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A Practical Competitive Market Model for Indivisible Commo

Author

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  • Zaifu Yang

    (Yokohama National University)

Abstract

A general and practical competitive market model for trading indivisible goods is introduced. There are a group of buyers and a group of sellers, and several indivisible goods. Each buyer is initially endowed with a sufficient amount of money and each seller is endowed with several units of each indivisible good. Each buyer has reservation values over bundles of indivisible goods above which he will not buy and each seller has reservation values over bundles of his own indivisible goods below which he will not sell. Buyers and sellers' preferences depend on the bundle of indivisible goods and the quantity of money they consume. All preferences are assumed to be quasi-linear in money and money is treated as a perfectly divisible good. It is shown in an extremely simple manner that the market has a Walrasian equilibrium if and only if an associated linear program problem has an optimal solution with its value equal to the potential market value. In addition, it is shown that the equilibrium prices of the goods and the profits of the agents are the optimal solutions of the linear program problem.

Suggested Citation

  • Zaifu Yang, 2001. "A Practical Competitive Market Model for Indivisible Commo," Cowles Foundation Discussion Papers 1317, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:1317
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    File URL: http://cowles.yale.edu/sites/default/files/files/pub/d13/d1317.pdf
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    Keywords

    Market; indivisibility; Walrasian equilibrium; linear program; potential market value;

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C68 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computable General Equilibrium Models
    • D4 - Microeconomics - - Market Structure, Pricing, and Design
    • D41 - Microeconomics - - Market Structure, Pricing, and Design - - - Perfect Competition
    • D46 - Microeconomics - - Market Structure, Pricing, and Design - - - Value Theory
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General
    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies

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