AGGREGATION WITH A NON-CONVEX LABOUR SUPPLY DECISION, UNOBSERVABLE EFFORT, AND RECIPROCITY (“GIFT EXCHANGE”) IN LABOR RELATIONS
The purpose of this note is to explore the problem of non-convex labour supply decision in an economy with reciprocity in labour 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 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 labour supply decisions, the elasticity of aggregate labour supply increases from unity to infinity.
 Hansen, G. 1985. Indivisible labor and the business cycle, Journal of Monetary Economics, 16: 309-327.
 Rogerson, R. 1988. Indivisible labor, lotteries and equilibrium, Journal of Monetary Economics, 21: 3-16.
 Vasilev, A. 2017. A Real-Business-Cycle model with reciprocity in labor relations and fiscal policy: the case of Bulgaria, Bulgarian Economics Papers 03-2017, Center for Economic Theories and Policies, Sofia University St. Kliment Ohridski, Sofia, Bulgaria.
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