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2014 | OriginalPaper | Chapter

6. Endowing Fundamental Values: Willingness to Pay

Author : Jean-Pierre Aubin

Published in: Time and Money

Publisher: Springer International Publishing

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Abstract

The concept of fundamental value mentioned by Turgot in his letter 6 − − 12 to Hume has known a recent revival under the name of “Willingness to Pay” for giving a value to public goods which cannot be exchanged, such as the evaluation of biodiversity (See [84, Hanemann], [78, Griffon], [125, Weber], [37, Évaluation économique de la biodiversité] de Brahic et J.-Ph. Terreaux and its bibliography, among an infinity of other publications on this topic).

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previous chapter Evolutions and Their Temporal Windows
next chapter Endowing Exchange Values: Adam Smith’s Invisible Man
Footnotes
1
Even when the set of solutions (x, w) contains more than one unique solution, inverse function theorems are available for providing the existence of solutions in a neighborhood of (x 0, w 0) and their stability (in the sense of pseudo-Lipschitz or Aubin property). See Chap. 3 of [24, Set-Valued Analysis] for a sufficient condition and Sect. 9.7 of [15, Viability Theory. New Directions] for a necessary and sufficient condition based on viability theory.
 
2
This is, in essence, another formulation of the Isaacs-Bellman dynamic optimality property for control problems, known since at least Constantin Carathéodory in calculus of variations (see Theorem 6.3.3, p. 98).
 
3
This is the consequence of the Quincampoix Theorem on the semi-permeability barrier property of viability kernels.
 
4
When the endowment function is only lower semicontinuous, the viability solution coincides with the Barron-Jensen/Frankoska viscosity solutions (see [28, Barron, Jensen] and [66‐69, Frankowska]). We do not elaborate these generalizations, since economic interpretation of this Hamilton–Jacobi equation do not play a major role in this study.
 
5
See Sect. 6.1, p. 219 of [24, Set-Valued Analysis]. Sleekness plays the role of continuous differentiability.
 
6
If the potential function U is only lower semicontinuous and sleek, we set
$$\displaystyle\begin{array}{rcl} \mathcal{U}(x,y)\;:=\; \left \{\upsilon \in cB\;\mathrm{and}\;D_{\uparrow }U(x)(\upsilon ) \leq \;\; y\right \}& & {}\end{array}$$
(6.35)
 
Literature
11.
Aubin J-P (2000) Mutational and morphological analysis: tools for shape regulation and morphogenesis. Birkhäuser
13.
15.
Aubin J-P, Bayen A, Saint-Pierre P (2011) Viability theory. New directions. SpringerCrossRef
24.
Aubin J-P, Frankowska H (1990) Set-valued analysis. Birkhäuser
28.
Barron EN, Jensen R (1990) Semicontinuous viscosity solutions for Hamilton–Jacobi equations with convex Hamiltonians. Comm Part Differ Equat 15:1713–1742
37.
Brahic E, Terreaux J-P (2009) Évaluation économique de la biodiversité. Quae
38.
Brosnan SF, Jones, Gardner M, Lambeth SP, Schapiro SJ (2012) Evolution and the expression of biases: situational value changes the endowment effect in chimpanzees. Evol Hum Behav 33:378–386CrossRef
66.
Frankowska H (1991) Lower semicontinuous solutions to Hamilton–Jacobi–Bellman equations. In: Proceedings of the 30th IEEE conference on decision and control, Brighton, UK
69.
Frankowska H (2010) Control under state constraints. In: Proceedeings of the International Congress of Mathematicians (ICM 2010), Hyderabad, India
78.
Griffon M, Griffon L (2011) Pour un monde viable: changement global et viabilité planétaire. Odile Jacob
84.
Hanemann MW (1991) Willingness to pay and willingness to accept: how much do they differ? Am Econ Rev 81:635–647
85.
Harbaugh WT, Krause K, Vesterlund L (2001) Are adults better behaved than children? Age, experience, and the endowment effect. Econ Lett 70(2):175–181CrossRef
92.
Kanngiesser P, Santos LR, Hood BM, Call J (2011) The limits of endowment effects in great apes (Pan paniscus, Pan troglodytes, Gorilla gorilla, Pongo pygmaeus). J Comp Psychol 125:436–445CrossRef
114.
Rockafellar RT, Wets R (1997) Variational analysis. Springer
125.
Metadata
Title
Endowing Fundamental Values: Willingness to Pay
Author
Jean-Pierre Aubin
Copyright Year
2014
Book
Time and Money

Print ISBN: 978-3-319-00004-6

Electronic ISBN: 978-3-319-00005-3

Copyright Year: 2014

DOI
https://doi.org/10.1007/978-3-319-00005-3_6