Three qualities of second-hand bicycles are available in equal numbers: high, medium, and low. There are many buyers and sellers, who value each quality of the bike differently. The value that each agent assigns to each quality of the bike is given below. Quality High Medium Low Buyer’s value 100 (high), 65 (medium), 30 (low) Seller’s value 75 (high), 60(medium) , 45 (low) Now assume that the sellers can offer a reimbursement of 50 to the buyer, payable if the bicycle breaks down. Bikes of high quality never fail; those of low quality always fail; those of medium quality fail 50% of the time. (iii) Suppose that all owners of high and low quality bikes offer reimbursement but owners of low quality bikes do not. Moreover, assume this to be common knowledge. Show that this is an equilibrium if the price satisfies 85 < p < 95. That is, show that none of the sellers is willing to change their behaviour, given actions of others. Is the resulting outcome socially optimal? (iv) Are there any other (possibly inefficient) equilibria in which trade occurs?
Three qualities of second-hand bicycles are available in equal numbers: high, medium, and low. There are many buyers and sellers, who value each quality of the bike differently. The value that each agent assigns to each quality of the bike is given below.
Quality High Medium Low
Buyer’s value 100 (high), 65 (medium), 30 (low)
Seller’s value 75 (high), 60(medium) , 45 (low)
Now assume that the sellers can offer a reimbursement of 50 to the buyer, payable if the bicycle breaks down. Bikes of high quality never fail; those of low quality always fail; those of medium quality fail 50% of the time.
(iii) Suppose that all owners of high and low quality bikes offer reimbursement but owners of low quality bikes do not. Moreover, assume this to be common knowledge. Show that this is an equilibrium if the price satisfies 85 < p < 95. That is, show that none of the sellers is willing to change their behaviour, given actions of others. Is the resulting outcome socially optimal?
(iv) Are there any other (possibly inefficient) equilibria in which trade occurs?
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