THE UNIVERSITY OF SYDNEY
School of Economics
ECOS3010 Monetary Economics
END OF SEMESTER EXAMINATION
SEMESTER 1, 2021
Instructions:
1. Under NO circumstances will late submission be accepted. No exam will
be accepted via emails. If you need accommodation for your exam due to injury,
illness, or misadventure, please apply for Special Consideration.
2. Answer all 4 questions in Part A. Each question is worth 5 marks. Answer
all 3 questions in Part B. Each question is worth 10 marks. The whole exam is
worth 50 marks.
3. Handwrite your answers using a dark pen on white paper, A4 size, then
scan your handwritten answer to create a single PDF and upload the PDF le.
Organise your answers section by section, in the same order as the questions
below, clearly labelling each part (a) , (b) , etc. Do not write the questions
again on your answer sheet. Show all working. Present your answers clearly and
concisely. Draw and label charts in a format that is accurate and comprehensive.
The way you organise your answers will be a factor in your overall mark.
4. Carefully explain your work.
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Section A: Question 1-4, answer True, False or Uncertain. Brie y explain your answer.
Each question 5 marks.
A1. In the Lucas price surprise model, if the young can observe the amount of young
individuals on his own island, the relationship between in ation and output must be negative
under random in ation.
A2. For a country in a currency union, scal policy is more important than monetary
policy.
A3. In the model of illiquidity, the Tobin e¤ect does not exist without banks.
A4. In the model of demand deposit banking, if a planner exists, the planner can o¤er
a consumption allocation that features full risk sharing.
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Section B: Question 5-7. Each question 10 marks.
5. Consider the standard OLG model with money. Individuals are endowed with 10
units of the perishable consumption good when young and nothing when old. There are
1000 individuals in every generation. Each generation has identical preferences where
u(c1; c2) = c1 c2:
There exists one asset in the economy money. The money supply grows at a gross rate
z every period, Mt = zMt1 where z 1. The new money created is used to nance
government purchases G in real terms. The initial old are endowed withM0 units of money.
We focus on stationary allocations.
(a) Find an individual s budget constraints when young and when old. Combine them
to form the individual s lifetime budget constraint. (2 marks)
(b) Solve for the optimal consumption allocation (c1; c2) chosen by the individual in a
stationary monetary equilibrium. (2 marks)
(c)Write down the government s budget constraint and show how government purchases
G depend on the growth rate of money supply z. (1 mark)
(d) Does the relationship between G and z resemble the La¤er curve Why or why not
(1 marks)
Now we introduce another asset into the economy nominal bonds. Nominal bonds are
issued by the government and pay a net nominal interest rate i in each period where i > 0.
The government imposes a legal restriction such that individuals must carry a real money
balance of at least q units of the consumption good from young to old. That is, the amount
of money held by a young individual should be at least worth q units of the consumption
good. Assume that q is a small number and exogenously given.
(e) Let bt denote a young individual s holding of the nomina bonds. Find an individual s
budget constraints when young and when old. (1 mark)
(f) Solve for the optimal choices of bond holding and consumption allocation (b; c1; c2).
(2 marks)
(g) Explain how the choices of (b; c1; c2) would change if q is very big but less than 10
Characterize the choices of (b; c1; c2) as much as you can.(1 mark)
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6. Consider the model of random relocation. There are two islands. In each period, N
of two-period lived individuals are born on each island and each young individual faces the
probability that he will be relocated to the other island when old. Before the second period
of an individual s life, he learns whether he will be relocated or not. We label the individuals
who are relocated as movers and those who stay as non-movers. In the rst period, there
are N initial old. Each individual is endowed with y units of a perishable consumption
goods when young and nothing when old. Preferences are such that individuals consume
only when old and the expected utility of an individual is given by
u(cm) + (1 )u(cn);
where (cm; cn) denote consumption for movers and non-movers, respectively. Two types of
assets are available in this economy: money and capital. The stock of money is a constant
M . Capital matures in one period, but it cannot move across islands, nor can claims on
capital be veri ed. If k units of capital are invested, xk units of the consumption goods can
be produced in the next period. Early liquidation of capital yields 0 unit of the consumption
goods. Capital fully depreciates after production.
(a) Without banks, write down an individual s budget constraint in each period of life.
Form an individual s lifetime budget constraint. (1 mark)
(b) Suppose that banks exist and can identify movers and non-movers. Describe how
banks o¤er deposit contracts to individuals. Show the budget constraint faced by a bank.
Use a diagram to illustrate the bank s budget constraint. Please carefully label your dia-
gram. (2 marks)
(c) Write down the resource constraint faced by a planner. Use the diagram you develop
in part (b) to add the planner s resource constraint and illustrate the planner s allocation.
(2 marks)
(d) Use the diagram that you develop in part (b) and part (c) to explain why a constant
money supply cannot achieve the planner s allocation. (1 mark)
Now consider an elastic currency regime where the government allows banks to issue
inside money backed by a bank s assets.
(e) Given that banks can issue inside money, how should a bank make portfolio choices
after taking deposits from individuals (1 mark)
(f) Following part (e), characterize an individual s consumption allocation as much as
you can. (2 marks)
(g) Explain how the consumption allocation that you nd in part (f) is compared with
the planner s allocation that you nd in part (c). (1 mark)
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7. Consider the model of demand deposit banking. There are 1000 three-period-lived
individuals born each period in overlapping generations. In the rst period, there are 1000
initial old and 1000 initial middle-aged. Each individual is endowed with 10 units of the
perishable consumption goods only when young. Preferences are such that no one consumes
when young, but everyone wants to consume in one of the next two periods of life depending
on their types. In particular, an individual is an early consumer who wants to consume in
the second period of life with probability 1=2 and is a late consumer who wants to consume
in the third period of life with probability 1=2. At the end of the rst period, an individual
learns his/her type. Moreover, an individual s type is not observed by anyone else, including
banks. There are two types of assets in this economy: storage and capital. Storage always
yields a gross return of 1 over one period. Capital produces X = 2 units of goods for each
good invested two periods after its creation. If capital is liquidated early, it can be sold at
a price vk = 0:8 and it costs = 0:1 goods per unit of capital to verify that capital is not
fake. Capital fully depreciates after production.
(a) Without banks, write down an individual s budget constraint in each period of life.
(1 mark)
(b) Suppose that banks exist. Show how banks can help both early consumers and late
consumers achieve more consumption. (2 marks)
(c) Following part (b), given that banks cannot observe a consumer/depositor s type,
would depositors have incentives to lie about their types Explain. (1 mark)
(d) Following part (c), explain why a bank run can occur if late consumers hear a rumour
that other late consumers are going to withdraw their deposits early from the bank. How
many people can be paid before banks run out of assets (2 marks)
(e) Can you identify one costless way to avoid the bank run that you nd in part (d)
Explain your answer. (1 marks)
Now we denote c1 as consumption by early consumers and c2 as consumption by late
consumers. The expected utility of an individual can be written as
0:5u (c1) + 0:5u (c2) ;
where u (ci) = (1=ci) for i = f1; 2g.
(f) When banks exist, what is the expected utility of an individual under the bank
contract that you nd in part (b) (1 mark)
(g) Can a bank potentially o¤er a better demand deposit contract than the one that
you nd in part (b) If so, give an example of a better contract and explain your answers.
(2 marks)
END OF EXAMINATION
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