The Homogenization of Heterogeneous Inputs: Comment
Abstract
In a recent article in this Review (1981), James Buchanan and Robert Tollison used a truncated neoclassical model to deduce the allocational effects of forced equal-pay schemes, including equal pay for (a) workers of the same trade, (b) workers in the same firm or industry, (c) workers who perform the same work, and (d) the minimum wage. The model that Buchanan and Tollison used is one in which firms hire a single unit of each type of input, each may be hired in competitive markets where their prices differ, each has the same marginal physical product within the firm, and there is within limits among inputs of different types. They also assume only human inputs, since they are interested in equal-pay schemes. The purpose of this comment is to show that, depending on their meaning of substitution within limits, their model is either inconsistent or incorrectly specified. The key to understanding the BuchananTollison model appears to lie with identifying a production function that corresponds to substitution within limits. The early masters of marginal productivity theory recognized that two separate assumptions could be made about production coefficients. They could be assumed fixed or variable. The assumption of fixed coefficients meant that there could be no among inputs in a production process. The assumption of variable coefficients was used to illustrate cases in which a change in the relative prices of inputs would prompt entrepreneurs to alter their production methods in order to substitute inputs whose relative prices had fallen for those whose relative prices had risen. If one assumed variable coefficients, the equilibrium conditions and the various marginal equalities could be easily traced. If one assumed fixed coefficients, the marginal conditions could not be expressed. As a substitute for marginal productivity, however, Marshall and others introduced the concept of net productivity. This was not satisfactory to mathematical purists. Moreover, it left the door open to the possibility of haggling over a surplus; since product exhaustion would not occur even at the margin in the typical case. The assumption of fixed coefficients has sometimes been expressed in terms of lumpiness or indivisibility.' It seems clear that Buchanan and Tollison do not use the term within limits to mean variable coefficients. Suppose that, by chance, a firm that faced variable coefficients hired only one unit of each input of different types and that these inputs had identical marginal value products. Suppose further that the firm, industry, and economy were in general equilibrium. Now let there be a general reduction in the wages of one type of input, perhaps as a consequence of a preference by owners of that input for less leisure. The relative price of the input would fall. In neoclassical theory, the firm would attempt to substitute more of this input for other inputs and would alter its production methods to do so. In Buchanan-Tollison's model, however, this is impossible by assumption, since only one unit of each input is hired. One must conclude that within limits does not mean variable coefficients. Now consider whether they mean fixed production coefficients. Although this appears to be their meaning, it will be shown that it is inconsistent with their analytical framework. Consider their graphical representation of a firm, which provides the reference for their verbal discussion. The relevant parts are reproduced in Figure 1. Note that inputs of different types are arranged in order of ascending supply prices. An input of one
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