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• W2005890408 abstract "The paper considers some implications of the depreciation rate of capital's being a variable subject to choice by its users. It is found that conventional results concerning the relationship between the interest rate and the price of capital (and, therefore, gross investment) do not change in an important way, while the same is not true with respect to total capital services, employment and output. For changes in the interest rate, variable depreciation magnifies the long-run effects on those variables; a preannounced output price change results in short-run changes of those same variables in a direction opposite to those of the long run. L'amortissement variable: quelques-unes des consequences qu'il implique. Ce memoire examine quelques-unes des implications d'un taux d'amortissement du capital qui varie selon le choix de ceux qui en font usage. II en ressort que les resultats usuels quant au rapport entre le taux d'interet et le prix du capital (et donc l'investissement brut) ne sont pas modifies d'une faqon importante. Cependant, tel n'est pas le cas pour le rapport entre le taux d'interet d'une part, et l'ensemble des services du capital, le niveau d'emploi et de production, d'autre part: l'amortissement variable magnifie les effets 'a long terme du taux d'interet sur ces variables; un changement pre-annonce du prix du produit va entrainer des changements A court terme dans ces variables dans une direction opposee a celle des changements A long terme. While in much of the standard theory of capital the rate of physical depreciation is taken to be a constant, there is a longstanding tradition that This is a shortened version of a paper written while on a visit to the University of Gottingen, West Germany during 1983, under a grant from the Deutsche Forschungsgemeinschaft. I am thankful to members of the economics seminar at Gottingen, R. Battalio, T.R. Saving, an anonymous referee, and, as always, to my colleagues at CEMA for their comments. Canadian Journal of Economics Revue canadienne d'Economique, XIX, No. I February fevrier 1986. Printed in Canada Imprime au Canada 0008-4085 / 86 / 99-113 $1.50 ? Canadian Economics Association This content downloaded from 157.55.39.58 on Wed, 16 Nov 2016 04:24:48 UTC All use subject to http://about.jstor.org/terms 100 Leonardo Auernheimer recognizes that, in fact, in most cases depreciation is a variable subject to economic choice by the user of the capital good.' The treatment of such choice relates to a rather general literature, covering topics ranging from the old concept of 'user's cost' to the analysis of idle capacity, but it can be also more precisely associated with the idea of the choice variable's being the 'intensity of use' and, with it, the flow of services and the rate of depreciation. Standard references are the works of Taubman and Wilkinson (1970a, b), Lucas (1970), and Calvo (1975). Here, the question concretely relates to the choice of a certain intensity of use which, when increased, on one side raises the level of services provided by a unit of capital, and on the other increases the rate at which capital depreciates. The purpose of this paper is to discuss some of the implications of variations in the intensity of use, the flow of services and the rate of depreciation. In particular, the analysis focuses on the extent to which standard conclusions derived from the conventional view (that is, treating the flow of services of the capital stock as strictly proportional to the stock and the rate of depreciation as fixed) need to be modified when the choice is possible. Of course, we should expect flexibility to matter; the question is for what, and in which manner. The results of this paper show that while some of the conventional results need no modification, in some instances the consequences of flexibility run contrary to what intuition would initially indicate, and in others its presence brings about, in the short run, results opposite to those relevant in the long run an outcome possible only when flexibility is present. The analysis is performed for both the steady state and the adjustment process, and within the simplest framework at the level of the industry, in a model similar to Taubman and Wilkinson's (1970b), the main difference being the use, in our case, of the assumption of rational expectations (perfect foresight, in a deterministic model) concerning the price of the capital good. In the discussion of both the short and the long run we use an assumption that clearly circumscribes the scope of the analysis, namely that the price of the industry output remains constant. From the analytical viewpoint the assumption greatly simplifies the results and at least allows to gain some feeling about the general direction of the results; furthermore, there is at least one important case the one analysed in the third section, below for which such an assumption is empirically relevant. It does, however, restrict the direct applicability of some of the results. The first section presents the framework and elaborates on some of the long-run results. The next section discusses the mechanics of the adjustment I Another treatment is the case in which the rate of depreciation is subject to choice only at the time at which the capital good is produced, remaining fixed from then on, and with a cost of production inversely related to the depreciation rate embodied in the good. See, for example Auernheimer and Saving (1977), Kamien and Schwartz (1974), and Swan (1970). Curiously enough, the literature on the two alternative treatments has developed quite independently, despite the fact that many of the questions addressed are essentially the same. See footnote 3, below. This content downloaded from 157.55.39.58 on Wed, 16 Nov 2016 04:24:48 UTC All use subject to http://about.jstor.org/terms Variable depreciation 101 process, and the third section analyses, as a particular application but one with important implications for policy, the consequences of a pre-announced exogenous change. The final section contains some concluding remarks. Continuous time is used throughout. THE FRAMEWORK AND THE COMPARATIVE STATICS Consider the case of a competitive industry producing commodity x, according to the production function" @default.
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• W2005890408 title "Variable Depreciation and Some of Its Implications" @default.
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