William Baumol — an economist who just died at the age of 95 — had a famous idea, commonly known as Baumol’s cost disease, that explains a lot about our modern world.

It explains why barbers make more in San Francisco than in Cleveland and why services such as health care and education keep getting more expensive. And it provides a possible explanation for why rich countries like America are devoting more and more of their workforces to low-productivity services, dragging down the economy-wide rate of productivity growth.

In the 1960s, Baumol was trying to understand the economics of the arts, and he noticed something surprising: Musicians weren’t getting any more productive — playing a piece written for a string quartet took four musicians the same amount of time in 1965 as it did in 1865 — yet musicians in 1965 made a lot more money than musicians in 1865.

The explanation wasn’t too hard to figure out. Rising worker productivity in other sectors of the economy, like manufacturing, was pushing up wages. An arts institution that insisted on paying musicians 1860s wages in a 1960s economy would find their musicians were constantly quitting to take other jobs. So arts institutions — at least those that could afford it — had to raise their wages in order to attract and retain the best musicians.

The consequence is that rising productivity in the manufacturing sector of the economy inevitably pushes up the cost of labor-intensive services like live musical performances. Rising productivity allows factories to cut prices and raise wages at the same time. But when wages rise, music venues have no alternative but to raise ticket prices to cover the higher costs.

This became known as Baumol’s cost disease, and Baumol realized that it had implications far beyond the arts. It implies that in a world of rapid technological progress, we should expect the cost of manufactured goods — cars, smartphones, T-shirts, bananas, and so forth — to fall, while the cost of labor-intensive services — schooling, health care, child care, haircuts, fitness coaching, legal services, and so forth — to rise. And this is exactly what the data shows:

Decade after decade, health care and education have gotten more expensive while the price of clothing, cars, furniture, toys, and other manufactured goods has gone down relative to the overall inflation rate — exactly the pattern Baumol predicted a half-century ago.

Baumol’s cost disease is a powerful tool for understanding the modern economic world. It suggests, for example, that the continually rising costs of education and health care isn’t necessarily a sign that anything has gone wrong with those sectors of the economy. At least until we invent robotic professors, teachers, doctors, and nurses, we should expect these low-productivity sectors of the economy to get more expensive.

While some argue that prices keep rising because the government subsidizes health care through programs like Medicare and college educations through student loans and grants, you see the same basic pattern with services like summer camps, veterinary services, and Broadway shows that aren’t hamstrung by government regulations and subsidies.

Of course, as the Atlantic’s Derek Thompson pointed out a few years ago, the cost of many of these services is actually rising faster than wages are growing, suggesting that Baumol’s disease isn’t the whole story. Universities, for example, have been hiring a growing army of administrators and building ever more lavish amenities to attract the best students. The growing incomes of the richest Americans are a major underlying factor here — rich people are buying services like Broadway shows, summer camp spots, and Harvard educations more quickly than anyone can expand the supply.

But even if we found a way to slow the rapid runup in costs for these kinds of services, we shouldn’t expect them to ever get steadily cheaper the way televisions and T-shirts do. These services are necessarily expensive because it takes a lot of human labor to provide them, and those human workers deserve to be paid well.

And as Steven Perlstein has argued, this has an important implication for government policy. Most of federal and state budgets are spent on services — law enforcement, education, health care, the courts, and so forth — that are subject to Baumol’s cost disease. Government spending on these categories has grown inexorably in recent decades, and many conservatives see this as a sign that there’s something badly wrong with how the government provides these services.

But Baumol’s work suggests another explanation: It was simply inevitable that these services would get more expensive over time, at least relative to private sector manufactured goods like televisions and cars. The rising cost of services is an unavoidable side effect of rising affluence generally. There’s probably no way to maintain our current standard of living while cutting the cost of these services back to the levels of the 1950s.

How rapid innovation can lead to slow growth

Looking at things this way suggests a possible answer to one of the biggest mysteries about the American economy: how seemingly rapid innovation can be coupled with slowing economic growth rates.

As manufacturing has gotten more efficient, the price of manufactured goods like T-shirts and televisions has fallen. At some point, our living rooms and closets get full and we don’t need any more of this stuff, so we spend less and less on it as prices fall.

What do we do with these savings? We spend it on stuff that’s not getting cheaper. If you live in a city like New York or San Francisco, that probably means paying ludicrously high rent. But for a lot of us, what’s eating up a larger and larger share of our budgets is those labor-intensive services that are rising in the chart above: education, health care, child care, meals out, and so forth.

As a result, more and more of our economy is devoted to producing these services, and more and more workers are focused on providing them

The problem is that if a large majority of your labor force is in low-productivity service sector jobs like nurses, lawyers, and nannies, then even rapid productivity growth in the manufacturing sector won’t have a big impact on the overall growth rate. In fact, innovation can make the situation even worse by causing consumers to shift even more of their spending into low-productivity services.

The counterargument here is that innovation could also automate service sector jobs, and some of that will undoubtedly happen. Taxi drivers, for example, are service workers who are likely to lose their jobs to self-driving cars within the next 15 years.

But a lot of service workers are doing jobs that are unlikely to ever be fully automated. Nobody wants a robot for a teacher or a nanny, for example. And even if we get software with advanced diagnostic capabilities, patients are still going to want doctors to explain the recommendations and nurses to provide hands-on care.

Hence, Baumol helps us understand not only today’s economy but also a likely path for the economy’s future. He explained why labor-intensive services get more and more expensive as the economy grows. And those kinds of services are likely to be the future of the global economy.