From Smith to Schumpeter: A Theory of Take-Off and Convergence to Sustained Growth

This paper develops a theory of the emergence of modern innovation-driven Schumpeterian growth. It uses a tractable model that yields a closed-form solution, consisting of an S-shaped (i.e., logistic-like) time path of firm size and a set of equations that express the relevant endogenous variables – GDP, product variety and product quality, consumption, the shares of GDP earned by the factors of production – as functions of firm size. It also obtains closed-form solutions for the dates of the events that drive the economy's phase transitions as functions of the fundamentals. The resulting path of GDP per capita consists of a convex-concave profile replicating the key feature of long-run data: an accelerating phase followed by a deceleration with convergence to a stationary growth rate. Compared to other availables theories, the paper focuses on the within-industry forces that regulate the response of firms and entrepreneurs to Smithian market expansion.