Variational analysis for the consumer theory (Q2442712)

The problem under investigation is the representation of the demand correspondence as a generalized derivative of the inverse utility function. The latter is the indirect utility function under some conditions on the original utility function. Under custom conditions of classical demand theory (finite dimensionality of the goods' space, continuity and non-satiety of preferences) the representation is the well-known Roy's identity. However, the author is guided by mathematical interest, and he considers the generalization of the economic motivated optimization problem in an abstract space without continuity assumption. Some rather skilled connections between the demand correspondence and different generalized derivative structures are obtained. The theoretical results are illustrated on three examples of famous consumers, Falstaff, Gavroche and Gargantua.