1. Environmental and Natural Resource Economics 3rd ed. Jonathan M
Environmental and Natural Resource Economics 3rd ed. Jonathan M. Harris and Brian Roach Chapter 5 – Resource Allocation Over Time
Copyright © 2013 Jonathan M. Harris

2. Figure 5.1a: Supply, Demand, and Marginal Net Benefit for Copper
Price
Supply
Ps = Q
$150 . e
$100
Demand
Pd = Q
$50
In the current period, equilibrium in the market for copper occurs at P =$100 and Q = This is also known as the static equilibrium.
100
200
Quantity of Copper

3. Figure 5.1b: Marginal Net Benefit for Copper
$150
$100
MNB = Q
$50
The marginal net benefit of copper in the current period is obtained by subtracting marginal costs (shown by the supply curve) from marginal benefits (shown by the demand curve).
100
200
Quantity of Copper

4. Figure 5.2: Allocation of Copper over Two Time Periods
Marginal Net Benefit
$100
$100
MNB1
MNB2
$75
$75
$50
PV [MNB2]
$50
$25
$25
To find the economic optimum allocation between two time periods, the marginal net benefit for the second period is discounted to obtain its present value, and this is compared to marginal net benefit in the first period. This is also known as the dynamic equilibrium. Q1 50
100
150
200
250 Q2
250
200
150
100 50
Quantity of Copper

5. Figure 5.3a: Optimal Intertemporal Resource Allocation
Marginal Net Benefit
$100
$100
MNB1
$75
$75
$50
PV [MNB2]
$50 A
$25
$25
The optimal intertemporal resource allocation occurs where MNB1 = PV[MNB2]. At this point total net benefit is equal to the two shaded areas (A + B). User costs are equal to $25. B Q1 50
100
150
200
250 Q2
250
200
150
100 50
Quantity of Copper

6. Figure 5.3b: Suboptimal Intertemporal Resource Allocation
Marginal Net Benefit
$100
$100
MNB1
$75
$75
PV [MNB2]
$50
$50 A1
$25
$25 B1
At a suboptimal allocation on Q1 = 200, Q2 = 50, total benefit is A1 + A2 + B1, and the area B2 represents a net loss as compared to the optimum allocation. B2 A2 Q1 50
100
150
200
250 Q2
250
200
150
100 50
Quantity of Copper

7. Figure 5.4a: Market for Copper with User Costs (first period)
Price
S’ with User Costs
$150
$112.5
Supply
$100
Demand
$50
If user costs are of $25 are included in the first period, the price rises to $ and the quantity consumed falls from 200 to 150. 50
100
150
200
250
Quantity of Copper

8. Figure 5.4b: Market for Copper (second period)
Price
$150
$125
$100
Demand
$50
With 100 units remaining in the second period, the price in that period will be $125. 50
100
150
200
250
Quantity of Copper

9. Figure 5.5: Intertemporal Resource Allocation with Different Discount Rates
Marginal Net Benefit
PV [MNB2] at:
$100 0%
MNB1 2%
$75 5% 7%
$50
10%
$25
15%
At higher discount rates, the intertemporal allocation of the resource shifts towards the first period, since the present value of the second period marginal net benefit is reduced.
20%
50% Q1 50
100
150
200
250 Q2
250
200
150
100 50
Quantity of Copper

10. Table 5.1: Intertemporal Resource Allocation with Different Discount RatesQ1 Q2 1
125 2
1.2
132
118 5
1.6
143
107
7.5
150
100 10
2.6
158 92 15 4
170 80 20
6.2
179 71 50
57.7
198 52
As the discount rate rises, the allocation shifts back towards the static equilibrium of 200 units consumption in the first period.

11. Figure 5.6: Hotelling’s Rule on Equilibrium Resource Price
According to Hotelling’s rule, the net price of a resource should rise at a rate equal to the discount rate.