Iterative methods for equilibrium search in the partial Arrow–Debreu–Stone exchange model
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 18 (2012) no. 3, pp. 201-207

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Iterative methods are proposed for equilibrium price search in the Arrow–Debre model with Stone's multiplicative utility functions. The methods converge under weak initial assumptions and allow for a conceptual interpretation in economic terms. Strict convergence theorems supported by numerical experiments are presented. The paper continues the author's investigations conducted earlier for Cobb–Douglas multiplicative functions.
Keywords: economic equilibrium, exchange model, multiplicative utility function, split methods.
L. D. Popov. Iterative methods for equilibrium search in the partial Arrow–Debreu–Stone exchange model. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 18 (2012) no. 3, pp. 201-207. http://geodesic.mathdoc.fr/item/TIMM_2012_18_3_a23/
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[1] Arrow K. J., Debreu G., “Existence of equilibrium for a competitive economy”, Econometrica, 25 (1954), 265–290 | DOI | MR

[2] Karlin S., Matematicheskie metody v teorii igr, programmirovanii i ekonomike, Mir, M., 1964, 835 pp. | Zbl

[3] Nikaido Kh., Vypuklye struktury i matematicheskaya ekonomika, Mir, M., 1972, 519 pp.

[4] Lankaster K., Matematicheskaya ekonomika, Sov. radio, M., 1972, 464 pp. | Zbl

[5] Makarov V. L., Rubinov A. M., Matematicheskaya teoriya ekonomicheskoi dinamiki i ravnovesiya, Nauka, M., 1973, 338 pp. | MR

[6] Intriligator M., Matematicheskie metody optimizatsii i matematicheskaya ekonomika, Progress, M., 1975, 597 pp.

[7] Shafer W. J., Sonnenschein H. F., “Some theorems on the existence of competitive equilibrium”, J. Economic Theory, 11 (1975), 83–93 | DOI | MR | Zbl

[8] Ekland I., Elementy matematicheskoi ekonomiki, Mir, M., 1983, 248 pp. | MR

[9] Eaves B. C., “Finite solution of pure trade markets with Cobb–Douglas utilities”, Math. Program. Study, 23 (1985), 226–239 | DOI | MR | Zbl

[10] Aliprantis C. D., Brown D. J., Burkinshaw O., Existence and optimality of competitive equilibria, Springer, Berlin, 1990, 296 pp. | MR

[11] Polterovich V. M., Ekonomicheskoe ravnovesie i khozyaistvennyi mekhanizm, Nauka, M., 1990, 254 pp.

[12] Popov L. D., “K metodam otyskaniya ravnovesiya v modelyakh Errou–Debre”, Dinamika neodnorodnykh sistem, Tr. In-ta sistemnogo analiza RAN, 30, no. 12, 2008, 116–124

[13] Streng G., Lineinaya algebra i ee primeneniya, Mir, M., 1989, 446 pp.