The Economics of Money, Finance, and Bank Runs — Complete Study Guide
The Econom ics of Money, Finance,
and B ank Ru ns
Lectures 1–11
Lectur e 1: B ank Ru ns and the Diam ond-Dybvig
Model
Chapter 1: In tr odu ction to Fin an cial Cr ises an d the System
Financial systems are essential for the functioning of our economy: they channel savings from
individuals to companies that want to invest and produce. However, the system is inherently fragile.
During the Great Financial Crisis (GFC) or 'Great Recession' of 2007–2008, we witnessed how the
collapse of a single seemingly modest institution, such as the American investment bank Lehman
Brothers, could trigger a global financial and economic meltdown.
When a crisis strikes, credit lending stagnates, and stock and housing markets collapse, resulting in
massive job losses in the real economy. Although we saw similar crises a century ago during the Great
Depression, these phenomena continuously repeat themselves. Even though the actors change—such as
the rise of so-called 'shadow banks' that operate outside the traditional deposit-taking model—the
fundamental mechanisms of instability remain identical.
In combating a crisis, eyes often turn toward the government. However, there is a crucial difference in
response time: fiscal interventions (such as parliamentary-approved bailouts) are slow and politically
fraught, whereas monetary policy (executed by the central bank) can react far more rapidly.
Chapter 2: The Essen ce of a B an k: Matu r ity Tr ansfor m ation
To understand the fragility of the financial system, we must examine the core function of a bank.
Conflict between Lecture Slide and Lecture Explanation
The slide shows a highly stylized balance sheet containing only two components: 'Loans' on the asset side
and 'Deposits' on the liability side. The professor explicitly emphasized that reality is far more complex: a
real bank balance sheet also contains equity (capital) and long-term bonds on the liability side, as well as
stocks and other investments on the asset side. The Diamond-Dybvig model deliberately strips away this
complexity to isolate the absolute essence of banking: maturity transformation.
Page 1 of 27
, The Economics of Money, Finance, and Bank Runs — Complete Study Guide
Maturity Transformation is the process by which a bank transforms short-term liabilities (deposits from
savers that are withdrawable at any time, 'on demand') into long-term assets (loans and mortgages to
businesses and individuals, which are repaid over decades).
This creates a fundamental liquidity problem. A bank can be fully solvent (its long-term loans are
profitable and safe), but it can still fail due to illiquidity (an acute shortage of cash) if all depositors
simultaneously demand their money back.
Chapter 3: The Diam on d-Dybvig Model (1983)
To analyze this phenomenon, we use the Diamond-Dybvig model from 1983. This theoretical framework
is so powerful that Ben Bernanke (former Fed Chair and Nobel laureate in 2022, alongside Diamond and
Dybvig) stated that this model perfectly describes the dynamics of the 2008 credit crisis and the bank
run on Northern Rock.
Model Ingredients and Assumptions
The model features one representative bank and many identical consumers, spanning three time
periods (T=0, 1, 2). There is no endogenous (self-created) risk by the bank; the bank acts purely as a
conduit.
T=0 (Start): All consumers are ex-ante identical and possess an initial endowment of exactly 1.
Utility: Consumers maximize their expected utility. The utility function is concave, implying diminishing
marginal utility (the first apple yields more utility than the twentieth) and therefore risk aversion. There
is no discounting (ρ = 1), meaning consumption today is intrinsically worth the same as consumption
tomorrow.
T=1 (The Shock): An exogenous preference shock (like 'manna from heaven') occurs. Consumers discover
their type:
• A fraction t becomes Type 1 (Early consumer): They want to consume NOW and assign zero value to
consumption at T=2. They are the 'unlucky' ones.
• A fraction 1 - t becomes Type 2 (Late consumer): They want to consume at T=2. They are the 'lucky'
ones.
Production Technology: Investments can be made with the following returns:
• Investment costs -1 at T=0.
• Liquidation at T=1 yields a return of 1 (the investment is liquidated prematurely; there is no gain).
• Waiting until T=2 yields a return of R, where R > 1.
Chapter 4: Tw o Possible Allocation s (Solu tion s)
We investigate two theoretical scenarios to understand how consumers make decisions: one in which
types are unobservable and one in which types can be observed.
Page 2 of 27
, The Economics of Money, Finance, and Bank Runs — Complete Study Guide
Solution 1: Types are UNOBSERVABLE (Autarky)
If types are invisible, binding contracts cannot be written because individuals can lie about their type. In
T=1, Type 1 will withdraw their deposit of 1 and consume it immediately. In T=1, Type 2 has no incentive
to lie and withdraw early: if they do, they receive 1, hold it until T=2, and consume 1. By waiting
honestly, they receive the higher return R.
