Adjustment costs and variable inputs in the theory of the competitive firm

Abstract

This paper has focused on a number of negative results that arise when we attempt to make the theory of the competitive firm “dynamic” by introduction of adjustment costs. Such generalizations of the theory of the firm have the benefit that they do allow a theory of investment behavior, which was touched on briefly. Investment-demand can be shown to be inversely related to capital stock and to the real rental ( r + μ) g, at least in a neighborhood of a long-run equilibrium point. Furthermore, we were able to show that the long-run demand for capital was inversely related to the rental. These inferences flow from the intertemporal optimization process. However, it appears that the intertemporal optimization theory is not capable of yielding a number of other inferences that are implied by the standard atemporal model. Though all behavior functions are homogenous of degree zero in prices, we were unable to demonstrate (a) the nonpositivity of own-wage effects on the demand for the variable factor either in the short-run or the long-run, (b) the nonnegativity of supply effects of a change in product price in either the short-run or the long-run or (c) that short run effects are less elastic than long-run effects. Furthermore, the intertemporal optimization theory does not, in general, yield symmetric long-run factor-demand functions, though F 23 ≡ 0 is a sufficient condition for that property; this asymmetry, of course, excludes the possibility of obtaining these long-run factor demand functions through optimization of any surrogate static profit function. A fairly weak and plausible sufficient condition for (a) was F 12 F 23 > 0. No such “reasonable” sufficient conditions for either (b) or (c) appear to exist. The economic reasons for these problems are essentially two. The ambiguity of the results for the variable factor (i.e., the issue (a)) and the asymmetry of long-run factor demands stem from the possibility, which the author regards as entirely plausible in practise, that a variable factor may not only contribute to production activities but also to the growth activities of a firm. Labor services may facilitate plant expansion as well as being useful in the production process itself. Such a possibility is entirely excluded from the static optimization model. The second reason for many of the ambiguities of the intertemporal model arises from the dual role of the firm as both an owner of a stock of productive capital goods and a producer of a finished product. In the firm's second capacity it “rents” capital services from itself in its first capacity and this internal relationship is “monopsonistic”. This appears to lie at the root of the sign ambiguities of the supply effects of a change in product price.