The cutoff policy of taxation when CRRA taxpayers differ in risk aversion coefficients and income: a proof

Under a cutoff policy, taxpayers can either report income as usual and run the risk of being audited, or report a "cutoff" income and hence pay a threshold tax that guarantees not being audited. Whereas the mainstream literature in this field assumes risk neutrality of taxpayers - with some notable exceptions like Chu (1990) and Glen Ueng and Yang (2001) - this paper assumes risk aversion instead: taxpayers have a Constant Relative Risk Aversion (CRRA) utility function and differ in terms of their relative risk aversion coefficient and income. The novel contribution of this work is that, under certain conditions, the cutoff is accepted by taxpayers with intermediate characteristics in terms of income and relative risk aversion. Contrary to the standard result in the literature, a full separation of types (the rich who accept the cutoff versus the poor who refuse it) does not arise. However, our results confirm that the cutoff policy violates equity, as only some taxpayers directly benefit. Nonetheless, the perception of this drawback may in practice be obfuscated because that exclusion does not necessarily affect only the poor.