Conclusion of Solution 1: Everyone acts strictly according to their true type. Every consumer faces a
large, volatile lottery at the outset: a probability t of an outcome of 1, and a probability 1 - t of an
outcome of R. Because agents are risk-averse, this uncertainty lowers their overall expected utility. This
reflects the mathematical property known in financial theory as Jensen's inequality.
Solution 2: Types are OBSERVABLE (Optimal Risk Sharing)
If we could observe each other's type at T=0, we could write an insurance contract before the shock
occurs. Because consumers are risk-averse, they want to reduce the variance of the lottery by sharing
risks.
Mathematical Calculation of the Optimal Allocation:
We maximize expected utility:
max_{c1, c2} E[u] = t · U(c1) + (1 - t) · U(c2)
Subject to the macroeconomic budget constraint:
t · c1 + ((1 - t) · c2) / R = 1
Explanation of the Budget Constraint: At T=0, total deposits equal 1. At T=1, a fraction t of the
population is paid c1. The remaining capital in the economy is then 1 - t · c1. This capital is invested until
T=2 and grows by the factor R. The total pool available at T=2 is thus R · (1 - t · c1). This amount must be
distributed over the remaining fraction (1 - t) of late consumers. Mathematically, c2 = (R / (1 - t)) · (1 - t ·
c1), which rewrites to the budget constraint above.
To calculate optimal consumption, we substitute c2 into the objective function and take the derivative
with respect to c1 (First-Order Condition / FOC):
FOC: t · U'(c1) + (1 - t) · U'(c2) · (R / (1 - t)) · (-t) = 0
t · U'(c1) - t · R · U'(c2) = 0 => U'(c1) = R · U'(c2)
Interpretation of the FOC (U'(c1) = R · U'(c2)):
The optimal solution demonstrates that 1 < c1* < c2* < R. This means late (lucky) types accept slightly
lower future consumption (c2* < R) in order to fund a higher payout for early (unlucky) types (c1* > 1).
The extreme lottery risk from Solution 1 is mitigated; outcomes are closer together, increasing expected
utility for everyone ex-ante.
However, the problem with Solution 2 is that it is unrealistic. In the real world, a bank employee cannot
read your type off your face (types are unobservable), and anyone could claim to be an early consumer.
Page 3 of 27
The Econom ics of Money, Finance,
and B ank Ru ns
Lectures 1–11
Lectur e 1: B ank Ru ns and the Diam ond-Dybvig
Model
Chapter 1: In tr odu ction to Fin an cial Cr ises an d the System
Financial systems are essential for the functioning of our economy: they channel savings from
individuals to companies that want to invest and produce. However, the system is inherently fragile.
During the Great Financial Crisis (GFC) or 'Great Recession' of 2007–2008, we witnessed how the
collapse of a single seemingly modest institution, such as the American investment bank Lehman
Brothers, could trigger a global financial and economic meltdown.
When a crisis strikes, credit lending stagnates, and stock and housing markets collapse, resulting in
massive job losses in the real economy. Although we saw similar crises a century ago during the Great
Depression, these phenomena continuously repeat themselves. Even though the actors change—such as
the rise of so-called 'shadow banks' that operate outside the traditional deposit-taking model—the
fundamental mechanisms of instability remain identical.
In combating a crisis, eyes often turn toward the government. However, there is a crucial difference in
response time: fiscal interventions (such as parliamentary-approved bailouts) are slow and politically
fraught, whereas monetary policy (executed by the central bank) can react far more rapidly.
Chapter 2: The Essen ce of a B an k: Matu r ity Tr ansfor m ation
To understand the fragility of the financial system, we must examine the core function of a bank.
Conflict between Lecture Slide and Lecture Explanation
The slide shows a highly stylized balance sheet containing only two components: 'Loans' on the asset side
and 'Deposits' on the liability side. The professor explicitly emphasized that reality is far more complex: a
real bank balance sheet also contains equity (capital) and long-term bonds on the liability side, as well as
stocks and other investments on the asset side. The Diamond-Dybvig model deliberately strips away this
complexity to isolate the absolute essence of banking: maturity transformation.
Page 1 of 27
, The Economics of Money, Finance, and Bank Runs — Complete Study Guide
Maturity Transformation is the process by which a bank transforms short-term liabilities (deposits from
savers that are withdrawable at any time, 'on demand') into long-term assets (loans and mortgages to
businesses and individuals, which are repaid over decades).
This creates a fundamental liquidity problem. A bank can be fully solvent (its long-term loans are
profitable and safe), but it can still fail due to illiquidity (an acute shortage of cash) if all depositors
simultaneously demand their money back.
