Crises and bailouts

Question 1

Which model states that government guarantees ensure stability of financial system?

Answer 1

The Diamond-Dybvig model

Question 2

Which model states that government guarantees lead to moral hazard?

Answer 2

The Kareken-Wallace model

Question 3

State the three basic assumptions of the Diamond Dybvig-model

Answer 3

• Some agents experience liquidity shocks (leading them to consume impatiently)
• Production technology is risk free but involve illiquid assets
• Banks transform illiquid assets into liquid deposits

Question 4

What can an agent to, in the Diamond-Dybvig model

Answer 4

Period 0
♠ decide whether to invest in the production technology or to deposit in a bank.

Period 1
♠ observe one’s liquidity shock
♠ decide on investment termination and deposit withdrawals
♠ if going to the bank – a random position in the bank queue
♠ consumption and storage decision

Period 2
♠ liquidate remaining investments and deposits ♠ consumption decision

Question 5

What is the expected utility of investing in the production technology (in the Diamond-Dybvig model)?

Answer 5

Probability (type 1) × goods × MU + Probability (type 2) × goods × MU

Question 6

State the formulas for “goods” that the bank must promise for people to use the bank (in the Diamond-Dybvig model)?

Answer 6

For impatient customers: good = q = bank’s promised return = goods returned from technology (= 1.5 in example)

For patient customers:
(Technology return period 2 * (q * (W/D))) / 1 - (W/D)

Question 7

What is the proportion of successful withdrawals in case of a bank run?

Answer 7

W* / D = 1 / q

Question 8

What is the expected utility in case of a bank run?

Answer 8

Proportion of successful withdrawals * (bank’s original utility function BUT with patient customers receiving the same number of goods as the impatient customers (1.5 in example))

Question 9

How do you find the acceptable probability of a bank-run?

Answer 9

Call the probability π, use π and 1-π to calculate expected value of having the bank with or without bank run, make it an inequality in relation to expected value of technology, then solve for π

Question 10

Remedies to bank runs

Answer 10

The government can offer deposit insurance – guaranteeing a gross return equal to q.

Banks can suspend convertibility if more than (0.5 D) depositors show up and want to withdraw in period 1.

Question 11

Name two basic assumptions of the Kareken-Wallace model

Answer 11

• No information asymmetries

* Complete markets – trade in state-contingent claims

Question 12

What formula describes the no-arbitrage condition in the Kareken-Wallace model?

Answer 12

P(A) + P(B) = 1 / (1+R)

Question 13

State the bank’s budget constraint in the Kareken-Wallace model

Answer 13

P(A) * Q(A) + P(B) * Q(B) = D

Question 14

State the banks basic profit formula in the Kareken-Wallace model

Answer 14

Profit = max{Q(S) – (1+r) D , 0 }

Question 15

State the formula for the value of Qbar in the Kareken-Wallace model

Answer 15

Qbar = D / (P(A) + P(B))

Question 16

State the formula for the bank’s expected profit in the Kareken-Wallace model

Answer 16

= π(A) × max{Q(A) –(1+r)D, 0} + π(B) × max{Q(B) –(1+r)D, 0}

Question 17

Why can you not simultaneously be in favor of the Kareken-Wallace model and the Diamond-Dybvig model?

Answer 17

Because the deposit insurance proposed by Diamond-Dybvig to avoid bank runs may distort investment incentives, as Kareken-Wallace point out