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ECOS 3010 Monetary Economics

THE UNIVERSITY OF SYDNEY
School of Economics
ECOS 3010 Monetary Economics
MID-SEMESTER EXAMINATION
April 24, 2020
Instructions:
1. Time allowed: 24 hours (Friday, April 24, 6 pm – Saturday, April 25, 5:59
pm, Sydney Time).
2. Answer all 4 questions in Part A. Each question is worth 1.5 marks.
Answer all 4 questions in Part B. Each question is worth 6 marks. The whole
exam is worth 30 marks.
3. TYPE your work (including all mathematical equations). Your work
must be submitted as a typed .pdf …le, no exceptions. Untyped work will not
be marked. You can draw a graph by hand, scan it, and include it as a …gure
in the PDF. Please don’t forget to include your name and student number.
4. Carefully explain your work.
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ECOS3010: Midterm Exam (Total: 30 marks)
Section A: Question 1-4, answer True, False or Uncertain. Brie‡y explain
your answer. (each question is worth 1.5 marks)
1. The lack of double coincidence of wants precludes people from using credit for transactions.
2. When the population is growing, …xing the price level is the optimal policy.
3. To …nance the same amount of government purchases, using a lump-sum tax is better
than using the in‡ation tax (money creation).
4. In the Lucas price surprise model where monetary policy is nonrandom, the young
can always infer which island they live on no matter how the young population is distributed
between the two islands.
— — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — –
Section B: Answer all 4 questions. Each question is worth 6 marks.
5. (6 marks) Consider the standard OLG model with money and growing population.
Individuals are endowed with y units of a perishable consumption good when young and
nothing when old. Individuals want to consume both when young and when old. Let
Nt = nNt1 and Mt = zMt1 for every period t, where Nt are the number of people born
in period t and Mt is the money stock in period t. Consider the case in which z and n are
both greater than 1. The money created each period is distributed as a lump-sum transfer
to each old individual worth at units of consumption goods. Each generation has identical
preferences where
u(c1;t; c2;t+1) = ln(c1;t) + ln(c2;t+1);
where c1;t is the amount of the good that is consumed in the …rst period of life by an
individual born in period t, and c2;t+1 is the amount the same individual consumes in the
second period of life. is the discount factor and 0 < < 1.
(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 (c 1; c 2) chosen by the individual in a
stationary monetary equilibrium. Note: express (c 1; c 2) as a function of exogenous parameters (z; y; ; n) in the model. at is not an exogenous variable. (2 marks)
(c) Solve for the social planner’s golden-rule allocation. Under what condition(s) will the
monetary equilibrium coincide with the golden-rule allocation? How would you interpret
your results? (2 marks)
6. (6 marks) Consider the Lucas price surprise model. The total population across the
two islands is constant over time. Half of the old individuals in any period live on each
of the islands. The old are randomly distributed across the two islands, independently of
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where they lived when young. The young are distributed unequally across the islands, with
1=4 of the young living on one island and 3=4 of the young living on the other island in
each period. Each island has an equal chance of having the large population of the young
in any single period. The money market clearing condition on island i is given by
Nili
t(pi t) = 1
pi t
Mt
2 ;
where Ni; lti and pi t represent the population of the young, labor supply and price on island
i, and Mt is the money supply in period t.
(a) Suppose that monetary policy is nonrandom and the growth rate of money supply is
zt = z. Use a graph to show how in‡ation and output are related and explain your answer.
(3 marks)
(b) Suppose that monetary policy is random such that zt = 1 with probability 1=2 and
zt = 4 with probability 1=2. What are the potential prices on the two islands? Would a
higher growth rate of money supply associated with a higher level of output? Explain your
answer. (3 marks)
7. (6 marks) Consider the standard OLG model with money. Individuals are endowed
with y units of a perishable consumption good when young and nothing when old. There
are N individuals in every generation. Each generation has identical preferences where
u(c1;t; c2;t+1) = (c1;t)1 2 + (c2;t+1)12 ;
where c1;t is the amount of the good that is consumed in the …rst period of life by an
individual born in period t, and c2;t+1 is the amount the same individual consumes in the
second period of life.
There exists one asset in the economy –money. The money supply grows at a constant
rate z; where Mt = zMt1 and z > 1. The new money created is used to …nance government
purchases of g goods per young individual in every period. The initial old are endowed with
M0 units of money. In the following, 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. (1 mark)
(b) Solve for the optimal consumption allocation (c 1; c 2) chosen by the individual in a
stationary monetary equilibrium. How do (c 1; c 2) depend on z? (1 mark)
(c) Find the government budget constraint. Express government purchases g as a function of z and other exogenous parameters in the model. (1 mark)
Now assume individuals do not receive any endowment when young or old. Instead,
each individual has to supply labour l1;t to produce output when young. Out of the goods
produced, each young individual consumes c1;t and sells the remaining goods to the old.
One unit of labour supply produces one unit of the consumption good. Each generation has
identical preferences where
u(c1;t; c2;t+1; l1;t) = (c1;t)1 2 + (c2;t+1)1 2 l1;t;
where c1;t is the amount of the good that is consumed in the …rst period of life by an
individual born in period t, and c2;t+1 is the amount the same individual consumes in the
second period of life.
(d) Find an individual’s budget constraints when young and when old. Combine them
to form the individual’s lifetime budget constraint. (1 mark)
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(e) Solve for the optimal consumption and labour supply (c 1; c 2; l1) chosen by the individual in a stationary monetary equilibrium. (1 mark)
(f) How do (c 1; c 2) depend on z? How does l1 depend on z? Brie‡y explain the intuition
for your answer. (1 mark)
8. (6 marks) Consider the following OLG economy with N individuals in each generation. Individuals are endowed with y units of the consumption good when young and
nothing when old. Fiat money is supplied by the government. The initial old are endowed
with M0 units of money. The growth rate of the money supply is z where Mt = zMt1 and
z > 1. Newly printed money is used to …nance government spending. Preferences are such
that individuals would like to consume in both periods of life and young individuals also
value government spending. That is, u(c1;t; c2;t+1; gt) = ln(c1;t +gt)+ ln c2;t+1, where gt
is the amount of government spending per young individual in real terms and gt < y. We
focus on stationary allocations.
(a) Write down the …rst- and second-period budget constraints of a typical individual
in period t. (1 mark)
(b) Combine the …rst- and second-period budget constraints to …nd the individual’s
lifetime budget constraint. (1 mark)
(c) Find the rate of return on money. (1 mark)
(d) Solve for the optimal choice of (c 1; c 2) in a stationary equilibrium. What is the level
of government spending g consumed by the young? (2 marks)
(e) How does a change in z a¤ect the optimal (c 1; c 2) and g? Explain. (1 mark)
END OF EXAMINATION
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