Equilibrium price as a coincidence point of two mappings

The existence of an equilibrium price vector in a nonlinear market model is analyzed. In the model, the demand and supply functions are obtained by maximizing the producer utility and profit, respectively. Sufficient conditions for the existence of an equilibrium price vector and its stability with respect to small perturbations in the model are given. The results are consequences of theorems on the existence and stability of coincidence points in the theory of $\alpha$-covering mappings.