AGGREGATION WITH A LABOUR-SUPPLY DECISION AND HABITS IN CONSUMPTION
The objective of this paper is to study the problem of a discrete labour supply decision in an artificial economy where the households feature habits in consumption. We demonstrate how lotteries a la Rogerson (1988) can be used to make consumption choices into convex sets, and then produce an equivalent aggregate household with convex labour supply. The presence of consumption habits does not affect the main results of the paper. As in Hansen (1985) and Rogerson (1988) and no consumption habits, with a discrete labor supply decision at individual level, the elasticity of hours worked at the aggregate level increases from one to an infinitely large value.
 Rogerson, R. 1988. Indivisible labor, lotteries, and equilibrium. Journal of Monetary Economics 21: 3-16. DOI:https://doi.org/10.1016/0304-3932(88)90042-6
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