IAI Actuarial Core Principles · Economic Modelling · Rational choice theory and utility
Meera has utility of wealth U(w) = ln(w). She holds wealth of Rs 1,00,000 and is offered a gamble: a 50% chance of ending with Rs 1,60,000 and a 50% chance of ending with Rs 62,500. What is the certainty equivalent of the gamble?
The certainty equivalent is Rs 1,00,000. With log utility, expected utility equals half the log of the product of the two outcomes, which is the log of the square root of 10^10, namely 1,00,000. Expected wealth of Rs 1,11,250 is higher because of risk aversion.
- ARs 1,00,000Correct
- BRs 1,11,250
- CRs 90,000
- DRs 81,250
- Rs 1,05,000
Explanation
Expected utility = 0.5 ln(160000) + 0.5 ln(62500) = 0.5 ln(160000 x 62500) = 0.5 ln(10^10) = ln(10^5). So the certainty equivalent is exp of that = Rs 1,00,000. The expected wealth of Rs 1,11,250 overstates it because of risk aversion.
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