Engel's law and growth with directed technical change

This paper presents a tractable endogenous two-sector growth model with non-Gorman intra-temporal preferences and directed technical change. One of the two consumption goods is a necessity whereas the other is a luxury. If the economy starts with a low initial stock of knowledge, households are relatively poor and a high expenditure share is devoted to necessities. Therefore in early phases of development technical innovations are mainly directed toward the necessity sector. According to Engel's law, growth in income increases the expenditure share of the luxury sector. Biased technical change constitutes another force that leads to shifts in expenditure shares. The resulting structural change is accompanied by increasing R&D investments in the luxury sector whereas investments in the necessity sector become less attractive. The asymptotic equilibrium consists of a nonbalanced constant growth path along which the Kaldor facts hold and growth is fully driven by the luxury sector.