The more negative is С , the more damped is the negative response of reported income to an increased tax rate, both because it scales down the labor supply response (which is zero if CJ2 = -C22) and because it reduces the positive avoidance response (the higher is 1C I, the more any labor supply decreases the attractiveness of avoidance). The reported income response is increased, though, because of the avoidance response itself, which is larger, ceteris paribus, the larger is 1/C • The net change is of ambiguous sign. The response of reported income to wage rate changes is, however, always lower than in the standard model, as long as Cl2/C22 is negative and D/S is non-negative, as I maintain is the usual case. To the extent that C12/C22 is negative, an increased wage rate makes avoidance more attractive, offsetting to some extent the induced increase in true income. As discussed above, more negative D (recall that S
One fascinating special case obtains when the cost of avoidance depends only on the taxpayer’s reported income (wL – A), which I will denote R. In this circumstance Ci = -C2, and
С = С = -С = С. This has the startling result of making — equal precisely to zero.
As it also makes — into exactly its value in the absence of taxes, taxation has no
(compensated) effect on labor supply. Furthermore, the compensated response of reported income (wL-А) to a change in w is always zero, because the increase in actual labor income will be exactly offset by an increase in avoidance. This occurs because, at the optimal amount of avoidance, С equals t. But if only reported income affects the cost of avoidance, increasing actual income will be as effective in reducing cost as reducing avoidance itself, so that = -C^.
This implies that С = -t or, in other words, there is an implicit subsidy to working equal to wt, which exactly offsets the explicit tax rate. Thus a (compensated) reduction in t reduces avoidance but leaves labor supply unchanged, and increases reported income concomitantly. credit