When justifying progressive taxes or any type of transfer people often use the idea of diminishing marginal utility. Now I am not against transfers, I think there are many good reasons justifying transfers, however DMU is not one of them.
- The utility from income differs between people and we can’t observe it. Furthermore, people with higher utility from income will work more – so if there is any “choice” in the work decision then DMU is not sufficient to ensure the optimality of progressivity.
- Liquidity constraints and the discrete nature of purchases ensures that even if we have diminishing marginal utility for individual products we cannot assume that marginal utility is falling in income.
Another possible critique of the DMU justification for transfers comes from prices. Assume for now that there are two types of people, poor and rich. Assume that poor people buy goods with perfectly price inelastic supply, and rich people buy goods with elastic supply.
In this case, any transfer from rich to poor would lead to no increase in the welfare of the poor – as the price of the goods they buy would simply increase by the amount their income has increased! However, there would be a welfare loss for the rich – as both the price and the quantity sold would fall. As a result, the transfer is pareto inferior.
Now this was an extremely simplistic, stylized cases. However, it does show us that if the supply of goods that the poor buy are sufficiently price inelastic relative to the goods that the “rich” buy then even in the case of diminishing marginal utility transfers may not be effective – because of price changes.
What we are using here is the fact that, the more elastic a (normal) good is, the greater the proportion of any income change will actually lead to an increase in “consumer surplus”. In the case where the supply is perfectly price inelastic, any increase in income simply increases firms profit.