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Endowing Fundamental Values: Willingness to Pay

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Time and Money

Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 670))

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Abstract

The concept of fundamental value mentioned by Turgot in his letter6 − − 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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Notes

  1. 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. 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. 3.

    This is the consequence of the Quincampoix Theorem on the semi-permeability barrier property of viability kernels.

  4. 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. 5.

    See Sect. 6.1, p. 219 of [24, Set-Valued Analysis]. Sleekness plays the role of continuous differentiability.

  6. 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)

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Authors and Affiliations

  1. VIMADES (Viabilité, Marchés, Automatique et Décision), Paris, France

    Jean-Pierre Aubin

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  1. Jean-Pierre Aubin
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Aubin, JP. (2014). Endowing Fundamental Values: Willingness to Pay. In: Time and Money. Lecture Notes in Economics and Mathematical Systems, vol 670. Springer, Cham. https://doi.org/10.1007/978-3-319-00005-3_6

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