This paper examines an economy with identical agents and indivisible labor, showing that such a setup leads to significant aggregate effects despite the disappearance of individual-level discontinuities when aggregated. It demonstrates that optimal allocations may involve lotteries over employment and consumption. The analysis reveals that even with a large number of identical agents, non-convexities in individual preferences can have major implications for aggregate responses to shocks. The economy behaves as if populated by a single agent with preferences not matching any individual. The paper also shows that introducing lotteries allows for decentralized market mechanisms and facilitates equilibrium computation. It further demonstrates that in such economies, aggregate fluctuations in hours of work can be larger than in purely neoclassical models. The paper also discusses the implications for aggregate fluctuations, showing that non-convexities may be crucial in explaining observed magnitudes of fluctuations in labor supply and real wages. It concludes that even with heterogeneous agents, the results hold, and that the elasticity of labor supply can be affected by the indivisibility of labor and the use of lotteries. The paper emphasizes the importance of considering non-convexities in economic models to better understand aggregate behavior.This paper examines an economy with identical agents and indivisible labor, showing that such a setup leads to significant aggregate effects despite the disappearance of individual-level discontinuities when aggregated. It demonstrates that optimal allocations may involve lotteries over employment and consumption. The analysis reveals that even with a large number of identical agents, non-convexities in individual preferences can have major implications for aggregate responses to shocks. The economy behaves as if populated by a single agent with preferences not matching any individual. The paper also shows that introducing lotteries allows for decentralized market mechanisms and facilitates equilibrium computation. It further demonstrates that in such economies, aggregate fluctuations in hours of work can be larger than in purely neoclassical models. The paper also discusses the implications for aggregate fluctuations, showing that non-convexities may be crucial in explaining observed magnitudes of fluctuations in labor supply and real wages. It concludes that even with heterogeneous agents, the results hold, and that the elasticity of labor supply can be affected by the indivisibility of labor and the use of lotteries. The paper emphasizes the importance of considering non-convexities in economic models to better understand aggregate behavior.