-
QUESTION
Moral Hazard in Credit Markets I
A competitive lender makes loans to a pool of borrowers that are identical. After borrowers have received their loans they choose one of two investment projects. Project G pays the borrower a rate of return of r(g) with probability p(g). With probability 1-p(g), the project earns a zero rate of return, the borrower defaults on the loan, and the lender receives back the initial loan amount. Project B pays the borrower a rate of return of r(b) with probability p(b). With probability 1-p(b), the project earns a zero rate of return, the borrower defaults on the loan, and the lender receives back the initial loan amount. We assume that r(g)p(b) and p(g)(1+r(g))>p(b)(1+r(b)).
The lender can’t distinguish between borrower types and so it charges all borrowers the same interest rate r(L). The lender lends an amount L and pays interest r(D)on funds acquired from depositors.
Q1. Which project would the lender prefer that the borrowers undertake?
Project B or Project G
Q2. Explain in words why your answer to the previous question is true.
Q3. Write down an expression for the profit that a borrower expects from Project G and submit an image file depicting your answer.
Q4. Suppose r(g)=0.08, r(b)=0.10, p(g)=0.99, p(b)=0.3, r(D)=0.02, L=100. Find the value for r(L)* such that the borrower is indifferent between projects G and B. Round to three decimal places.
Q5. Either by hand or using a computer, graph the lender’s expected profit function E(π^L) for values of r(L) between 0.00 and 0.10. Make sure axes and r(L)* are clearly labeled.
Q6. Explain in words what is happening to the borrowers’ behavior at the discontinuity in the lender's profit function that you graphed in the previous question.
| Subject | Business | Pages | 6 | Style | APA |
|---|
Answer
-
Moral Hazard in Credit Markets
Question A
The borrower has two options on investing either in Project B or G. Project G pays the borrower a rate of return r(g) with a probability p(g) whole project B pays a rate of return of r(b) with a probability p(b). If the borrower does not get any return, then the project fails and the borrower is not able to repay back either the principal or the interest amount. In this case, the borrower will be indifferent in which project to undertake or invest.
The lender lends an amount of L and charges rl interest rate from the borrow. The lender has to pay an equivalent of rp on deposit. Therefore, the payoff to the lender when the borrower undertakes project G is derived as follows.
PLs.g = PsL + Ps.rl.L – L -Lrp
The payoff to the lender when the borrower undertakes project B is derived as follows:
PLs.b= PbL +Pb.rl.L – L-Lrp
As Pg>Pb the payoff to the lenders when Project G is undertaken is greater than the payoff when Project B is undertaken.
Question B
The profit to the borrower when project G is undertaken is derived as follows:
P(s.g) = L +PsL(rs) – PsL_ PsL(rl)
Question C
The profit to the borrower when project B is undertaken is derived below.
P(s.s) = L+Ps.L(rs) – PsL – PsL(rl)
Question D
When the borrower is indifferent between the project, the payoff from the two projects will be equivalent to: Ps.g = Ps.s
L +PsL(rs) – PsL_ PsL(rl) = L+Ps.L(rs) – PsL – PsL(rl)
100 + (0.3* 100*0.10) – (100*0.3) – (100*0.3*rl) = 100 +(0.99*100*0.08) – (100*0.99) – (100*0.99*rl)
1+0.03-0.3-0.3rl = 1+0.0792-0.99-0.99rl
0.73-0.3rl = 0.0892-0.99rl
0.6408 = -0.68rl
Answer rl = -0.984
Question E
Question 6
The graph indicates that as better rates of return are offered, the borrower increase the amount until that point where he is indifferent between project B and G.
References