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: r i,j,t < r t * ; for grade i, location j, time t. Or the rate of return on oil-in-the-ground (G i,j, ) has a risk-and-tax adjusted rate of return equal to that of comparable assets as long as G i,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 1.We can do it by bruit force by constructing many supply and demand curves. Not fun. 2.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. 6 Outcome of efficient competitive market (however complex but finite time) Maximization of weighted utility function: Economic Theory Behind Modeling = 1. Basic theorem of “markets as maximization” (Samuelson, Negishi) 2. This allows us (in principle) to calculate the outcome of a market system by a constrained non-linear maximization.

7. Specific Tools 1.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). 2.EXCEL “Solver,” which is convenient but has relatively low power. - I will use this for the Hotelling model. 3.GAMS software. Has own language, proprietary software, but very powerful - This will be used later in global warming models, specifically Yale-DICE model.

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

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