When the tax-exempt asset is an argument in the utility function In this subsection we will briefly discuss another permutation, which will turn out to have an interesting connection to the simple model of Section 3. Assume that the outside asset X appears as an argument in the utility function. Formally, this means that we reformulate (16), with X as an argument in the utility function, and with p- 0:
where X is now an ordinary consumption good. In practice, we may think of X as housing, or some consumer durable. This model gives a representation of how housing appears in the labor supply decision of an individual in an economy with full interest deductibility; model (16) above has a closer resemblance to a world where X is raw land (which gives a constant yield of the consumption good, but which does not appear in the utility function). Working out the first-order conditions gives us solutions for the supply of labor, £(t, w, г, X), and for the demand for housing, X(r, w, r, X). These solutions will differ from those in section 3 in the sense that both first-order conditions of (24) will involve marginal utilities. Several implications follow.
First, since marginal utilities are different for different individuals, there will be no equalization of taxable incomes. But for standard utility functions high-wage individuals will consume more housing than they would have done if interest expenses had not been tax deductible. Thus the distribution of taxable income will be compressed relative to the wage distribution.
Second, consider an econometrician who ignores the fact that there are two consumption goods (с and X), and incorrectly specifies the model as
where r(X – X) is regarded as exogenously given non-labor income. Clearly, the implied labor supply function £(r, w,r(X- X)) will be mis-specified, too. The problems associated with this are not really due to the econometrician’s neglect of tax arbitrage per se, but rather to neglecting the fact that there are two consumption goods instead of one. The implications for the econometrics of labor supply of introducing a tax deductible good in the utility function is discussed by Triest (1992). cash payday loans