# Examples 9.1 through 9.3 all assume zero initial wealth. For each utility function determine the…

Examples 9.1 through 9.3 all assume zero initial wealth. For each utility function determine the maximum value of probability α such that the risky choice is preferred.

((Example 9.1 Suppose α = .5 and U(w) = w in the setting described in Table 9.1 or 9.2. Following expression (9.1) we have the following evaluations:

and we see that ω(a1) > ω(a2) regardless of initial wealth. This is probably the format in which you first encountered expected utility analysis. The utility of the outcome is the outcome itself (here adjusted for initial wealth). This linearity implies risk neutrality, but that is getting ahead of the story.))

((Example 9.3 Continuing the saga, now consider the third utility measure in Table 9.3: U(w) = − exp(−ρ·w), along with ρ = 0.001. Using zero initial wealth we find the following:

and conclude ω(a2) > ω(a1). Repeating for the case wi = 500, we do not alter the preference for a2 as we have ω(a2) = −.47711 > ω(a1) = −.47769.

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