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In this paper, the author presents a theory that unifies the role of demand and production to investigate conditions that make this relation a bell-shape. Under the optimality assumption and when establishments operate in the same market, the author quantifies a simple algebraic condition on demand and production elasticity's that governs the relation between productivity and input size. The case where establishments face different demands is also considered using a simple trade model and the implications are shown to be qualitatively the same. Supportive evidence is obtained from plant-level data on ready-mix concrete. Findings of this paper have important implications on how productivity dispersion and size distribution are formed within industries.
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