1. Economics of exhaustible resources Economics 331b Spring 2011 1

2. Agenda Monday: Energy primer Wednesday: Hubbert curve and Hotelling theories Thursday pm: Lint will show you how to use spreadsheets and Solver Friday: snow day Monday: Hotelling v. Hubbert Sometime next week: A pset on using spreadsheets and numerical optimization. 2

3. Questions about exhaustible resources 1.What is the optimal (efficient) price of the resource? 2.Is it an “essential” resource? - Question of elasticity of substitution between resource and other inputs. Is there a backstop technology? At what price? 3.Is the use of the resources “sustainable”? - This refers to whether net investment in the economy is positive. - E.g., investment in capital greater than disinvestment in value of resources 3

4. 4 McKelvey diagram on resources

5. Hubbert concerns the Q Hotelling concerns the P Can they be married into a happy P-Q couple? 5 Two important approaches

6. 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. 6

7. Hubbert theory 7 Q max = Maximum producible resources P(t) = production

8. Hubbert curve for US Data source: Oil production for EIA. Hubbert curve fit by Nordhaus. 8

9. Hotelling theory: Derives the price of an exhaustible resource Let’s work through an example Assume demand = 10 per year (zero price elasticity) Resources: 100 units of costless oil unlimited amount of “backstop oil” at $100 per unit Discount rate = 5 % per year Questions: 1.What is the efficient allocation over time? Q and P? 2.What would be the market pricing in a competitive market? 3.How do (1) and (2) compare? 9

10. Solution quantities 10

11. Solution prices 11

12. 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) 12

13. 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) 13

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15. Next step We next will build a little economic model of the world oil industry using geological data, demand data, and solving using numerical optimization. This will give you a chance to learn numerical optimization. 15

16. Why we will learn numerical optimization 1.You will use to build a little economy-climate change model and optimize your policy. 2.You have learned the theory (Lagrangeans etc.), so let’s see how it is applied 3.Optimization is extremely widely used in modern analysis: - statistics, finance, profit maximization, engineering design, sustainable systems, marketing, sports, just everywhere! 4.It is fun! 16

17. Standard Tools for Numerical Optimization in Economics and Environment 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). [For picture, see http://en.wikipedia.org/wiki/File:NewtonIteration_Ani.gif] 2.EXCEL “Solver,” which is convenient but has relatively low power. - I will use this for the Hotelling model. [proprietary version is better but pricey.] 3.GAMS software (LP and other). Has own language, proprietary software, but very powerful. - This is used in many economic integrated assessment models of climate change. GAMS software. Has own language, proprietary software, but very powerful. 4. MATLAB and similar. 17