Aggregation with a Non-Convex Labour Supply Decision, Unobservable Effort, and Reciprocity (“Gift Exchange”) in Labor Relations

<p>The purpose of this note is to explore the problem of non-convex labour supply decision in an economy withreciprocity in labour relations (gift exchange) a la Danthine and Kurmann (2010), and explicitly perform theaggregation 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 inRogerson (1988) can be used to convexify consumption sets, and aggregate over individual preferences. With adiscrete labour supply decisions, the elasticity of aggregate labour supply increases from unity to infinity.</p>