Economics of exhaustible resources

Economics 331b Spring 2011 1

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.

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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

McKelvey diagram on resources

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Two important approaches

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

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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.

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Hubbert theory

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

3,600 3,200 2,800 2,400 2,000 1,600 1,200 800 400 0 00 10

Hubbert curve for US

US crude oil production Hubbert curve 20 30 (peak 1976; total = 222; cum to date = 197) 40 50 60 70 80 90 00 10 Data source: Oil production for EIA. Hubbert curve fit by Nordhaus.

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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?

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Solution quantities

12 10 8 6 4 2 0 0 Low cost Backstop 5 10 15

Year

20 25 30 10

Solution prices

200 180 160 140 120 100 80 60 40 20 0 0 5 10 15

Year

Supply price low cost Market price 20 25 30 11

Hotelling theory

• Let r t = net price of oil in ground = p t = price of oil t – extraction cost t – e 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 ground for grade i, location j, time t.

= return on oil in the • Note that arbitrage condition holds only when production is positive (price-quantity duality condition) 12

Real crude oil prices (2010 $ per barrel) 200 100 80 60 50 40 30 20 10 50 55 60 65 70 75 80 85 90 95 00 05 10 Data source: Oil price data from EIA and BLS. Price deflation by CPI from BLS.

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200 100 80 60 50 40 30 20 Real oil price 10 1975 Hotelling growth at r = 3% per year 1980 1985 1990 Hotelling line 1995 2000 Real oil price 2005 2010 14

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.

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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

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