Over the last 10,000 years, growth in per capita world GDP has been increasing. Growth in per capita GDP was approximately zero from the dawn of civilization to about 1500, increased to 0.08% a year between 1500 and 1760, doubled during the next hundred years, and increased even further during the nineteenth and twentieth centuries. Today, worldwide per capita GDP is growing by a little over 3% per year.

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Could economic growth become even faster? Yes. Let’s take a look again at our measure off technological progress, A. We can summarize what we have said about the factors causing A to increase in a simple equation:

A (ideas) = Population × Incentives × Ideas per hour

In words, the number of new ideas is a function of the number of people, the incentives to innovate, and the number of ideas per hour that each person has. Of course, this equation is not meant to be exact—it’s just a way of thinking about some of the key factors driving technological growth. So let’s go through each of the factors and think about what they imply for the future of economic growth.

The number of people is increasing, which is good for idea generation. More important, the number of people whose job it is to produce new ideas is increasing. In all the world today, there are perhaps 6 million scientists and engineers, of which 1.3 million come from the United States. These 1.3 million represent about one-half of 1% of the U.S. population, a surprisingly small percentage. Yet for the world as a whole, the ratio of scientists and engineers to population is much lower.

Today, because much of the world is poor, thousands of potentially great scientists will spend most of their lives doing backbreaking work on a farm. If the world as a whole were as wealthy as the United States and could devote the same share of population to research and development as does the United States today, there would be more than five times as many scientists and engineers. Thus, as the world gets richer, more people will be producing ideas, and because of spillovers, these ideas will benefit everyone.

The incentives to innovate also appear to be increasing. Consumers are richer and the world is becoming one giant integrated market because of trade; each of these factors boosts the incentives to innovate.

The incentives to innovate also increase when innovators can profit from their investments without fear of expropriation. The worldwide improvement in institutions—that is, the movement toward property rights, honest government, political stability, and a dependable legal system—has been very positive for both innovation and economic growth.

We know the least about the last factor in the equation, the number of ideas per hour or how easy it is to come up with new ideas. In some fields, we are unlikely to ever know much more than we know now. For thousands of years, scientists periodically discovered new human organs, but the last new organ to be found was identified in 1880 (the parathyroid gland). Don’t expect more breakthroughs in this field, no matter how hard we look. In some places and times, knowledge grows by leaps and bounds, and in others it stagnates. We don’t always know why. When the law of diminishing returns applies to ideas in general as well as to capital, then economic growth will be much slower. There are at least two reasons, however, for thinking that diminishing returns is not the usual state of affairs.

First, many ideas make creating other ideas easier. Sadly, the authors of this book can remember the day when answering even simple questions like who won the 1969 World Series could not be answered without going to a library, consulting a card catalog (don’t ask), looking for the appropriate book in the stacks, and then (if the book hadn’t been checked out) finding the answer. Today, you can probably find the answer using Google on your cell phone faster than you can read this paragraph. (By the way, it was the New York Mets in one of the greatest upsets in baseball history.) Since we still have many new ideas about creating even more ideas, it does not seem that ideas production has come close to diminishing returns.

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The second reason to think that the number of ideas per hour is not yet strongly diminishing comes from one of the pioneers of the economics of ideas, Paul Romer. (Romer is not only a distinguished theorist of ideas, he is a first-class idea entrepreneur; he started Aplia, the online economics test bank and tutorial system that many of you use and that is a good example of an idea that makes learning new ideas easier.) Romer points out that ideas for production are like recipes and the number of potential recipes in the universe is unimaginably vast:

The periodic table contains about a hundred different types of atoms, which means that the number of combinations made up of four different elements is about 100 × 99 × 98 × 97 = 94,000,000. A list of numbers like 6, 2, 1, 7 can represent the proportions for using the four elements in a recipe. To keep things simple, assume that the numbers in the list must lie between 1 and 10, that no fractions are allowed, and that the smallest number must always be 1. Then there are about 3,500 different sets of proportions for each choice of four elements, and 3,500 × 94,000,000 (or 330 billion) different recipes in total. If laboratories around the world evaluated 1,000 recipes each day, it would take nearly a million years to go through them all.4

True, many of the recipes are going to be like chicken liver ice cream (not that good), but the field of ideas that we can explore is so large that diminishing returns may not set in for a very long time.

Putting all this together, economic growth might be even faster in the future than it has been in the past. There are more scientists and engineers in the world today than ever before and their numbers are increasing both in absolute terms and as a percentage of the population. The incentives to invest in R&D are also increasing because of globalization and increased wealth in developing countries such as China and India. Better institutions and more secure property rights are spreading throughout the world.

We have reason to be optimistic about the future of economic growth but, of course, nothing is guaranteed. In the twentieth century, two world wars diverted the energy of two generations from production to destruction. When the wars ended, an iron curtain isolated billions of people from the rest of the world, reducing trade in goods and ideas—to everyone’s detriment. World poverty meant that the United States and a few other countries shouldered the burden of advancing knowledge nearly alone. We must hope that this does not happen again.