Econ 208

Marek KapickaLecture 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 ProblemTiming

A Liquidity ProblemPreferences

An Example of Early Consumers

A Liquidity ProblemPreferences

A Liquidity Problem1. Autarkic Solution2. Market Solution3. Efficient Solution4. Banking Solution

1. Autarkic Solution

1. Autarkic SolutionThe Budget Constraint

1. Autarkic Solution

A Liquidity Problem1. Autarkic Solution2. Market Solution3. Efficient Solution4. Banking Solution

2. A Market SolutionMarket 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 SolutionMarket vs. Autarky

Autarkic choices

Market Equilibrium

A Liquidity Problem1. Autarkic Solution2. Market Solution3. Efficient Solution4. Banking Solution

3. The Efficient SolutionWhat is efficiency?

3. The Efficient SolutionSocial planner’s problem Social planner:

Maximize the expected utility

Subject to

WLOG assume that late consumers only consume in period 2

3. The Efficient SolutionSocial Planner’s problem Social planner:

Maximize the expected utility

First order condition

3. The Efficient SolutionCase 1: Too little liquidity in the market solution

Market Equilibrium

Efficient Solution

3. The Efficient SolutionCase 2: Too much liquidity in the market solution

Market EquilibriumEfficient Solution

3. The Efficient SolutionCase 3: The right amount of liquidity in the market solution

Market Equilibrium = Efficient solution

3. The Efficient SolutionWhat next? In general, the market solution is

not efficient How to get efficiency?

Can banking improve on the market solution?

A Liquidity Problem1. Autarkic Solution2. Market Solution3. Efficient Solution4. Banking Solution

5. Banking SolutionA note on Information Structure

5. Banking Solution

5. Banking SolutionEquilibrium 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 SolutionEquilibrium without runs Maximize the expected utility

First order condition

Identical to the social planner’s problem

The (good) equilibrium is efficient!

5. Banking SolutionEquilibrium without runs

5. Banking SolutionEquilibrium without runs

Equilibrium without runs

5. Banking SolutionEquilibrium with runs

5. Banking SolutionEquilibrium with runs

Suppose that everyone decides to withdraw in period 1

Since

1. Not everyone in can be paid in period 12. Those who wait until period 2 will get

nothing The bank will become insolvent

5. Banking SolutionEquilibrium 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)