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Endogenous Prices in a Riemannian Geometry Framework

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  • François Gardes

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, UP1 - Université Paris 1 Panthéon-Sorbonne, PSE - Paris School of Economics - ENPC - École des Ponts ParisTech - ENS Paris - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique - EHESS - École des hautes études en sciences sociales - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, UCO - Université Catholique de l'Ouest)

Abstract

Economic agents decide often under different price conditions (named endogenous prices), and moreover these individual price systems may depend on their previous choices. Such a situation appears for instance for consumers' choices under constraints which imply virtual costs or when non-monetary resources add to the monetary budget constraint. In case where no market exist which regulates these prices and make them converge toward a common price for all agents, observed differences appear between the social distribution of consumer expenditures and their change over time which are modelized here using Riemannian geometry. Observations in a cross-sectional survey are supposed to constitute a Riemannian surface (where each point is associated with a particular price system). Social differences are measured along the geodesics of the Riemannian surface, while changes over time correspond to movements along their tangent spaces (characterized by constant endogenous prices). The Riemannian curvature of the consumption space is thus estimated comparing the derivatives over the surface (corresponding to cross-section differences) to those of the tangent plane (corresponding to the time changes). The Riemannian curvature being shown to be non-null for the Polish consumers surveyed in a four years Polish panel, implies that usual econometric methods based on a unique metric over the (cross-sectional) consumption space are inadequate to estimate geodesics (corresponding to optimal choices) on the Riemannian surface. The curvature of the survey can be linked to changes in latent endogenous prices over the Riemannian surface, which are for instance full prices in a domestic production framework. Finally, the Riemannian structure is used to study the path dependency of consumers' choices.

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  • François Gardes, 2021. "Endogenous Prices in a Riemannian Geometry Framework," Post-Print halshs-03325414, HAL.
  • Handle: RePEc:hal:journl:halshs-03325414
    Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-03325414
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    References listed on IDEAS

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    8. Mundlak, Yair, 1978. "On the Pooling of Time Series and Cross Section Data," Econometrica, Econometric Society, vol. 46(1), pages 69-85, January.
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    10. Anil Alpman & François Gardes & Noel Thiombiano, 2017. "Statistical Matching for Combining Time-Use Surveys with Consumer Expenditure Surveys: An Evaluation on Real Data," Post-Print halshs-01529699, HAL.
    11. Duncan, G.J. & Gardes, F. & Gaubert, P. & Starzec, C., 1998. "A Comparison of Consumption Models Estimated on American and Polish Panel and Pseudo-Panel Data," Papiers du Laboratoire de Microéconomie Appliquée 1998-09, Université Panthéon-Sorbonne (Paris 1).
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    Keywords

    spatial autocorrelation; Riemannian geometry; curvature; virtual price; full price; path dependency;
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