IAI Actuarial Core Principles · Economic Modelling · Rational choice theory and utility
An individual has utility U(w) = ln(w) and faces a 50:50 gamble giving final wealth of Rs 4,00,000 or Rs 1,00,000. What is the certainty equivalent wealth?
The certainty equivalent is Rs 2,00,000. With log utility it equals the geometric mean of the outcomes, the square root of 4,00,000 times 1,00,000. This is below the expected wealth of Rs 2,50,000, reflecting risk aversion.
- ARs 2,50,000
- BRs 2,00,000Correct
- CRs 1,50,000
- DRs 3,00,000
- Rs 1,00,000
Explanation
E[U] = 0.5 ln(4,00,000) + 0.5 ln(1,00,000) = 0.5 ln(4x10^10) = ln(2,00,000). The certainty equivalent solves ln(CE) = E[U], so CE = Rs 2,00,000. The expected wealth of Rs 2,50,000 is the distractor from ignoring risk aversion.
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