Department of Economics

University of Delaware

Working Paper #2008-01

A Short Note on Marshall’s Third Law of Derived Demand:  Why Does Labor’s Share Interact with the Elasticity of Substitution to Decrease the Elasticity of Labor Demand?

Saul D. Hoffman

ABSTRACT

The third Marshall-Hicks-Allen rule of elasticity of derived demand purports to show that labor demand is less elastic when labor is a smaller share of total costs.  As Hicks and then Bronfenbrenner showed more than four decades ago, this rule is not quite correct, and actually is complicated by an unexpected negative relationship involving labor’s share of total costs and the elasticity of substitution. The standard intuitive explanation for the exception to the rule, due to Stigler, describes a situation rather different than the one described in Marshall’s rule.  In this paper, I show first, that the exception to the law is genuine, and second, why the unexpected relationship between labor’s share of total cost, the elasticity of substitution, and the elasticity of labor demand holds.

JEL Codes: J010, J200