Last month’s announcement by U.N. demographers that the world’s population had reached 7 billion reignited fears that our overcrowded planet is running out of space, food, and other resources to support us all. It’s a replay of the doomsday scenario made fashionable more than 200 years ago by Thomas Malthus and popularized by Paul Ehrlich’s 1968 bestseller, The Population Bomb. But in many places—including the U.S.—the real problem is too few births, not too many people, making it hard for nations and communities alike to support their oldest citizens.

There’s no doubt that the world’s population is soaring. It took nearly all of human history—until the early 1800s—to amass the first billion people. The second billion took only about 100 years. Lately we’ve been adding a billion humans about every dozen years.

The population is expanding because people are living longer nearly everywhere, not because they’re having more kids. Life expectancy in the U.S. now stands at 78, up from 68 in 1950. It’s even higher in places like Japan (83), Australia (82), and France (81).

As longevity has increased, birth rates have fallen. Back in 1960, the total fertility rate—the average number of children born to a woman over her reproductive years—was 3.65 in the U.S. Today American women average just 2.1 kids, the minimum needed to replenish the existing population without immigrants. The fertility rate is even lower in most other wealthy countries, including Korea (1.1), Italy (1.4), and Japan (1.4). Only a handful of high-income countries (Iceland, Israel, and a few oil-rich states in the Middle East) can boast birth rates high enough to expand their populations. Birth rates are even declining in lower-income countries. In India, the fertility rate fell from 4.6 to 2.7 over the past three decades.

With people living longer and having fewer kids, societies around the world are growing older. Here at home, 13 percent of Americans are age 65 or older, up from 8 percent in 1950. Twenty years from now nearly one in five Americans will have celebrated his or her 65th birthday. Certain counties are already much grayer. Seniors now make up 34 percent of residents in Charlotte County, Florida, for example.

The growing domestic imbalance between the young and old creates several challenges. At the national level, Medicare and Social Security taxes paid by a stagnating workforce must fund benefits for a growing number of retirees, threatening to bankrupt those programs. Local and state governments need to fund more services that enable seniors to age in private residences, like home care, home-delivered meals, and transportation for people who can’t drive to supermarkets and doctors’ offices. And if more young people aren’t on the horizon, we’re going to have to push back the start of old age to keep more adults in their sixties and seventies productively employed, paying taxes, and off the pension rolls.