Some Notes on Progression and Risk-Taking

Abstract

These notes examine the effect of tax progression on an individual facing a choice under uncertainty. The analysis of the impact of proportional taxes in such circumstances has been well developed-see Mossin (1968) and Stiglitz (1969) for the cases involving atemporal risk. Little work has been done on more general tax schedules and their effect; see, however, Allingham (1972) for a thorough examination of the effect of progression on work/leisure choice. The problem is dealt with here by using a linear tax schedule and considering the effects on the demand for risky assets of a compensated increase in the marginal tax rate (MTR). Two different approaches to compensation are examined in detail. The principal results are as follows: (a) Increase the MTR and compensate the individual so that his expected tax payment is constant. Then, unlike the case of an increase in a proportional income tax, may or may not increase, even though relative risk-aversion is increasing, -absolute risk aversion decreasing. Here, risk-taking is understood to be equivalent to Domar and Musgrave's (1964) concept of social risk-taking, i.e. the purchase of risky assets; see also Stiglitz (1969, p. 269). (b) Increase the MTR and compensate the individual so that expected utility is constant. Then the effect on is exactly that which would occur in the case of proportional taxation and a zero return on riskless assets. (c) If increases with a compensated increase in MTR (in the sense of result (a)) for all values of the MTR less than unity, then there is no linear tax schedule that will maximize risk-taking.