Exercise 3: Consider two households, A and B. They must decide whether to purchase a bench that they would jointly own. The price of the bench is €40. The value of the bench to each household is privately known. What Is known to all Is that
- Household A values the bench €80 with probability p €10,11 and €0 with probability (1 — p).
- Household B values the bench E120 with probability q EPA] and €0 with probability (1 — q).
They decide to meet and report what the bench is worth to them. They also agree to the following rule. Let a €
- Explain, in a few lines and using words as opposed to a mathematical proof, whether the variables p or q should be high or low to facilitate honest reports of a high valuation.
- Assume that p = q = 0.8. Is the bench ever ordered? And, If so, how much does each household pay for it? (Prove all answers.)
- Let p = q = 0.8, and assume now that households A and B amend the rules in such a way that they now agree to the following:
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