Aggregation with 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 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 micto-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.