# Ruhr Economic Papers

Ruhr Economic Papers #354

### Generating Random Optimising Choices

by Jan Heufer

TU Dortmund, 07/2012, 12 S./p., 8 Euro, ISBN 978-3-86788-408-2 DOI: 10.4419/86788408

download### Abstract

This paper provides an efficient way to generate a set of random choices on a set of budgets which satisfy the Generalised Axiom of Revealed Preferences (GARP), that is, they are consistent with utility maximisation. The choices are drawn from an approximate uniform distribution on the admissible region on each budget which ensures consistency with GARP, based on a Markovian Monte Carlo algorithm due to Smith (1984). This procedure can be used to extend Bronarsâ€˜ (1987) method as it can be used to approximate the power of tests for conditions for which GARP is a necessary but not sufficient condition (e.g., homotheticity, separability, risk aversion, etc.). For example, it allows to approximate the probability that a set of random choices which happens to satisfy GARP is also consistent with homotheticity. The approach can also be applied to production analysis and nonparametric tests of cost minimisation.

JEL-Classification: C14, C63, D11, D12

Keywords: Cost minimisation; GARP; hypothesis testing; Monte Carlo methods; nonparametric tests; test power; random optimal choices; revealed preference; utility maximisation