We propose a new approach to studying the existence of an economic equilibrium in dynamic market models, where equilibrium is understood as a market situation where the total demand for goods is equal to the total supply of these goods. From the mathematical point of view, an equilibrium state is a solution to a system of differential equations with an initial condition and a constraint on the derivative with nonnegative components. To obtain the existence conditions, we use the theory of covering mappings and coincidence points.