6. The value of information Aa Aa Marissa wants to buy her brother a new sweater
ID: 1148292 • Letter: 6
Question
6. The value of information Aa Aa Marissa wants to buy her brother a new sweater for his birthday, Marissa thinks there is a 70% chance that her brother wears a size medium, but there is also a 30% chance he wears a size large. The following table shows the payoff (in utils) to Marissa from giving the sweater depending on Marissa's brother's true size and on the size Marissa purchases. You can see that if she purchases the incorrect size, Marissa will get no utility from giving the sweater. True Sweater Size Options (1) Buy size medium (2) Buy size large Medium Large 30 30 The expected payoff from buying the size medium sweater is large sweater is , and the expected payoff from buying a size therefore, she should choose to buy the size sweater. Suppose Marissa could call her dad to find out the correct size, but Marissa is extremely busy, and she knows that the call would turn into a very long conversation. If making the phone call costs Marissa 10 utils, but allows her to make the right choice with certainty, the net payoff after the call is expected utility gain from information Assuming Marissa is risk-neutral, the outweigh the cost.Explanation / Answer
Expected payoff from the first type of sweater is = (0.7*30)+(0.3*0)=21. Expected payoffs from large sweater is = (0.7*0)+(0.3*30)=9. Thus as the expected payoff in the first case is greater she should choose to by the first type of sweater.
The net payoff after the call is 30-10=20. This is as she will now get 30 with certainty and we net off the costs that she bears due to the call. The expected utility gain from this additional information is thus 30-21=9 utils. This is the difference in the two states.
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