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ECOS3010 economy

创建日期：2024-06-03 17:23:23

所属分类：经济Economics

标签： ECOS3010

economy.

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ECOS3010: Tutorial 2 (Answer Key)

Question 1-5. Answer True, False or Uncertain. Briey explain your answer.
1. According to RBAs denition of monetary aggregates, M1 includes more assets than
M3 does.
False. According to RBAs denition of monetary aggregates, M3 includes M1 plus all
other deposits in the economy. So M3 includes more assets than M1 does.
2. Suppose that the government increases money supply and gives new money to the
old in every period. Comparing monetary equilibrium with the golden rule allocation, we
nd that all future generations achieve a lower level of utility but the initial old enjoys a
higher level of utility in the monetary equilibrium.
False. When the government increases money supply and gives new money to the old in
every period, the allocation in the monetary equilibrium is not the golden rule allocation. In
particular, all future generations in the monetary equilibrium achieve a lower level of utility.
The initial old also achieve a lower level of utility because c2 in the monetary equilibrium
is lower than c2 at the golden rule allocation.
3. Suppose that money supply grows at a constant rate z (z > 1). Comparing monetary
equilibrium and the golden rule allocation, we nd that individuals consume too much when
young and too little when old in the monetary equilibrium.
True. In a monetary equilibrium, ination makes young individuals trade less goods
for money. As a result, the old have less money to purchase goods. Comparing monetary
equilibrium with the golden rule allocation, we nd that individuals consume too much
when young and too little when old.
4. Suppose that the population grows at a constant rate n (n > 1) and money supply
grows at a constant rate z (z > 1), the value of money falls over time.
Uncertain. When the population grows at a constant rate n and money supply grows
at a constant rate z, we can derive moneys rate of return as vt+1=vt = n=z. If n < z, the
value of money falls over time. If n > z, the value of money increases over time. And if
n = z, the value of money stays constant.
5. When the population is growing, xing the price level is the optimal policy.
False. When the population is growing, moneys rate of return is given by vt+1=vt = n=z.
The allocation in the monetary equilibrium is generally not the golden rule allocation. The
optimal policy requires that an individuals budget constraint is identical to the planners
resource constraint. It implies that we need z = 1 for a monetary equilibrium to achieve the
golden rule allocation. In this case, the value of money increases over time and the price
level actually falls over time.
(Note that for question 4 and question 5, my explanation uses the expression of vt+1=vt.
If you cannot memorize the exact expression of vt+1=vt, it is ne to explain your answer in
words as long as the intuition is correct.)
6. Let Nt = nNt1 and Mt = zMt1 for every period t, where z and n are both greater
than 1. The money created each period is used to nance a lump-sum subsidy of at goods
to each young individual.
(a) Find the equation for the budget constraint of an individual in the monetary equilib-
rium. Graph it. Show an arbitrary indi¤erence curve tangent to the budget constraint and
indicate the levels of c1 and c2 that would be chosen by an individual in this equilibrium.
An individuals rst- and second-period budget constraints are
c1 + vtmt y + at and c2 vt+1mt:
1
Combining these two period budget constraints together, we derive the lifetime budget
constraint
c1 +
vt
vt+1
c2 y + at :
The value of money is derived from the money market clearing condition (when aggregate
money supply equals aggregate money demand),
Nt (y + a
c1) = vtMt ! vt = Nt (y + a
c1)
Mt
:
It follows that moneys rate of return is
vt+1
vt
=
Nt+1(y+ac1)
Mt+1
Nt(y+ac1)
Mt
=
Nt+1
Nt
Mt
Mt+1
=
n
z
:
We can update our budget constraint as
c1 +
z
n
c2 y + a:
Graphically, we can draw the budget constraint and label point A as the allocation
in a monetary equilibrium. The consumption bundle (c1; c2) at point A maximizes an
individuals utility subject to the budget constraint.
c1
c2
A
c*1
c*2
y+a
(y+a)n/z
(b) On the graph you drew in part (a), draw the resource constraint. Take advantage of
the fact that the resource constraint goes through the monetary equilibrium (c1; c2). Label
your graph carefully, distinguishing between the budget and resource constraints.
We rst derive the resource constraint faced by the planner,
Ntc1 +Nt1c2 Nty ! c1 + 1
n
c2 y:
We add the resource constraint to the graph and label the golden rule allocation as point
B.
2
c1
c2
A
c*1
c*2
y+a
(y+a)n/z
B
ny
y
(c) Show that the monetary equilibrium does not maximize the utility of the future
generations. Support your assertion with references to the graph you drew of the budget
and feasible constraints.
We can clearly see from the graph that there are feasible points that are preferred by the
future generations to (c1; c2). One such point is point B which is the golden rule allocation.
Point B lies on a higher indi¤erence curve than (c1; c2). This shows that given the resource
constraint (or feasible constraint), the stationary monetary equilibrium (c1; c2) does not
maximize the utility of future generations. Furthermore, the initial old also prefer a point
like B since it gives them higher second-period consumption than c2.
(Note that we use the term "feasible constraint" and the term "resource constraint"
interchangeably.)
7. Consider an overlapping generations model with the following characteristics: Each
generation is composed of 1; 000 individuals. The money supply changes according toMt =
2Mt1. The initial old own a total of 10; 000 units of money (M0 = $10; 000). Each
period, the newly printed money is given to the old of that period as a lump-sum transfer.
Each individual is endowed with 20 units of the consumption good when born and nothing
when old. Preferences are such that individuals wish to save 10 units when young at the
equilibrium rate of return on money.
(a) What is the gross real rate of return on money in this economy (vt+1=vt)?
To derive the rate return on money, we rst need to nd the value of money. The money
market clearing condition is
N (y c1) = vtMt ! vt = N (y c1)
Mt
:
It follows that
vt+1
vt
=
N(yc1)
Mt+1
N(yc1)
Mt
=
Mt
Mt+1
=
1
2
:
The rate of return on money is 1=2. The value of money falls by a half every period.
(b) How many goods does an individual consume when young (c1)?
Individuals allocate their endowments between consumption and saving when young.
The rst-period budget constraint is
c1 + vtmt y:
When individuals save 10 units when young, it means that vtmt = 10. Given that y = 20;
3
we have c1 = y vtmt = 10. The consumption when young is 10 units of good.
(c) How many goods does an individual receive as a transfer (a)?
From the government budget constraint, the transfer is from the newly printed money.
In aggregate,
Na = vt (Mt Mt1) = vt

