Answer to Question #271008 in Macroeconomics for Mehwash Sk

Question

11 1. Recall the lemons problem at the start of the chapter. Some used cars are peaches, worth $3,000 to buyers and $2,500 to sellers, and some are lemons,. worth $2,000 to buyers and $1,000 to sellers. There is a fixed supply of cars and unlimited demand. Suppose there are twice as many peaches as lemons. Assume buyers can't tell the quality of a given car, while sellers can. What do the supply and demand curves look like? In the text, we asserted that markets clear at $2,666.67. Are there other market clearing prices?

 

Answer 1

Given,

Plum cars worth to buyers = $3000

Plum cars worth to sellers = $2500 

Lemon cars worth to buyers = $2000

Lemon cars worth to sellers = $1500 

If the lemon car is x and peach cars are double of lemon cars, it will be 2x. So there are $3x (2x+ x$ ) cars in the market. 

The peaches car in the market is in the ratio $=\frac{2}{3} (\frac{2x}{3x})$

The lemon car in the market is in the ratio $= \frac{1}{3} (\frac{x}{3x})$

Since sellers have perfect knowledge about the cars' quality, but buyers have no knowledge about the cars' quality, so it creates the problem of asymmetric information where one agent has more information about a product than other agents and that agent uses that information for its gain.

 

The demand curve shows that the demanded quantity of the good decreases with an increase in the price or vice versa.

The supply curve shows that the supplied quantity of the good decreases with a decrease in the price or vice versa.

The demand is unlimited and supply is fixed of used cars, so the demand curve is downward sloping but the supply is vertical to a fixed quantity of car Q. 

The market clears where demand (D) is equal to supply (S), so the market-clearing price is $2,666.67 where the D curve cuts the S curve. 

Since the buyers do not about the quality of the used cars, they will be ready to buy at the price equal to the average quality. 

The proportion of the plum and lemon cars is $\frac{2}{3}$ and $\frac{1}{3}$ , the average quality will be,

Average quality (willingness to pay)= $\frac{2}{3}$(A peach car worth to buyer)$+\frac{2}{3}$ (A lemon car worth to buyer)

                           $= \frac{2}{3} \times (3000) + \frac{1}{3}\times (2000)\\ = \frac{(6000+ 2000)}{ 3}\\ = \$2666.67$

Since we have seen the market-clearing price is the same as the price for average quality, so there will not be other market clearing prices as at that price demand is the same as supply.