Consider a local used car market with an unlimited number of buyers, 50 sellers of high-quality...

Consider a local used car market with an unlimited number of buyers, 50 sellers of high-quality cars, 30 sellers of medium-quality cars and 20 sellers of low-quality cars. Each seller offers up to 1 car for sale. Sellers of high-quality cars value their car at $15,000, sellers of medium-quality cars at $7,000, and sellers of low-quality cars at $3,000. Buyers value high-quality cars at $20,000, medium-quality cars at $10,000, and low-quality cars at $5,000.
Answer the following questions according to the lemon’s model that we discussed in class.
If buyers and sellers are symmetrically and fully informed about the quality of the cars, ...
(a) ... how many “submarkets” for cars will there exist? (1 mark)
(b) ... what is the total surplus generated in the market for cars? That is, what is the total surplus generated in all “submarkets” together?
If sellers are fully informed about the car quality but buyers do not know the car quality, ...
(c) ... how many “submarkets” for cars will there exist? (1 mark)
(d) ... will high quality cars be traded in the market equilibrium? Explain your answer.
(e) ... can medium quality cars be traded in a market equilibrium? Explain your answer.
(f) ... what is the total surplus generated in the market for cars, assuming as many cars as possible are traded in market equilibrium? (1 mark)
(g) Compute the difference between the total surplus of (b) and the total surplus of (f). In the scenario with asymmetric information from (c) - (f), is the market for used cars efﬁcient? Explain your answer.
(h) Which sellers gain and which sellers lose if we move from the symmetric information situation of (a)-(b) to the asymmetric information situation in (c)-(f)? How much do they gain or lose?

Solutions

Expert Solution

(a) For all qualities of cars, the valuation of the buyer is larger than the valuation of the respective seller. Therefore, three submarkets will exist: one where high quality cars are bought and sold, one where medium quality cars are bought and sold and one where low quality cars are bought and sold.

(b) Total surplus generated when a high quality car is sold = valuation of buyer - valuation of seller = 20000 - 15000 = $5000

Total surplus generated in the high quality car market = number of high quality car sellers * surplus generated when a high quality car is sold = 50*5000 = $2,50,000

Total surplus generated when a medium quality car is sold = valuation of buyer - valuation of seller = 10000 - 7000 = $3000

Total surplus generated in the medium quality car market = number of medium quality car sellers * surplus generated when a medium quality car is sold = 30*3000 = $90,000

Total surplus generated when a low quality car is sold = valuation of buyer - valuation of seller = 5000 - 3000 = $2000

Total surplus generated in the low quality car market = number of low quality car sellers * surplus generated when a low quality car is sold = 20*2000 = $40,000

Total surplus generated in all three markets = 2,50,000 + 90,000 + 40,000 = $3,80,000

Total surplus generated in all three markets is $3,80,000.

(c) If buyers cannot observe the quality of the car, only one market will exist where buyers and sellers meet to buy and sell cars. This is because buyers can no longer observe the quality of the car and hence cannot distinguish between them.

(d) Buyer's valuation of a car in the common market = valuation for high quality car * probability that car is high quaility + valuation for medium quality car * probability that car is medium quaility + valuation for low quality car * probability that car is low quaility

Now, probability that car is of a particular quaility = number of sellers of that quality car/ total number of sellers

Therefore,

Buyer's valuation of a car in the common market = 20,000*50/100 + 10,000*30/100 + 5000*20/100

= 10,000 + 3000 + 1000 = $14,000

Therefore, a buyer is willing to pay a maximum of $14,000 for a car when he is not able to observe car quality. But the valuation of a high quality car for the seller is $15,000 which means that the least price he will sell the car for is $15,000. So, he will never sell the car in this market. Therefore, high quality cars are not traded.

Rahul Sunny answered 1 month ago

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