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2022 | OriginalPaper | Chapter

6. Price Formation: General Equilibrium

Authors : Sabiou M. Inoua, Vernon L. Smith

Published in: Economics of Markets

Publisher: Springer International Publishing

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Abstract

This chapter extends the theory to multiple markets where, as in classical economics, wealth is explicitly treated as one of the determinants of reservation prices in market realizations.

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previous chapter Price Formation: Partial Equilibrium

next chapter Financial Instability: Re-tradable Assets and Speculation

For a recent multiple-market model of double-auction dynamics, see Asparouhova et al. (2020).

Since the horizon \(T\) is assumed given, it will be usually omitted. Yet it is important to keep in mind that the economy’s supply and demand apply to a given period \(\{ 0,...,T\} ,\) which includes the case where the limit \(T = \infty\) is considered. In all rigor, we should index the distribution of unit by \(T,\) writing, for example, \(M_{T}\) and \(N_{T} .\)

This is a standard property of line integration. See, for example, Apostol (1969, ch. 10).

A technical detail is omitted in the differentiation under the integral (or expectation) sign.

To wit: “A market…is theoretically perfect only when all have perfect knowledge of the conditions of supply and demand, and the consequent ratio of exchange; and…there can only be one ratio of exchange of one uniform commodity at any moment” (Jevons (1871 [1888], p. iv).

For a review of the neoclassical models of price adjustment and stability, see Negishi (1962), Hahn (1982), and Fisher (2013). Hahn, in his review of neoclassical price dynamics, said: “we shall have to conclude that we still lack a satisfactory descriptive theory of the invisible hand” (Hahn, 1982, p. 746).

For a review of SMD theorem and related aggregation literature see Shafer and Sonnenschein (1982). See also Kirman (1989) and Rizvi (2006).

Hotelling (1932).

In the mathematical theory of dynamics, an equilibrium, when it exists, derives from a dynamical representation of a system: it is not decided a priori and rationalized a posteriori.

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Asparouhova, E., Bossaerts, P., & Ledyard, J. O. (2020). Price formation in multiple, simultaneous continuous double auctions, with implications for asset pricing (Social Science Working Paper 1450). California Institute of Technology. https://resolver.caltech.edu/CaltechAUTHORS:20200727-111303655

Barbashin, E., & Krasovskii, N. (1961). On stability of motion in the large. Dokl. Akad. Nauk. USSR, 86(3), 453–456.

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Hotelling, H. (1932). Edgeworth’s taxation paradox and the nature of demand and supply functions. Journal of Political Economy, 40(5), 577–616.CrossRef

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Title: Price Formation: General Equilibrium
Authors: Sabiou M. Inoua
Vernon L. Smith
Publisher: Springer International Publishing
Book: Economics of Markets
Print ISBN: 978-3-031-08427-0

Electronic ISBN: 978-3-031-08428-7

Copyright Year: 2022
DOI: https://doi.org/10.1007/978-3-031-08428-7_6