Inflation and Farm Tractor Replacement in the U.S.: A Simulation Model: Reply

Two recent contributions to this Journal (Chisholm; Kay and Rister) have been concerned to extend the literature on the replacement problem to encompass the real world decision milieu of the farmer via taxation considerations. These extensions, while welcome and useful, seem to us to be incomplete in the inflationary world of the 1970s: specifically, they make no explicit allowance for the link between optimal replacement age and the nature of the allowances permitted by the taxation authorities in an economy with rising prices. We would suggest that inflation has not been so negligible in most developed economies that it can be disregarded in this aspect of farm decision making. The principal purpose of this note, then, is an attempt to extend further the tax-adjusted replacement model to embrace relevant considerations of inflation. We shall extend the results of Kay and Rister, but whereas previous contributions have utilized discrete time models, we shall use a continuous time model. It may be noted that Perrin developed a continuous time depreciation model, but without consideration of taxation and inflation. His examples, however, utilized discrete, annual models only. It finds the optimal replacement age exactly, an advantage of some importance in its own right, but more important, one which enables the sensitivity of replacement to changes in other conditions to be assessed with greater precision.