Abstract
This paper studies dynamic models of production and exchange on graph with consideration of transportation costs. Using graph and set of matrices, we introduce superlinear multivalued mappings which describe the exchange ratio in considered system. Effective trajectories of these models are studied. It is shown that trajectories can be constructed using the simplest equilibrium type mechanisms. Characteristics of effective trajectories in Neumann type models are given. Conditions for the existence of equilibrium state of the considered model are found.
Highlights
A lot of works appeared lately dealing with the applications of graph theory to some models of economic dynamics [1,2,3] and related extremal problems [2, 4,5,6,7,8,9]
The results obtained in this work allow applying well-known facts about graph theory to some models of production and exchange
It is shown that the characteristic prices can be considered as equilibrium prices in some distribution models
Summary
A lot of works appeared lately dealing with the applications of graph theory to some models of economic dynamics [1,2,3] and related extremal problems [2, 4,5,6,7,8,9]. Conditions for the existence of equilibrium state of the considered model are found. We consider production mappings which define the Neumann-Gale model [10].
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