### The Great Debate on Inequality: Stiglitz versus Krugman

Economics Nobel laureate Joseph Stiglitz is the chief alarmist warning that income and wealth inequality in the U.S. is a very serious threat to the economy. So it comes as a surprise that his fellow Nobelist Paul Krugman – Stiglitz’s intellectual comrade-in-arms – disagrees with him. Their disagreement goes to the heart of today’s economic problem.

We frequently read about inequality, and the statistics often take the same form. Reports try to shock us by showing how unequal a particular society is. A recent article I saw described South Africa’s continuing problems, including economic inequality. To demonstrate how unequal South Africa’s society is, the article said: “The top 10% of the population takes home 58% of the country’s annual income, while the bottom half receives less than 8%.”

When I read statements like that, I wonder, “How bad is that?” Of course the upper percentage of income earners or wealth holders will have more than that percent of the money. The only way the upper 10% could have exactly 10% of the money, for example, is if everybody’s income or wealth were the same.

That, of course, is highly unlikely – unless equality were forced on society by the government, as Communist governments tried to do. But even then, inequality persists.

Given that we know that the upper x% will have more than x% of money – say it has y% – how big does y% have to be before our jaws should drop? And how big does y% have to be before it becomes a problem?

And what, exactly, is the problem?

**Inequality from the bottom up**

Italian statistician and sociologist Corrado Gini invented the Gini coefficient, a handy device for making comparisons in wealth inequality, a century ago. It may have lain dormant for a while, but suddenly we are hearing about it everywhere. (For a brief explanation of the Gini coefficient and the Lorenz curve on which it is based, see the Appendix.)

Imagine a country with 10 million people – call it Equalia – where everyone has the same amount of money, $10,000. Its wealth distribution curve (its “Lorenz curve” – see Appendix) looks like the straight dashed green line in Figure 1. The Gini coefficient is zero – perfect equality.Now suppose that Clyde, one of the denizens of Equalia, stumbles on a vein of 2,000 tons of pure gold. He stakes a claim. The gold is worth $100 billion. So now the wealth of Equalia has doubled, but Clyde has half of it, while everyone else has an equal amount. The Lorenz curve looks like the solid blue line in Figure 2.

Now the Gini coefficient is 0.5, because the areas of the two triangles are the same. (If Clyde had come into an infinite amount of wealth instead of only $100 billion, the Gini coefficient would approach its maximum value of one.)

That 0.5 is a rather high Gini coefficient, about the same as Zimbabwe’s, but not as high as Hong Kong’s. Is that bad?

First of all, it won’t stay that way. Clyde will spend some of his new wealth, which means other people in Equalia will get it – and the Gini coefficient will decrease.

This leads us to Krugman’s disagreement with Stiglitz. But first, let’s recap Stiglitz’s arguments.