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.
I would like to express my thanks to the co-authors, Yoshinori Shiozawa and Masashi Morioka, who read this chapter and gave me helpful comments.
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Notes
- 1.
The origin of the word “vector” comes from the Latin vehere (carrying). A vector is often indicated by a bold character x or \(\vec {x}\) with an arrow over the character, but this chapter uses the normal character x.
- 2.
See Shiozawa (2016).
- 3.
The relation that z is greater than or equal to s can be expressed as the case z = max{z, s}.
- 4.
Scarf (1959) p.197.
- 5.
Regarding the “process analysis,” see Chap. 1, Sect. 5, “Methodology of Analysis.”
- 6.
See Eq. (6.7).
- 7.
See Table 6.1.
- 8.
Keynes (1936) pp.195–6.
- 9.
Regarding the “loosely connected system,” see Chap. 1, Sect. 4, “Environment of Economic Activities.”
- 10.
- 11.
See Chap. 2, Sect. 3, “Some Characteristic Features of the System.”
- 12.
- 13.
Regarding the evolutionary features, see Chap. 1, Sects. 1, 2, and 3.
- 14.
See the Theorems 1 and 2 in Chap. 4 and Morioka (2005).
- 15.
Since A is a 13 × 13 matrix, Φ is a 26 × 26 matrix.
- 16.
See Chaps. 3, 4, and 5.
- 17.
In this chapter, we did not perform experiments regarding the traverses with different growth rates and cases where demand is partitioned due to inventory shortages.
- 18.
Regarding the “micro-macro loop,” see Chap. 1, Sect. 5, “Methodology of Analysis.”
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Shiozawa, Y., Morioka, M., Taniguchi, K. (2019). Significance of Nonlinearity and Many Goods Models. In: Microfoundations of Evolutionary Economics. Evolutionary Economics and Social Complexity Science, vol 15. Springer, Tokyo. https://doi.org/10.1007/978-4-431-55267-3_6
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