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The Stochastic Matrix and Linear Programming

Author

Listed:
  • John Hartwick

Abstract

We take a stochastic matrix (or Markov matrix) and place the matrix in a linear programming framework. The dual program is in a sense a novel “completion†of the stochastic matrix formulation. We identify the primal linear program (LP) as a “quantity†program (based on a key eigenvalue) and the dual program as a “price†program (turning on an eigenvalue of the transpose matrix). Our approach is to present detailed numerical examples, examples based on particular 3 x 3 stochastic matrices. We do not present new types of evolution “descending from†a stochastic matrix. The linear programming framework provides a novel way to envisage a stochastic matrix and its transpose.

Suggested Citation

  • John Hartwick, 2026. "The Stochastic Matrix and Linear Programming," Working Paper 1545, Economics Department, Queen's University.
    • Handle: RePEc:qed:wpaper:1545
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    File URL: https://www.econ.queensu.ca/sites/econ.queensu.ca/files/wpaper/qed_wp_1545.pdf
    File Function: First version 2026
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    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • Y8 - Miscellaneous Categories - - Related Disciplines
    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology

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