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Why Thomas Piketty's capital gulf gets a bit complicated when you look at the numbers.

Inequality in the United States, Europe, and elsewhere has become a hot topic since the global economic downturn highlighted the stark differences between rich and poor. Thomas Piketty's widely-reviewed (and, to hear him tell it, widely misunderstood) best-selling book has illustrated just how wide the disparities are in income and wealth. His data show that the gaps are at their widest since the waning days of the Gilded Age, which was not capitalism's finest hour. But how much these gaps really matter in practice is a bit more complicated.  
Which inequality are we talking about?
The term inequality is often used without specifying what is being measured or how. For example, income inequality and wealth inequality are distinct; one measures an annual flow, and the other a quantity at some point in time. Which one you care about may depend on the costs and benefits of each kind. I happen to think wealth inequality is more important because it's more likely to determine your access to economic opportunities, but intelligent people can differ on this point.
Measures of income inequality can also give different results. One might compare the incomes of the top 10 percent to the bottom 10 percent, while another might use a calculation like a Gini coefficient that looks at the entire distribution. Here, the choice of metric is more philosophical; you might care more about the difference between the richest and poorest people in your country than you do about what happens in between, or vice versa.
What are the benefits and costs of inequality?
Inequality is a fundamental part of the capitalist system, at least as viewed by economists. The possibility of earning different incomes and accumulating different levels of wealth gives people incentives to work hard and realize their productive potential. In theory, this makes the pie bigger for everyone, even if it's not shared completely evenly.
But inequality also has costs, as recent research has begun to suggest. If money plays a role in the allocation of opportunity, then inequality may make it more likely that a rich, stupid kid gets a chance -- say, a place at an elite university -- that would have been better exploited by a poor, smart kid. Moreover, there are probably social costs to huge disparities in wealth. 
Even if the people at the bottom enjoy a decent standard of living in absolute terms, the contrasts with the lifestyles of rich may lead to resentment, unrest, or worse.
Even if the people at the bottom enjoy a decent standard of living in absolute terms, the contrasts with the lifestyles of rich may lead to resentment, unrest, or worse. And that's a big "if." Here, in the supposedly wealthy United States, there are still millions of kids who experience hunger sometime during the year.
The overall relationship between inequality and average living standards probably looks something like the curve proposed by Arthur Laffer for tax rates and tax revenue. If you have complete equality, then living standards may fall short of their maximum, since people will have less incentive to work. If you have complete inequality -- that is, all wealth in the hands of one person -- then everyone else is stuck once more with the same wealth: nothing. As essentially slaves, their incentives to be productive will be just as bad, unless there's some chance they could be that one person at the top in the future. In fact, both extremes look a lot like North Korea, which isn't exactly an economic heavyweight.
Is there any scientific evidence for these relationships between inequality and living standards?
Anecdotally, the rapid growth in post-socialist economies suggests that too little inequality may indeed have been a problem. But, according to the International Monetary Fund, extreme inequality can also detract from economic growth. It may also be the case that changes in inequalityare associated with lower growth rates, perhaps because of the disruptions that can cause or accompany the changes themselves. Every economy almost certainly has a peak in its inequality Laffer curve, that is, the level of inequality where living standards are at their highest, all other things equal. We just don't know where it is yet.
If inequality is bad, what can we do about it?
There are quite a few options, but for me they all fall into two categories. First are policies that make inequality irrelevant to opportunity in society. These include efforts to improve early childhood education, nutrition for poor children, and access to the admissions process at top colleges; the idea in each case is to make sure every kid has a chance to be evaluated on his or her merits. This category also includes initiatives to reduce the influence of money in politics, so that even poor candidates would have a shot. Doing so might make the electoral process more meritocratic and economically efficient, compared to the current situation where wealth can seem like a prerequisite for mounting a campaignSome of these policies can take effect quickly, but others -- especially those aimed mainly at kids -- could take a generation or more to make a dent in inequality.
Options in the second category attack inequality directly. Among these are progressive taxes on income and wealth. They're always controversial, since their objective may appear to be bringing people at the top of the economic totem pole down, rather than lifting the bottom up. On the other hand, they can change the distributions of income and wealth much more quickly.
All of these policies seek to reduce the economic distortions that come with inequality. But it's worth thinking about how these policies might create new distortions along the way. Programs for children cost money, and tax rates would have to rise to pay for them. Progressive income and wealth taxes may distort decisions about working and saving, though it's not clear which are worse in this respect. My own proposal tries to reduce these distortions with a hybrid tax on both income and wealth that uses a sliding scale for rates.
What's the bottom line?
The recent surge of interest in inequality is healthy for the global economy, as well as for Piketty's book sales. Even as inequality diminishes between countries, it's rising within many around the world. It will be useful to know how much inequality may hurt our living standards in the long term, and whether the possible remedies might be just as costly. Stay tuned.
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