Information about price and income elasticities of demand is not without interest for economists and policymakers. At the moment, there are many methods of estimating these elasticities but the estimates given by the various systems are often very different and there is no basis for deciding which is the most accurate. This study attempts to throw some light on the characteristics of the estimating methods which are now commonly used. Four estimators are taken and each is applied in turn to a number of sets of stochastic consumption data where the elasticities are already known. By doing this, it is hoped to discover how accurately the elasticities are estimated in a variety of circumstances and whether the results can tell us anything about the structure of the underlying demand relationships. Section II below describes the estimating methods used and the reasons for choosing them; Section III tells how the data were produced, Section IV describes the results of applying the estimators to the data; Section V is an application of the results to Irish data and Section VI draws conclusions.