Knowledge that Transforms

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.

Judith Lave and Lester Lave, in their article in this Review, have proposed two imaginative, if simple, techniques for estimating cost functions in multiproduct, multiservice industries. Both techniques rest on the assumption that output mix varies among firms but is constant over time within any one firm. The first proposed technique involves two stages of analysis and allows a simple cost function to differ among firms. In the first stage a cost function is estimated for each firm. In the second stage a search is made for the factors causing variation among the estimated individual firm cost function parameters. The second proposed technique is based on the more limited assumption that, apart from the intercept term, all firms have the same cost function. Here the data are pooled and a single cost function estimated. Lave and Lave, in the course of analysis, conclude that their dichotomous first technique is too inflexible, given their particular problems and opt for the second method. Despite their discarding of the first technique, others have been tempted to try it out and I think some discussion of this proposed estimation procedure is in order.1 I think this discussion will also have some bearing on the Laves' second method. The Laves' search for the causes of variation among individual cost functions involves taking firm cost function parameters and regressing them on various sets of independent variables in an effort to find significant relationships. Research workers using such a procedure should be aware that it is unusual in that before these regressions are ever run, an estimate of the variance of each dependent variable is available. Such knowledge may well be unpleasant. If on testing the hypothesis of homogeneity of variance using likelihood ratio methods, the null hvpothesis is rejected, then the problem of heteroscedasticity in regressions using estimated parameters as dependent variables must be confronted. The now classical results indicate that applying ordinary least squares to an equation with a heteroscedastic error structure, while giving unbiased estimates of the coefficients of the independent variables, is nonetheless an inefficient method. Also, using the usual formula to calculate sampling variances may well involve an overstatement of the true sampling variances. Given the comparatively low I-statistics reported in the Laves' Tables 1, 2, and 3, the possibility exists that many of the variables reported as significant were really not at all significant. What can be done about this problem of heteroscedasticity? Since estimates of the variance of each observation on the dependent variable are available, a straightforward procedure would imply weighting each observation on all variables used in the secondstage equation by the inverse of the estimated standard error of the dependent variable. This weighting technique, of course, is nothing more than an application of generalized least squares, where an estimate of the variance-covariance matrix is used in place of the true variance-covariance matrix. One may well wonder whether the twostage procedure is necessary at all. After all in the Laves' case, the linear second-stage equation (4) can easily be substituted into the linear first-stage equation (3). Unfortunately, to the extent that the variances of the stochastic terms in the first-stage cost equations are hospital specific, the fundamental equation resulting from this substitution will still contain a heteroscedastic error structure. Interestingly enough, * The University of Michigan. I would like to thank Takeshi Amemiya for good advice and Judith Lave and Lester Lave for providing the data used in the analysis in this paper. I See for example, J. G. Williamson. With increased interest in the last ten years in models where it is assumed that the parameters have a stochastic component, it is not surprising that there also be increased interest in models where the parameters are subject to systematic variation.

In contemplating the future course of economic growth in the West, scientists are divided between one group crying and another which denies that species' existence. One persistent concern has been that man's economic activities would reach a scale where the global climate would be significantly affected. Unlike many of the wolf cries, this one, in my opinion, should be taken very seriously. The present article will first give a brief overview of the climatic implications of economic activity with special reference to carbon dioxide, and then will present possible strategies for control. A more complete report with references to the literature on climatic change is contained in Nordhaus (1976). It is thought that the economic activities which most affect climate are agriculture and energy. Of these, the latter is probably more significant, is certainly more easily analyzed, and will be discussed here. In the energy sector, emissions of carbon dioxide, particulate matter, and heat are of significance for the global climate.