1. Consider a two period model of resource use in which the inverse demand curve is P = 40-2.0Q. The marginal cost of extraction is $9. The total resource stock is 20 units. The discount rate (r) is 20%.
2. Calculate the optimal resource allocation between the periods. Calculate the marginal user cost in period 1 and period 2. (10 points)
3. Illustrate the effect of a decrease in the discount rate to 10%. What is the impact on the resource allocation and the marginal user cost. Explain the outcome relative to the answer in part (a). (10 points)
4. Now suppose that the stock of remaining resources grows from period one to period two by a factor of 2*r (twice the discount rate). Explain how this would affect the optimal allocation (show graphically, mathematically and/or in words). Will the optimal allocation for period 1 increase or decrease when compared to the model in which the remaining resource in period 2 does not grow? What is the impact on marginal user cost in period 1? (10 points).