Economic Models of Optimal Energy Use under Global Environmental Constraints

Abstract

Part 1 of this paper presents simple control models on the use of fossil fuels and the global environmental problems caused by carbon dioxide accumulation. The reference model assumes that energy is the only productive factor in the economy and that energy use causes carbon dioxide accumulation which lowers productivity. Consumption of the single good in the economy causes a flow of utility. The policy maker acts to maximize the integral of the discounted utility stream. The single state variable is carbon dioxide concentration. Unique features of the model are the very general production function and the assumption that the pollutant does not affect utility directly.

Conditions which assure the existence of an optimal equilibrium for these models are discussed. In order to focus on policy directed changes such models are specified to be solvable numerically and applied to specific issues of interest. A specific form involves the assumption that the negative impact of carbon dioxide accumulation occurs abruptly at specific levels of atmospheric carbon dioxide.

Part 2 pursues in depth some specific aspects of optimizing economic models for fossil fuel use given carbon dioxide accumulation, e.g. technical progress, international co-operation and structural uncertainty. We develop a taxonomy of technical progress situations and show that depending on the assumptions the optimal steady state CO₂ concentration may rise or fall with increases in the steady state level of progress.

Two cases of international co-operation in controlling CO₂ accumulation are examined, the co-operative and non-co-operative case. In the non-co-operative situation the critical level is reached sooner, even though the region concerned about CO₂ always emits less carbon than in the co-operative case. Major results pertain to uncertainty. Here we show, supported by numerical examples, that a “certainty equivalent” treatment of uncertainty can lead to significantly higher than optimal estimates of the desirable level of fossil fuel use as compared to a proper full treatment of uncertainty.

The contents of this paper are the author’s sole responsibility. They do not necessarily represent the views of the Oxford Institute for Energy Studies or any of its Members.

Acknowledgement: This is to thank O. von dem Hagen, University of Oldenburg, for checking some of the formulas, discovering some mistakes and recalculating Table 1. All remaining errors are mine.