Compare two versions of the two-period depletable resource model that differ only in the treatment of marginal extraction cost. Assume that in the second version the constant marginal extraction cost is lower in the second period than the first (perhaps due to the anticipated arrival of a new, superior extraction technology). The constant marginal extraction cost is the same in both periods in the first version and is equal to the marginal extraction cost in the first period of the second version. In a dynamic efficient allocation, how would the extraction profile in the second version differ from the first? Would relatively more or less be allocated to the second period in the second version than in the first version? Would the marginal user cost be higher or lower in the second version? Why?

a. Consider the general effect of the discount rate on the dynamic efficient allocation of a depletable resource across time. Suppose we have two versions of the two-period model discussed in this chapter. The two versions are identical except for the fact that the second version involves a higher discount rate than the first version. What effect would the higher discount rate have on the allocation between the two periods and the magnitude of the present value of the marginal user cost?

b. Explain the intuition behind your results.

c. Consider the effect of population growth on the dynamic efficient allocation of a depletable resource across time. Suppose we have two versions of the two-period model, discussed in this chapter, that are identical except for the fact that the second version involves a higher demand for the resource in the second period (e.g., the demand curve shifts to the right due to population growth) than the first version. What effect would the higher demand in the second period have on the allocation between the two periods and the magnitude of the present value of the marginal user cost?

d. Explain the intuition behind your results.