Empirical Isoquants and Observable Optima: Cobb and Douglas at Seventy

The theory of production and derived demand for factor inputs seems abstract because of its dependence on unobservable marginal products. Seventy years ago, Charles Cobb and Paul Douglas showed that if the production function is linearly homogeneous, the theoretical propositions can be illustrated by observable wages and average products. This paper argues that economists can exploit this linkage between theory and observation to make production theory come alive in real-world data. A multicountry data set is used to illustrate how information on output per worker, output per unit of capital, and input prices can trace out theoretically defensible isoquants and labor demand curves. Choice of high capital-labor ratios are shown to be driven by relative wages across nations. Comparison of unit labor costs across nations demonstrates that high wages need not imply competitive disadvantage in international trade. Countries with inefficient input allocations are shown to be importers and/or highly protectionis, whereas countries with efficient input allocations are exporters. All these concepts are motivated by two-dimensional plots of real-world data that replicate textbook theoretical treatments with remarkable consistency. The paper closes with examples of how these plots have been used in classroom settings.