Robert Martin and I have a new working paper available at SSRN. From the abstract:
The effect of rising net attendance prices on college students and their families is a contested issue. Traditionally, this financial burden is measured by the share of income taken by the net price of attendance. Recently, some claim the residual real income left after paying for college should be the measure of this financial burden: if residual real income increases, the household must be better off. Using a household utility function we demonstrate that the residual income argument is flawed since the substitution effect leads to an increase in non-college expenditures regardless of the change in utility. On the other hand, we find that changes in utility are a function of the share of income accounted for by the net attendance price and the ratio of the growth rate in net price to the growth rate in income.
In general, household utility declines as net price increases for low income households and for households with slow growing incomes. Hence, rising real net attendance price is a "regressive tax" that is particularly burdensome for low income households. Further, when net price increases, households substitute away from college attendance, causing increases in expenditures for composite commodities, regardless of whether or not household utility is increasing or decreasing. Therefore, changes in expenditures for other goods tell us nothing about the burden imposed by rising net attendance prices. Finally, the model suggests a variety of empirical results for measuring changes in affordability. We also pursue these results in the paper.