# TAX ARBITRAGE: The Simple Model 2

If tax arbitrage is possible, things become quite different. Taxpayers can create a wedge between taxable income and labor income in a number of ways. Here, we will consider an economy with two types of assets, tax-exempt and taxable claims. We will assume that no other form of wealth exists, and that the claims are inside assets, that is, all individuals can issue both types of claims. This last assumption is of course a strong simplification (we will relax it in section 4), but it serves the useful purpose of illuminating the essence of the problem.

Denote by r the risk-free interest rate on taxable claims, and by p the risk-free interest rate on tax-exempt claims. As no individual has any initial wealth, a positive holding of taxable claims must be balanced by a negative holding of tax-exempt claims of the same amount, and vice versa. As a matter of convention, we use X to denote borrowing against taxable claims. In line with a conventional global income tax we assume that the interest expense rX is fully deductible when calculating taxable income add comment.

Taxable income В is thus (w£ – rX), and the tax paid6 is T(w£ – rX). Throughout we will assume that the tax schedule is continuously differentiable, that 0 < 7′( ) < 1 > and that the tax schedule is progressive in the sense that T”(,)> 0.7 An individual with a wage rate w solves the following optimization problem:

Equation (4) is our arbitrage condition, saying that the after-tax interest rate on taxable claims must equal the interest rate on tax-exempt claims. Since all individuals face the same relative asset yield p f r in a perfect capital market, equation (4) implies that all individuals will have the same marginal tax rate T'(w£ – rX). Also, since the marginal tax rate is a monotone function of taxable income, everybody will report the same taxable income: