Recipes and Economic Growth: A Combinatorial March Down an Exponential Tail

New ideas are often combinations of existing goods or ideas, a point emphasized by Romer (1993) and Weitzman (1998). A separate literature highlights the links between exponential growth and Pareto distributions: Gabaix (1999) shows how exponential growth generates Pareto distributions, while Kortum (1997) shows how Pareto distributions generate exponential growth. But this raises a "chicken and egg" problem: which came first, the exponential growth or the Pareto distribution? And regardless, what happened to the Romer and Weitzman insight that combinatorics should be important? This paper answers these questions by demonstrating that combinatorial growth in the number of draws from standard thin-tailed distributions leads to exponential economic growth; no Pareto assumption is required. More generally, it provides a theorem linking the behavior of the max extreme value to the number of draws and the shape of the tail for any continuous probability distribution.