Piku faces a lottery with outcomes of ₹24, ₹12, ₹48 and ₹6 given by the following probability distribution
| Lottery Outcome | ₹24 | ₹12 | ₹48 | ₹6 |
|---|---|---|---|---|
| Probability of Outcome | 2/6 | 3/6 | 1/6 | 0 |
She is indifferent between the lottery and receiving ₹28 with certainty. Given the information we can conclude that Piku is a
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Answer: (A)
Step 1 - Compute the lottery's expected value.
Step 2 - Compare to the certainty equivalent. Piku is indifferent between this lottery and a certain ₹28. Her certainty equivalent (CE) is therefore 28.
Step 3 - Interpret. Since , Piku requires a certain amount that is actually MORE than the lottery's expected value to give up the gamble — equivalently, she values the risky lottery MORE than its expected monetary value. This is the signature of risk-loving (convex utility) behavior: a risk-averse person would instead have a certainty equivalent BELOW the expected value (they'd accept less than the EV for the safety of certainty), while a risk-neutral person's CE would equal the EV exactly.
Since here, Piku displays risk-loving preferences. Therefore the answer is (A) risk lover.
Students sometimes default to 'risk averse' as the more commonly-discussed/intuitive risk attitude in textbooks without carefully comparing the DIRECTION of the CE-vs-EV gap here — the fact that the certain amount (28) is HIGHER than the expected value (22) is the specific, counter-intuitive signal that must be caught to correctly identify risk-loving rather than risk-averse behavior.
Choice under uncertainty has come up 27 times in 7 exams since 2007.
This question is on Risk aversion, certainty equivalent and risk premium, part of Choice under uncertainty in Microeconomics.
How the shape of utility reveals attitude to risk and how much a person would pay to avoid it.
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Question from the GATE 2021 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.