Assuming that the Capitalist Spirit model provides a roughly correct description of the behavior of wealthy households, a natural question to ask is what the model implies about the relationship between accumulation behavior and taxes. Returning to the parameterized version of the model in which p = 2 and a = 7 = 1, if bequests (or wealth) are taxed at rate r then the equation for optimal consumption becomes:
Figure 7 shows the effect on consumption if bequest taxes are increased from 40 percent to 80 percent. Consider first the curve labelled r = .4, which shows the optimal amount of consumption for consumers facing a 40 percent bequest tax if bequests are not constrained to be positive. The actual consumption function, of course, is the minimum of the 45 degree line and this curve. The point of intersection of this curve and the 45 degree line, labelled u;i, reveals the level of lifetime wealth at which consumers begin to leave positive bequests.
When the bequest tax is raised to 80 percent, the amount of consumption shifts up, as indicated in the curve labelled r = .8. The point at which consumers begin leaving bequests, is substantially higher than when the tax rate was 40 percent.
Hence, it is useful to think of the effects of raising the bequest tax by considering three categories of consumers. The first are those with lifetime wealth less than uj\. They leave bequests under neither tax regime, so their behavior is unaffected by the tax increase. The second region is those consumers with lifetime wealth between and 0J2. These are the consumers who would leave bequests if the bequest tax were only 40 percent, but prefer to consume all of their lifetime wealth when the bequest tax rises. Finally, consumers with lifetime wealth greater than uj2 will leave bequests even when the bequest tax is 80 percent. However, at any level of lifetime wealth the size of the bequests they leave is reduced by an amount equal to the gap between the two consumption curves. It is simple to show that as lifetime wealth goes to infinity the fraction of lifetime wealth bequeathed approaches 100 percent even with the higher bequest taxes. This is the region of the model presumably corresponds best to the circumstances of fabulously wealthy people like Bill Gates.
Because the effect of taxes on consumption depends on the distribution of consumers across the different levels of lifetime income, the aggregate effect of bequest taxes in this model is impossible to judge in the absence of evidence (or assumptions) about the distribution of lifetime income (and information about the parameters of the model). If most bequests come from people with < wt < then an increase in the bequest tax could reduce bequests almost to nothing. If, on the other hand, most bequeathed wealth comes from consumers with very large amounts of lifetime income, increasing the bequest tax might have very little effect on either consumption or (pre-tax) bequests.