Question

In: Economics

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?

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 7 months ago

Consider a market for used cars. There are 100 sellers and 100 buyers. The sellers know...

Consider a market for used cars. There are 100 sellers and 100 buyers. The sellers know the qualities of their cars, but the buyers only know that the quality θ of each used card is uniformly distributed over interval [0, 1]. The seller’s value of a car with quality θ is θ. (Thus, market supply is S(p) = 100p for 0 ≤ p ≤ 1 and S(p) = 100 for p > 1.) Each of 50 buyers values a car...

Consider a market with 22 sellers and 21 buyers. Of 22 sellers, there are 15 "high-cost"...

Consider a market with 22 sellers and 21 buyers. Of 22 sellers, there are 15 "high-cost" sellers with production costs of $30 per unit and 7 "low-cost" sellers with costs of $10 per unit. Of 21 buyers, there are 14 "high-value" buyers with values of $40 per unit and 7 "low-value" with values of $20 per unit. For this market, identify and graph the demand and supply curves. Finally, predict the equilibrium price and quantity in the market.

Consider a market in which there are many potential buyers and sellers of used cars. Each...

Consider a market in which there are many potential buyers and sellers of used cars. Each potential seller has one car, which is either of high quality (a plum) or low quality (a lemon). A seller with a low-quality car is willing to sell it for $4,500, whereas a seller with a high-quality car is willing to sell it for $8,500. A buyer is willing to pay $5,500 for a low-quality car and $10,500 for a high-quality car. Of course,...

Consider a market for used cars. There are many sellers and even more buyers. A seller...

Consider a market for used cars. There are many sellers and even more buyers. A seller values a high quality car at 800 and a low quality car at 200. For any quality, the value to buyers is m times the value to sellers, where m > 1. All agents are risk-neutral. Sellers know the quality of their own car, but buyers only know that 2/3 of the cars are low quality and the remaining 1/3 of them are high...

In a used cars market, there are many car sellers with even larger number of car...

In a used cars market, there are many car sellers with even larger number of car buyers. A car priced at 800 is considered high quality to the seller, a car at 200 is considered low quality to the seller. To a buyer, for any quality of a car, the value to the buyer is x times the value to the sellers. x>1. Sellers have information about the quality of their own car, whereas buyers know 2/3 of cars are...

Consider the market for used cars and let X = value of the car. Sellers know...

Consider the market for used cars and let X = value of the car. Sellers know the value of the car they sell and their utility is U(X) = X. Buyers only know that car value is uniformly distributed on (50,150) and their utility is 1.5×X. Suppose the posted price for used cars is 90. Will consumers buy a car at this price? Explain.

Consider a market with 30 sellers and 30 buyers. Of 30 sellers, there are 10 ”high-cost” sellers with production costs of $25 per unit and 20 ”low-cost” sellers with costs of $5 per unit.

Consider a market with 30 sellers and 30 buyers. Of 30 sellers, there are 10 ”high-cost” sellers with production costs of $25 per unit and 20 ”low-cost” sellers with costs of $5 per unit. Of 30 buyers, there are 15 ”high-value” buyers with values of $30 per unit and 15 ”low-value” buyers with values of $10 per unit.a.) Identify the demand schedule for this market.b.) Identify the supply schedule for this market.c.) Graph the demand and supply schedules for this...

For a market to be competitive, why is it important that there be buyers and sellers...

For a market to be competitive, why is it important that there be buyers and sellers and easy entry and exit?

A market consists of groups of buyers and sellers of a good or service. Market equilibrium...

A market consists of groups of buyers and sellers of a good or service. Market equilibrium represents the price at which the quantity of goods supplied is balanced with the quantity of goods consumers are willing and able to buy. Consider the market for iPads. What could change the quantity of iPads consumers are willing and able to purchase? Identify examples of three events since 2010 that have caused changes in the iPad market's equilibrium. For each event, decide whether...

In a market there are 10 sellers and 4 buyers and the opp cost for seller...

In a market there are 10 sellers and 4 buyers and the opp cost for seller is $3.00 and opp cost for the buyer is $10.00. Then what will be the price that trade will take place at? Explain why. What will a price that buyers will say NO to (if any)? What will be a price that seller will say NO (if any)?