Chapter 3: The Diam on d-Dybvig Model (1983)
To analyze this phenomenon, we use the Diamond-Dybvig model from 1983. This theoretical framework
is so powerful that Ben Bernanke (former Fed Chair and Nobel laureate in 2022, alongside Diamond and
Dybvig) stated that this model perfectly describes the dynamics of the 2008 credit crisis and the bank
run on Northern Rock.
Model Ingredients and Assumptions
The model features one representative bank and many identical consumers, spanning three time
periods (T=0, 1, 2). There is no endogenous (self-created) risk by the bank; the bank acts purely as a
conduit.
T=0 (Start): All consumers are ex-ante identical and possess an initial endowment of exactly 1.
Utility: Consumers maximize their expected utility. The utility function is concave, implying diminishing
marginal utility (the first apple yields more utility than the twentieth) and therefore risk aversion. There
is no discounting (ρ = 1), meaning consumption today is intrinsically worth the same as consumption
tomorrow.
T=1 (The Shock): An exogenous preference shock (like 'manna from heaven') occurs. Consumers discover
their type:
• A fraction t becomes Type 1 (Early consumer): They want to consume NOW and assign zero value to
consumption at T=2. They are the 'unlucky' ones.
• A fraction 1 - t becomes Type 2 (Late consumer): They want to consume at T=2. They are the 'lucky'
ones.
Production Technology: Investments can be made with the following returns:
• Investment costs -1 at T=0.
• Liquidation at T=1 yields a return of 1 (the investment is liquidated prematurely; there is no gain).
• Waiting until T=2 yields a return of R, where R > 1.
Chapter 4: Tw o Possible Allocation s (Solu tion s)
We investigate two theoretical scenarios to understand how consumers make decisions: one in which
types are unobservable and one in which types can be observed.
Page 2 of 27
, The Economics of Money, Finance, and Bank Runs — Complete Study Guide
Solution 1: Types are UNOBSERVABLE (Autarky)
If types are invisible, binding contracts cannot be written because individuals can lie about their type. In
T=1, Type 1 will withdraw their deposit of 1 and consume it immediately. In T=1, Type 2 has no incentive
to lie and withdraw early: if they do, they receive 1, hold it until T=2, and consume 1. By waiting
honestly, they receive the higher return R.
Conclusion of Solution 1: Everyone acts strictly according to their true type. Every consumer faces a
large, volatile lottery at the outset: a probability t of an outcome of 1, and a probability 1 - t of an
outcome of R. Because agents are risk-averse, this uncertainty lowers their overall expected utility. This
reflects the mathematical property known in financial theory as Jensen's inequality.
Solution 2: Types are OBSERVABLE (Optimal Risk Sharing)
If we could observe each other's type at T=0, we could write an insurance contract before the shock
occurs. Because consumers are risk-averse, they want to reduce the variance of the lottery by sharing
risks.
Mathematical Calculation of the Optimal Allocation:
We maximize expected utility:
max_{c1, c2} E[u] = t · U(c1) + (1 - t) · U(c2)
Subject to the macroeconomic budget constraint:
t · c1 + ((1 - t) · c2) / R = 1
Explanation of the Budget Constraint: At T=0, total deposits equal 1. At T=1, a fraction t of the
population is paid c1. The remaining capital in the economy is then 1 - t · c1. This capital is invested until
T=2 and grows by the factor R. The total pool available at T=2 is thus R · (1 - t · c1). This amount must be
distributed over the remaining fraction (1 - t) of late consumers. Mathematically, c2 = (R / (1 - t)) · (1 - t ·
c1), which rewrites to the budget constraint above.
To calculate optimal consumption, we substitute c2 into the objective function and take the derivative
with respect to c1 (First-Order Condition / FOC):
FOC: t · U'(c1) + (1 - t) · U'(c2) · (R / (1 - t)) · (-t) = 0
t · U'(c1) - t · R · U'(c2) = 0 => U'(c1) = R · U'(c2)
Interpretation of the FOC (U'(c1) = R · U'(c2)):
The optimal solution demonstrates that 1 < c1* < c2* < R. This means late (lucky) types accept slightly
lower future consumption (c2* < R) in order to fund a higher payout for early (unlucky) types (c1* > 1).
The extreme lottery risk from Solution 1 is mitigated; outcomes are closer together, increasing expected
utility for everyone ex-ante.
However, the problem with Solution 2 is that it is unrealistic. In the real world, a bank employee cannot
read your type off your face (types are unobservable), and anyone could claim to be an early consumer.
Page 3 of 27
