In this paper, we investigate the existence of equilibrium in several market models. In these models the supply and the demand functions are determined by the price elasticity coefficients of goods presented on the market. We obtained necessary and sufficient conditions for the existence of equilibrium in the market model without import. Also we obtained sufficient conditions for the existence of equilibrium in the open market model as corollaries of theorems on coincidence points for mappings of metric spaces. Conditions on the uniqueness and nonuniqueness of equilibrium in open and closed market models in the form of conditions on model parameters are obtained.