Everybody with a full income w + rX less than the right-hand side of (22) will be in a constrained optimum, while everybody with a full income that is greater than or equal to the right-hand side will be in an unconstrained optimum. Inherently poor individuals will face a binding credit constraint and a nonlinear tax system, and they will supply labor according to (21). Inherently rich individuals will face a perfect capital market and a linearized tax system, and they will supply labor according to (19).
We can now integrate (20) over all unconstrained individuals to obtain aggregate land demand. In equilibrium, this has to be equal to the total quantity of land available (which we for simplicity set equal to unity) read more:
where F(w, X) now is a joint cumulative distribution function. Equation (23) gives a solution for the endogenous variable r , or rather for the price of land, since r =rP.
To sum up, when we assume that the tax-exempt asset is not an inside asset, but an outside one which can be held in positive amounts only, some of the more striking predictions from the simple model in section 3 disappear. Taxable incomes and effective marginal tax rates will now be the same only for that segment of the population which is at an interior portfolio optimum – an affluent subgroup consisting of those with high wages and/or large land endowments. Less affluent individuals do not hold the tax-exempt asset, and their taxable incomes vary across individuals.
Another observation is that constraints on short sales make it less likely that the introduction of tax arbitrage (via a policy decision, or as the consequence of technological innovation in financial markets) produces utility gains at both tails of the wage distribution. Although high-wage and low-wage individuals have strong incentives to engage in asset trade, the quantity constraint prevents low-wage individuals from going short in the tax-exempt asset. As a consequence, only high-wage individuals can reap the full reward from tax arbitrage.
Finally, and very much in line with the analysis of the preceding section, we can not rule out the possibility that the introduction of tax arbitrage leads to such a boost to the labor supply of high-wage individuals, that the government could lower taxes. When the income tax distorts the labor supply decision of high-ability individuals to a great extent, everyone may thus benefit from the introduction of tax arbitrage.