My previous post, which answered the question, “Why has growth has been speeding up?” made no use of the concept of excludability. So why did I make such a big deal about partial excludability in my 1990 paper? At least since Marshall handed down his Principles of Economics (arguably since Adam Smith told the story of the pin factory), economists have fretted about how to reconcile the increasing returns associated with what Smith called increases in “the extent of the market” with the obvious fact that in real economies, lots of firms of all sizes compete with each other. One of most important things about growth theory that I learned from Chad Jones is that this question is separable from the question about why the growth rate has been speeding up. Speeding up follows from the 2 key properties of production possibilities that I emphasized in that post–combinatorial explosion and nonrivalry. These are facts about the physical world that nature gives to us, provided we recognize that part of what nature gave us was the amazing capacity to humans was the ability to codify things we learn in words that other humans understand. What Chad pointed out in an aside that I will never forget is that that to understand speeding up, it is enough to take a specification of the production possibilities, attach an objective function, and just solve a social planner’s problem. All the reasonable proposals for decentralizing an equilibrium have a path for growth that is qualitatively similar to the path that solves the planner’s problem. If your production possibilities give you a solution to the planner’s problem with a growth rate that speeds up, you will be able to come up with a decentralized version that does so too.

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