Upcoming in Class

1. Upcoming in Class • Homework #5 Due Monday • Extra Credit Writing Assignment Oct. 16th • Writing Assignment Due Oct. 23rd • Final Exam (optional) • Tuesday December 10 – 3:10-5:10pm

2. Chapter 5 – Resource Allocation over Time • A renewable resource is supplied on a continuing basis by ecosystems, such as forests, fisheries, wind energy, solar energy. • Non-renewable resources are available in a fixed supply, such as metal ores, coal, and oil.

3. Chapter 5 – Resource Allocation over Time • How should we optimally use a non-renewable resource over time? • Opportunity Cost – the benefit of the next best alternative • The net benefits of using the resource tomorrow are today’s opportunity costs.

4. Assumptions Fixed supply of coal. Consider two time periods only Demand (marginal WTP) is constant over time and MC is the marginal cost of extraction. Chapter 5 - A Two-Period Model

5. A Two-Period Model • If supply is sufficient to meet demand, then a static efficient solution will provide the optimal allocations over time, regardless of the discount rate. • For example, if the total supply of coal resource is 30 or more, what will be the efficient quantities for each period?

6. A Two-Period Model – Insufficient Supply • If supply is not sufficient we must determine the optimal allocation using the dynamic efficiency criterion: maximize the present value of net benefits. • Suppose instead, the total supply of coal is 20 units. • What will be the efficient quantities for each period?

7. Two period model • A two period model can be illustrated graphically by flipping the graph of period 2 such that the zero axis for the period 2 net benefits is on the right side, rather than the left. • The size of the box represents the resource constraint. • Any point on the horizontal axis sums to the amount of the resource constraint (=20 units).

8. Dynamic Efficiency • The dynamically efficient allocation will satisfy the condition that the present value of the marginal net benefit from the last unit in period 1 equals the present value of the marginal net benefit in period 2. • This allocation will maximize the present value of net benefits.

9. A Two-Period Model – Insufficient Supply • The net benefits in each period is the portion of the area under the demand curve and above the supply curve or the area under the marginal net benefit curve (which is the demand curve minus the marginal cost).

10. Discount Rate • The annual rate at which future benefits or costs are discounted relative to current benefits or costs. • PV(MNB2) = MNB2/(1+r)n • n=number of years between periods • r=discount rate

11. Change in discount rate A higher discount rate will favor the present. The amount allocated to the second period falls as the discount rate rises.

12. Chapter 5 - Problems • Assume the demand conditions are the same, but let the discounted rate be 0.10 and the marginal cost of extraction be $2. Total supply available = 20. How much would be produced in each period in an efficient allocation? • Assume the discount rate is 0.2. What happens to the efficient allocation? • Assume the discount rate is 0.5. What happens to the efficient allocation?

13. Marginal User Cost • Marginal user cost is the opportunity cost caused by intertemporalscarcity. • The marginal user cost for each period in an efficient market is the difference between the price and the marginal extraction cost. • MUC1 = 2 and MUC2=2 *(1+r)

14. Hotelling's Rule and Scarcity • Hotelling's Rule • Marginal user cost rises over time at the rate of discount causing efficient prices to rise over time and thus reflecting scarcity. • Scarcity • Scarcity rent is producer surplus that exists in the long run due to fixed supply or increasing costs

15. Upcoming in Class • Homework #5 Due Monday • Extra Credit Writing Assignment Oct. 16th • Writing Assignment Due Oct. 23rd • Final Exam (optional) • Tuesday December 10 – 3:10-5:10pm