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How to Compute Equilibrium Prices in 1891



Irving Fisher's Ph.D. thesis, submitted to Yale University in 1891, contains a fully articulated general equilibrium model presented with the broad scope and formal mathematical clarity associated with Walras and his successors. In addition, Fisher presents a remarkable hydraulic apparatus for calculating equilibrium prices and the resulting distribution of society's endowments among the agents in the economy. In this paper we provide an analytical description of Fisher's apparatus, and report the results of simulating the mechanical/hydraulic "machine," illustrating the ability of the apparatus to "compute" equilibrium prices and also to find multiple equilibria.

Suggested Citation

  • William C. Brainard & Herbert E. Scarf, 2000. "How to Compute Equilibrium Prices in 1891," Cowles Foundation Discussion Papers 1272, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:1272

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    References listed on IDEAS

    1. Morris, Stephen & Shin, Hyun Song, 1998. "Unique Equilibrium in a Model of Self-Fulfilling Currency Attacks," American Economic Review, American Economic Association, vol. 88(3), pages 587-597, June.
    2. Frankel, David M. & Morris, Stephen & Pauzner, Ady, 2003. "Equilibrium selection in global games with strategic complementarities," Journal of Economic Theory, Elsevier, vol. 108(1), pages 1-44, January.
    3. Carlsson, Hans & van Damme, Eric, 1993. "Global Games and Equilibrium Selection," Econometrica, Econometric Society, vol. 61(5), pages 989-1018, September.
    4. Obstfeld, Maurice, 1996. "Models of currency crises with self-fulfilling features," European Economic Review, Elsevier, vol. 40(3-5), pages 1037-1047, April.
    5. Stephen Morris & Hyun Song Shin, 2000. "Global Games: Theory and Applications," Cowles Foundation Discussion Papers 1275R, Cowles Foundation for Research in Economics, Yale University, revised Aug 2001.
    6. Douglas W. Diamond & Philip H. Dybvig, 2000. "Bank runs, deposit insurance, and liquidity," Quarterly Review, Federal Reserve Bank of Minneapolis, issue Win, pages 14-23.
    7. Levine, David K & Pesendorfer, Wolfgang, 1995. "When Are Agents Negligible?," American Economic Review, American Economic Association, vol. 85(5), pages 1160-1170, December.
    8. Giancarlo Corsetti & Paolo Pesenti & Nouriel Roubini, 1998. "What Caused the Asian Currency and Financial Crisis? Part I: A Macroeconomic Overview," NBER Working Papers 6833, National Bureau of Economic Research, Inc.
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    Cited by:

    1. Chuangyin Dang & Yinyu Ye & Zhisu Zhu, 2011. "An interior-point path-following algorithm for computing a Leontief economy equilibrium," Computational Optimization and Applications, Springer, vol. 50(2), pages 223-236, October.
    2. Bruno Codenotti & Kasturi Varadarajan, 2005. "Market Equilibrium in Exchange Economies with Some Families of Concave Utility Functions," Computational Economics 0503001, EconWPA.
    3. Jain, Kamal & Vazirani, Vijay V., 2010. "Eisenberg-Gale markets: Algorithms and game-theoretic properties," Games and Economic Behavior, Elsevier, vol. 70(1), pages 84-106, September.
    4. Donald J. Brown, 2014. "Approximate Solutions of the Walrasian Equilibrium Inequalities with Bounded Marginal Utilities of Income," Cowles Foundation Discussion Papers 1955, Cowles Foundation for Research in Economics, Yale University.
    5. Devanur, Nikhil R. & Garg, Jugal & Végh, László A., 2016. "A rational convex program for linear Arrow-Debreu markets," LSE Research Online Documents on Economics 69224, London School of Economics and Political Science, LSE Library.
    6. K. Vela Velupillai & Stefano Zambelli, 2010. "Computation in Economics," ASSRU Discussion Papers 1001, ASSRU - Algorithmic Social Science Research Unit.
    7. Giocoli, Nicola, 2005. "Mathematics as the role model for neoclassical economics (Blanqui Lecture)," MPRA Paper 33806, University Library of Munich, Germany.
    8. Velupillai K. Vela, 2011. "The Phillips Machine, the Analogue Computing Tradition in Economics and Computability," Economia politica, Società editrice il Mulino, issue 1, pages 39-62.
    9. K. Vela Velupillai, 2010. "Introduction to the Phillips Machine and the Analogue Computing Tradition in Economics," ASSRU Discussion Papers 1008, ASSRU - Algorithmic Social Science Research Unit.

    More about this item


    Fisher; general equilibrium; hydraulic apparatus; equilibrium prices; computable general equilibrium; algorithms;

    JEL classification:

    • D58 - Microeconomics - - General Equilibrium and Disequilibrium - - - Computable and Other Applied General Equilibrium Models
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C68 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computable General Equilibrium Models
    • B13 - Schools of Economic Thought and Methodology - - History of Economic Thought through 1925 - - - Neoclassical through 1925 (Austrian, Marshallian, Walrasian, Wicksellian)
    • B31 - Schools of Economic Thought and Methodology - - History of Economic Thought: Individuals - - - Individuals


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