2. Suppose that the demand and supply curves for aluminum, a nonrenewable resource, in the current time period are given as:
Demand: \( Q_{d}=(200-P) / 0.4 \) or \( P=200-0.4 Q_{d} \)
Supply: \( Q_{s}=(P-80) / 0.6 \) or \( P=80+0.6 Q \) s,
where \( Q \) is million tons and \( P \) is the price per ton.
a. Solve for the equilibrium price and quantity in the current time period. Present a supply-and-demand graph showing the supply and demand curves and the equilibrium point.
b. Determine the marginal net benefit curve for aluminum and show this on a new graph.
c. Assume there are 150 million tons of aluminum to be divided between the current time period and the future, and the future marginal net benefits will be the same as in the current generation. Further, assume that the future period is 25 years into the future and the discount rate is \( 4.5 \% \). Using the discount formula, we divide future benefits by \( (1.045)^{25} \), which equals 3.0 . In other words, the future marginal net benefit function will need to be divided by 3 to obtain the present value of future benefits. Solve for the efficient allocation of aluminum between the two generations. Show this allocation on a graph similar to Figure 5.4.
d. Calculate the appropriate resource depletion tax in the current time period. What will be the price of aluminum in the current time period with the resource depletion tax?
