Measures of economic well‐being are often needed for geographically small areas, as economic indicators may be distributed unevenly among the subsets of relatively small regions. We consider small area estimation of average equivalized income. Disposable household income data are usually available only for a sample of households, typically too small to provide reliable estimates for small regions. We consider a small area estimation technique that is robust to outliers, produces results consistent with design weighted estimates obtained for larger areas and yield maps with approximately no shrinkage. The proposed methodology is applied to the Local Labour Systems in Tuscany (Italy).