## A GENERAL MODEL OF THE BEHAVIORAL RESPONSE TO TAXATION: Some Examples

A concrete example nicely illustrates the important points.

A few aspects of these calculations are worth noting. First of all, the compensated tax elasticity of labor supply is only six-tenths of what it would be in the standard model. Furthermore, the compensated elasticity of labor supply with respect to w and (1-t), which are equal in the standard model, are not in the general model; the elasticity with respect to (1-t) is significantly lower; this is because an increase in t also generates an increasing avoidance faciltation effect, dampening the pure tax effect. Note also that the tax elasticity of avoidance is less than one because of the indirect effect on the cost of avoidance via induced changes in labor supply. add comment

Because generalizing the model dampens the standard labor supply response but adds an avoidance response, the implications for the elasticity of taxable income (wL-А) are not obvious.
With this avoidance cost function and these parameters, —— is – wL while it is — in the traditional model. If the standard labor supply response is small (S —> -oo), then the S taxable income responsiveness is likely to be larger in the general model because of the additonal avoidance response. If the standard labor supply response is large, the fact that this is dampened in the general model could make the taxable income response lower.The avoidance cost function С = a — (a) is a special case of the class of cost-of-avoidance functions C = awL“YA1+ 5, which share the characteristic that there is a simple relationship between the marginal effect of avoidance on real substitution behavior — the avoidance-facilitating effect – and the fraction of the potential tax base avoided. In this case the avoidance-facilitating effect is as follows, using the fact that at an interior solution C2 = t:

reduction in the effective tax rate is proportional to the fraction of the tax base avoided and two parameters of the cost-of-avoidance function. A special case of this cost function is one in which the per-unit cost of avoidance is a function of the relative amount of avoidance, i.e. where у = 5,