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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 knowledge stock, 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.
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