TAX ARBITRAGE: The Simple Model 4

We can obtain some characterizations of the equilibrium. Integrating (5) over all individuals, and using the Miller equilibrium condition (8), yields B(p !r)~ wt, where w£* is the average labor income in the economy. Substituting this back into (5), we obtain the individual’s demand for tax deductions in general equilibrium:
As we should expect, individuals with a higher-than-average labor income have a positive demand for tax deductions, while the opposite holds for those with lower-than-average income. Individuals with average labor income will not participate in the arbitrage process. Also, when the tax system is purely redistributive, and when the government’s budget is balanced, there is a simple relation between the curvature of the tax schedule and the relative asset yield. An often adopted measure of the degree of tax progression is the measure of residual tax progression more:
Our assumptions about the marginal tax rate imply that 0 w6708-10
In equilibrium the relative asset yield equals the degree of tax progression of the formal bracket schedule.
A logarithmic example. So far our analysis is fairly general. It turns out, however, that we can obtain surprisingly simple closed-form solutions for a particular parameterization of the model, namely a logarithmic utility function of the form
We also assume that the tax system is characterized by constant residual progression in the sense that v in (10) is a constant. As shown by Jakobsson (1976), this means that disposable income out of a taxable income В is an exponential function of B: