The Neoclassical Production Function: Reply - Gallaway, Lowell E.; Shukla, Vishwa (American Economic Review, 1976)
The comments of Kazuo Sato and P. Garegnani indicate a technical problem in our original analysis. Its effect is to make it possible for reswitching to occur even though what Sato calls our capital-intensity condition is satisfied, provided that the factor price contours in question are quite similar in nature. Thus, as Sato notes, our condition only definitely reduces the possibility of reswitching. Unfortunately, all this may be simply a minor exegesis of what is perhaps a trivial question. Let us explain that statement. Consider the standard case of a full-employment steady-state economy (constant population and labor force) in which alternative two-commodity indecomposable production systems are available. Assume that producers will choose the technique that is profitable. Conventionally, this is taken to mean that they will choose the productive technique that will provide the highest rate. For example, Luigi Pasinetti states: Clearly, on grounds of profitability, that technique will be chosen which-for any given wage rate-yields the higher rate of profit (p. 507). In a micro-economic context one would not quarrel with this proposition. A given investment in capital goods will be the higher the rate of return on the investment. However, at our highly aggregated (economy wide) level of analysis of the meaning of capital and the nature of the production function, this is not so obvious. At the heart of the Cambridge (England) criticism of neoclassical analysis is the proposition that capital in an aggregate sense can only be measured through the use of some pricing numeraire which itself is functionally related to the level of wage and (interest) rates. In this highly interdependent world (illustrated by the twocommodity indecomposable production systems under discussion), it is alleged that the straightforward neoclassical propositions break down because of the interrelationship between the value of capital and the (interest) rate. Unfortunately, the analysis upon which this conclusion has been based appears to have ignored the fact that at the aggregate level the phrase more profitable has an added dimension that is lacking at the micro-economic level. This added dimension is the opportunity to employ capital. In the models under analysis the rate of and the quantity (in value terms) of capital employed are simultaneously determined. Together, they explain the volume of profits per head associated with a given technique and wage-profit rate combination. Since net output per head for any technique is constant (at the level of the wage rate associated with zero rate), profits per head may be calculated by subtracting any wage rate on the factor price contour from the zero wage. We have done this for Sato's example (Garegnani's would do just as well) and the results are shown in Table 1. They are fascinating in that they indicate that at any rate the most technique from the standpoint of profits per head is technique I. But, how important is this? Quite; in a macromodel that assumes 1) full emplovment and 2) that capital is used solely for the purpose of producing the commodities included in the model.' Together, these conditions imply that profits per head are a measure of the total profits associated with the use of any technique. This means that switching from technique I to technique II in Sato's example as the rate falls below .595 involves adopting a production system that yields