Question 4 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) (i) What is the efficient outcome in this market? Equivalently, which types of bikes should change their owners to maximise the social welfare?
Question 4
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)
(i) What is the efficient outcome in this market? Equivalently, which types of bikes should change their owners to maximise the social welfare?
Suppose that the buyers do not know the quality of any particular bicycle for sale, but the sellers do know the quality of the bike they sell. The price at which a bike is traded is determined by demand and supply. Each buyer wants at most one bicycle.
(ii) Assuming that each buyer purchases a bike only if its expected quality is higher than the price, and each seller is willing to sell their bike only if the price exceeds their valuation, what is the equilibrium outcome in this market?
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