Competitive Production and Increases in Risk

Abstract

The theory of the firm is a monumental achievement of neoclassical economics. Without this engine of analysis, it would be difficult, if not impossible, to comprehend the pricing, output, and input decisions of firms as they respond to routine events like the imposition of a tax, the opening of a new market, a technical innovation, and a sudden shortage of a key factor of production. It is remarkable that this theory has been successful in explaining behavior that to a large extent is motivated by both profit and risk when the theory itself has only explicitly considered the profit motive. This is not the place to dwell on the evolution of economic theory; it suffices to note that there are many important economic phenomena that the purely deterministic theory does not explain.' The purpose of this note is to elucidate the way in which risk influences the output decisions of riskaverse entrepreneurs and the number of riskneutral firms in a competitive industry. In both cases, the predicted behavior differs from that of the deterministic theory. In our study we shall restrict attention to the behavior of firms in a single period 2 setting. The firm has no control over price and, because storage makes no sense, simply sells all of its output at the going price. The source of uncertainty is the requirement that the firm produce before price is known, where the price is a random variable with a known probability distribution. The firm chooses output to maximize its expected utility. It is well-known that, in the presence of uncertainty, the optimal output of the risk-averse firm is less than that of the riskneutral firm; moreover, increases in risk aversion, in the sense of Arrow and John Pratt, lead to further diminutions in output. On the other hand, for a fixed degree of risk aversion, the change in output induced by a mean-preserving increase in risk depends on the shape of the cost curve as well as the sign of the third derivative of the utility function u and the sign of the second derivative of qu'(q). Next, competitive industry behavior under uncertainty is analyzed. In order to isolate the effect of uncertainty, firms are assumed to be risk neutral. We show that both the optimal number of firms in the industry and excess capacity increase as industry output becomes riskier. Results like this are important for probabilistic economics, for it would be unfortunate if the vitality of the stochastic theory of the firm relied solely on the controversial assumption of risk aversion.3

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