Ayudantia 6

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Macroeconomía II – Problem Set
TA Session 6
Professor: Caio Machado (caio.machado@uc.cl)
TA assigned: Wei Xiong (wxiong@uc.cl)
Some of those exercises will be solved on the ayudantia of October 19, 2018.
Goods and money markets
Exercise 1
Consider the basic model of equilibrium in the goods market, which has the following
assumptions: (i) all firms produce the same good that can be used for consumption,
investment or by the government; (ii) the economy is closed; (iii) firms are willing to
supply any amount of the good at a given price level.
Consumption (C) is given by
C = c0 + c1(Y − T ),
where Y denotes the income, T denotes taxes (minus government transfers) and c0 > 0
and c1 ∈ (0, 1) are parameters. Investment is exogenous and fixed at some level I and the
same applies to government spending, denoted by G.
1. What is the equilibrium level of output Y ?
2. Only on this item, suppose that there is some regulation that forces the government
to run a balanced budget. That is, G must always be equal to T . Therefore, any
increase in government spending must be compensated by an equal increase in taxes.
Can the government still affect the level of output using fiscal policy (i.e., changing
G and T , but keeping the budget balanced)? Explain.
3. Now suppose that T depends on Y , according to
T = t0 + t1Y, with t0 ≥ 0, and t1 ∈ (0, 1).
Compute the equilibrium level of output Y . Compare the government spending
multiplier you got in Item 1 with the one you got here. Which multiplier is larger?
Macroeconomía II, 2018/2 1
Exercise 2
Suppose that when the nominal interest rate i is larger than zero the money demand (Md)
is given by
Md = $Y (0.25− i),
where the nominal income $Y is $100. When i = 0, agents will demand at least 0.25× $Y
units of money, but are indifferent between holding any amount of money equal or larger
than 0.25× $Y . Suppose the supply of money is $20.
1. What is the equilibrium interest rate?
2. What is the equilibrium interest rate when the money supply is $30?
3. What happens to the equilibrium nominal interest rate when the central bank in-
creases the money supply from $30 to $40?
4. Suppose the money supply is $25 and the nominal income $Y increases from $100
to $200. Will the equilibrium nominal interest rate increase? Show what happens
using a demand and supply graph.
Exercise 3
Consider the model of Chapter 3 in Blanchard, where investment and government are
fixed at I and G, respectively, and consumption is given by
C = c0 + c1(Y − T )
where Y denotes real output and T are taxes, and c0 > 0 and c1 ∈ (0, 1). Answer true or
false to the statements below, justifying your answers.
1. An increase of 500 units in government expenditure has the same effect on equilib-
rium output as a decrease of 500 units in taxes.
2. An increase of 10% in G always leads to an increase of 1/(1− c1)% in output.
3. The higher the marginal propensity to consume, the higher the increase in GDP
after a marginal decrease in taxes.
4. Suppose taxes are a fraction of total income, i.e., T = τY . The government spending
multiplier is larger than when T is fixed.
Macroeconomía II, 2018/2 2
5. Suppose the government runs a balanced budget always, i.e.,T = G. An increase of
one unit in G causes an increase of one unit in output.
6. Suppose there are two group of people in a country (of equal size and each earns
half of the total income). One group has a marginal propensity to consume higher
than others. A policy that taxes the group with the low propensity to consume and
transfer the amount to the group with the high propensity to consume will increase
output.
IS-LM
Exercise 4
Consider the basic IS-LM model where the central bank fixes the money supply. Suppose
country A is at the liquidity trap, as described in the graph below.
0
LM
IS
Output, Y
Interest
rate, i
Equilibrium
Now consider the following idea:
“Imagine that the Fed were to announce that, a year from today, it would pick a digit
from zero to 9 out of a hat. All currency with a serial number ending in that digit would
no longer be legal tender. Suddenly, the expected return to holding currency would become
negative 10 percent.
That move would free the Fed to cut interest rates below zero. People would be delighted
to lend money at negative 3 percent, since losing 3 percent is better than losing 10.” Gregory
Mankiw, NY Times, April 18, 2009
Macroeconomía II, 2018/2 3
(http://www.nytimes.com/2009/04/19/business/economy/19view.html)
Assume that country A initially has notes with 10 different colors and the total value
of the currency of a given color is the same across colors. Based on the idea above,
the central bank implements the following policy. Every year the central bank chooses
randomly one color (with equal probability for each) and all notes with that color lose
its value. Every time the central bank picks the currency color that will have its legal
tender status withdrawn, it immediately puts the same amount of money back in the
economy in notes created with a color not yet used (think that money is thrown from a
helicopter). Thus, the money supply is fixed. People in that country only use currency to
make transactions.
1. How would that policy affect the equilibrium output in this economy? You can use
your intuition to answer it, or you can base it on your answer to item 3 below.
2. Draw the money demand curve of this economy before and after the policy.
3. In the same graph, draw the IS and LM curves before and after the policy. (Obs:
the IS and LM curves before the policy are already drawn in the graph above, but
draw it again to compare with the new equilibrium).
Exercise 5
In a graph, represents what happens in the IS-LM after each of the shocks below. Explain
how the transition between the old equilibrium and the new equilibrium occurs, plotting
in a graph the path of the nominal interest rate i and output Y . To derive the transitions,
assume that money markets are always in equilibrium, while goods markets can be not in
equilibrium during the transition. Assume that the bank central fixes the money supply
(assumption A1 in class).
