Calculus: Should Isaac Newton Earn Royalties?

It is common intuition that knowledge and ideas drive growth. But if economics were intuition and nothing more, it would not be a profession. This is the story of how a group of young economists created a revolution in technical economics by recognizing how central knowledge-driven technological change is to economies, and more importantly, modeling its effects. They transformed economics from a dismal and tremendously boring science about land, labor and capital to a field with boundless possibility: a field about people, ideas and things.1

The basic units of economic theory are the factors of production. Taught in every introductory economics class, they are land, labor and capital. These categories were once thought to be all encompassing.1 Formulated in the seventeenth century, these endogenous variables2 enabled classical economists to argue about everything that they thought they should argue about.  On the other hand, from the very dawn of economics, some things were considered to be well outside the domain of economic analysis. For example, consumer preferences were always taken as a given. They lay outside economic models and were considered exogenous variables.1,2

However, this way of arranging economic thought was not watertight. Foremost among the inconsistencies in this way of thinking was a family of irritating effects that defied conventional modeling, known as increasing returns to scale.1,2

Economists have always been comfortable with the idea of decreasing returns to scale. This idea is simple and ubiquitous in everyday life: everyone knows watering a plant too much will make it die. 1

In contrast with this idea of decreasing returns to scale is increasing returns to scale, which is the phenomenon of decreasing average cost.1,2 It sets in when the same input generates an increasing amount of output on the margin. Adam Smith gives a famous example in the “Wealth of Nations” of a pin factory, in which he implies that the only reason costs fall is because of division of labor. He accompanies this with the cryptic statement ‘…the division of labor is limited by the extent of the market.’ As economic journalist David Warsh notes, ‘It does not make sense to invent a hammer to hammer in a single nail.’1 In our single nail world, there will be no hammer factories, no division of labor in hammer production – a single consumer is the entire market.

However, throughout the nineteenth century, it became clear that increasing returns did not only relate to division of labor and the extent of the market but also had much to do with the output of machines.1

In any industry where the cost of getting one more new customer was negligible, like railroads or telecommunications, increasing returns tore competitive forces to shreds.1 Such industries were soon declared ‘natural monopolies’—markets that would necessarily lead to government intervention to maintain competition.1,2 Natural monopolies were considered by economists to be exceptions to the rule and so were relegated to footnotes, all but forgotten, gradually receding from the eyes of the field, dragging away with them the problem of increasing returns. Growing formalization of the economic method disguised this blind spot in economics, making the issues associated with it obscure and almost impossible to discuss.1

The question of what was causing these increasing returns was left out of academic discourse until 1990, when a thirty-six-year old Chicago economist named Paul Romer published a new mathematical model that sought to reconcile knowledge with increasing returns and growth.1

‘Endogenous Technological Change’ made an interesting claim: ‘…the distinguishing feature… of technology as an input is that it is neither a conventional nor a public good…it is a non-rival… partially excludable good.’ 3

This sentence in an innocuous academic paper tucked away in the corner of a highly technical journal of mathematical economics represented the culmination of years of work by Romer and started a rearrangement of the very fabric of economic theory. It did this by supplementing the definition of public goods and private goods with the concept of rivalry and non-rivalry.1

A rival good is corporeal, meaning that its owner can consume it only once. On the other hand, a non-rival good is non-corporeal and can be consumed over and over again. The difference between rivalry and non-rivalry corresponds to the difference between objects and ideas.1 A steak, which can only be consumed once, is an example of an atom or a rival good. Calculus is a classic example of a bit or an idea. It is non-rival because Newton’s invention and consumption of it does not preclude our consumption of it – we can do so using any blueprint such as a textbook.

Romer melded rivalry with partial excludability and opened up ideas or bits for economic analysis. From intellectual property to trade secrets, from patents to piracy, ‘Endogenous Technological Change’ unlocked a strange new world rife with possibility.1

This paper is a classic. To understand why, we must go back in time to Memorial Day Weekend, 1988, when the foremost economists in the emerging field of growth theory gathered at the Buffalo Hilton Hotel. Here, Romer presented a precursor to ‘Endogenous Technological Change,’ and laid claim to being the first economist to solve the puzzle of economic growth.1

Paul Romer in 2005

Apart from Paul Romer, the meeting included famed scholars such as Gary Becker, Kevin Murphy, Paul Krugman, Dale Jorgenson, and Robert Barro. It was here that Romer presented the findings of what would be published as ‘Endogenous Technological Change.’

