Perfect competition without slater condition: the equivalence of non-standard and contractual approach
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Perfect competition without slater condition: the equivalence of non-standard and contractual approach
Publication type
Valery Marakulin 
Occupation: Associate Professor
Affiliation: Novosibirsk State University
Address: Russian Federation, Novosibirsk
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.
equilibrium with random prices, survival assumption (Slater condition), perfect competition, fuzzy core, fuzzy contractual allocations, Edgeworth equilibria
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1. Aliprantis C.D., Brown D.J., Burkinshaw O. (1989). Existence and Optimality of Competitive Equilibria. Berlin, New York: Springer-Verlag.

2. Anderson R.M. (1992). Non-Standard Analysis with Applications to Economics. In: Hildenbrand W., Sonnenschein H. (eds.). “Handbook of Mathematical Economics”. Vol. IV. Amsterdam: North-Holland, 2145–2208.

3. Aumann R.J. (1964). Markets with a Continuum of Traders. Econometrica, 32, 1–2, 39–50.

4. Brown D.J., Robinson A. (1975). Nonstandard Exchange Economies. Econometrica, 43, 41–55.

5. Davis M. (1977). Applied Nonstandard Analysis. New York: Wiley.

6. Debreu G., Scarf H.E. (1963). A Limit Theorem on the Core of an Economy. International Economic Review, 4, 235–246.

7. Hildenbrand W. (1974). Core and Equilibria of a Large Economy. Princeton/New Jersey: Princeton University Press.

8. Konovalov A.V., Marakulin V.M. (2006). Equilibria without the Survival Assumption. Journal of Mathematical Economics, 42, 198–215.

9. Loeb P.A. (2000). An Introduction to Non-Standard Analysis. In: Loeb P.A., Wolff M. (eds.) “Nonstandard Analysis for the Working Mathematician”. Dordrecht: Kluwer Academic Publishers.

10. Marakulin V.M. (1988). An Equilibrium with Nonstandard Prices and Its Properties in Mathematical Models of Economy. Preprint No. 18. Novosibirsk: IM SB of USSR Academy of Sciences (in Russian).

11. Marakulin V.M. (2011). Contracts and Domination in Competitive Economies. Journal of the New Economic Association, 9, 10–32 (in Russian).

12. Marakulin, V.M. (2012). An Abstract Equilibrium Analysis of Economic-Mathematical Models. Novosibirsk: SB Russian Academy of Science Publisher (in Russian).

13. Marakulin V.M. (2013). On the Edgeworth Conjecture for Production Economies with Public Goods: A Contract- Based Approach. Journal of Mathematical Economics, 49, 3, 189–200.

14. Marakulin V.M. (2014). On Contractual Approach for Arrow – Debreu – McKenzie Economies. Economics and Mathematical Methods, 50 (1), 61–79 (in Russian).

15. Rashid S. (1987). Economies with Many Agents: An Approach Using Nonstandard Analysis. Baltimore: Johns Hopkins University Press.