Question

Suppose your utility function is u(x)-VX Consider the following two games: 1. You have a 1/4 chance of winning 25 and a 3/4 chance of winning 1 2. You have a 2/3 chance of winning 7 and a 1/3 chance of winning 4 What is the expected value and the expected utility of these games?

Answer 1

1) u(x) = $\sqrt{}$ x

expected value= $\sum$ x* P(x)

=1/4 *25 + 3/4*1 = 7

expected utility = $\sum$ P(x) * u(x)

=1/4 * $\sqrt{}$ 25 + 3/4 * $\sqrt{}$ 1 = 2

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2)

expected value= $\sum$ x* P(x)

=2/3 * 7 + 1/3 * 4

=18/3

expected utility = $\sum$ P(x) * u(x)

2/3 * $\sqrt{}$ 7 + 1/3 * $\sqrt{}$ 4

=(2/3) ( $\sqrt{}$ 7 + 1)

=1.2244