Time allowance: 2 hours. Answer one question from Part A and three ques_x005f tions from Part B. Each question carries 25 percent of the total mark. Please,
explain your answers. A numerical answer without explanation will not give
you full credit.
In cases where a student answers more questions than requested by the ex amination rubric, the policy of the Economics Department is that the student’s
first set of answers up to the required number will be the ones that count (not
the best answers). All remaining answers will be ignored.
Part A
Question A.1
Illustrate the different theories of banking crises. Discuss the role of deposit
insurance in preventing bank runs.
Question A.2
Illustrate the main characteristics of the financial system in a developed or
developing economy (you can choose the specific country on which you focus).
Part B
Question B.1
In our economy there are three dates t = 0, 1, 2 and a single, all-purpose
good at each date. There is a continuum of ex-ante identical agents of measure
1. Each has an endowment of one unit of the good at time t = 0 and nothing at
dates t = 1, 2. There are two assets, a short asset and a long asset. The short
asset produces one unit of the good at date t + 1 for every unit invested at date
t = 0, 1. The long asset produces R = 1.5 units of the good at date 2 for every
unit invested at date 0. If instead it is liquidated at date 1, it produces r = 0.5.
At date 0 each agent is uncertain about his preferences over the timing of
consumption. With probability 1/2 he expects to be an early consumer, who
only values consumption at date 1. With the complementary probability he
expects to be a late consumer, who only values consumption at date 2. Note that
he never values consumption at date 0. Each agent has preferences represented
by a Von Neumann-Morgenstern utility function, with
u(c) = ln c .
ECON3023 TURN OVER
1
Suppose there is a bank operating in a perfectly competitive sector (e.g.,
because of free entry). At date 0 the agents deposit their endowments in the
bank. The bank allocates all agents’ endowments in a portfolio of x units of the
long asset and y units of the short asset. The portfolio (x, y) must satisfy the
budget constraint x + y ≤ 1. Let c1 denote the amount consumed at date 1 by
an early consumer and c2 denote the amount consumed by a late consumer at
date 2. Note that he will consume either c1 or c2 but not both.
a) What is the banking solution That is, what portfolio and consumption
levels will the bank choose
b) Explain why with this solution a bank run is possible.
c) Suppose the government wants to introduce a deposit insurance. What
levels of consumption (c1, c2) should it offer to the consumers to avoid a bank
run
d) Finally, suppose agents’ preferences are represented by u(c) =
2+3c
c
. Is
a bank run still possible
Question B.2
Consider an economy with three dates t = 0, 1, 2 and a single, all-purpose
good at each date. There is a continuum of ex-ante identical agents of measure
1. Each agent has an endowment of one unit of the good at date t = 0 and
nothing at dates t = 1, 2. In order to provide for future consumption, each
agent can invest in two assets, a short asset and a long asset. The short asset
produces one unit of the good at date t + 1 for every unit invested at date
t = 0, 1. The long asset produces R = 1.5 units of the good at date 2 for every
unit invested at date 0 (and produces nothing at date 1).
At date 0 each agent is uncertain about his preferences over the timing
of consumption. With probability 1/2 he expects to be an early consumer,
who only values consumption at date 1. With the complementary probability
he expects to be a late consumer, who only values consumption at date 2.
Note that he never values consumption at date 0. Each agent has preferences
represented by a Von Neumann-Morgenstern utility function u(c) (with u
0 (c) >
0 and u
00 (c) < 0).
Suppose that the agents can invest in the two assets and can trade the long
asset at date 1, i.
e., after they learn whether they are early or late consumers.
Let P be the price of the long asset at date 1. At date 0 each agent invests the
amount x in the long asset and the amount y in the short asset. The portfolio
(x, y) must satisfy the budget constraint x + y ≤ 1. Let c1 denote the amount
consumed at date 1 by an early consumer and c2 denote the amount consumed
by a late consumer at date 2. Note that he will consume either c1 or c2 but not
both.
ECON3023 CONTINUED
2
a) What is the feasible consumption set for each agent
b) Find the equilibrium in this economy, i.e., the price, the portfolio decisions
and the consumption levels. Explain carefully why this is an equilibrium.
c) Find out the feasibility constraints in the case of a benevolent social
planner who maximizes the agents’ expected utility. Illustrate such constraints
in a graph. In the same graph, show the equilibrium market allocation.
d) Suppose agents’ relative risk aversion is lower than 1 (for any level of c). Is
consumption at time 1 in the market solution higher or lower than in the efficient
solution [You need to give a mathematical proof for your answer, without
making further assumptions on the utility function — e.g., do not assume a
CRRA utility function.]
Question B.3
In our economy there are three dates t = 0, 1, 2 and a single, all-purpose
good at each date. There is a continuum of ex-ante identical agents of measure
1. Each has an endowment of one unit of the good at time t = 0 and nothing
at dates t = 1, 2. The agent will consume either at date 1 or at date 2 but
not in both. In order to provide for future consumption, he can invest in two
assets, a short asset and a long asset. The short asset produces one unit of
the good at date t + 1 for every unit invested at date t = 0, 1. The long asset
produces R = 1.2 units of the good at date 2 for every unit invested at date 0
and produces nothing at date 1.
At date 0 each agent is uncertain about his preferences over the timing of
consumption. In particular there are two types of agents: early consumers and
late consumers. Early consumers only value consumption at date 1 and late
consumers only value it at date 2. There are two states of nature, denoted by
s = L, H. The probability of being an early consumer is different in the two
states. At time 0, an agent expects to be an early consumer with probability
λs and a late consumer with probability 1 λs. Let λL = 0.04, λH = 0.06 and
Pr(λL) = 0.9 and Pr(λH) = 0.1 (in other words, state L occurs with probability
0.9 and state H with probability 0.1). Of course, the state of nature becomes
observable at time 1. Moreover, let the agents’ preferences be represented by
the logarithmic utility function: u(c) = ln c.
ECON3023 TURN OVER
3
Suppose that the agents can invest in the two assets at time 0 and can trade
the long asset at time 1, i.e., after they learn the state of the world and whether
they are early or late consumers.
a)State the agent’s problem and the first order condition (FOC), assuming
the problem has an interior solution. [You only have to write the FOC, not
solve it.]
b) Suppose in equilibrium both prices are cash-in-the-market: what is their
expression What is an index of price volatility And if they are not both cash in-the-market, how do your answers change [You only need to write the ex pressions, not derive the exact prices.]
c) Explain why cash-in-the-market prices do not reflect the asset fundamen tal value and in which sense low liquidity determines high volatility.
d) Suppose that the agents are risk neutral. State the agent’s problem.
Explain how to determine the optimal portfolio in equilibrium. [You do not
need to compute the portfolio, just explain the condition to derive it.]
e) If agents are risk neutral, do you expect higher or lower volatility compared
to the case of a logarithmic utility function: u(c) = ln c [You do not need to
compute the price volatility, but give a clear explanation.]
ECON3023 END OF PAPER