hree 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 65 30

Seller's value 75 60 45

(i) What is the efficient outcome in this market? Equivalently, which types of bikes should change their owners to maximise the social welfare?

[3 marks]

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?

[7 marks]

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 fail50%of the time.

(iii) Supposethatallownersofhighandlowqualitybikesofferreimbursementbutownersoflowqual- ity bikes do not. Moreover, assume this to be common knowledge. Show that this is an equilibrium if the price satisfies85< 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?

[6 marks] [9 marks]