied to environmental resources such as the atmosphere and the oceans? Would the same kind of conclusions about optimal depletion apply or not?

We can modify the interperiod allocation model to deal with the issue of intergenerational allocation of resources. Suppose a generation is thirty-five years, and we are concerned with only two generations.
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

(a) Draw a demand and supply graph showing the equilibrium price and quantity consumed in this generation in the absence of any consideration of the future. Now 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 net benefit (benefit minus cost)
algebraically.

(b) Suppose that the 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 annum, which for thirty-five years works out to (1.04)35, which is approximately equal to 4. Total oil supply for both generations is limited to 100 units. Calculate the efficient allocation of resources between the two generations and show this graphically. (Set marginal benefits equal for the two periods, remembering to include the discount rate.)

(c) What is marginal user cost for this efficient allocation? If you include this user cost in your original supply and demand graph, what is the new equilibrium? What is the scarcity rent? If the demand curve is the same in the second generation, what will the price and quantity consumed in that period be?

(d) How would the answers differ if we used a zero discount rate? What can you conclude from this example about the general problem of allocation of resources over long periods?