Aggregation with non-convex labor supply, unobservable effort, and efficiency wages of the no-shirking type

The purpose of this note is to explore the problem of non-convex labor supply decision in an economy with imperfect observability of work effort, and the need to use efficiency wages to prevent shirking as in Shapiro and Stiglitz (1984). In addition, the paper and explicitly performs the aggregation presented in Vasilev (2017) without a formal proof, and thus provide - starting from micro-foundations - the derivation of the expected utility functions used for the aggregate household. We show how lotteries as in Rogerson (1988) can be used to convexify consumption sets, and aggregate over individual preferences. With a discrete labor supply decisions, the elasticity of aggregate labor supply increases from unity to infinity.