Weakening the Strong Convexity of Preferences

In general models, the strong quasi-concavity of the objective function, which is sufficient for theoretical properties of demands in consumer theory, is often arbitrary and weaker global concavity conditions are desirable. We propose a new global concavity condition that implies, for models with several nonlinear constraints, the local uniqueness and the smoothness of the decision functions as well as the negativity of the generalised substitution matrix. This condition can be used to specify general and flexible economic models and is easier to check than the strong quasi-concavity or the usual second order conditions over the whole domain.