Dynamics of Markups, Concentration and Product Span

We develop a model with a finite number of multi-product firms that populate an industry together with a continuum of single product firms, and study the dynamics of this industry that arises from investments in the invention of new products. Consistent with the available evidence, the model predicts rising markups and concentration and a declining labor share. We then examine the dynamics of market shares and product spans in response to improvements in the technologies of the multi-product and single product firms, and the impact of these changes on the steady state distribution of market shares and product spans. Our model predicts the possibility of an inverted-U relationship between labor productivity and product span in the cross-section of firms, for which we provide suggestive evidence. It also predicts that rising entry costs of single-product firms may flatten the relationship between labor productivity and market shares of the large multi-product firms.