The Stochastic Matrix and Linear Programming

John Hartwick ()

No 1545, Working Paper from Economics Department, Queen's University

Abstract: 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.

Keywords: stochastic matrices; linear programming; the transpose; evolution (search for similar items in EconPapers)
JEL-codes: B4 C6 Y8 (search for similar items in EconPapers)
Pages: 6 pages
Date: 2026-05
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