Upcoming in Class Homework #5 Due Next Tuesday Oct. Homework #6 Due Oct. 25 Writing Assignment Due Oct. 27th

Non-renewable Resources We will eventually run out. How should we optimally use a non-renewable resource over time? The benefits today means we can’t using it tomorrow. Opportunity Cost – the benefit of the next best alternative

Chapter 5 - A Two-Period Model Assumptions Fixed supply of coal Consider two time periods only Total supply is 30 tons Demand (marginal WTP) is constant: Calculate NB = P – MC = 6 – 0.4 Q

The Allocation of an Abundant Depletable Resource The Allocation of an Abundant Depletable Resource. (a) Period 1 (b) Period 2

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 the efficient quantities for each period?

A Two-Period Model – Insufficient Supply If total supply amount is 20, regardless of discount rate, what efficiency criterion can we use?

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. 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.

Dynamic Efficiency 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).

A Two-Period Model – Insufficient Supply The present value for a two-period model is the sum of the present values in each of the two years. The present value 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).

Maximizing Net Benefit Total net benefits are represented in the shaded area. r=.10 Optimal quantity for period 1 = 10.238, period 2 = 9.762 Total PVNB = (1/2)*(6+1.905)*10.238+(1/2)*(1.905+5.45)*9.762 =$76.366

The Dynamically Efficient Allocation

Discount Rate The annual rate at which future benefits or costs are discounted relative to current benefits or costs. PV = NB2/(1+r)n-1

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.

Marginal User Cost The opportunity cost caused by intertemporal scarcity is called the marginal user cost (MUC). The marginal user cost for each period in an efficient market is the difference between the price and the marginal extraction cost. MUC1 = 1.905 and MUC2 =1.905(1+r)= 2.095

Scarcity Marginal user cost rises over time at the rate of discount causing efficient prices to rise over time and thus reflecting scarcity. -Hotelling’s Rule A higher discount rate will favor the present. The amount allocated to the second period falls as the discount rate rises. Scarcity Rent is producer surplus that exists in the long run due to fixed supply or increasing costs

The Efficient Market Allocation of a Depletable Resource: The Constant-Marginal-Cost Case. (a) Period 1 (b) Period 2

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? R=0 6-0.4q R=0.1 5.45 - 0.36q R=0.2 5-.33q R=0.5 4-.26q

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 $4. Total supply available = 20. How much would be produced in each period in an efficient allocation? What would be the marginal user cost in each period? Would the static and dynamic efficiency criteria yield the same answers for this problem? Why?

Chapter 5 - Problem Assume the demand conditions are the same, but let the discounted rate be 0 and the marginal cost of extraction be $4. Total supply available = 10. How much would be produced in each period in an efficient allocation? What would be the marginal user cost in each period? Would the static and dynamic efficiency criteria yield the same answers for this problem? Why?