Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

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

Keywords

  • Clarke differential
  • Greenberg-Pierskalla differential
  • directionally Lipschitzian
  • quasiconcave function
  • max-formula
  • envelope theorem
  • affine Gateaux differentiability

Mathematics Subject Classification

26B25, 26E15, 90C26, 49J52

Suggested citation

S. Cerreia-Vioglio, F. Maccheroni, M. Marinacci, L. Montrucchio. “On the Equality of Clarke and Greenberg-Pierskalla Differentials.” Journal of Convex Analysis 29 (2022), No. 2, 459–480. https://doi.org/10.68381/jca29028

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Published by Heldermann Verlag, 2022. Rights now held by Banach Press.