Econ 208

1. Econ 208 MarekKapicka Lecture 15 Financial Intermediation

2. 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

3. 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

4. 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

5. A Liquidity ProblemTiming • Time • Two assets: • Liquid, short-term (short) asset • unit of consumption in period t can be converted to unit of consumption in period • Illiquid, long-term (long) asset • unit of consumption in period can be converted into units of consumption in period • Long asset yields more in the long run, but nothing in the short run!

6. A Liquidity ProblemPreferences • Liquidity preference: Two types of consumers: • Early consumers: only want to consume in period 1 • Late consumers: are indifferent about the timing of consumption • The consumer learns about his type at the beginning of period

7. An Example of Early Consumers

8. A Liquidity ProblemPreferences • Probability of being early: • Preferences of a consumer: expected utility • Trade-off: investing in long asset yield higher return but does not insure against the risk of being an early consumer

9. A Liquidity Problem • Autarkic Solution • Market Solution • Efficient Solution • Banking Solution

10. 1. Autarkic Solution • The consumer has initial wealth • Invests fraction in the short (liquid) asset • Chooses to maximize

11. 1. Autarkic SolutionThe Budget Constraint

12. 1. Autarkic Solution • If the utility is logarithmic, the solution is • If increases, increases • If increases, decreases

13. A Liquidity Problem • Autarkic Solution • Market Solution • Efficient Solution • Banking Solution

14. 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

15. 2. A Market SolutionMarket vs. Autarky Market Equilibrium Autarkic choices

16. A Liquidity Problem • Autarkic Solution • Market Solution • Efficient Solution • Banking Solution

17. 3. The Efficient SolutionWhat is efficiency? • Pareto Efficiency: What would a social planner, not bound by markets, do? • Social planner: • Choose feasible consumption • Choose the amount and the society invests in illiquid (long) and liquid (short) assets

18. 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

19. 3. The Efficient SolutionSocial Planner’s problem • Social planner: • Maximize the expected utility • First order condition

20. 3. The Efficient SolutionCase 1: Too little liquidity in the market solution Market Equilibrium Efficient Solution

21. 3. The Efficient SolutionCase 2: Too much liquidity in the market solution Efficient Solution Market Equilibrium

22. 3. The Efficient SolutionCase 3: The right amount of liquidity in the market solution Market Equilibrium = Efficient solution

23. 3. The Efficient SolutionWhat next? • In general, the market solution is not efficient • How to get efficiency? • Can banking improve on the market solution?

24. A Liquidity Problem • Autarkic Solution • Market Solution • Efficient Solution • Banking Solution

25. 5. Banking SolutionA note on Information Structure • It is reasonable to assume that agent’s type is private information • Only the agent knows if he is early or late • No one else cannot observe it • The (late) agents will not want to misrepresent their type if . • This inequality holds in the efficient allocation

26. 5. Banking Solution • A bank • Collects depositors’ investments at time 0 • Invests in a portfolio • Offers to pay consumers (A deposit contract) • Free entry into the banking sector • Banks maximize investors’ expected utility

27. 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

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

29. 5. Banking SolutionEquilibrium without runs • To make the problem interesting, we assume that • We also assume that the illiquid asset can be liquidated in period 1 to yield

30. 5. Banking SolutionEquilibrium without runs Equilibrium without runs

31. 5. Banking SolutionEquilibrium with runs • Assume that the bank operates under a sequential service constraint: • Everyone who comes to the bank in period 1 is paid , until bank resources are depleted • The liquidated value of all the bank’s assets is

32. 5. Banking SolutionEquilibrium with runs • Suppose that everyone decides to withdraw in period 1 • Since • Not everyone in can be paid in period 1 • Those who wait until period 2 will get nothing • The bank will become insolvent

33. 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)