Конференции ИВТ СО РАН

Abstracts

Summary

Problems of an asymptotic stability on Lyapunov of process of forming of the prices in the good's markets with the trade mediators, based on Samuelson model, are investigated.

In work [1] for modelling dynamics of the prices in the real good's markets with trade mediators the following system of the differential equations is offered

$$ frac {dp_j^d} {dt} = alpha_j^d [q_j^d (p^d)-q_j^s (p^s)], $$ begin {equation} frac {dp_j^s} {dt} = alpha_j^s [q_j^d (p^d)-q_j^s (p^s)], end {equation} $$ p^d (0) =p _ {(0)} ^d, p^s (0) =p _ {(0)} ^s, quad alpha_j^d, alpha_j^s> 0, quad j = overline {1, n}. $$

One of the basic suppositions of a considered system is that modification prices of the demand $ (p_j^d (t)) $ and prices of the supply $ (p_j^s (t)) $ proportionally to excess of volumes of demand $ (q_j^d (t)) $ above the supply $ (q_j^s (t)) $ in a point ( day) $t $. Initial significances $p_j^d (0) $ and $p_j^s (0) $ are assumed known numbers; positive constants $ alpha_j^d $ and $ alpha_j^d $ are coefficients of adjustment of the prices for the goods $j $.

The given system is generalization of Samuelson model [2] for the good's markets with mediators. Conditions at which the trajectory of a system gives sequence prices of the demand and prices of the supply, converging to the equilibrium prices [3] are formulated. The proof of stability is obtained at the supposition, that Lyapunov function of systems of the differential equations [4] is not necessarily differentiated.

The work is supported by Russian Foundation for Basic Research, Projects 03-06-80247.

References:

[1] Algazin G. Information technologies of system compromise in regulation of good's markets with trade mediators // Joint issue on materials of International conference < Computing and information technologies in a science, engineering and education >. Part-1. Novosibirsk - Almaty-Ust-Kamenogorsk: EKSU, 2003. (in Russian).

[2] Samualson P. Foundation of economic analysis. Cambridge, Massachusetts, 1948.

[3] Algazin G. Competitive equilibrium with intermediaries in Walrasian model // Proceedings of the third All-Russian conference on financial and actuarial mathematics and related fields. Krasnoyarsk: ICM SB RAS, 2004 (at the printer's, in Russian).

[4] Barabash E. Functions of Lyapunov. M.: The Science, 1970. (in Russian).

Note. Abstracts are published in author's edition

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