Perfect competition without slater condition: the equivalence of non-standard and contractual approach

Marakulin, Valery

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Экономическая теория, Экономика и управление народным хозяйством, Математические и инструментальные методы экономики, Мировая экономика

UDC

33 Экономика. Народное хозяйство. Экономические науки

Publisher

Russian Academy of Sciences

Date of publication

14.11.2018

Public year

2018

Perfect competition without slater condition: the equivalence of non-standard and contractual approach

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GOST	Marakulin V. Perfect competition without slater condition: the equivalence of non-standard and contractual approach // Economics and the Mathematical Methods. – 2018. – V. 54. – Issue 1 C. 69-91 . URL: https://sochum.ru/s042473880000005-4-1/
MLA	Marakulin, Valery "Perfect competition without slater condition: the equivalence of non-standard and contractual approach." Economics and the Mathematical Methods. 54.1 (2018).:69-91.
APA	Marakulin V. (2018). Perfect competition without slater condition: the equivalence of non-standard and contractual approach. Economics and the Mathematical Methods. vol. 54, no. 1, pp.69-91

Annotation

In the neoclassical Arrow–Debreu model under the conditions of perfect competition every allocation from the core allows price decentralization, i.e. it is an equilibrium allocation. Moreover, espetially in the conditions, under which the core and equilibria coincise and are called perfect competition. However, in all the known models of perfect competition the theorem of the core coincidence and equilibria is proved exclusively under the survival assumption, which implies that Slater’s condition for consumer’s problem is fulfilled. How important is this additional requirement and what will happen if it is discarded? The paper is addressing this problem. The classical Debreu – Scarf approach is analyzed and is compared with the contractual model of perfect competition developed early by the author. It is shown that the most accurate model of this is provided by the contractual approach; namely, this is a concept of fuzzy contractual allocation which provides stability with respect to the signing of a new contract and an asymmetric partial break of already existing ones. Under weak assumptions, it is proved that these allocations coincide with those with nonstandard prices. In this case implemented allocations generally are different from the elements of the classical core in perfect competition conditions (Edgeworth equilibria). However, in the case when model assumptions (indecomposability) provide the survival assumption for non-standard equilibria, the contractual approach coincides with the classical one.

Economics and the Mathematical Methods. 2018 Issue 1

About authors

Valery Marakulin

Institute of Mathematics S.L. Sobolev

References

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