Microfoundations of Evolutionary Economics pp 291-323 | Cite as

# Significance of Nonlinearity and Many Goods Models

*S*,

*s*) Inventory Control Policy in the Economy as a Whole

## Abstract

This chapter examines what economic consequences can be induced in the entire economy when many different enterprises in the economy implement production based on inventory control, which is referred to as the (*S*, *s*) policy.

The first section describes the features of a contemporary society that is characterized by an enormous number of different kinds of commodities. To theoretically contemplate an economy with these many kinds of commodities, the concepts of vector space and nonlinearity are explained in the Introduction. The second section of this paper explains the (*S*, *s*) inventory control policy theory developed by Scarf (The optimality of (S,s) policies in the dynamic inventory problem. In: Arrow KJ, Karlin S, and Suppes P (eds) Mathematical methods in the social sciences 1959. Stanford University Press, Stanford, 1959). Since Scarf’s model is a model that focuses on one kind of goods, it does not consider the movements of the entire economy. We discuss this crucial point with respect to Scarf (The optimality of (S,s) policies in the dynamic inventory problem. In: Arrow KJ, Karlin S, and Suppes P (eds) Mathematical methods in the social sciences 1959. Stanford University Press, Stanford, 1959) and develop the Scarf model into a many kinds of goods model. The sequence of events and the determinant processes of our model are precisely explained. Next, the third section shows the quantity adjustment processes based on the (*S*, *s*) policy model. The mathematical solutions of a one kind of goods and two kinds of goods models are shown, and next, the results, which are different results from the one kind of goods and the two kinds of goods, by the more than three kinds of goods model are discussed. In the fourth section, certain of the results obtained by numerical experiments conducted by the author are explained, and the effects of the number of commodities are discussed.

## Keywords

Many kinds of goods Vector space Nonlinearity Inventory shortage Numerical experiments (S s) Policy model## References

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