Koopmans activity analysis as an optimal control problem

Abstract

The usefulness of the Leontief input-output model, Leontief (1966), for decision making at the firm level has been well demonstrated, see Kaplan (1973) and the references cited in that article. But there are two major limitations of the Leontief model. First, there is a one-to-one correspondence between one activity for each output, that is only one activity or manufacturing process is used to produce a single output or product. And second, it is a static model. This article removes the first limitation by introducing the Koopmans model, Koopmans (1951). The second limitation is overcome by using the Von Neumann dynamic growth model, Von Neumann (1945–46). The primary objective of this article is to demonstrate from a micro-economic point of view that Koopmans production activities may be represented as the Von Neumann growth model and analysed in the state-space format within the framework of control theory and the Pontryagin maximum principle. This results in a more meaningful and robust dynamic model with enhanced analytical power.