Question

1. A loan buyer in a secondary market believes that x% of the loans are high quality, and the rest are low quality. The buyer values high quality loans at $40,000 and low quality at $35,000. Banks selling loans value high quality loans at $38,750 and value low quality at $33,444. If the buyer cannot observe the bond's type, then the maximum price the buyer will pay is equal to the seller's value of high quality loans when x is

a) 65%

b) 75%

c) 79%

d) 85%

2. A financial intermediary is hired to make a transaction "go forward". The intermediary can do a good job that costs the intermediary $13,450, or do a bad job that costs $0. If the intermediary does a good job the transaction will go forward. If the intermediary does a bad job the transaction will go forward with probability 0.82, and will fail with prob. 0.18. The customer can't observe the intermediary's job choice and simply pays the intermediary $X if the transaction goes forward and pays $0 if it fails. What is the minimum X the customer must pay in order to persuade the intermediary to do a good job?

a) X = $70,555

b) X = $74,723

c) X = $78,880

d) X = $80,115

Answer 1

1.) If the expected value of the loans will be greater than 38750 then buyers will pay:

Expected value of loan =

[X(40,000) +(1-X).(35,000) ]> 38750

(40,000X + 35,000 - 35,000X ) > 38750

5000X > 3750

X > 3750/5000

X > 0.75

Or 75%

The correct option is b.) 75%

2) Two options with intermediary

Consumer has to pay the intermediary such that it cannot differentiate between the good and the bad or if the payoffs from good as well as bad are equal enough, and it could meet the cost of intermediary then we can assure that there will be "go forward case only"

Consumer must pay

=( Cost of good job to intermediary/ The probability of the failure

= 13450/0.18

= 74722.22

= $74722.23 (approx.)

The correct option is b) X = $74723.