Yet something is missing. Why was it that, next to innovation in the 19th century, especially after the first quarter with its wars, innovation was so paltry throughout the 18th? The answer may be that something may have grown to multiply or amplify the faint impulses of innovation – to potentiate the democracy and the vitalism that were already present at relatively high levels by the last quarter of the century. But what might that something be? Economic historians appear not to have identified it. Why did innovation come earlier to Britain, America, and possibly Belgium than to France and Germany? We do not have to share de Tocqueville’s impression that culture is everywhere the same to wonder whether differing intensities of the above forces argued to be central – the corporation, democracy, vitalism, and economic freedom – can wholly or largely explain why France and Germany got their dynamism later that the others.
The missing piece, which is obvious once one hits on it, is population density – the number of working-age persons in the country, excluding remote areas. Not many innovations in a country can be encouraged by its culture and promoted by its institutions if there are few minds. (Why, then, are Icelanders, with their small numbers, not backward and therefore poor? The reason is their proficiency in English and Scandinavian languages virtually integrate them into the economies of America and Europe.) Having more persons, all energized by vitalism and encouraged by democratic limits on arbitrary powers, surely increases the total number of new ideas being generated, even it leaves unchanged the number per generator. Further, if the resulting new products and methods generally lead not to private use by the developers but to adoptions over the country – to diffusion – the end result is an increase in the number of innovations: the new products developed by companies themselves and those developed by other companies, which grew in number with the increased population. Thus, the more people there are in a rather integrated country to inspire, develop, market, and try out new ideas, the greater is its prospective rate of indigenous innovations per capita – provided the necessary institutions and culture are in place. (Why, then, was China, despite a population far greater than that of Britain or America, not generating many innovations in the 19th century? Or earlier? There was a phenomenal abundance of entrepreneurs in China’s cities in the 18th century, the Irish economist Richard Cantillon reported in his 1755 study. The reason is China was seriously lacking in the economic institutions or the economic culture of both needed for innovation, indigenous or exogenous. It is far less lacking in the 21st century.) If the economy of the West experiences more innovations per capita now than 100 years ago, it is mainly because there are many more people engaged in innovation in that economy; it does not follow that every (or any) subpopulation of a given size generated more new products and methods.
The benefits of increased population come not only from more creations, most of them available for adoption by others. If new ideas and new products based on them are striking a country, they are likely to spread faster through the economy the more dense the population is – just as heat travels faster when there are more molecules and a disease is apt to spread faster (and farther) through the world the greater the population size. Ideas are communicated very much like diseases. More people, more relays. Also: more people, bigger market. The Beatles could play 1,000 nights in Hamburg, that city being big enough, but not Liverpool.
It's the cities and their role in facilitating the exchange and development of ideas. Yes, it's Jane Jacobs but in the hands of a masterful economist. Phelps' broad brush uses a generalized population density measure but notice that he has to arrived at his story, having carefully explored the others contenders.
Urban economists have for most of the history of the field modeled the journey to work as the spatial organizing principle. Recently, they have rediscovered Jane Jacobs. The exchange of ideas is a key dynamic force.
Aggregating capital (as many economic theorists do) does great harm because we get economic growth if capital markets screen projects so that we get the good ones and do not invest in the bad ones. But we should no sooner aggregate land. Location matters and sites have peculiar advantages. We want an assignment of activities to sites such that producers (including individuals) go where they think they can be productive. This includes where they can burnish their thoughts and ideas. Ray Oldenburg wrote about this. Look at the title of his book.