Econ 208

1. Econ 208 Marek Kapicka 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

6. A Liquidity ProblemPreferences

7. An Example of Early Consumers

8. A Liquidity ProblemPreferences

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

10. 1. Autarkic Solution

11. 1. Autarkic SolutionThe Budget Constraint

12. 1. Autarkic Solution

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?

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

26. 5. Banking Solution

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

30. 5. Banking SolutionEquilibrium without runs Equilibrium without runs

31. 5. Banking SolutionEquilibrium with runs

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)