On the stability and solution sensitivity of a consumer problem
Speaker: Vu Thi Huong

Time: 9h00, Wednesday, January 18, 2017
Room 4, Building A14, Institute of Mathematics, 18 Hoang Quoc Viet, Cau Giay, Hanoi
Various stability properties and a result on solution sensitivity of a consumer problem are obtained in this paper. Focusing on some nice features of the budget map, we are able to establish the continuity and the locally Lipschitz continuity of the indirect utility function, as well as the Lipschitz-H\"older continuity of the demand map under a minimal set of assumptions. The recent work of Penot [J. Nonlinear Convex Anal. 15 (2014), 1071--1085] is our starting point, while an implicit function theorem of Borwein [J. Optim. Theory Appl. 48 (1986), 9--52] and a theorem of Yen [Applied Math. Optim. 31 (1995), 245--255] on solution sensitivity of  parametric variational inequalities are the main tools in our proofs.