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A new variable dimension simplicial algorithm for computing economic equilibria onS n ×R m1+

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Abstract

In this paper, a new variable-dimension simplicial algorithm is developed to compute economic equilibria on the Cartesian product of then-dimensional unit price simplexS n and them-dimensional production activity spaceR m+ . The algorithm differs from other algorithms in the number of directions in which the algorithm may leave the starting point. More precisely, the algorithm has 2n+m+1–2 rays to leave the starting point, whereas the other algorithms have at most 2m(n+1) rays. The path of points generated by the algorithm can be interpreted as a globally and universally convergent price and production adjustment process. The process as well as the convergence condition are much more natural and economically meaningful than the adjustment processes obtained by other simplicial algorithms. Furthermore, we apply the algorithm to economies with linear production, economies with constant returns to scale, and economies with increasing returns to scale.

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Authors and Affiliations

  1. Department of Econometrics and CentER, Tilburg University, Tilburg, Netherlands

    A. J. J. Talman (Professor) & Z. Yang (Doctoral Student)

  2. Institute of Socio-Economic Planning, University of Tsukuba, Tsukuba, Ibaraki, Japan

    Y. Yamamoto (Professor)

Authors
  1. A. J. J. Talman
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  2. Y. Yamamoto
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  3. Z. Yang
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Additional information

Communicated by F. Zirilli

This work is part of the VF-Program “Competition and Cooperation.”

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Talman, A.J.J., Yamamoto, Y. & Yang, Z. A new variable dimension simplicial algorithm for computing economic equilibria onS n ×R m1+ . J Optim Theory Appl 87, 679–701 (1995). https://doi.org/10.1007/BF02192139

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