# TAX ARBITRAGE: The Simple Model 3

This is intuitively reasonable. With unlimited tax arbitrage, high-income individuals issue taxable claims and hold tax-exempt claims, while low-income individuals hold taxable claims and issue tax-exempt claims. This process continues until all taxable incomes, and hence all marginal tax rates, are equalized. From an efficiency point of view, we may also note that this implies that

In the presence of tax arbitrage, individual marginal rates of substitution between consumption and leisure are proportional to the marginal rate of transformation (i.e., the wage rate). The factor of proportionality is to be regarded as a tax wedge, since p and r are unequal.
Combining (3), (4), and the budget constraint in (2) gives us labor supply t and asset demand X (or, rather, the demand for interest deductions rX):

Note that the labor supply function (6) does not contain a vectorarbitrage in a perfect asset market, we thus no longer need to bother about the curvature of the tax schedule. All individuals are now confronted with the same linear tax system, with an effective marginal tax rate equal to I-pir. Here, one might of course ask why the government would choose a non-linear tax schedule if arbitrage would automatically make the effective tax schedule linear. The answer is either that the non-linear statutory schedule might be the result of some public choice mechanism that is outside the present model; or that the government, having not (yet) read this paper, incorrectly believes that it can impose a non-linear schedule.

The relative asset yield is determined by invoking equilibrium in the asset market. We assume that all agents have identical preferences and differ only with respect to the wage rate w which, assuming a linear production technology, is the individual’s marginal and average productivity. In a Miller (1977) equilibrium, with purely inside assets, if follows that т like the standard supply function (1) did; in fact, it only contains the two scalars pir and w. With tax

where F(w) is the cumulative distribution function of wages. This condition determines pir and thereby the effective marginal tax rate in the linearized tax schedule. It follows readily that an individual’s labor supply in general equilibrium, t, depends not only on her own wage but also on various moments of the overall wage distribution. Asset trade tends to link the labor supply decision to the wage structure, much in the same way as considerations of envy and interdependent utility can produce demand and supply functions that depend on measures of relative income. payday loan companies