Journal of Convex Analysis 29 (2022), No. 2, 459--480
Copyright Heldermann Verlag 2022
On the Equality of Clarke and Greenberg-Pierskalla Differentials
Simone Cerreia-Vioglio
Department of Decision Sciences, Università Bocconi, Milano, Italy
simone.cerreia@unibocconi.it
Fabio Maccheroni
Department of Decision Sciences, Università Bocconi, Milano, Italy
Massimo Marinacci
Department of Decision Sciences, Università Bocconi, Milano, Italy
Luigi Montrucchio
Collegio Carlo Alberto, Università di Torino, Torino, Italy
We study the relations for quasiconcave and continuous functions between the two important notions of Clarke and Greenberg-Pierskalla differentiability. As an application, we generalize the classic Roy's identity of consumer theory.
Keywords: Clarke differential, Greenberg-Pierskalla differential, directionally Lipschitzian, quasiconcave function, max-formula, envelope theorem, affine Gateaux differentiability.
MSC: 26B25, 26E15, 90C26, 49J52.
[ Fulltext-pdf (185 KB)] for subscribers only.