Academic journal article Academy of Strategic Management Journal

Output Decisions of Firms under Uncertainty: Some Micro-Theoretic Analysis

Academic journal article Academy of Strategic Management Journal

Output Decisions of Firms under Uncertainty: Some Micro-Theoretic Analysis

Article excerpt

INTRODUCTION

Traditionally, risk-return models have been used in portfolio theory. The theory of the firm under uncertainty has not been analyzed with the risk-return approach except for few works such as the mean-standard deviation model of Hawawini (1978). Expected utility approach seems to be popular in this field of study notwithstanding the intuitive appeal of the risk-return dichotomy in the business world.

This paper is a theoretical re-exploration of various risk-return models to the output decision making of a competitive firm facing uncertainty in the product price. Our attempt here is to find if different results do arise under risk-return vs. expected utility approaches. The results of the risk-return models in this paper are compared to those of the expected utility literature. One important difference in the results is that the risk-return approach requires some restrictions on the cost function of the firm whenever the assumption of decreasing absolute risk aversion is required in the expected utility approach in order to obtain deterministic comparative statics results.

The remainder of the paper is structured as follows. Section 2 presents a brief review of some related literature. Section 3 is on the output decisions of a competitive firm under product-price uncertainty within mean-general risk model, and mean-standard deviation model. Section 4 concludes by comparing the major findings of this paper with the corresponding results in the expected utility approach.

LITERATURE REVIEW

Mills (1959) studies a monopolist under uncertainty and is one of the earliest works introducing uncertainty in microeconomics. But Mills' work suffers from serious limitations, such as, assumption of risk neutrality. Zabel (1970) is a generalization of Mills' article in some respects. Zabel uses multiplicative form of uncertainty instead of additive separability of uncertainty. Sandmo (1971) and Baron (1970) deal with a competitive firm facing an uncertain price of its product. These two articles are complementary to each other. The marginal impact of changing the distribution of price is studied by Sandmo but not by Baron, while Baron studies the effect of an increase in risk aversion which Sandmo ignores. Sandmo finds that the overall-impact of uncertainty is to reduce output assuming that the marginal cost is rising. However, Sandmo himself could not determine the sign of the marginal impact of uncertainty (for example the effect of a mean-preserving spread). But this problem was later taken up by Ishi (1977) who showed that nondecreasing absolute risk aversion is a sufficient condition for the marginal impact to be in the same direction as the overall impact.

Baron proves that, "... optimal output is a nondecreasing function of the firm's index (Arrow-Pratt measure) of risk aversion." Moreover, an increase in fixed cost decreases output for decreasing absolute risk aversion. Baron also concludes that if risk aversion is prevalent, as seems reasonable, prices are higher and outputs are lower than if firms were indifferent to risk. Finally, Baron finds that under uncertainty it is possible for the short run supply function of the risk averse firm to have a negative slope. This is a result which cannot occur in deterministic microeconomic theory. Baron (1971) demonstrates that for an imperfectly competitive firm under uncertainty the strategies of offering a quantity or changing a fixed price yield different results. Leland (1972) considers three alternatives behavioral modes under uncertainty, and claims that the result of Baron (1970) and Sandmo (1971) are special cases of his more general results. Lim (1980) addresses the question of ranking these behavioral modes under risk neutrality.

Batra and Ullah (1974) follow Sandmo heavily except that they use a production function and adopt an input approach instead of an output approach. As shown by Hartman (1975,1976), the Batra and Ullah paper suffers from a partial approach in deriving their conclusions about the overall impact of uncertainty on input demands considering both inputs simultaneously. …

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