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

摘要

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)