Nonhomothetic preferences and rent sharing in an open economy

We develop a framework for studying how differences in the level and/or dispersion of per-capita income affect trade structure and welfare in a two-country model. Thereby, we embed nonhomothetic preferences into a home-market model with two sectors of production and one input factor. We associate the outside good with a necessity and the differentiated good with a luxury, and we assume that heterogeneity of income arises due to heterogeneity of households in their effective labor supply. We then show that in line with the home-market effect countries have a trade surplus in the good for which they have relatively higher domestic demand, making the country with a higher level and/or dispersion of per-capita income a net-exporter of luxuries. The structure of trade is irrelevant for welfare in the open economy if both sectors pay the same wage. If, however, the sector producing luxuries pays a wage premium due to rent sharing, there are feedback effects of trade on the level and dispersion of per-capita income, which can lead to losses from trade in the country net-exporting necessities. In an extension of our model, we show that our results remain intact when we allow for positive assortative matching of workers featuring high effective labor supply with jobs offering high wages in the sector of luxuries. In a second extension, we show that the assumption of nonhomothetic preferences seems less important when supply-side differences are the main motive for inter-industry trade.