Question

) In class, we developed a simple two-period model of dynamically efficient etraction of a nonrenewable resource with a finite stock of 20 units, constant marginal extraction costs of 2.0, and constant demand given by the inverse demand function: p = 8 - 0.4 q Everything remains as before (including the 10% interest rate), except for the demand for the resource. We now change the situation in the following manner: we know in period 1 that due to technological change, the demand for the resource will decrease in period 2. Hence, there are now different demand functions for each period. In particular, inverse demand functions for the two periods are: p1 = 8 - 0.4 q1 p2 = 6 - 0.4 q2 a) What is the socially optimal quantity of resource extraction in the two periods? This part of the question can be satisfactorily approached with a carefully drawn graph. But, in addition, if you're comfortable using some simple algebra, you can get more precise answers by setting up the appropriate equations. (HINT: Solve graphically and mathematically) b) Compare your optimal extraction in period 1 to the optimal period 1 extraction we derived in class for the case of constant demand. Explain the logic (intuition) behind the similarity or difference. c) What is the optimal real (current) price of the resource in the two periods? d) Compare your optimal price in period 1 to the optimal period 1 price we derived in class for the case of constant demand. Explain the logic (intuition) behind the similarity or difference. e) What is the marginal user cost (or scarcity rent or shadow price) of the resource in the two periods? f) Comment on the applicability of the simple Hotelling Rule developed in class to the context of a nonrenewable resource for which demand is not constant over time. Can you offer any intuition about what's going on?

Answer 1