Journal article: Luxembourg is a small open economy with a set of particular features, including rather limited competition in the domestic goods market, strong union power, and a segmented labour market for resident and non-resident workers. In this paper we develop a medium scale DSGE model that captures these features, calibrate it to mimic the actual behaviour of the key macroeconomic aggregates, and use it to conduct policy experiments aimed at relaxing some of the existing rigidities in the goods and labour market.