2.3 Act Immediately
An alternative policy is to act immediately, by saving an amount in the first period to finance a proportion, γ, of the anticipated cost. Thus, the tax rate in period 1 is given by:
(6)
Then in the second period, if the event does not happen, this revenue can be used to lower the tax rate below the planned rate needed to finance b2. Hence the tax rate in period 2 becomes:
(7)
If the event does happen, then the rate becomes:
(8)
As before, it is assumed that b1 is not also adjusted. For simplicity, it is further assumed that income in each period is not affected by the tax policy. [13]
Expected social welfare from acting immediately is:
(9)
The final line in (9) reflects the fact that, if the event does not take place, the accumulated fund can be used to reduce the second period’s tax rate below τ2 (rather than being used, for example, to increase expenditure on other items). It can easily be seen that when γ = 0, (9) reduces to (5). Hence waiting is simply an extreme form of acting immediately, and it is necessary only to solve (9) for the value of γ that maximises E (W | act). Furthermore, as p approaches 1, gamma approaches the tax smoothing case discussed in Appendix B.
Notes
- [13] In addition to standard incentive effects, there is some debate about whether the use of a fund would increase or reduce income growth.
