Heterogeneity and the moral case for progressive taxation

Reading the piece discussed in the preceding post led to another, more substantive, thought. The traditional view espoused by Piketty assumes that everyone shares the same utility function. In such a world, the marginal utility of income is lower for high income individuals than low income individuals.

Suppose, though, that utility functions exhibit heterogeneity rather than uniformity. Specifically, suppose that there are two arguments in the utility function - goods and leisure. For simplicity, make the cross partial zero, though mucking with the cross partial is interesting here too. Now suppose that individuals vary on the relative importance of the two arguments. Some individuals really like leisure - they are the ones we worry about when writing papers on optimal unemployment insurance - and some really like market goods. At an given income level, the individuals with a high taste for market goods will have higher marginal utilities of income than those with a high taste for leisure. They will also, in most any reasonable sort of model, have higher incomes because they will be more willing to trade of leisure for income.

In this model, individuals sort into income levels based on their marginal utility of income. As a result, the traditional rationale for progressive taxation that assumes a representative agent falls apart, or at least gets a bit woozy and stumbles around running into the walls and furniture.

Surely someone has already written this down, but it was a new thought for me.