1) The inverse demand curve for a nonrenewable resource is given by Pd=14-0.25q, and the supply curve is Ps=7+0.25q. Assume there are 0 extraction costs, 30 total units of the resource available for extraction over two time periods, and a discount rate of 5%
a. set up the problem (show your formulas!) and solve for P1,q1,p2 andq2. Remember–first solve for the marginal net benefit equation!
b. What are user costs at the efficient extraction level? Again, reference your marginal net benefit function? Explain what this user cost represents.
c. Now suppose that extraction costs are $1. Set up the problem that would allow you to solve for P1, P2, q1 and q2 (you do not need to solve for these quantities again).
d. Intuitively (again, you do not need to solve the full problem), how will p1，p2, q1, q2, and the user cost differ from the solution in part a?
e. Explain why, in an optimal (resource-rent maximizing) solution, marginal net benefits of extraction must be equal across all time periods. HOW does this relate to Hotelling’s rule, which states that