Adverse Selection Problem Set

Adverse Selection Problem Set

Clean Version

Due April 11...

1) Suppose that the net value of profit π of the mortgage to the bank as a fraction of its principal is equal to four years' interest minus the chance of default:

π = 6r - d

And suppose that the homeowners and homebuyers who come to the bank have a chance of default which is:

d = x + 24r²

a. Solve for profits as a function of the interest rate charged by the bank and the parameter x.
b. Suppose competition between banks drives the interest rate in the market down to the minimum interest rate at which banks do not make losses. What, then, is the market interest rate as a function of the background default probability x?
c. For what background default probabilities x does the market collapse completely?

2) What would your answers to (1) be if the coefficient in front of r in the profit equation were not 6 but 10?

3) What would your answers to (1) be if the coefficient in front of r in the profit equation were not 6 but 2?

4) Suppose that the demand for mortgage loans by "good borrowers" is given by:

D = 4000(0.1 - r)

where D is total demand in billions of dollars and an r of 5% means r=0.05. Suppose further that the demand for mortgage loans by "bad borrowers" is simply some parameter y. Banks earn a net rate of interest of 0 on the loans they make to bad borrowers. Banks earn the posted rate of interest on the loans they make to good borrowers.

a. Suppose y = 2000 and the cost of funds to banks is perfectly elastic at 1%. What volume of loans are made in equilibrium? How many go to good borrowers? How many to bad borrowers?
b. Suppose Suppose y = 2000 and the cost of funds to banks is perfectly elastic at 2%. What volume of loans are made in equilibrium? How many go to good borrowers? How many to bad borrowers?
c. Suppose Suppose y = 2000 and the cost of funds to banks is perfectly elastic at 3%. What volume of loans are made in equilibrium? How many go to good borrowers? How many to bad borrowers?
d. Suppose Suppose y = 2000. What is the maximum cost of funds to banks at which any loans at all are made? How many loans are made at that cost, and what interest rate do the banks try to charge?

5) How would your answers to (4) be different if the bad borrower parameter y = 1000?

6) How would your answers to (4) be different if the bad borrower parameter y = 3000?

7) Consider George Akerlof's article, "The Market for 'Lemons'." What were the two major things you got out of reading it? Write one paragraph explaining each.

8) Consider the article "Leveraged Losses Lessons from the Mortgage Market Meltdown." What were the two major things you got out of reading it? Write one paragraph explaining each.

Comments

[Dena Fehrenbacher]

So this is due on April 11, even if we do not have lecture that day?

[Tim Wang]

Is the first part supposed to read "Suppose ... is equal to SIX years' interest minus the chance of default" since the equation is π = 6r - d?