If Ann's utility function is U = W⁰.⁵,and she invests in a business which can yield $6,400 with probability 1/5,and $3600 with probability 4/5,then her expected wealth is
A) $1280.
B) $2880.
C) $4160.
D) $5840.

Question

Quizplus · Accepted Answer

The expected value of the investment is:

E(W) = (1/5)*$6,400 + (4/5)*$3600 = $4,000

Using Ann's utility function, we can find her expected utility:

U($4,000) = ($4,000)^0.5 = $63.25

To find the best choice(s), we need to compare the expected utility of the investment to the utility of not investing, which is just the square root of Ann's wealth:

U(wealth) = W^0.5

Assuming Ann has an initial wealth of $0, her utility without investing is:

U($0) = ($0)^0.5 = $0

Since U($63.25) > U($0), Ann should invest in the business to maximize her expected utility.

Note that we can also see this by comparing the expected wealth of the investment ($4,000) to Ann's initial wealth ($0). Since the expected wealth of the investment is greater than her initial wealth, she should invest.

If Ann's Utility Function Is U = W⁰