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The purpose of this paper is to study a new concept of equilibrium, called equilibrium with quantity targets, in an economy with increasing returns to scale. This concept is introduced by E. Dierker and W. Neuefeind (J. Math. Econom. 17 (1988)). We extend this definition to the case of a general production model and we provide an existence theorem. Furthermore we state an existence result in the particular model considered by Dierker and Neuefeind which improves their result.

International audience; We prove a fixed-point theorem for set-valued mappings defined on a nonempty compact subset X of Rn which can be represented by inequality constraints, i.e., X={x in Rn| f(x) < 0}, f locally Lipschitzian and satisfying a nondegeneracy assumption outside of X. This class of sets extends significantly the class of convex, compact sets with a nonempty interior. Topological properties of such sets X are proved (continuous deformation retract of a ball, acyclicity) as a consequence of a generalization of Morse's lemma for Lipschitzian real-valued function defined on Image n a result also of interest for itself.