Aggregation with sequential indivisible and continuous labor supply decisions and an informal sector

The purpose of this paper is to explore the problem of non-convex labor supply decision in an economy with both discrete and continuous labor decisions. In contrast to the setup in Vasilev (2016a), here each household faces a sequential labor market choice - an indivisible labor supply choice in the market sector, and conditional on non-working in the official sector, a divisible hours choice in the informal sector. We show how lotteries as in Rogerson (1988) can again be used to convexify consumption sets, and aggregate over individual preferences. With a mix of sequential discrete and continuous labor supply decisions, aggregate disutility of non-market work becomes separable from market work, and the elasticity of the latter increases from unity to infinity.