Mt Mt
2

=
1
2
vtMt:
To nd the value of vtMt, we use the money market clearing condition
vtMt = N (y c1) = 1000 (20 10) = 10; 000:
It follows that the amount of the transfer in real terms is given by
a =
1
2vtMt
N
=
1
2 10; 000
1000
= 5:
(d) How many goods does an individual consume when old (c2)?
From an individuals second-period budget constraint,
c2 vt+1mt + a:
Recall that vtmt = 10. We can derive the value of vt+1mt as
vt+1mt =
vt+1
vt
vtmt =
1
2
10 = 5:
Therefore, we have
c2 = vt+1mt + a = 5 + 5 = 10:
The second-period consumption is 10 units of good.
(e) What is the price of the consumption good in period 1 in dollars (p1)?

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ECOS3003 ELEC6252 C2511C PHY328 EC1060 ECON32202 COMP4002-E1 MATH3063 EFIMM0124 QBUS2310 ECON4411 FUNDAMENTALS ACCT20001 18YX RPM COMP 2711 QBUS6600 BUSS5221 ST3189 FIT1047 MAT344 EGB375 MATH60013 MATH96011 COMP3557 MAST20029 ECM159 EAE1011 ENSCEN 105 SECTION A STA 141C SOSE 2022 PAM006 COMP0048 M40007 ISOM2500 CMPE 142 A06472 MCC150 ACST 8083 GEOG6087 ECON920 FINM7008 ENVENG 4110 COMPSCI 361 ENGRCEE 21 PHYS 1112 ACF2100 ECMM108 COMPS267F MAT00050M MAST30025 CSIT970 MSCI 224 INT202 PUBL0054 MSDM5004 BMAN 21020 BMAN21020 MGMT1002 MATH11150 LAWS7023 ACTL30002 CIVL3340 MATH1002 ECON 8069 COMPSCI 351 IBUS7302 STAT4528 CHEM1101 STAT3925 BUSN 7008 Comp 3120 ECOS2040 SWEN90010 ENGN6528 ECM158 ECON20022 COMP6452 Calculation CITS1401 S1889112 BUS 351 ACTL30008 FIT2091 ECON6002 IBUS6020 PHI 001 ECON30290 MATH7501 ECON10004 MFIN7017 ISYS90043 LAWS7012 ECON30025 COMP30023 COMM1190 ECOM20001 GSBS6009 STAT 337 EMET8002 ECOM90001 ECOM30001 FINC 2012 BUSINESS ENGCV512 ECO 101H1 IB9520 FINM 3008 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