Taxation and Risk-Taking: An Expected Utility Approach

It is a popular notion that higher taxes tend to discourage risk-taking. In economic theory, however, the conclusions in this respect have been somewhat different. Thus, Tobin in his celebrated Liquidity Preference as Behavior Towards Risk 3 and Musgrave in his text-book 21 come to the conclusion that an increase in a proportional tax rate will, with full loss offset, increase the holding of the risky asset in a portfolio of a given size. Musgrave's analysis of the no-loss-offset case leads to the result that the direction of the effect is indeterminate. In this article these problems are re-examined on the basis of expected utility theory. There are two reasons why such a re-examination is justified. One is that it seems desirable to develop the analysis under assumptions about the investor's preference structure less restrictive than those made by Musgrave and Tobin. The other is that in spite of the greater generality of the expected utility approach, it is possible to sharpen some of the old conclusions, to derive some new ones, and to correct some erroneous ones. The analysis is inspired largely by the elegant treatment of portfolio choices by Arrow in 1. The Pratt-Arrow measures of absolute and relative risk aversion are employed at various points in the analysis, and some familiarity with these concepts is assumed. (See Appendix.) Without any serious loss of generality, the discussion is restricted to portfolio choices involving two assets only. It is assumed, however, that the yield on one of these is non-stochastic, i.e. known with certainty. It may be true that in the real world no such asset exists, but when a general utility function is used this assumption is necessary in order to get a relatively simple measure of risk-taking, simply by using the amount invested in the riskless asset. One might of course compute and compare, say, the means and variances of two portfolios; but when it is not assumed that the investor is satisfied by letting himself be guided by the portfolio mean and variance only, it is clearly not to be expected that his behaviour can be summarized by these alone. The following notation is employed: