Question: This is a variant of the Lemon's problem. A student has a used book whose value can be any real number between $0 and $10

This is a variant of the Lemon's problem.

A student has a used book whose value can be any real number between $0 and $10 to the student (uniform distribution, average is $5). The student observes the value. There is a potential buyer who does not observe the value and makes an offer to the student. The student observes the offer and decides whether to accept or reject the offer. The book worth 50% more to the buyer than to the seller. The buyer's utility is the difference between the value of the book to the buyer and the price he pays to the seller. What is the buyer's expected utility if the buyer offers $4?

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