We live in a world of broken models. To understand why world leaders can’t easily fix the sputtering global economy, you have to realize that the economic models on which the United States, Europe and China relied are collapsing. The models differ, but the breakdowns are occurring simultaneously and feed on each other. The result is that the global recovery flags, while pessimism and uncertainty mount.

Take the United States. The U.S. economic model was consumer-led growth. From the early 1980s until the mid-2000s, what propelled the economy was rising wealth — stocks, bonds, real estate — that encouraged households to spend and borrow more. Feeling richer, people traded up for better cars, homes and vacations. Everyone could afford or aspire to “luxury.” Businesses responded by investing in more malls, restaurants, hotels, factories and start-ups.

Of course, this is now ancient history. The popping of the credit bubble depressed home values, stocks and jobs. Recently, the Federal Reserve reported that the net worth of the median U.S. household — the one exactly in the middle — fell 39 percent from 2007 to 2010 to $77,300, a level that, when adjusted for inflation, equaled the early 1990s. (Net worth is the difference between what someone owns and owes.)

Feeling and being poorer, Americans have cut back. Their buying is muted. They’re trying to repay debt and rebuild wealth. A new study from the National Bureau of Economic Research found that declines in household balance sheets — that is, wealth — caused almost two-thirds of the 6.2 million jobs lost from March 2007 to March 2009. To grow faster, the U.S. economy can’t rely on large gains in consumer purchases.

What’s to replace it? There are three possibilities: higher exports, more business investment and higher government spending. Weak economies elsewhere hinder exports. Businesses won’t invest unless there’s stronger demand. And more reliance on government means bigger budget deficits, a policy that inspires powerful political resistance.

It turns out that, once your economic model goes bust, it’s not easy to build a new one. The obstacles are at once economic, social and political.

The same thing is happening in Europe. The European model rested on two assumptions.

First, the success of the euro — the single currency used by 17 countries — would continue. The euro had delivered low interest rates in the countries that used it, causing housing and consumption booms in Ireland, Greece, Spain and elsewhere. These in turn fed the demand for exports from Germany and other countries. Everyone benefited.

Second, slow but steady economic growth sufficed to support generous welfare states. Tax revenue kept budget deficits at manageable levels.

Once these assumptions shattered — as they did in the wake of the 2008-09 financial crisis — the model stopped working. Economic growth fell; budget deficits rose. Investors became worried, so low interest rates vanished for weaker countries. The fragile equilibrium between slow economic growth and expensive welfare states came undone.

Europe has been thrown into turmoil. Its leaders dash from one crisis to another. The search for a new approach is proving (again) contentious and elusive.

China’s situation seems less dire, though the country’s secrecy makes guesses hazardous. It has followed an export-led growth model, supported by periodic government stimulus programs. The trouble is that sluggish economies in the United States and Europe — two major markets — have reduced demand for Chinese goods and fueled political opposition to allegedly subsidized imports. And China’s stimulus programs may have reached a point of diminishing returns.

Altogether, the United States, Europe and China represent about half the world economy. But their situations are not isolated. Brazil, India and some other major countries are also discovering that their economic policies need recalibrating.

Everything feeds on everything else. There is no longer a large source of strong economic growth in the world to stimulate and support struggling economies. Not surprisingly, the latest World Bank forecast has the global economy growing only 2.5 percent in 2012, down from 4.1 percent in 2010.

Time may cure some of these problems. After all, economies move in cycles. In the United States, debts may be paid down. Housing prices may stabilize. Businesses may develop new products that spur investment. Elsewhere, pent-up demand may provide relief.

But the fact that what’s happening in so many places is an assault on long-held expectations and practices — economic and social models — suggests that finding a path forward could be time-consuming, tortuous and, possibly, inconclusive. If so, stalemate becomes an independent source of frustration and fear.