Capital Aggregation in Vintage Models

Abstract

This is an unpublished paper on the problem of capital aggregation in vintage models, which was presented at the First World Congress of the Econometric Society in Rome in 1965. At the beginning of his investigation, Gorman set out the problem in the primal with constant‐returns‐to‐scale technologies, but after some work he recognized that the solution is related to a concept that he had encountered in differential geometry––the edge of regression, and this led him to reformulate the problem in the dual. The Appendix contains a very detailed treatment of duality and the relationship between production functions and profit functions (Gorman uses the negative of the profit function, which he calls the loss function. Theorem 1 (in the Appendix) is a general equivalence between production and profit functions, while Theorem 2 extends this to production functions with fixed factors and gross profit functions; this leaves, as is usual in these arguments, a certain asymmetry in the duality, as quantities are usually non‐negative whereas prices are positive. Theorem 3 uses a boundedness assumption to establish a full duality.