Exercise 3: Consider two households, A and B. They must decide whether to purchase a bench...

 

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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 ● They decide to meet and report what the bench is worth to them. They also agree to the following rule. Let a € [0,1]. A reports $0 i. ii. Household A values the bench €80 with probability p E[0,1] and €0 with probability (1 - p). Household B values the bench €120 with probability q E[0,1] and €0 with probability (1-q). iii. A reports $80 B reports $0 Bench is not purchased Bench is purchased A pays $40 B reports $120 Bench is purchased B pays $40 Bench is purchased A pays $40a B pays $40(1-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: 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 ● They decide to meet and report what the bench is worth to them. They also agree to the following rule. Let a € [0,1]. A reports $0 i. ii. Household A values the bench €80 with probability p E[0,1] and €0 with probability (1 - p). Household B values the bench €120 with probability q E[0,1] and €0 with probability (1-q). iii. A reports $80 B reports $0 Bench is not purchased Bench is purchased A pays $40 B reports $120 Bench is purchased B pays $40 Bench is purchased A pays $40a B pays $40(1-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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There are 2 house holds A and B They must decide whether to purchase bench that a Price of bench is ... View the full answer