A scalar metric of the real quantity of capital and the Cambridge capital controversy

In the course of the long capital theory dispute known colloquially as the Cambridge capital controversy, the central claim advanced by post-Keynesian critics of the neoclassical theory of production and distribution was that there does not exist a mathematically consistent and usable scalar metric of the real quantity of capital composed of heterogeneous commodities. Their claim was that heterogeneous commodities can only be aggregated on the basis of their values and that this leads to insoluble problems for the neoclassical theory, including circular dependence of the profit rate and capital price/value, reswitching and capital reversing, and lack of convergence to, and uniqueness of, distribution equilibria. I employ a novel parameterization of a two-good model of production—consumption good and capital good—to compose the well-understood scalar value of capital in consumption good as the product of a necessary price of capital, determined independently of value and quantity, and a real scalar quantity—the “integrated labor time of production of the capital,” the labor time required for its production with reproduction of capital inputs. If the post-Keynesians were incorrect about their central claim, that would, at the very least, require reconsideration of their critique to place it on a firmer theoretical footing.