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Publicly traded companies are fundamental units of contemporary economies andmarkets and are important mechanisms through which humans interact with theirenvironments. Understanding the general properties that underlie the processesof their growth has long been of interest, yet fundamental debates about theeffects of firm size on growth have persisted. Here we develop a scalingframework that focuses on company size as the critical feature determining avariety of tradeoffs, and use this to reveal novel systematic behavior acrossthe diversity of publicly-traded companies. Using a large database of 31,553 UScompanies over nearly 70 years, and 3,160 Chinese companies over 24 year, weshow how the dynamics of companies expressed as scaling relationships leads toa quantitative, analytic theory for their growth. This theory produces severalpredictions that are in good agreement with data for both the US and China,whose markets have strikingly different histories and underlying structures. Inboth cases sales scale sublinearly with assets and exhibit nearly identicalexponents leading, surprisingly and nontrivially, to assets that grow as apower law in time rather than exponentially, as often assumed. On the otherhand, liabilities scale linearly in the US (exponent of $1.0$) butsuperlinearly in China (exponent of $1.09$). We show that such smalldifferences in scaling exponents can have a significant impact on the characterand long-term evolution of growth trajectories. These results illustrate thatwhile companies are part of a larger class of growth phenomena driven byincomes and costs that scale with size, they are unique in that they growfollowing a temporal power-function which sets them apart from organisms,cities, nations, and markets, whose growth over time is often exponential.

Scaling laws and a general theory for the growth of public companies