Aggregation with a mix of indivisible and continuous labor supply decisions: the case of home production

This note explores the problem of non-convex labor supply decision in an economy with both discrete and continuous labor decisions. In contrast to the setup in Mc-Grattan, Rogerson and Wright (1997), here each household faces an indivisible labor supply choice in the market sector, while it can choose to work any number of hours in the non-market sector. We show how lotteries as in Rogerson (1988) can again be used to convexify consumption sets, and aggregation over individual preferences. With a mix of discrete and continuous labor supply decisions, disutility of non-market work becomes separable from market work, and the elasticity of the latter increases from unity to infinity.