Aggregation with a non-convex labor supply decision, unobservable effort, and reciprocity ("gift exchange") in labor relations

The purpose of this note is to explore the problem of a non-convex labor supply decision in an economy with reciprocity in labor relations ("gift exchange") a la Danthine and Kurmann (2010), and explicitly perform the aggregation presented in Vasilev (2017) without a formal proof, and thus provide - starting from micro-foundations - the deriva- tion 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 aggre- gate over individual preferences. With a discrete labor supply decisions, the elasticity of aggregate labor supply increases from unity to infinity.