Energy Price Uncertainty and Optimal Factor Intensity: A Mean-Variance Analysis

Abstract

THE DRAMATIC INCREASE in energy prices in the 1970s has stimulated interest in the effect of energy prices on the demands for various factors of production. In analyzing the choice of energy-using characteristics of capital, it is important to recognize that a firm's energy-capital ratio is much more flexible prior to undertaking a capital investment than it is after the capital is put in place. In this paper we examine factor intensity choices in a stochastic putty-clay model. Ex ante, when the firm is making investment decisions, the price of energy is unknown. The energy/capital ratio is flexible ex ante and the firm chooses the optimal energy intensity based on the probability distribution of energy prices. Ex post, the energy/capital ratio is fixed and the price of energy is known. The firm cannot adjust the energy/capital ratio but can choose not to use its capital if the realized price of energy is too high.2 Recently, Kon [3] has studied factor demands in a stochastic putty-clay model in which the price of output is random and the prices of factors of production are known with certainty. In this paper, we focus on the effects of energy prices and thus treat factor prices as random and the output price as known with certainty. This difference in the source of randomness appears to make little difference in the comparison of optimal factor intensity under certainty and under uncertainty; indeed Proposition 1 in this paper corresponds to Kon's Proposition 1. In this paper we then go on to examine the effects on optimal factor intensity of changes in the mean and variance of the price of energy.3 The option to shut down during unfavorable price regimes plays an important role in our analysis. In Section 1 we develop a stochastic putty-clay model and compare a risk-neutral firm's behavior under certainty and uncertainty. The effects on energy-intensity of changes in the mean and variance of energy prices are analyzed in Section 2.