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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, UniversitÓ Bocconi, Milano, Italy
simone.cerreia@unibocconi.it

Fabio Maccheroni
Department of Decision Sciences, UniversitÓ Bocconi, Milano, Italy

Massimo Marinacci
Department of Decision Sciences, UniversitÓ Bocconi, Milano, Italy

Luigi Montrucchio
Collegio Carlo Alberto, UniversitÓ 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.

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