1 ECON/FRE 374 – Practice Questions for Midterm Questions: 1) Consider a three-period model of nonrenewable resource extraction. Lay out the maximization problem in a way analogous to the two-period model in the lecture notes, and determine the explicit expression for user cost. 2) Consider the extraction of a known stock problem for nonrenewable resource. Assume the existence of only two periods: t0 and t 1 . Let the (inverse) demand functions of the two periods be: p0 = 15 – q0 and p 1 = 15 – q 1 . Let the marginal extraction costs be MC0 = 5 + q0 and MC 1 = 5 + q 1 . And let the rate of discount r = 0.05. a) If there is no limitation on the total quantity of this nonrenewable resource, what is the socially optimal extraction each period? (Show both graphically and numerically). b) Now suppose there is a limitation on the total quantity of this nonrenewable resource: q0 + q 1 ≤ 8. What are the optimal extraction at t0 and optimal extraction at t 1 ? (Show both graphically and numerically)
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