This working paper presents a simple and locally optimal test statistic for the Pareto law. The test is based on the Lagrange multiplier (LM) principle and can be computed easily once the maximum likelihood estimator of the scale parameter of the Pareto density has been obtained.

A Monte Carlo exercise shows the good small sample properties of the test under the null hypothesis of the Pareto law and also its power against some sensible alternatives. Finally, a simple application to urban economics is performed. An appendix presents derivations and proofs.