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

Figure 5.1a: Supply, Demand, and Marginal Net Benefit for Copper Price Supply Ps = 50 + 0.25Q $150 . e $100 Demand Pd = 150 - 0.25Q $50 In the current period, equilibrium in the market for copper occurs at P =$100 and Q = 200. This is also known as the static equilibrium. 100 200 Quantity of Copper

Figure 5.1b: Marginal Net Benefit for Copper $150 $100 MNB = 100 - 0.5Q $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

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

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

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

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 $112.50 and the quantity consumed falls from 200 to 150. 50 100 150 200 250 Quantity of Copper

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

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

Table 5.1: Intertemporal Resource Allocation with Different Discount Rates Q1 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.

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.