ECON 107 University of California Moral Hazard in Credit Markets Questions

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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_grg with probability p_gpg. With probability 1 ? p_g1?pg, 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_brb with probability p_bpb. With probability 1 ? p_b1?pb, 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 < r_brg p_bpg>pb, and p_g(1 + r_g) > p_b(1 + r_b)pg(1+rg)>pb(1+rb).

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Homework: Moral Hazard in Credit
Markets II
Q1
6 Points
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 rg ? with probability pg ?. With probability 1?pg ?, 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 rb ? with probability pb ?. With
probability 1?pb ?, 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 rg ? < rb ?, pg ? > pb ?, and
pg ?(1 + rg ?) > pb ?(1 + rb ?).
The lender can’t observe in which project the borrower invests and
so it charges all borrowers the same interest rate rL ?. The lender
lends an amount L and pays interest rD ? on funds acquired from
depositors.
??
Suppose that when rL ? > rL
the lender requires the borrower to
post collateral. Let cL ? denote the collateral-to-loan ratio. That is,
cL ? = C/L. And let c?L ? denote the minimum collateral-to-loan ratio
such that the borrower is indifferent between projects G and B
??
even though rL ? > rL
.
Round all numeric answers to at least three decimal places.
Q1.1
2 Points
Suppose rg ? = 0.08, rb ? = 0.10, pg ? = 0.99, pb ? = 0.4, rD ? =
0.02, L = 100. Find the value for rL? ? such that the borrower is
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indifferent between projects G and B. Round to three decimal
places.
???? ???????
0.066
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Q1.2
1 Point
Suppose that the lending rate is rL ? =
0.16. Find c?L ?.
0.094
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Q1.3
1 Point
Suppose that the lending rate is rL ? =
0.20. Find c?L ?.
0.134
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Q1.4
2 Points
Explain in words why the imposition of a collateral requirement
eliminates the moral hazard problem in the model.
The collateral requirement requires borrower to make some
part of his assets as the collateral, and if he cannot repay the
money he borrowed before the due date, then he will lose his
collateral. This can reduce the moral hazard problems because
when those who choose not to repay the money, will also lose
even more when losing their collateral.
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???? ???????
Q2
11 Points
A competitive lender lends an amount L and faces a cost of
obtaining funds equal to:
C(L) = (1 + ? ? L) ? L.
The interest rate on loans is rL ?. Suppose that only a fraction p(rL ?)
of borrowers repay their loans, where:
p(rL ?) = e?0.965?rL
?
As we have been assuming, borrowers that default pay the lender
nothing. Answer the following.
Round all numeric answers to at least three decimals places.
Q2.1
1 Point
Derive an expression for the loan supply function that specifies the
quantity of loans supplied Ls as a function of the lending rate rL ?.
Assume ?
= 0.00001. Show your work.
Submit your answer as an image file.
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Q2.2
1 Point
What will be the quantity of loans supplied for rL ? =
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15.0188
???? ???????
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Q2.3
1 Point
What will be the quantity of loans supplied for rL ? =
0.025?
28.3887
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Q2.4
1 Point
What will be the quantity of loans supplied for rL ? =
0.05?
27.0155
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Q2.5
1 Point
max
Find the value of lending rate rL
that maximizes the quantity of
loans supplied? (You can find this either using a graphing tool or
with calculus)
Enter your answer here
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Q2.6
4 Points
Suppose the demand for loans is given by:
3
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Ld =
3 ?
rL ?
????
???????
Either
by hand
or using a computer, construct a plot of the
equilibrium and identify the equilibrium lending rate, the quantity of
loans supplied, and the quantity of loans demanded on your plot.
You graph does not have to be to scale.
Submit your answer as an image file.
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Q2.7
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2 Points
For the previous question, was there equilibrium credit rationing?
???? ???????
Explain how you know.
No, because equilibrium credit rationing means there is more
demand than the supply of loans, so the graph of the supply
curve and the demand curve will have no intersection, however,
in the previous question, the two graphs have an intersection.
So there isn’t an equilibrium credit rationing.
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Q3
2 Points
A bank in your area – 1st Anthill Bank – is offering home mortgages.
You learn that a loan applicant with $50,000 annual income and
cash for a $20,000 downpayment, can receive a $100,000 home
loan with an 8% interest rate. Your annual income is $50,000 and
you only have enough cash for a $10,000 downpayment. Suppose
that you apply for a $100,000 loan from 1st Anthill. The loan officer
reviews your financial information and will only lend you the funds
at an interest rate of 10%.
Based on the information provided, is there credit rationing in this
scenario? Clearly explain why or why not.
No, there isn’t, because even though the interest of the loan for
those who cannot pay $10,000 for the downpayment is higher,
the 1st Anthill Bank still keeps the quantity that they used to
supply, and doesn’t refrain from lending, so the demand of the
loan cannot be more than the supply.
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Q4
4 Points
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Banks engage in number of activities that help to limit the problems
of adverse selection and moral hazard. For each of the following,
????whether
???????
identify
the measure taken is intended reduces moral
hazard or adverse selection.
Q4.1
1 Point
Banks screen loan applicants by checking their credit histories and
verifying their employment.
? Adverse selection
? Moral hazard
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Q4.2
1 Point
Banks write contracts that specify what borrowers are allowed to
purchase with the borrowed funds and what other types of actions
must undertake, e.g., mortgage contracts require borrowers to
purchase a fire insurance policy for the purchased home.
? Adverse selection
? Moral hazard
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Q4.3
1 Point
Banks require that borrowers post collateral as part of the loan
agreement.
? Adverse selection
? Moral hazard
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Q4.4
1 Point
Banks form relationships with borrowers so that borrowers don’t
always have to be subjected to the full screening process each
time they take out a loan.
? Adverse selection
? Moral hazard
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