Aggregation with a non-convex labor supply decision and habits in consumption

The purpose of this paper is to explore the problem of non-convex labor supply decision in an economy where households feature consumption habits. We show how lotteries as in Rogerson (1988) can again be used to convexify consumption sets, and aggregate over individual preferences. The presence of habits in consumption does not affect the results. 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 unity to infinity.