Question 2. Bank Run. Consider the Diamond-Dybvig model we discussed in class. Suppose marginal utility of consuming c is given by c-². Gross interest rate is R = 1.5. Time preference is ẞ = 0.9. Probability of becoming first type is λ = 0.2. a) What is the efficient consumption level of type 1 (c)) and type 2 ( c). You need to solve for optimality condition and resource constraint. Answer must be numeric. b) Explain why 1 < c^, and c½ < R is better than c₁ = 1 and C2 = R. c) Now consider the contract we discussed in class that the bank offers. Suppose r₁ = 1. Explain why there wouldn't be a bank run in this situation. Why this is not a desirable contract?

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Chapter4: Utility Maximization And Choice
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Question 2. Bank Run. Consider the Diamond-Dybvig model we discussed in
class. Suppose marginal utility of consuming c is given by c². Gross interest
rate is R = 1.5. Time preference is ẞ = 0.9. Probability of becoming first type
is λ = 0.2.
a) What is the efficient consumption level of type 1 (c†) and type 2 (
c). You need to solve for optimality condition and resource constraint.
Answer must be numeric.
b) Explain why 1 < c†, and c½ < R is better than cı
=
1 and C2
=
R.
c) Now consider the contract we discussed in class that the bank
offers. Suppose ri
-
1. Explain why there wouldn't be a bank run in
this situation. Why this is not a desirable contract?
Question 3. Yield Curve. Find the data on yield curve on website of the
Department of the Treasury (link). Plot the yield curve for 2015-10-13 and
2015-11-10.
a) Explain how the yield curve changed? What is the underlying
reason for this change?
b) What is the impact of the chage of the yield curve on bank
profitability and balance sheet?
c) Now, we will focus on 2022 and 2023. Calculate the average yield
of 10 year government bond in February 2022 and February 2023. What
is the change in price of 10 year government bond? What is the impact
on balance sheet of a bank with high share of securities on its balance
sheet. Discuss it's impact on the possibility of a bank run.
Transcribed Image Text:Question 2. Bank Run. Consider the Diamond-Dybvig model we discussed in class. Suppose marginal utility of consuming c is given by c². Gross interest rate is R = 1.5. Time preference is ẞ = 0.9. Probability of becoming first type is λ = 0.2. a) What is the efficient consumption level of type 1 (c†) and type 2 ( c). You need to solve for optimality condition and resource constraint. Answer must be numeric. b) Explain why 1 < c†, and c½ < R is better than cı = 1 and C2 = R. c) Now consider the contract we discussed in class that the bank offers. Suppose ri - 1. Explain why there wouldn't be a bank run in this situation. Why this is not a desirable contract? Question 3. Yield Curve. Find the data on yield curve on website of the Department of the Treasury (link). Plot the yield curve for 2015-10-13 and 2015-11-10. a) Explain how the yield curve changed? What is the underlying reason for this change? b) What is the impact of the chage of the yield curve on bank profitability and balance sheet? c) Now, we will focus on 2022 and 2023. Calculate the average yield of 10 year government bond in February 2022 and February 2023. What is the change in price of 10 year government bond? What is the impact on balance sheet of a bank with high share of securities on its balance sheet. Discuss it's impact on the possibility of a bank run.
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