6. The value of information

Alyssa wants to buy her brother a new sweater for his birthday. Alyssa thinks there is a 90% chance that her brother wears a size medium, but there is also a 10% chance he wears a size large. The following table shows the payoff (in utils) to Alyssa from giving the sweater depending on Alyssa's brother's true size and on the size Alyssa purchases. You can see that if she purchases the incorrect size, Alyssa will get no utility from giving the sweater.

See table below:

The expected payoff from buying the size medium sweater is

, and the expected payoff from buying a size large sweater is

; therefore, she should choose to buy the size sweater.

True Sweater Size Options Medium Large (1) Buy size medium 30 0 (2) Buy size large 0 30