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New conditions for the existence of equilibrium prices

We study the existence of equilibrium price vector in a supply-demand model taking into account the transaction costs associated with the sale of products. In this model, the demand function is the solution to the problem of maximizing the utility function under budget constraints. The supply function is the solution to the problem of maximizing the profit (with given transaction losses) on the technology set. We establish sufficient conditions for the existence of the equilibrium price vector, which are consequences of some theorems in the theory of covering mappings. | Yugoslav Journal of Operations Research 28 (2018), Number 1, 59–77 DOI: https://doi.org/10.2298/YJOR170212021A NEW CONDITIONS FOR THE EXISTENCE OF EQUILIBRIUM PRICES Aram V. ARUTYUNOV Department of Nonlinear Analysis and Optimization, RUDN University, 6 Miklukho-Maklaya St, Moscow, 117198, Russian Federation arutun@orc.ru Natalia G. PAVLOVA Department of Nonlinear Analysis and Optimization, RUDN University, 6 Miklukho-Maklaya St, Moscow, 117198, Russian Federation natasharussia@mail.ru Aleksandr A. SHANANIN Moscow Institute Of Physics and Technology, 9 Institutskiy per., Dolgoprudny, Moscow Region, 141701, Russian Federation Dorodnicyn Computing Centre, FRC CSC RAS, 40 Vavilova St., Moscow, 119333, Russian Federation Department of Nonlinear Analysis and Optimization, RUDN University, 6 Miklukho-Maklaya St, Moscow, 117198, Russian Federation alexshan@yandex.ru Received: February 2017 / Accepted: October 2017 Abstract: We study the existence of equilibrium price vector in a supply-demand model taking into account the transaction costs associated with the sale of products. In this model, the demand function is the solution to the problem of maximizing the utility function under budget constraints. The supply function is the solution to the problem of maximizing the profit (with given transaction losses) on the technology set. We establish sufficient conditions for the existence of the equilibrium price vector, which are consequences of some theorems in the theory of covering mappings. Keywords: Economic Equilibrium, Demand Function, Supply Function, Transaction Costs, Coincidence Points, Covering Mappings. 60 A. Arutyunov, et al. / New Conditions for the Existence of Equilibrium Prices MSC: 91B50, 91B52, 91B55. 1. INTRODUCTION The existence of equilibrium is still one of the most important questions in the study of economic models. The concept of economic equilibrium was first formulated by Leon Walras [1]. He established a law, that implies the equality of the .