Hotelling v. Hubbert : How (if at all) can economics and peak oil be reconciled?

1. Hotelling v. Hubbert:How (if at all) can economics and peak oil be reconciled? Economics 331b

2. What is the issue? The Hubbert peak-oil theory posits that for any given geographical area, from an individual oil-producing region to the planet as a whole, the rate of petroleum production tends to follow a bell-shaped (normal) curve. There is no explicit economics in this approach.

3. Hotelling theory Oil is developed and produced to meet the arbitrage condition for assets: ri,j,t< rt* ; for grade i, location j, time t. Or the rate of return on oil-in-the-ground (Gi,j,) has a risk-and-tax adjusted rate of return equal to that of comparable assets as long as Gi,j, > 0.

4. Approach for Hotelling Let’s construct a little oil model and see whether the properties look Hubbertian. Technological assumptions: • Four regions: US, other non-OPEC, OPEC Middle East, and other OPEC • Ultimate oil resources (OIP) in place shown on next page. • Recoverable resources are OIP x RF – Cumulative extraction • Constant marginal production costs for each region • Fields have exponential decline rate of 10 % per year Economic assumptions • Oil is produced under perfect competition  costs are minimized to meet demand • Oil demand is perfectly price-inelastic • There is a backstop technology at $100 per barrel

5. How to calculate equilibrium • We can do it by bruit force by constructing many supply and demand curves. Not fun. • Modern approach is to use the “correspondence principle.” This holds that any competitive equilibrium can be found as a maximization of a particular system.

6. Economic Theory Behind Modeling 1. Basic theorem of “markets as maximization” (Samuelson, Negishi) Maximization of weighted utility function: Outcome of efficient competitive market (however complex but finite time) = 2. This allows us (in principle) to calculate the outcome of a market system by a constrained non-linear maximization.

7. Specific Tools • Some kind of Newton’s method. • Start with system z = g(x). Use trial values until converges (if you are lucky and live long enough). • EXCEL “Solver,” which is convenient but has relatively low power. - I will use this for the Hotelling model. • GAMS software. Has own language, proprietary software, but very powerful - This will be used later in global warming models, specifically Yale-DICE model.

8. Estimates of Petroleum in Place Department of Energy, Energy Information Agency, Report #:DOE/EIA-0484(2008)

9. Petroleum supply data Sources: Resource data and extraction from EIA and BP; costs from WN

10. Demand assumptions Historical data from 1970 to 2007 Then assumes that demand function for oil grows at 2 percent for year (3 percent output growth, income elasticity of 0.67). Price elasticity of demand = -0.5 Conventional oil and backstop are perfect substitutes.

11. Solution technique

12. Picture of spreadsheet

13. Results: Price trajectory

14. Results: Output trajectory How differs from Hubbert theory: 1. Much later peak 2. Not a bell curve; slower rise and steeper decline

15. Rate of price change