Non-homothetic preferences and growth

We observe that countries at low levels of income invest at lower rates than those at higher levels of income. This paper explains this fact as a consequence of Engel's law, i.e. that there is an inverse relation between expenditure and its proportion spent on food. It introduces non-homothetic preferences based on Engel's law in a simple Solow model. These preferences imply rates of net investment that increase with the level of income as we approach the steady state. Increasing investment rates imply a positive correlation between growth rates and the level of income, at low levels of income, rather than an inverse relation, as the usual Solow model implies. The existence of a positive correlation between income growth rates and income levels, at low levels of income in the presence of this type of preference, has already been shown in a previous paper for a closed economy. The purpose of this paper is to show that this positive correlation persists when we introduce trade into the model.