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

In the standard textbook model of the effect of income taxation on labor supply,1 the individual maximizes utility, which is a function of income, or consumption of goods, and labor supply, subject to a budget constraint affected by taxes:

where Y is income, L is labor supply, t is a proportional tax rate, w is the wage rate, and M is non-labor income, presumed for simplicity to be untaxed. The Slutsky equations for the response of labor supply are as follows:

where 5L/3M is the effect of income on labor supply, holding prices constant, and S is the substitution effect (i.e., the rate of change of the slope of the indifference curve between consumption and leisure, here defined to be a negative number). Note that (2a) and (2b) are isomorphic, as (2b) is just (2a) multiplied by -(1 – t)/w; the net-of-tax wage rate is all that matters for labor supply, and changes in w and t that leave w(l -1) unaffected are not material.

Now generalize this problem by allowing the individual to reduce income subject to tax from wL to (wL – A), at a cost of С. I will refer to A as avoidance. If there were no cost to avoidance, it would be pursued by all individuals until tax liability were zero (or, with a strictly flat tax rate and refundable taxes on losses, into the negative range). In this general formulation the cost of avoidance depends, with increasing positive marginal cost, on the amount of avoidance itself. It may also depend inversely on the amount of true income earned. I will refer to this phenomenon as the “avoidance-facilitating” value of true income. fast payday loans

The individual’s problem becomes

subject to Y = wL – t(wL – A) – C(wL, A) + M.

I have already argued that < 0 and C2 > 0. It is likely that the marginal cost of avoidance is increasing, so that С^ > 0. As long as the avoidance-facilitating quality of true income (C^) has diminishing returns, then >0. С is a critical parameter, as it captures the interaction between true income and avoidance in the avoidance technology. I will focus on the case where С < 0, so that more avoidance increases the avoidance-facilitating value of a given amount of true income; this seems to me the most likely case, although it is ultimately an empirical question.