Here, 0<v<l, and a lower value of v means a higher degree of progressivity, in the sense of disposable income being a more concave function of taxable income. For a given v, we use the parameter p to ensure a balanced budget, and for simplicity, we only deal with a purely redistributive tax system. One can easily show that within our tax arbitrage model, where everybody has the same taxable income, this implies
This corresponds to the supply function of the standard model (1), and it exhibits the well-known property that with logarithmic preferences and no initial wealth, labor supply is independent of the wage rate w.
In the arbitrage-economy, individual labor supply becomes
in partial equilibrium. We see that in an arbitrage-economy, modeling labor supply as (13) gives an incorrect functional form for the labor supply function. Using the general equilibrium condition (8), we can also solve for endogenous taxable income B(p / r):
where w is the average wage rate, and where we have used the fact that pi r = v . Substituting this into the partial equilibrium supply function (14), and using (12), gives us labor supply t in general equilibrium:
Now, labor supply does depend on the wage rate even with logarithmic preferences and no other wealth. Thus in the arbitrage-economy the response to changes in v will be different for different individuals. Comparing labor supply in the arbitrage and noarbitrage economies, it follows that tax arbitrage leads to lower labor supply for less able individuals (w/w > 1), and to higher labor supply for the relatively able ones.
Efficiency and tax incidence
The introduction of tax arbitrage could be the result of a conscious policy decision by the government, like deregulating the capital market, or making certain transactions legal that were not permitted under the earlier legislation. Or it could be the result of technological developments in financial markets that make various kinds of asset trade possible at a reasonably low transaction cost. In either case, it is interesting to know who would gain and who would lose from the introduction of tax arbitrage. installment payday loans