Exam Microeconomics of Banking

Prof. Dr. Isabel Schnabel
Johannes Gutenberg University Mainz
Exam
Microeconomics of Banking
Summer term 2007, 01.08.2007, 11.30 a.m. –13.00 p.m.
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Microeconomics of Banking
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1. Credit rationing (45 points)
100 identical entrepreneurs need to finance an indivisible investment project, which
requires an investment of one unit. Entrepreneurs can choose between two investment projects. The first project yields a return of RG = 2 with probability πG = 0.8,
and otherwise a return of zero. The other project yields a return of RB = 2.2 with
probability πB = 0.6, and zero otherwise. The project choice can be observed only
by the entrepreneur. The projects shall be financed through banks, which offer loans
to the entrepreneurs at an interest rate r (i. e., a gross interest rate of 1 + r) and
finance themselves through deposits, whose interest rate is rd (corresponding to a
gross interest rate of 1 + rd ). The projects of the 100 entrepreneurs are uncorrelated, such that the law of the large numbers applies and that (approximately) just
the share of πG or πB of the projects is successful. Hence, you can assume that
the loan portfolio of the bank is safe. There is perfect competition in the banking
sector.
(a) Efficient project choice (3 points) Which project should be carried out
from a social welfare perspective?
(b) Project choice of an entrepreneur (7 points)
(b1) What is the expected profit of an entrepreneur as a function of the loan rate r
if the entrepreneur chooses the “good” project?
(b2) What is the expected profit of the entrepreneur as a function of the loan rate
r if the entrepreneur chooses the “bad” project?
(b3) What is the critical loan rate r crit , above which the entrepreneur chooses the
“bad” project?
(c) Gross earnings and profits of the bank (15 points)
(c1) What is the expected gross return (before subtracting interest payments on
deposits) of the bank per invested unit as a function of the loan rate r?
(c2) Depict graphically the expected gross return of the bank per invested unit as a
function of the loan rate r. Write down the function values of the most important
points of the function in your graph. At which point reaches the gross return of the
bank its maximum value?
Microeconomics of Banking
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(c3) What is the expected profit of the bank per invested unit as a function of the
loan rate r and the deposit rate rd ?
(c4) Show that perfect competition in the banking sector implies that banks will
d
d
or 1 + r = 1+r
, respectively. Explain why
require a gross loan rate of 1 + r = 1+r
πG
πB
the loan rate is always higher than the deposit rate.
(d) Credit rationing
(9 points)
(d1) Assume that the market-clearing loan rate is 0.3. Which loan rate will the bank
offer? Which project will the entrepreneur choose? Is there credit rationing? Use
your graph from (c 2) to answer the question.
(d2) Answer the questions from (d1) for the case that the market-clearing loan rate
is 0.5.
(d3) Answer the questions from (d1) for the case that the market-clearing loan rate
is 1.2.
(e) Collateral (11 points) Assume now that each entrepreneur has to provide
collateral C in order to obtain a loan. Th collateral will be transferred to the bank
if the project is not successful. The liquidation value of collateral is equal to zero,
i. e., the collateral has no value for the bank.
(e1) What is the expected profit of an entrepreneur as a function of the loan rate r
and collateral C if the entrepreneur chooses the “good” project?
(e2) What is the expected profit of an entrepreneur as a function of the loan rate r
and collateral C if the entrepreneur chooses the “bad” project?
(e3) What is now the critical loan rate r crit as a function of C, above which the
entrepreneur chooses the “bad” project?
(e4) Explain why the provision of collateral mitigates the problem of credit rationing.
Microeconomics of Banking
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2. True or false? (25 points)
Are the following statements true or false? Explain your results economically. Correct answers do not yield any points if the explanation is missing or wrong.
(5 points each)
1. In the model by Diamond and Dybvig (1983), “late” consumers are strictly
worse off under liquidity insurance than in the market solution, therefore, they
will not be willing to deposit their money in the bank in period 0.
2. If in the model by Diamond and Dybvig (1983), first-best consumption of
the “early” consumer C1∗ is larger than first-best consumption of the “late”
consumer C2∗ , the first-best solution cannot be implemented by a financial
intermediary.
3. Consider the model by Diamond (1984). In the case of a direct financing
relationship between investors and entrepreneurs using a contract with nonmonetary penalties, it does not matter for the level of social welfare how high
the penalty is chosen because there will be no penalty payment in equilibrium.
4. In the model by Diamond (1984), the involvement of a financial intermediary
can only lead to an increase in social welfare if the bank finances several
entrepreneurs.
5. In the model by Bester (1985), “bad” types have to provide particularly high
collateral.
3. The trade-off between competition and stability in the
banking system (20 points)
Topics was not covered in class.