Writing about Tyler’s argument got me thinking some more about Will’s argument on price indices. That is, that true inequality hasn’t risen as much as we think because of price decline in the goods that poor people buy.

My reaction was that this isn’t appropriate because poor people are only buying those things because they are poor. If real incomes had in fact risen they would be buying different things. However, now I think my argument was wrong. Here is my example.

Suppose there are two Pete and Sam. Pete has an income of $10 a month which he uses to buy one potato. Sam has an income of $100 a month which he uses to buy one steak.

Then suddenly there is a big techno-social global revolution. The end result of which is that potatoes cost $5, steaks still cost $100, Pete still makes $10 but now Sam makes $200.

Pete can now buy two potatoes and Sam can buy two steaks.

If we ignored the fact that that the two had different consumption patterns we would say that inequality had doubled. Sam is now making twice the income as Pete. However, when we look at real consumption Pete is eating two potatoes and Sam is eating two steaks.

We can’t say that income inequality hasn’t risen because we don’t know that an additional potato adds as much relative happiness as an additional steak.

With this limited set of goods its even possible that inequality has fallen. An addition potato could be relatively better than an additional steak. With a more complete set of goods this becomes unlikely because Sam probably could arrange a basket that contained an additional potato and more steak if he wanted. The fact that he chooses not to suggests that an additional steak is better than an additional potato.

However, we can say that inequality hasn’t risen as much as we would think had we not accounted for the change in relative prices between what Pete buys and what Sam buys.

It does matter that goods Pete buys are cheaper. Even with a more complete set of goods it wouldn’t be right to chalk up all the difference to hedonic effects. That is, it wouldn’t be right to say that the price difference between steaks and potatoes must mean that now steaks are 20 times as good a source of food as potatoes when before the economic shift steaks were only 10 times as good.

By that same token we shouldn’t simply say that the difference in the price of food at Wal-Mart and Whole Foods only represents the fact that shopping at Whole Foods is much better than shopping at Wal-Mart. Lower income folks really do have more. We don’t know how much more but some more.