Ideas and R&D: the Romer model, creative destruction and Jones

Economists classify goods by two properties. A good is rival if its use by one person prevents its use by another: a loaf of bread, a lathe. It is excludable if others can be prevented from using it. A lathe is both. An idea, such as the design of the lathe, is not rival: a million firms can use the same blueprint at once. It may be partly excludable, through patents, secrecy or the need to learn how to use it.

Non-rivalry changes the arithmetic of production. To double output of a physical good you replicate the factories and workers: constant returns to the rival inputs. But the blueprint does not have to be replicated; it is paid for once. So output rises more than in proportion to all inputs, including ideas: there are increasing returns to scale. Increasing returns are incompatible with perfect competition (each input cannot be paid its marginal product without exhausting more than output), so a model with ideas needs imperfect competition. That is why endogenous growth theory assumes increasing returns and imperfect competition, which UGC NET 2023 asks directly.

Take an economy with a labour force L split between two uses: L_Y workers produce goods and L_A researchers produce ideas. Output uses the stock of ideas A, and the stock grows with the number of researchers and with the stock itself:

The second equation says that a researcher produces θA new ideas a year, which is proportional to the stock A: the more that has been discovered, the more productive each researcher is (“standing on the shoulders of giants”). The growth rate of ideas is

Output Y = A L_Y with L_Y constant grows with A. There is a trade-off: a larger share of researchers raises growth but lowers output now, since fewer people make goods. A society chooses how many to put into research.

Joseph Schumpeter (1942) argued that capitalist growth is a process of creative destruction: new products and methods destroy the value of old ones, and the prospect of temporary monopoly profit is what drives the entrepreneur. His idea was a theme in the development textbooks long before it entered formal growth models.

Aghion and Howitt (1992) turned it into a model. Each product line has a quality, and research is a gamble: with a probability proportional to the number of researchers a firm invents a product better than the current best by a fixed factor (> 1), and takes over the market. The old leader loses its profit. The average growth rate is the arrival rate of innovations, which is proportional to the number of researchers, times the log size of each step:

where λ is the arrival rate per researcher, L_R the number of researchers and γ > 1 the size of an improvement. Grossman and Helpman (1991) built two versions of the same idea, a model of quality ladders like this one, and one of expanding variety, where growth comes from an ever-growing number of different products. Exams test the labels: GATE 2026 matches Schumpeter with creative destruction and Grossman–Helpman with the expanding-variety model.

In the Romer model g = θ s_R L: growth rises with the size of the economy. A country with twice the population, and the same research share, should grow twice as fast. Two facts go against this. Large countries do not grow faster than small ones. And the number of researchers in the United States and other rich economies has risen many times since the 1950s, with no sign of a rise in growth. Charles Jones (1995) made the point.

His fix changes one number. Let the production of ideas be

With φ = 1 this is Romer (with λ = 1). With φ < 1 the existing stock still helps, but less than in proportion: the best ideas are found first and new ones get harder to find (“fishing out”), and ideas in parallel research may duplicate one another (λ < 1). Take the growth rate of A, Ȧ/A = θL_A^λA^φ−1. For this to be constant, A^1−φ must grow at the same rate as L_A^λ. Taking growth rates and letting researchers grow at the population rate n:

This is semi-endogenous growth. Growth comes from research, and a larger population produces more ideas, but the growth rate is pinned down by n. A higher share of workers in research raises the level of the stock of ideas, and growth speeds up for a while, then falls back: a level effect like Solow’s. Subsidising research has no permanent effect on growth. Kremer (1993) took the long view of the same relationship: over a million years the world’s rate of technological progress tracked the size of its population.

Both versions start with growth of 2% and 10% of workers in research. At year 40 the research share rises (set it with the slider). In Romer’s model (a fixed population, φ = 1) growth jumps to a new rate and stays there: a growth effect. In Jones’s model (φ = 1/2, population growing at 1%) growth jumps and then drifts back to 2%, the rate set by n: a level effect. Watch the second chart too: both leave the economy with a higher stock of ideas, but only one of them with a higher rate of increase.

Because ideas are non-rival, the best static price for using one is zero. But then no one would pay to invent it. Growth models resolve the conflict with temporary monopoly power: patents let an inventor charge above marginal cost for a time, and the profits repay the research cost. The price is a static inefficiency, since monopoly prices reduce use below the efficient level. The gain is a faster flow of new ideas.

Three further results shape policy discussions. Spillovers: because inventors do not capture all the benefit of an idea (others build on it), the market tends to produce too little research, which is the case for subsidies. Business stealing: in Schumpeterian models an innovator destroys the old leader’s profit, which a social planner would not count as a gain, so the market can also produce too much research. Which effect wins is an empirical question. And openness: a larger market and the flow of ideas across borders raise the payoff to invention, which is one argument for trade and for protecting intellectual property in a way that spreads, not blocks, knowledge.

Questions on Schumpeter, Romer, innovation and idea production, from JAM, GATE, UGC NET, JNU and Hyderabad. The Delhi School’s research-sector problem, with a labour share λ in R&D, is in Lesson 14.