EFIMM0051 Introduction to the Microeconomics of Banking TB1 2024
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TB1 2024
UNIT CODE: EFIMM0051
UNIT NAME: Introduction to the Microeconomics of Banking
DEADLINE: 24th October 2023 before 13:00
SUBMIT TO BLACKBOARD UNIT SUBMISSION POINT
Overview
• Your summative coursework represents 20% of the final mark for the unit.
• The coursework is in the form of a group presentation.
• Penalties will apply if the coursework is submitted late.
Microeconomics of Banking: Tutorial 2
Exercise 1 Maturity Transformation 100 points
Maturity transformation is one of the key functions of a modern banking system. This exercise builds on the model of liquidity transformation derived in the lecture and studies how maturity transformation makes banks vulnerable to bank runs.
Consider the model from the lecture:
. A competitive bank with access to a long term technology yielding R > 1 per unit of investment at the inal stage t = 2 and λ per unit of investment at the interim stage t = 1.
. In addition, there are M depositors with one unit of endowment each.
. At t = 0, borrowers and banks know that the borrower has a consumption need c1 at t = 1 with probability π and a consumption need c2 at t = 2 with probability 1 - π .
. Borrowers are risk neutral so that their utility function from the perspective of t = 0 is U = πc1 + (1 - π)c2 .
. At t = 0, borrowers deposit their endowment at the bank against the bank’s promise of receiving c1 when withdrawing at t = 1 and c2 when withdrawing at t = 2.
. At the sametime, t = 0, the bank invests I of borrowers’ deposits into the long term technology and saves M - I.
1.1 Liquidity Transformation: Optimal Allocation 20 points
Repeat the derivation of the optimal deposit schedule (c1(F)I , c2(F)I ) from the lecture.
1.2 Beneit of Financial Intermediation 20 points
Recall the solution of autarky from the lecture. Provide, in few sentences, the intuition of liquidity transformation and how it serves depositors.
1.3 Bank Run total of 60 points
Extend the model by an unexpected liquidity shock to depositors. Therefore use the following notation. At t = 0, when agreeing on the deposit schedule (c1 , c2 ) and when making the investment I, both bank and depositors believe that a portion of π depositors will withdraw at t = 1 and 1 - π at t = 2. Now instead, assume that at t = 1, banks and depositors learn that a share π、> π of depositors want to withdraw at t = 1, i.e. more depositors than expected want to withdraw at t = 1. Since investment in the long term technology I is already decided at t = 0, the bank has to liquidate L of the long term technology in order to satisfy the increased deposit withdrawals. Recall, liquidation at t = 1 yields a per unit return of ` < 1.
For your derivations assume that I = (1 - π)M so that c2 = R and c1 = 1. Proceed as follows:
1.3.1 15 points
Determine how much of the long term technology has to be liquidated L in order to satisfy the increased deposit withdrawals π、Mc1 .
1.3.2 15 points
Given the liquidation L of the long term technology, how much can depositors with- draw at t = 2 at most. Determine c2(、)(π、).
1.3.3 15 points
Depositors who are supposed to withdraw c2(、)(π、) at t = 2 want to withdraw c1 at t = 1 instead if c2(、)(π、) < c1. Show for which level of π、, t = 2 depositors withdraw at t = 1 as well.
1.3.4 15 points
Interpret briely the above threshold for π、.
2023-10-24