Convergence Properties of a Pies-Type Algorithm for Non-Integrable Functions.

Abstract

An algorithm for determining the market equilibrium in the presence of non-integrable but differentiable excess demand functions is developed. This can be reviewed as a variant of the Project Independence Evaluation System Algorithm. A sequence of approximate market equilibria are obtained by constructing integrable excess demand functions. Conditions for the existence and uniqueness of the solutions are demonstrated. It is shown further that the sequence converges to the true market equilibrium if a matrix related to the demand elasticities has a spectral radius less than one. There is a close analogy to known methods for iterative solution of nonlinear equations. Geometric interpretations and some effects of coordinate transformation are discussed. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1977
Accession Number
ADA053440

Entities

People

  • Caulton L. Irwin

Organizations

  • Stanford University

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  • Air Platforms
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Algorithms
  • Convergence
  • Coordinate Systems
  • Differential Equations
  • Equations
  • Linear Programming
  • Mathematical Programming
  • New York
  • Numerical Analysis
  • Operations Research
  • Optimization
  • Partial Differential Equations
  • Sequences
  • Theorems
  • United States
  • United States Government
  • West Virginia

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  • Industrial Economics
  • Linear Algebra