Staging a performance of Shakespeare's "Henry IV, Part II" takes a lot of people and a lot of time. There are dozens of roles to fill. You need theater support staff. You need rehearsals. And performing the play takes, well, as long as it takes.

What struck two Princeton economists, William J. Baumol and William G. Bowen, was not that performing "Henry IV, Part II" requires all that time and effort, but that it has always been that way. Nearly a half-century ago, Baumol and Bowen observedthat Shakespearean theater hasn't grown much more productive since the Bard of Avon directed operations himself.

That's not true of other industries, of course. Productivity in farming or steelmaking is vastly higher than it used to be. Baumol's and Bowen's famous insight was that these disparities in rates of productivity growth have a striking result.

Rising productivity in most sectors of the economy gives workers' wages ever more purchasing power. Some of these wages are spent on the goods that keep getting cheaper: food, automobiles, clothing and so on. Yet some goes on purchases in "stagnant" industries: tickets to Shakespearean plays, doctor visits and college tuition. As workers earn more in inflation-adjusted income, Baumol and Bowen predicted in 1965, they will be forced to fork over ever-larger shares of it to industries afflicted by "Baumol's disease" -- the inability to increase productivity.

Baumol and Bowen's prediction was dead accurate. Consumer prices for admission to movies, theaters and concerts have risen roughly 60 percent since 1999, well above the broader rate of inflation. Health-care and education spending have soared.

Are these cost increases a problem? In a bookpublished last year, Baumol argued they aren't. We will always be able to afford the increased costs, he reasoned, because they are caused by the increases in our own incomes. It's our good fortune to be productive enough to spend so much on health care, education, and the performing arts.

That's debatable. Higher spending on health care and education haven't yielded much: Are we really healthier or smarter than we would be with cheaper versions of those services? And this raises a broader point: If the trend Baumol described is so beneficial, why try to halt or deflect it?

Efforts to do just that are under way. What we have begun to see, in fact, is the outbreak of war against Baumol's disease. And the fight is coming from business and government, both of which have large and growing incentives to find a cure. The question is whether these efforts will be strong enough to defeat one of the most accurate and significant economic predictions of the last century.

The private sector's interest is obvious. When stagnant industries control a large share of spending, they become targets for disruption. Businesses see big incentives to find cost-saving innovation. But government has incentives of its own. Taxpayers shoulder a large share of medical and education expenses, so Baumol's disease threatens perpetual tax increases and the crowding out of other public spending.

Two main fronts have opened up in the war against Baumol's disease: online education and the Affordable Care Act.

Despite the shortcomings of current online programs, the emerging wave of innovation poses the greatest challenge to how we educate since Horace Mann. The ultimate promise of services such as Coursera, edX and Udacity is to remake the model of education. If they succeed, they will do so by transforming education from a rationed service into one that's widely accessible, eliminating the limits to the scale of education as we know it now. This prompts the thought that Baumol's disease might be a reflection of the fact that education and health care are the last two major service industries to develop scalable products.

The battle is on in medicine as well. One of the central goals of President Barack Obama's Affordable Care Act is to reduce cost inflation in health care -- in other words, to cure Baumol's disease. The program is designed to do that through a wide variety of mechanisms, including a shift away from fee-for-service medicine, better management of chronic diseases and cuts to public spending on hospitals and prescription drugs.

One major private-sector effort comes from pharmacy chains, which are expanding into in-store health-care clinics. The Wall Street Journal reported last month that Rite Aid Corp., CVS Caremark Corp. and Walgreen Co. are all starting or expanding such ventures this year. Full-service hospitals are incredibly expensive and inefficient places to deliver routine care and other basic medical services. Clinics are poised to be a big part of the war on Baumol's disease.

We may already be winning. Cost inflation in health care has slowed substantially in recent years, running at roughly 4 percent since 2009. Less noticed has been an equally large slowdown in education-cost inflation: The consumer price index's education component is also growing at roughly 4 percent, the slowest on record. And, at least for higher education, the forecast is for inflation to keep falling.

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Evan Soltas at