Econ 208 Marek Kapicka Lecture 15 Financial Intermediation

Announcements PS5 will be posted today, due next Thursday before the section (3pm) Give them directly to Xintong, or to her mailbox Read “Zero sum debate” – the Economist article about capital taxation

Why Financial Crises? Key insight: Banks are here to transform illiquid assets to liquid liabilities Depositors prefer to withdraw deposits easily (preference for liquidity) Borrowers need time to repay the loans Tension between both sides of the balance sheet: If everyone wants to withdraw deposits, there is not enough resources

A Liquidity Problem 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

A Liquidity Problem Preferences

An Example of Early Consumers

A Liquidity Problem Preferences

A Liquidity Problem 1. Autarkic Solution 2. Market Solution 3. Efficient Solution 4. Banking Solution

1. Autarkic Solution

1. Autarkic Solution The Budget Constraint

1. Autarkic Solution

A Liquidity Problem 1. Autarkic Solution 2. Market Solution 3. Efficient Solution 4. Banking Solution

2. A Market Solution Market vs. Autarky 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: 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 Autarkic choices Market Equilibrium

A Liquidity Problem 1. Autarkic Solution 2. Market Solution 3. Efficient Solution 4. Banking Solution

3. The Efficient Solution What is efficiency?

3. The Efficient Solution Social planner’s problem Social planner: Maximize the expected utility Subject to WLOG assume that late consumers only consume in period 2

3. The Efficient Solution Social Planner’s problem Social planner: Maximize the expected utility 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 Market Equilibrium Efficient Solution

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? In general, the market solution is not efficient How to get efficiency? Can banking improve on the market solution?

A Liquidity Problem 1. Autarkic Solution 2. Market Solution 3. Efficient Solution 4. Banking Solution

5. Banking Solution A note on Information Structure

5. Banking Solution

5. Banking Solution Equilibrium without runs Later on, we’ll see that banks are prone to runs, but ignore it for now The bank maximizes the expected utility Subject to

5. Banking Solution Equilibrium without runs Maximize the expected utility First order condition Identical to the social planner’s problem The (good) equilibrium is efficient!

5. Banking Solution Equilibrium without runs

Equilibrium without runs

5. Banking Solution Equilibrium with runs

Suppose that everyone decides to withdraw in period 1 Since 1. Not everyone in can be paid in period 1 2. Those who wait until period 2 will get nothing The bank will become insolvent

5. Banking Solution Equilibrium with runs A payoff matrix: late consumer (rows) vs every other late consumer (columns): Note: the run/run payoff is the expected payoff There are two equilibria: No run/No run (good equilibrium) Run/Run (bad equilibrium) RunNo Run Run No Run