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Power method tâtonnements for Cobb-Douglas economies

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  • Vladimir Shikhman
  • Yurii Nesterov
  • Victor Ginsburgh

Abstract

We consider an economy with consumers maximizing Cobb–Douglas utilities from the algorithmic perspective. It is known that in this case finding equilibrium prices reduces to the eigenvalue problem for a particularly structured stochastic matrix. We show that the power method for solving this eigenvalue problem can be naturally interpreted as a tâtonnement executed by an auctioneer. Its linear rate of convergence is established under the reasonable assumption of pairwise connectivity w.r.t. commodities within submarkets. We show that the pairwise connectivity remains valid under sufficiently small perturbations of consumers’ tastes and endowments. Moreover, the property of pairwise connectivity holds for almost all Cobb–Douglas economies.
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Suggested Citation

  • Vladimir Shikhman & Yurii Nesterov & Victor Ginsburgh, 2018. "Power method tâtonnements for Cobb-Douglas economies," LIDAM Reprints CORE 2956, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvrp:2956
    Note: In : Journal of Mathematical Economics, 75, 84-92, 2018
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    3. Wang, Jingfan & Tchapmi, Lyne P. & Ravikumar, Arvind P. & McGuire, Mike & Bell, Clay S. & Zimmerle, Daniel & Savarese, Silvio & Brandt, Adam R., 2020. "Machine vision for natural gas methane emissions detection using an infrared camera," Applied Energy, Elsevier, vol. 257(C).

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