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On the Stability and Solution Sensitivity of a Consumer Problem

Vu Thi Huong (), Jen-Chih Yao () and Nguyen Dong Yen ()
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Vu Thi Huong: Vietnam Academy of Science and Technology
Jen-Chih Yao: China Medical University
Nguyen Dong Yen: Vietnam Academy of Science and Technology

Journal of Optimization Theory and Applications, 2017, vol. 175, issue 2, No 14, 567-589

Abstract: Abstract 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–Hölder continuity of the demand map under a minimal set of assumptions. The recent work of Penot (J Nonlinear Convex Anal 15:1071–1085, 2014) is our starting point, while an implicit function theorem of Borwein (J Optim Theory Appl 48:9–52, 1986) and a theorem of Yen (Appl Math Optim 31:245–255, 1995) on solution sensitivity of parametric variational inequalities are the main tools in our proofs.

Keywords: Consumer problem; Producer problem; Budget map; Indirect utility function; Demand map; Continuity; Lipschitz–Hölder continuity; 91B16; 91B42; 91B38; 46N10; 49J53 (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s10957-017-1164-6

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