Session 2 Natural Resource Economics

a) Fossil fuel. Describe the key characteristics of world supply of fossil fuel. You should answer questions like; How large are known and expected reserves of the different types of fossil fuel relative to current and future consumption? In current prices, approximately how large is the value of these stocks? How large is the share of world energy production that comes from fossil fuel? How costly is extraction now and in the future? How geographically concentrated are reserves? Discuss the “peak oil” controversy?

Some possibly useful reading:

BP Statistical Review of World Economy

An assessment of World Hydrocarbon Resources (Rogner -97)

World Energy Outlook 2008

World Energy Outlook 2010 Executive Summary

b) The production function The central feature of the neoclassical framework is the production function. With only capital and labor as inputs, the dominant functional form used has typically been a Cobb-Douglas (unitary-elasticity) formulation. When fossil energy is added as an input into the aggregate production function, however, one also has to take a stand on how the three arguments should be nested. One possibility is that the production function is Cobb-Douglas in all three arguments, i.e., F(A,K,L,E)=AK α L1-α-Eθ with α<1 and θ<1. This formulation is for instance used by Nordhaus in the RICE-model.
Describe the main implications of the above Cobb-Douglas function. Describe also how data can be used to evaluate whether the Cobb-Douglas function has empirical support. Suggest alternative functional forms for the production function. Why is the production function important when it comes to welfare analysis of climate change?

Some possibly useful reading:

Griffin, James M. and Paul R. Gregory. "An intercountry translog model of energy substitution responses." American Economic Review, 1976, Vol. 66 No.5: pp.845-857.
Hudson, Edward A. and Dale W. Jorgenson (1974). "U.S. energy policy and economic growth, 1975-2000." Bell Journal of Economics, 1974, Vol. 5: pp. 461-514.
Hassler, Krusell, Olofsson,"Energy-Saving Technical Change", mimeo IIES

c) The equilibrium price path for a natural resource in finite supply? What is the Hotelling formula, which Hotelling provided as an answer to this question, and how does one derive it? Specify the assumptions, and try to find as general a case as possible for stating and deriving it. What is the "Hotelling rent" earned on a resource?

It is useful to concretize by looking at a specific model (though the insights behind the Hotelling formula are quite general). Suppose, for example, that you are looking at a one-sector growth model where an aggregate production function specifies the resource as an input (the obvious example here is that fossil fuel, because it can be used to produce energy, which is used in production of most goods and services). Suppose also that there is some technology for extracting the resource---though an important special case that you need to discuss is the case where the resource extraction cost is zero at all times (a "cake-eating" problem). How would you then calculate the equilibrium price path for the resource? The Hotelling formula specifies an equation that relates the price of the resource in t to that in t+1. The Hotelling rent is the value of the total remaining resource at t.

Some possibly useful reading:

Hotelling, Harold. “The economics of exhaustible resources.“, Journal of Political Economy, 1931, Vol. 39, : pp. 137-175.

Solow, Robert M. “Intergenerational Equity and Exhaustible Resources“, The Review of Economic Studies, 1974, Vol. 41: pp. 29-45.

Stiglitz, Joseph. “Growth with Exhaustible Natural Resources: Efficient and Optimal Growth Paths“, The Review of Economic Studies, 1974, Vol. 41: pp. 123-137.

Golosov, Hassler, Krusell and Tsyvinski, "Optimal taxes on fossil fuel in general equilibrium", mimeo IIES