Econ 208
Marek Kapicka
Lecture 15
Financial Intermediation
Announcements
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PS5 will be posted today, due next
Thursday before the section (3pm)
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Give them directly to Xintong, or to her
mailbox
Read “Zero sum debate” – the
Economist article about capital taxation
Why Financial Crises?
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Key insight: Banks are here to transform
illiquid assets to liquid liabilities
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Depositors prefer to withdraw deposits easily
(preference for liquidity)
Borrowers need time to repay the loans
Tension between both sides of the
balance sheet:
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If everyone wants to withdraw deposits,
there is not enough resources
A Liquidity Problem
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How to choose between liquid and illiquid
assets?
Liquid assets: can be converted into
immediate consumption without any costs
Illiquid assets: it is costly to convert them
into immediate consumption
People have preference for liquidity: they
are unsure when they need to consume
A Liquidity Problem
Timing
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A Liquidity Problem
Preferences
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An Example of Early Consumers
A Liquidity Problem
Preferences
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A Liquidity Problem
1.
2.
3.
4.
Autarkic Solution
Market Solution
Efficient Solution
Banking Solution
1. Autarkic Solution
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1. Autarkic Solution
The Budget Constraint
1. Autarkic Solution
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A Liquidity Problem
1.
2.
3.
4.
Autarkic Solution
Market Solution
Efficient Solution
Banking Solution
2. A Market Solution
Market vs. Autarky
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In a market, early consumer are
allowed to sell long assets and buy
short assets
We don’t have time to go through this,
but one can show:
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Market can achieve more risk sharing than
autarky
We will see that with banks we can do
even better than that
2. A Market Solution
Market vs. Autarky
Market Equilibrium
Autarkic choices
A Liquidity Problem
1.
2.
3.
4.
Autarkic Solution
Market Solution
Efficient Solution
Banking Solution
3. The Efficient Solution
What is efficiency?
3. The Efficient Solution
Social planner’s problem
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Social planner:
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Maximize the expected utility
Subject to
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WLOG assume that late consumers only
consume in period 2
3. The Efficient Solution
Social Planner’s problem
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Social planner:
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Maximize the expected utility
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First order condition
3. The Efficient Solution
Case 1: Too little liquidity in the market solution
Market Equilibrium
Efficient Solution
3. The Efficient Solution
Case 2: Too much liquidity in the market solution
Efficient Solution
Market Equilibrium
3. The Efficient Solution
Case 3: The right amount of liquidity in the
market solution
Market Equilibrium
= Efficient solution
3. The Efficient Solution
What next?
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In general, the market solution is not
efficient
How to get efficiency?
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Can banking improve on the market
solution?
A Liquidity Problem
1.
2.
3.
4.
Autarkic Solution
Market Solution
Efficient Solution
Banking Solution
5. Banking Solution
A note on Information Structure
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5. Banking Solution
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5. Banking Solution
Equilibrium without runs
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Later on, we’ll see that banks are prone
to runs, but ignore it for now
The bank maximizes the expected utility
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Subject to
5. Banking Solution
Equilibrium without runs
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Maximize the expected utility
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First order condition
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Identical to the social planner’s problem
The (good) equilibrium is efficient!
5. Banking Solution
Equilibrium without runs
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5. Banking Solution
Equilibrium without runs
Equilibrium without
runs
5. Banking Solution
Equilibrium with runs
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5. Banking Solution
Equilibrium with runs
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Suppose that everyone decides to
withdraw in period 1
Since
1.
2.
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Not everyone in can be paid in period 1
Those who wait until period 2 will get
nothing
The bank will become insolvent
5. Banking Solution
Equilibrium with runs
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A payoff matrix: late consumer (rows) vs
every other late consumer (columns):
Run
No Run
Run
No Run
Note: the run/run payoff is the expected payoff
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There are two equilibria:
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No run/No run (good equilibrium)
Run/Run (bad equilibrium)