Input Decisions of Competitive Firms Under Uncertainty : Some Comparative Analyses Using Risk-Return Models 183 INPUT DECISIONS OF COMPETITIVE FIRMS UNDER UNCERTAINTY : SOME COMPARATIVE ANALYSES USING RISK-RETURN MODELS

The theory of the firm under uncertainty has been usually studied using the expected utility approach. This paper applies various mean-risk models to the input decision making of a competitive firm facing product price uncertainty. The risk formulation used in this paper includes a prespecified target level of profit, similar to those discussed in Fishburn (1977). Furthermore, the measure of risk-aversion used in this model indicates the relative weight given by the agent to the risk component of the mean-risk objective function. The expected utility results require decreasing absolute risk aversion as a sufficient condition. But the corresponding sufficient condition in the risk-return model of this paper is the ratio of wages to marginal productivity of labor that is at least as large as the sum of average input cost and average target level of profit. Increases in input prices and firm's risk aversion reduce input demands resulting in lower output. INTRODUCTION This topic is of particular importance because business firms are exposed to more intense competition causing them to lose their product-pricing power to increase total profit. As a result, their product-demand conditions are more uncertain making product prices highly unpredictable. Consequently, firms need to allocate and utilize inputs in the production process to minimize production cost to enhance competitiveness. The topic is also interesting and merits an indepth theoretical analysis because firms now face more uncertainties because of i) rising product price competitiveness ii) unexpected input supply disruptions, iii) higher competition in input procurements and pricing, iv) uncertain technological progress that unpredictably alters market dynamics and v) fragmentation in the production process (outsourcing). Because of these factors, firms need to pay closer attention to efficient input allocations and utilizations thereof to reduce both variable and fixed costs. In short, to be competitive, firms have to be cost-efficient in an uncertain market environment. This paper thus analyzes efficient input decisions by firms under uncertainty. For example, GM and Ford have been facing steep price competition from foreign auto-suppliers like Japanese Toyota and Honda. To reduce cost, GM and Ford outsource various components. They are also forced to downsize their U.S. workforce and reduce capital expenditures. Colossal losses and shrinking market-share have raised their risk aversion. As a result, the hiring of auto workers and capital outlays Southwestern Economic Review 184 are declining which reduce auto production by GM and Ford in the U.S. This phenomenon conjecturally accords well with the major findings of this paper. Risk-return models have been used extensively in portfolio theory. The theory of the firm under uncertainty has not been analyzed with the risk-return approach except for a limited number of works, such as, the mean-standard deviation model of Hawawini (1978). The expected utility approach has become popular in this field of study notwithstanding the intuitive appeal of the risk-return dichotomy in the business world. This paper applies various risk-return models to the input decision making of a competitive firm facing uncertain product prices. The results of the riskreturn models are compared to those of the expected utility literature. The risk-return approach requires moderate restrictions on the cost function of the firm. The expected utility approach requires a more stringent assumption of decreasing absolute risk aversion in order to obtain deterministic comparative static results. Our attempt is to explore whether different results arise under risk-return vs. expected utility approaches. The remainder of the paper is organized as follows. Section II presents literature review. Section III is about the purpose of the paper and basic assumptions of the models. Section IV discusses mean-general risk model. Section V is about mean-standard deviation model. Finally, section VI offers conclusions. 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 Input Decisions of Competitive Firms Under Uncertainty: Some Comparative Analyses Using Risk-Return Models 185 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. Batra-Ullah also assume concavity of the production function and decreasing absolute risk aversion to show that the marginal impact of uncertainty in terms of mean-preserving spread is to reduce input demands. Hartman (1975) criticizes the partial approach adopted by Batra-Ullah and in his 1976 article, Hartman also relaxes the assumption that all inputs are chosen before the product price is observed. He claims that the results of Batra-Ullah and Sandmo are rather sensitive to that particular assumption. Korkie(1975) comments that Leland’s conclusion is the result of the assumption called the principle of increasing uncertainty. Blair (1974) also discusses some implications of random input prices on the theory of the firm. Arzac (1976) allows for substitution between expected profit and safety, and proposes the following objective: Maximize x + g (α), g' < 0, g'' < 0. , where α is the probability that profit falls below a disaster level. This criterion satisfies the continuity axiom but only its linear form satisfies the independence axiom and is compatible with utility theory ( Markowitz (1959) and Arzac (1976)). Arzac also applies the safety-first approaches to the theory of the firm under uncertainty and concludes the following: a) The overall impact of uncertainty is to lower output. b) Maximizing the certainty equivalent profit has the same comparative statics properties as the certainty model. c) If suitable empirical evidence on the firm's past responses to changes in the profit tax rate and in lump sum taxes and subsidies are available, then an almost complete discrimination among the alternative criteria can be made. A survey of stochastic dominance principle which is used in comparative statics analyses of this paper is found in Levy (1992). Examples of various applications of this principle in investment decision making are available in Levy and Robinson (1998), Kim (1998) and Kjetsaa and Kieff (2003). Empirical works on this principle are reported in Porter and Gaumnitz(1972) and Barret and Donald (2003). Gotoh and Konno (2000) study relationship between Third Degree Stochastic Dominance and Mean –Risk Analyses. PURPOSE OF THE PAPER AND BASIC ASSUMPTIONS OF THE MODELS In this paper we study the choice of inputs of a competitive firm facing uncertainty in the product price, assuming that the firm has a subjective probability distribution for the product price. First, we list the basic assumptions underlying all the models to follow. Second, we study the general risk formulation and derive some comparative static Southwestern Economic Review 186 results. Third, the mean-standard deviation model is used which gives stronger results. Finally, we compare the results of the mean-risk models with those of the corresponding expected utility models. Basic Assumptions (a) We consider two variable inputs, capital (K) and labor (L). (b) There is no fixed cost. (c) The firm is a price taker in the probabilistic sense for its product price (p). The subjective probability distribution of p is F (p), the probability density function is f(p), and the mean is p . (d) The prices of inputs (w for L, and r for K) are given parameters with certainty to the firm. The follow