# Confusions about calculations in Utility Theory Paper

Recently I was improving my knowledge of Utility Functions in finances. I stumped upon very nice (yet quite old) article: "An Introduction to Utility Theory" by John Norstad (1999). What drove my attention was charts in section 4. They represent utility functions of wealth:

• First chart (figure 2): $- \dfrac{10^6}{w^3}$
• Second chart(figure 3): $-\dfrac{10^{10}}{w^5}$

(So basically $-\dfrac{10^{2c}}{w^c}$) with c as chosen constant)

Purely for learning purpose I was trying to recreate his example (by using Excel/R) from section 4 (details on page 7). In same page author stated that expected utility (of 105) will be equal to -0.98. It is also shown under figure 2 in table:

  Wealth   Utility
$90 -1.37 Bad outcome$100   -1.00   Current wealth
$105 -0.98 Expected outcome$120   -0.58   Good outcome


I run test and with those values and for \$105 it does not match. Using$- \frac{10^6}{105^3}$I get -0.86. What is surprising other stated values are calculated correctly (90, 100, 120). At first I though it is nothing more than some kind of typo, but when I checked the second formula used to draft function in figure 3 the same situation occurred. For table: Wealth Utility$90   -1.69   Bad outcome
$100 -1.00 Current wealth$105   -1.05   Expected outcome