Question

Suppose there are only two types of cars in the used car market q=0 and q=1.

Half the cars are q=0 and the other half are q=1.

Buyers still cannot tell the quality but they are aware of the quality distribution.

Sellers are willing to accept any price p≥0, but prefer to receive a higher price.

If buyers do not know q, then they are willing to pay p=10000*Q+500

where Q is the average quality of the cars in the market. Suppose that sellers

can get their car certified by having it tested by a third party.

Denote y as the number of certifications.

Let the cost of each certification be $750 for cars of quality q=1 and $4180

for cars of quality q=0. If buyers believe that the certification signals the quality,

then they are willing to pay p=10,500 for signal of high quality and p=500

for the signal of low quality.

Find the range for the number of certifications (y) such that there is

a separating equilibrium.

In addition, what will be the price in the pooling equilibrium?

Please show all work/steps!

Answer 1

Solution :-

Given data:

Suppose there are only two types of cars in the used car market q=0 and q=1.Half the cars are q=0 and the other half are q=1.

Here we have to find out the range for the number of certifications (y) such that there is a separating equilibrium. and the price in the pooling equilibrium.

Now consider as the seller has 50 cars.

i.e, we can say that 25 cars of q=0 and remaining 25 are from q=1.

Hence, the range of certification (y) will be at least 25, i.e, 50% of the total number of cars for separating equilibrium.

	Q=0	Q=1
Certification cost	$4,180	$750
Car quantity	25	25
Total certification cost	= $4,180 * 25 = $104,500	= $750 * 25 = $18,750
Total car selling cost	= 500 * 25 = $12,500	= 10,500 * 25 = $262,500
Loss / profit.	= $12,500 - $104,500 = -$92000 (Loss)	= $262,500 - $18,750 = $243,750 (Profit)
Net profit	= $243,750 - $92000 = $151,750

Here choose the same action in pooling equilibrium agents with the differing characteristics.. Then we will consider average quality of the total cars.

Now, without certification:

Assume that q = 0.5.

Then, Price, P = 10000*Q+500

Price, P = 10000*(0.5)+500

Price, P = 5000 + 500

Price, P = $5500.

Price in the pooling equilibrium, P = $5,500.