Romer’s paper blew away the others, for it was here that intellectual property was first characterized within the context of growth theory, and knowledge was described both as an input and output of production.1 The paper began by asserting that it was the accumulation of knowledge, rather than physical capital, that was economically important.1,3,4 The raw materials used to produce a given good had remained, Romer asserted, more or less the same for a long time. What had changed were the ‘instructions’ that we used to combine them. This is where he introduced the concept of non-rivalry in the context of instructions or knowledge. From the very beginning, he had been attracted to non-rivalry because it could explain Smith’s hypothesis that the division of labor is limited by the extent of the market. Allyn Young had sought only to understand division of labor in terms of specialization, but now, Romer implied, he had isolated the mechanism that related division of labor and market size: the fixed cost of finding a new set of instructions. It was uneconomical to create a new kind of genetic engineering to modify a solitary fish, but the bigger the market, the more copies of the new design could be sold. The cost was fixed, which means it was irrelevant how many times the design was used: its non-rivalry meant that it could be used over and over again at no additional cost.1 Because the market for knowledge was capable of supporting a great number of specialists who could provide input indefinitely to the final product, Romer concluded that knowledge brought increasing returns and was therefore economically crucial.

The Buffalo model showed that opening markets to technology (and thus implicitly to new instructions) did not just improve welfare but the rate of growth itself. However, Romer warned that the economics of making ideas was very different from the economics of making things, because ideas could be copied without cost.1

This led to the second innovation of the model: giving up the elegant convex mathematics of Chicago School perfect competition and using a monopolistic competition assumption instead. The presence of intellectual property meant the existence of trade secrets. It meant product differentiation and price making, and that certain producers could make things that others couldn’t. But remember the most important property of Romer’s concept of knowledge: no secret remains secret for long, even with the protection of law. He wrote, ‘As is quite clear from the experience of video tape recording (a technology developed by firms in the United States, refined by firms in Japan, and used by firms in Korea, technological innovation can be copied and used without the consent of the developer.’ He called these effects spillovers.1

Romer’s analysis of the way knowledge was structured had many implications: the most important of these implications was that apart from the traditional concerns of economic policy, governments would soon have to formulate policies for the creation and dissemination of knowledge. There was a trade-off – a balance would have to be found between providing incentives to inventors to continue generating new ideas (by making intellectual property laws strong), and on the other hand, ensuring that these laws still allowed for flexibility so that spillovers could occur, knowledge could be copied, and new knowledge could be generated.

Those in the room at the Buffalo Hilton in the summer of 1988 knew that the field had been irreversibly changed. What Romer’s paper had done was rework the factors of production and carve economics along new and completely different lines. The familiar idea of scarcity, of land, labor, and capital, was augmented by a new idea of abundance: people, ideas, and things.1


  1. David Warsh, Knowledge and the Wealth of Nations: A Story of Economic Discovery (New  York:Norton, 2007)
  2. Elhanan Helpman, The Mystery of Economic Growth (Boston: Harvard University Press,  2004)
  3. Paul Romer, Endogenous Technological Change, Journal of Political Economy, Vol. 8, No.5, Part 2 (1990) S71 – S102
  4. David Warsh, Meeting of Minds Sharpens Ideas, Boston Globe, May 8 1994, accessed November 7th, 2011,
  5. Paul Romer, Increasing Returns and Long-Run Economic Growth, Journal of Political Economy Vol. 4, (1986) 1002-1007
  6. Akerman, Scott. “Calculus III,” flickr, taken on Nov 23, 2008,
  7. Doerrb. “Paul Romer in 2005,” Wikimedia Commons, uploaded on May 19, 2008,

Akshat Goel is a second-year student at the University of Chicago majoring in Economics and Sociology. Follow The Triple Helix Online on Twitter and join us on Facebook.