On the Equivalence of Input and Output Market Marshallian Surplus Measures

Abstract

In a series of papers which has appeared in this Review the following question is raised: Given a change in the vector of unit factor prices, to what is the resulting change in Marshallian surplus (in the factor markets) equal? As is probably now well-known, the first two papers in this series, written by Richard Schmalensee (1971) and Daniel Wisecarver, answered the above question incorrectly. Indeed, James Anderson and Schmalensee (1976), in two separate papers, discussed the error of the first two papers. Anderson answers the question correctly under the assumptions of linear homogeneous and single output production, competition, and a change in only one factor price. Schmalensee corrects his previous paper by correctly answering the question under the assumptions of general single output production, competition, and a change in only one factor price. However, Schmalensee does not completely answer the question under monopolistic conditions and, as a result, appears to believe that it may be possible to infer Marshallian surplus change in the final output market from Marshallian surplus change in the factor markets. The basic purpose of this article is to demonstrate the answers for both the monopoly and competitive cases under conditions more general than those of the above authors. In particular, the answers are derivable regardless of how many factor prices are changed and regardless of the number of final outputs which these factors produce. The approach employed in the last two papers cannot provide this generalization. I will show that, under monopoly conditions, the change in Marshallian surplus in the factor markets (due to a factor-price vector change) is precisely equal to the change in monopoly profits that occurs because of the factor-price vector change. Also, it will be shown that under competitive conditions the Marshallian surplus change in the factor markets is precisely equal to the change in Marshallian surplus (measured in the final output markets) plus the change in producer's surplus (i.e., industry profits) which is the correct answer arrived at by both Anderson and Schmalensee in his second paper under the above mentioned restrictive conditions. The generality of the answers is demonstrated by utilizing (i) what W. Erwin Diewert (p. 12) has called Shephard's Lemma (for example, see Paul A. Samuelson, p. 68; Ronald W. Shephard, p. I 1; or Daniel McFadden p. 5), and (ii) the profit function from which the factor demands are derived.

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