04.05.2023 Banks III#

last Lecture: Credit Market Failures

Wealth and Credit#

Decisions by the Banks and Lenders

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Contributions by Lender

  • Collateral (Sicherheit)

  • equity (Eigenkapital)

reduces Risk for Bank => higher lending

2 Period Model#

  • \(y_1\) and \(y_2\) (income now and then)

  • \(c_1, c_2\) (consumption)

  • saving possible today

  • interest rate r

Constraint#

Consumption Possibilities $\( c_1 + s = y_1 \\ c_2 = y_2 + (1+r)s \\ \implies s = \frac{y_2-y_2}{1+r} \\ \)\( Lifetime budget constraint (LBC) \)\( \underbrace{c_1 + \frac{y_2-y_2}{1+r}}_{\text{present value of consumption}} = \underbrace{y_1+ \frac{y_2}{1+r}}_{\text{present value of income}} \)$

Preferences#

Consumer Preferences: \(U(c_1, c_2)\)

  • consumption smoothing advised

  • maximization

Equilibrium#

\[ \max U(c_1, c_2) s.t. \ c_1 + \frac{y_2-y_2}{1+r}= y_1+ \frac{y_2}{1+r} \]

Example (Saver):

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Problem: Credit-rationed borrowers (borrow limit)

  • not able to perfectly smooth from future to present

  • every possibility to borrow is used

  • every extra income is consumed today

=> marginal propensity to consume \(c=1\)

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Roles of Banks#

Goal: maturity transformation: short-run to long run

Problem: Liquidity Risk

  • fractional reserves not enough for customers demand

  • panic -> bank run

Solution: Lender of Last Resort (LOLR)

Objectives of LOLR:

  • interdependence in banking sector (uncertainty spreads)

    • negative spillover effect

  • avoid moral hazard (Too big to fail)

Lending and Inequality#

  • inly some people are able to prfit by lending

  • credit rationing do not profit from borrowing