3.2 An Alternative Welfare Function
The application of the Epstein-Zin specification for the welfare function in this context involves the certainty equivalent of Y ε = Z1/(1- ε where:
(29)
The welfare function is:
(30)
- Figure 7: Optimal Gamma for Epstein-Zin Preferences: Alpha = 0.5
Using the Epstein-Zin welfare function, the optimal choice of γ is shown in Figure 7 for two risk aversion parameters and a value of α = 0.5. Other values are, as earlier, y1 = 5000, b1 = 2000, β = 600 and gy = gb = r = 0.5. The cost values are assumed to be CL = 600 and CH = 1000. The very high degree of risk aversion does produce a different, and somewhat concave, surface compared with the lower risk aversion. However, the effect of risk aversion becomes much smaller as the two costs are reduced and as the value of α is increased. The concavity in the case of very high risk aversion may be associated with the increase in the certainty equivalent beyond p2 = 0.5 (the point of maximum uncertainty regarding the high cost alternative), allowing for a lower current tax rate.