While the aggregation literature deals with the question of whether a well-behaved aggregate production function can be generated from micro production functions for the purpose of building theoretical models and for empirical testing, the Cambridge-Cambridge debates were about the measurement of capital as it relates to the interdependence of prices and distribution. Both problems can be present at once, but they are not the same issues. The discussions took place during the 1950s, 1960s and 1970s between Joan Robinson and her colleagues at Cambridge, UK, and Paul Samuelson and Robert Solow at Cambridge, USA. The debates were, in the final analysis, about different value theories, the classical versus the neoclassical, and how these theories explain prices and distribution. The debates centered around the question of whether one can use an aggregate measure of capital (Joan Robinson’s 1953-54 famous question “in what unit is ‘capital’ to be measured?”) in a macroeconomic production function without running into apparently paradoxical phenomena (e.g., reswitching and reverse capital deepening). It was concluded that the notion of an aggregate production function is more than dubious. In a widely cited paper, Paul Samuelson (1961-1962) showed that under some admittedly strict conditions, one could think of an aggregate production function as a parable. However, a few years later, Garegnani (1970) showed that Samuelson’s neoclassical aggregate production function, supposedly the antithesis of the classical approach, was theoretically valid only if Ricardo’s labor theory of value, which neoclassical economics contemptuously rejects, is strictly true. What a cold shower!
See the paper by Cohen and Harcourt in the Winter issue of the Journal of Economic Perspectives (2003) and the comments on this paper in the Fall 2004 issue of the same journal.