Dynamic Allocation of a Nonrenewable Resource

1. Dynamic Allocation of a Nonrenewable Resource

2. Natural resources • Renewable resource • Nonrenewable resource

3. Natural resources – are we running out? • Thomas Malthus • Limits to Growth

4. Natural resources – are we running out? • Technological advances • Substitution and conservation

5. Nonrenewable Resource • Issues: • What is the efficient rate of resource extraction over time? • What does this rate of extraction imply for natural resource costs over time?

6. Nonrenewable Resource • A nonrenewable resource is depletable; only a limited stock is available. • A unit of the resource produced today is gone forever.

7. Nonrenewable Resource • Two features: • 1) Stock of a nonrenewable resource is fixed • 2) Not producing has an opportunity cost

8. Nonrenewable Resource • A depletable resource is both a product and an asset • Product: once produced, it can be sold at the market price • Asset: kept in the ground, it can rise in value (capital gain)

9. Nonrenewable Resource • Issues: • Do I produce the resource, or keep it in the ground one more year? • Do I spread production evenly from one year to the next?

10. Efficient Intertemporal Allocation • Choose production allocation over time so as to maximize the present value of benefits minus costs

11. Efficient Intertemporal Allocation • Two types of cost to consider • 1) Production cost • 2) Opportunity cost – due to depletion

12. Efficient Intertemporal Allocation • Production cost • Expense of extracting the resource • Cost of exploration, drilling, production

13. Efficient Intertemporal Allocation • Opportunity cost • If a bbl is NOT produced, an opportunity cost arises • The amount that could have been earned by producing, selling the oil, and investing the proceeds

14. Efficient Intertemporal Allocation • Opportunity cost • This cost is measured by marginal resource rent • Also called marginal user cost • Value of a bbl of the resource in the ground

15. Efficient Intertemporal Allocation • Criteria for NOT producing: compare the rate of growth of marginal resource rent with the interest rate

16. Efficient Intertemporal Allocation • Rate of growth (ROG) of marginal resource rent is (r2/r1)-1 • Example: • r1 = $48 and r2= $49 • (r2/r1)-1 = 0.0208 = 2.1%

17. Efficient Intertemporal Allocation • If (r2/r1)-1> i , keep the marginal bbl in the ground another year. • Example: i = 1% and ROG r = 2.1%. Keep the marginal bbl in the ground another year.

18. Efficient Intertemporal Allocation • If (r2/r1)-1 < i , produce the marginal bbl this year. • If i = 2.5% and ROG r = 2.1%, produce the marginal bbl and invest the proceeds.

19. Efficient Intertemporal Allocation • In equilibrium: (r2/r1)-1 = i • We are indifferent between producing the marginal bbl this year or waiting until next year.

20. Efficient Intertemporal Allocation • The equilibrium condition (r2/r1)-1 = i implies that marginal resource rent will grow at the rate of interest.

21. Efficient Intertemporal Allocation • Hotelling rule: (economist Harold Hotelling) assuming sufficient demand, resource rent will rise over time at the rate of interest.

22. Efficient Intertemporal Allocation • Goal: allocate production over the years so as to maximize PV of net benefits

23. Rule: allocate production so that the PV of net benefits from the marginal bbl is equal in all years.

24. This means that the PV of marginal resource rent will be equal in all years.