A decision maker is indifferent between the certainty equivalent(y^) of 15 perce

Question

A decision maker is indifferent between the certainty equivalent(y^) of 15 percent improvement and "achieving 10-percent or 35-percent improvement with 50-50 percent chance," or the indifference statement: .5(.10) + .5(.35) ~ .15. If v(.35) and v(.10) = .48, please sketch the corresponding utility function in the graph below. Besides struggling to wrap my head around the complexity of this problem, I'm not even making a dent in understanding how they got v(.35) = 85 and v(.10) = .48...or what even v means. Despite the solution and graph shown below from study guide.

Explanation / Answer

v(.35) = 0.85 and v(.10) = 0.48 is given and you said that you have got the solution but not able to understand how it come.

Certainty Equivalent: The amount of payoff that an agent would have to receive to be indifferent between that payoff and a given gamble is called that gamble's 'certainty equivalent'

Thus as per this question, it is given that a person is having an X amount and there is a 50% chance that he will get 10% return and 50% chance that he will get 35% return and the certainity equivalent in this example is given as 15% return. And 'v' in example is the Utility derived from the returns (payoff) received i.e. if a person gets 10% returns then the utility is 0.48 and when the return is 35% then the utility is 0.85

Also when the return is 15% (certainity equivalent) then as you have calculated the utility derived by an individual is 0.665

Thus joining the three points on the graph we get required utility function on the graph.

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