An individual faces wealth Rs. 10 lakh with probability 0.75 and Rs. 7 lakh with probability 0.25. With utility , the individual will buy full insurance by paying a premium of Rs. _______ lakh (round off to 2 decimal places).
2 marksMicroeconomicsChoice under uncertaintyInsurance, risk sharing and intertemporal choiceHardabout 3 min
IIT JAM 2022 Question 51: Choice under uncertainty
Answer and worked solution
Answer: 0.56 to 0.60
Expected utility is . The certainty equivalent solves , so lakh.
Full insurance guarantees the high wealth net of the premium, . The individual will pay up to the point of indifference, , giving lakh, within the accepted range. (Because is convex the person is risk loving, so the premium is below the actuarially fair premium of .)
Plain-text version
An individual faces wealth Rs. 10 lakh with probability 0.75 and Rs. 7 lakh with probability 0.25. With utility U(w) = w³, the individual will buy full insurance by paying a premium of Rs. _ lakh (round off to 2 decimal places).
Also written as: An individual faces wealth Rs. 10 lakh with probability 0.75 and Rs. 7 lakh with probability 0.25. With utility U(w) = w^3, the individual will buy full insurance by paying a premium of Rs. _ lakh (round off to 2 decimal places).
Choice under uncertainty has come up 27 times in 7 exams since 2007.
What this question tests
This question is on Insurance, risk sharing and intertemporal choice, part of Choice under uncertainty in Microeconomics.
How insurance and saving let people smooth consumption across states and over time.
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