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CMA Intermediate · Management Accounting · Decision Theory

An investor has a utility function U(W) = square root of W, where W is the outcome in Rs lakh. She is offered a venture giving Rs 64 lakh with probability 0.5 and Rs 16 lakh with probability 0.5, or a certain sum. What is the certainty equivalent of the venture, and what is her attitude to risk?

The certainty equivalent is Rs 36 lakh and she is risk averse. Expected utility is 0.5 times 8 plus 0.5 times 4, which is 6, and the sum with a utility of 6 is 36. This is below the expected value of 40, indicating risk aversion.

  1. ARs 40 lakh; risk neutral
  2. BRs 36 lakh; risk averseCorrect
  3. CRs 40 lakh; risk averse
  4. DRs 36 lakh; risk seeking

Explanation

Expected utility = 0.5x8 + 0.5x4 = 6. Certainty equivalent = 6 squared = 36. Expected monetary value is 40, which exceeds the certainty equivalent of 36, so she would accept less than the EMV for certainty, showing risk aversion. Using 40 as certainty equivalent ignores the utility curvature.

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