Assume your utility function is the cube root. Your initial wealth is $10k, and

Question

Assume your utility function is the cube root. Your initial wealth is $10k, and you are looking at a prospect of either losing $1000 with certainty, or losing $2000 or $0 with a 50-50 chance.

What is the difference between the utiilty of the certain outcome and the uncertain outcome? Enter answer accurate to 3 decimal places.

Hint: calculate the utility of the certain wealth outcome. Then calculate the expected value of the uncertain outcome in utility. Then find the difference!

Think also which alternative should you prefer, if you are an expected-utility maximizer.

Explanation / Answer

Certaininty means 1 or 100%

cube root of 1 = 1

Utility of certain outcome = 1000*1 = $1000.

Utility of the uncreratin outcome: cube root of 0.5 is 0.7937 and cube root of 0 is 0

Utility of uncertain outcome = 0.7937*2000 + 0 = $1587.4

Difference between the utility outcomes = 1587.4 -1000 = 587.40

If you are an expected utility maximzer the alternative of losing $2000 or $0 with a 50-50 chance is better since it has an utility outcome of 1587.40 as against 1000 of the certain approach

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