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Money and Banking

Spring 2016

Midterm Exam

Question 1 [18 points]

Consider an economy with three dates (T=0, 1, 2) and the following investment opportunity. If an agent invests $1 in a project at T=0, the project yields $2 at T=2. The project can be liquidated at T=1 but early liquidation yields $1 at T=1.

An agent has $1 and can be of two types. With probability 0.5 the agent is a type-1 consumer and with probability 0.5 the agent is a type-2 consumer.

If an agent is a type1-consumer, he only values consumption at T=1 and his utility function is

where c1 is the amount consumed at T=1. If an agent is a type-2 consumer, he values consumption at both T=1 and T=2 according to the utility function

where c1  and c2  are the amounts consumed at T=1 and T=2, respectively.

a)         What is the expected utility of the agent? [3 Points]

Now consider a bank that invests in these projects. There are N=1000 agents. All agents are identical ex ante in the above sense. Suppose they all deposit $1 each with the bank. The bank offers the following demand deposit contract (d1, d2) where d1  is the amount and agent can withdraw at T=1 and d2  is the amount he can withdraw at T=2.

b)         Suppose d1=1.25. What is the amount d2 that the bank can offer an agent who withdraws at T=2? What is the expected utility of an agent? [3 Points]

For all subsequent questions, suppose the bank offers the deposit contract (d1, d2)=(1.25, 1.5).

c)         A type-2 consumer expects that 680 agents will withdraw at T=1.What is the best

response of the type-2 consumer, i.e. does he has an incentive to run to the bank and withdraw at T=1? [4 Points]

Suppose the government wants to provide deposit insurance or suspend convertibility of demand deposit into cash if too many agents are withdrawing.

d)        What is the maximum number of withdrawals at T=1 that the government can allow for so as to prevent a type-2 consumer from withdrawing at T=1? [6 Points]

e)         What is the minimum amount of deposit insurance that the government needs to provide so as to prevent a type-2 consumer from withdrawing at T=1? [2 Points]

Consider the following economy with three dates (t=0, 1, 2). A firm needs to raise $100 to finance a project at t=0. At t=2, the project can be a failure and pays off nothing or a success which generates $400. The probability of failure is 0.2 and the probability of success is 0.8.

There is an early consumer who has $100 at t=0 and the utility function

There is a late consumer who has $300 at t=1 and the utility function uL = cL0  + cL1  + cL2 .

Suppose the firm issues equity at t=0. At t=1, the equity market reveals whether the project is a success or failure.

a)         What equity contract does the firm offer the early consumer so as to get $100? [4 Points]

b)        What is the expected profit of the firm? [1 Points]

Now suppose the firm seeks bank finance. The bank provides loans to firms and keeps information secret. At t=2 the bank is liquidated and consumers who have deposits with the bank get back what the bank owns at t=2.

The bank offers the early consumer the following demand deposit contract. If the early consumer deposits $100 at t=0, he can withdraw $100 at t=1.

c)         What loan contract does the firm offer the bank so as to get $100 from the bank? [4 Points]

d)        What is the expected profit of the firm? [1 Points]

Free banks in the Free Banking Era issued banknotes. Similarly, national banks in the National Banking Era issued banknotes.

a)         What did free banks use to back their banknotes? [2 Points]

b)        What happened during a bank run in the Free Banking Era and what was the main reason for bank runs? [4 Points]

c)         What happened during a bank run in the National Banking Era? How was it different from a bank run in the Free Banking Era and what were the reasons for the differences? [6 Points]

After the experiences in the Free and National Banking Eras, and in particular, the Great Depression, the banking industry was highly regulated up to 1980s.

d)        What were the main regulations that bank holding companies were facing in that period? [4 Points]

In the late 1980s deregulations ofthe banking industry set in. This led to many bank mergers and an industry consolidation.

e)         What triggered deregulations and the change in banking? [4 Points]