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

2. Hubbert concerns the Q Hotelling concerns the P Can they be married into a happy P-Q couple? 2

3. Hubbert theory 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

4. Hubbert curve for US Data source: Oil production for EIA. Hubbert curve fit by Nordhaus. 4

5. Hotelling theory Let r t = net price of oil in ground = p t – e t = price of oil t – extraction cost t Oil is developed and produced to meet the arbitrage condition for assets: r t * = market rate of return on assets = r i,j,t = return on oil in the ground for grade i, location j, time t. Note that arbitrage condition holds only when production is positive (price-quantity duality condition) 5

6. Data source: Oil price data from EIA and BLS. Price deflation by CPI from BLS. 200 100 80 60 50 40 30 20 10 50556065707580859095000510 Real crude oil prices (2010 $ per barrel) 6

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8. Arranged marriage of Hotelling and Hubbert Let’s construct a little Hotelling-style 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 8

9. 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. 9

10. 10 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.

11. Specific Tools for Finding Solution 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 is used in many economic integrated assessment models of climate change. 11

12. Department of Energy, Energy Information Agency, Report #:DOE/EIA-0484(2008) Estimates of Petroleum in Place 12

13. Petroleum supply data Sources: Resource data and extraction from EIA and BP; costs from WN 13

14. Demand assumptions Historical data from 1970 to 2008 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 Backstop price = $100 per barrel of oil equivalent. Conventional oil and backstop are perfect substitutes. 14

15. Solution technique 15

16. Picture of spreadsheet 16

17. Results: Price trajectory 17

18. Results: Price trajectory and actual 18

19. Results: Output trajectory How differs from Hubbert theory: 1. Much later peak 2. Not a bell curve; slower rise and steeper decline 19

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21. Further questions Why are actual prices above model calculations? Why is there so much short-run volatility of oil prices? Since backstop does not now exist, will market forces induce efficient R&D on backstop technology? 21