On the Mechanics of Firm Growth

When the rate at which any given blueprint can be replicated is subject to decreasing returns, it is optimal to replicate high-quality blueprints more quickly than low-quality blueprints. The cost of introducing high-quality “start-up” blueprints will also rise with the rate at which they are introduced, and so low-quality blueprints will continue to enter the population. This naturally leads to persistent heterogeneity in blueprint quality. If quality begets quality and firms are identified with collections of blueprints derived from the same initial blueprint, then firms grow at a constant mean rate along the balanced growth path. A firm size distribution with the thick right tail observed in the data can then arise only when the number of blueprints in the economy grows over time. When calibrated to match the firm entry rate and the right tail of the size distribution, a homogeneous quality version of this model implies that the median age among firms with more than 10,000 employees is about 750 years. If the relative quality of a firm’s blueprints depreciates over time, then firm growth rates are not constant but slow down with age. If the successful replication of new blueprints is rapid but noisy, and high relative quality is sufficiently persistent, this version of the model can explain high observed entry rates, the thick-tailed size distribution, and the relatively young age of large U.S. corporations.