## A GENERAL MODEL OF THE BEHAVIORAL RESPONSE TO TAXATION: Proportional Labor Income Taxation 2

The first-order conditions for this problem are: Expression (4b) states that avoidance should be increased until its marginal cost, С , equals its marginal return of t. The first-order condition (4a) is the usual one that labor supply is optimal when the marginal rate of substitution of labor for income equals the net-of-tax wage rate. The critical aspect of the general model is that the net-of-tax wage rate includes an implicit subsidy to working equal to wC(, due to the fact that earning more income lowers the marginal cost of avoiding taxes bv that amount. The implications of this can be drawn out by examining the Slutsky equations for the response of labor supply and avoidance to the tax rate and wage rate, which are summarized in Table l:

Comparative Static Results in the General Model of Labor Supply Response to Taxation The value of D reflects the homogeneity of the avoidance technology. When D is zero, the cost per dollar of avoidance depends only on the amount of avoidance as a ratio to true labor income. If D is negative, the cost per unit of avoidance increases for-a given А/wL as A and wL increase. Note that when D is zero, the wage rate effect on labor supply (though not the tax rate effect) is essentially the same as in the standard model.5 The more negative is D, the lower is the (generally positive) value of — . This occurs because as w increases, a proportionate increase aw у in A becomes more costly per unit of wL, making the wage rate increase that much less of an dL increased incentive than otherwise. Similarly, a positive value of D increases — aw и

For most of what follows, I will concentrate on the substitution effects of changes in w and t. Note, though, that the income effect terms are modified to reflect that the tax rate affects income by an amount proportional to the tax base, which is now wL-А, and the wage rate affects income proportionally to the implicit net-of-tax rate (1-t-Cy. The income derivative itself, dh/dM, is also altered, being S/(D+S) times as large as in the standard model. The income effect, —, is equal to -w-^-f-^-1. This reflects the fact that an increase in non-labor
at с22 \ J
income has no direct effect on the marginal conditions determining A. If, though, M changes L, then that will change A through its effect on C2. credit