Suppose that there are two types of cars,good and bad.The qualities of cars are not observable but are known to the sellers.Risk-neutral buyers and sellers have their own valuation of these two types of cars as follows:
$$\begin{array} { | l | l | l | }
\hline \text { Types of Cars } & \text { Buyer's Valuation } & \text { Beller's Valuation } \
\hline \text { Good } & & \
\text { (50\% probability) } & 5,000 & 4,500 \
\hline \text { Bad } & & \
\text { (50\% probability) } & 3,000 & 2,500 \
\hline
\end{array}$$ Now suppose that sellers value a good car at $4,500 and a bad car at $2,500,and quality is not observed by the buyers.What is the highest price that risk-neutral buyers will offer for a used car if they recognize adverse selection?

Question

Suppose that there are two types of cars,good and bad.The qualities of cars are not observable but are known to the sellers.Risk-neutral buyers and sellers have their own valuation of these two types of cars as follows:
$$\begin{array} {  | l | l | l | } 
\hline \text { Types of Cars } & \text { Buyer's Valuation } & \text { Beller's Valuation } \
\hline \text { Good } & & \
\text { (50\% probability) } & 5,000 & 4,500 \
\hline \text { Bad } & & \
\text { (50\% probability) } & 3,000 & 2,500 \
\hline
\end{array}$$ Now suppose that sellers value a good car at $4,500 and a bad car at $2,500,and quality is not observed by the buyers.What is the highest price that risk-neutral buyers will offer for a used car if they recognize adverse selection?

Quizplus · Accepted Answer

Since buyers cannot observe the quality of the car, they will expect to pay the average value of both types of cars, which is ($5,000+$3,000)/2 = $4,000. However, sellers who know the quality of the car will only sell a good car if the price is greater than or equal to $4,500 and a bad car if the price is greater than or equal to $2,500. Given this information, buyers will recognize that any car offered for less than $4,000 is likely to be a bad car (since sellers would not offer good cars at that price), and they will therefore not be willing to offer more than the value of a bad car, which is $3,000. Therefore, the highest price that risk-neutral buyers will offer for a used car is $3,000.

Suppose That There Are Two Types of Cars,good and Bad