Factor Demand with Output Price Uncertainty

Abstract

The effects of output price uncertainty on a competitive firm's supply and factor demands have recently been explored under the assumption that all decisions are made before the price is observed. Agnar Sandmo has shown that a risk-averse, competitive firm with a nonrandom cost function will produce a smaller output if the price is random than it would if the price were known with certainty to equal its mean. Raveendra Batra and Aman Ullah and I have extended the analysis by considering the effects of output price uncertainty on factor demands. Among other things, Batra and Ullah show that the firm will choose its inputs to minimize the cost of producing whatever level of output is chosen. This result, combined with the Sandmo result that the presence of uncertainty reduces output, implies that the effects of uncertainty on factor demands depend on what effect the decreased output due to uncertainty has on the cost minimizing levels of inputs. Except for the rare case of inferior factors, the presence of uncertainty reduces factor demands. Finally, it is clear from these analyses that if the firm is risk neutral, the uncertainty has no effect on supply and factor demands. In this paper I relax the assumption that all inputs are chosen before the output price is observed. My conclusions show that the results noted above are really rather sensitive to that particular assumption. A simple two-input, one-output model of the firm is employed. One of the inputs, which I call capital, is quasi fixed in the sense that it must be chosen before the output price is observed. The other input, which I call labor, is variable since it is not chosen until the output price is observed. Clearly, this implies that the level of output is not determined until its price is known. Although labor may be a name for the variable input in view of the recent discussions of its character, it seems apparent that in many situations there are inputs which can be varied on short notice. By allowing a variable input in this sense we considerably alter the situation facing the firm. If, after observing the output price, it turns out that the firm made a poor choice regarding the quasi-fixed factor, it is able to partially adjust by choosing an appropriate level of the variable input. This ability to make adjustments for what, ex post, appears to be a decision is totally lacking if all inputs must be chosen before the uncertainty is resolved. In Section I the basic model is presented. In Section II the analysis for a risk-neutral firm is carried out, and Section III contains an example. In Section IV the analysis is extended to a risk-averse firm. The final section contains some brief concluding comments.

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