Let us first consider a regime where no tax arbitrage is possible. The indirect utility of an individual with a wage rate w, i.e., the utility resulting from labor supply (1) and its corresponding consumption, is denoted by V(w) . Similarly, the indirect utility of the same individual under a regime where tax arbitrage is possible (i.e., the utility resulting from labor supply С and its corresponding consumption) is denoted by VA {w), where the subscript stands for ’’arbitrage”. The change in utility from introducing arbitrage is thus A = Va (w) – V(w) more.

Assume now that the tax schedule is the same for the two cases (this assumption will be relaxed shortly). Then the introduction of tax arbitrage can make nobody worse off, as everybody can abstain from engaging in asset trade and supply exactly the same amount of labor as before. If someone nevertheless would choose to engage in asset trade, it would be only because this would yield higher utility. The change in relative price between consumption and leisure, being earlier equal to w( 1 – T'(w£)), and being now equal to wp / r, would be greatest for people at the tails of the wage distribution.

Thus these people would have the strongest incentives to trade with each other, high-income earners issuing taxable claims and purchasing tax-exempt ones, and low-income earners doing the converse. People with average income w£ would however have nobody to trade with, and no incentive to do so. Thus they would supply the same amount of labor as before, and set X – 0.

The utility gain from introducing tax arbitrage would therefore be greatest at the tails of the wage distribution10, and zero at the mean, as is illustrated by the solid curve in Figure 1. Note, however, that this reasoning is based on the assumption of an unchanged tax schedule. This is obviously unrealistic. Since the very purpose of tax arbitrage is to reduce taxes, it is reasonable to assume that the introduction of arbitrage would lead to a government budget deficit. In order to maintain budget balance, the government would thus have to raise taxes.