Quantifying Non-monotonicity in Productivity-Input Relations

It is stylized that productivity and input size should relate positively and monotonically in the long run. In this paper, I present 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, I quantify a simple algebraic condition on demand and production elasticities 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.