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This paper illustrates how fluctuations in aggregate economic activity can result from many small, independent shocks to individual sectors. The effects of the small independent shocks fail to cancel in the aggregate due to the presence of two non-standard assumptions: local interaction between productive units (linked by supply relationships), and non-convex technology. We also argue that neither feature on its own would suffice. In the case of a simple model, we explicitly calculate the distribution of aggregate activity in the limit of an infinite number of independently disturbed sectors.