1. A permanent increase in G.
2. A permanent increase in M .
Exercise 6
Answer the questions below considering the following modifications of the standard IS-LM
model seen in class in which t the central bank fixes the money supply (assumption A1).
Macroeconomía II, 2018/2 4
http://www.nytimes.com/2009/04/19/business/economy/19view.html
1. Derive the IS curve assuming that the investment does not depend on the interest
rate. What is the impact of monetary and fiscal policy in this case?
2. Derive the LM curve assuming that the money demand does not depend on the
interest rate. What is the impact of monetary and fiscal policy in this case?
3. Derive the LM curve assuming that the demand for real balances does not depend
on income. What is the impact of monetary and fiscal policy in this case?
4. Suppose Md/P = aY , where a > 0. Derive the LM curve when a→∞.
Exercise 7
Answer the questions below using the IS-LM model for a closed economy in which the
central bank fixes the money supply.
1. Suppose a country wants to reduce its fiscal deficit, but at the same time, it does
not want to reduce output. Suggest a policy (or a mix of policies) that could achieve
those objectives. Explain it using the IS-LM diagram.
2. Suppose now that a government decides to increase spending (G), but to keep the
fiscal deficit constant it also increases a lump-sum tax (T ) in the same amount.
Using the IS-LM diagram, explain the effect of these policies.
3. Suppose the central bank increases the money supply in a permanent way at some
date τ . Represent the new equilibrium in the IS-LM diagram, as well as the transition
for the new equilibrium. To show the transition, plot output and the nominal interest
rate as a function of time. When analyzing the transition, assume that money
markets are always in equilibrium, while goods markets adjust slow.
Mundell-FlemingExercise 8
Consider an open economy characterized by the following equations:
C = c0 + c1 (Y − T )
I = d0 + d1Y
Macroeconomía II, 2018/2 5
IM = m1Y
X = x1Y ∗
where, C denotes consumption, Y denotes the domestic income, I denotes investment,
IM and X are the quantity of imports and exports, respectively. The parameters m1 and
x1 are the propensities to import and export. Assume that the real exchange rate is fixed
at a value of 1 and treat foreign income, Y ∗, as fixed. Also assume that taxes, T , are fixed
and that government purchases, G, are exogenous (i.e., decided by the government). Note
that differently from the standard Mundell-Fleming model seen in class, here we assume
that investment does not depend on the interest rate.
1. Write the equilibrium condition in the market for domestic goods and solve for Y .
2. What is the government spending multiplier? (Assume that 0 < m1 < c1 + d1 < 1)
3. What is the change in net exports when government purchases increase by one unit?
4. Suppose the government decides to close the economy, not allowing trade with the
rest of the world (i.e., IM = X = 0). Find the government spending multiplier. Is
it larger or smaller than the multiplier you found in item 2? Explain, in words, why
the two multipliers are different.
Exercise 9
Suppose a country operates under a fixed exchange rate regime and has perfect capital
mobility. At date t, the central bank spends 100 units of local currency buying domestic
bonds in an open market operation. Suppose that between dates t + 1 and t financial
investors had time to fully react to the open market operation.
1. Is the monetary base at t+1 larger, equal or smaller than the monetary base at date
t?
2. Did the central bank balance sheet change between dates t + 1 and t? If yes, how
did it change?
Exercise 10
To answer the questions below use the Mundell-Fleming model of an open economy.
Macroeconomía II, 2018/2 6
1. Suppose a country has perfect capital mobility and operates under a flexible exchange
rate regime. Suppose the country is in a severe recession, and policymakers are
looking for a policy (or a mix of policies) to increase output. Moreover, they would
like to ensure net exports will not be affected by those policies. Changing the
exchange regime from flexible to fixed is not a posssibility. How could this country
increase output without affecting net exports? Explain using graphs and words.
2. Suppose now a country that has perfect capital mobility and operates under a fixed
exchange rate regime. Suppose there is a sudden exogenous increase in the demand
for exports (say that the income in the rest of the world increased). What will be the
effect of this higher demand for exports on the amount of foreign currency reserves
of the central bank? Explain using graphs and words.
Macroeconomía II, 2018/2 7
Proposed exercises
Exercise 11
1. Consider a bond that promises to pay $100 in one year. What it is the interest rate
on the bond if its price today is $80, $95 and $110?
2. Suppose there are no costs associated with storing currency. Explain why the nom-
inal interest rate cannot go below zero.
Exercise 12
The government of a country, after years running large fiscal deficits, is forced to reduce
its deficit in a given year. Increasing taxes takes a lot of time and it is not an available
option in the short run. Using the IS-LM model where the central bank fixes the nominal
interest rate, explain how this country could avoid a fall in output in the short run.
Exercise 13
Take two countries that are identical except for the behavior of the central bank: in country
A the central bank fixes the nominal interest rate (and adjusts the money supply to achieve
it), while in country B the central bank fixes the money supply. Initially, both countries
are at an equilibrium in which the interest rate and output are the same. Suppose both
countries experience the same reduction in goverment spending. Which country will suffer
a larger output loss? Explain your answer using the IS-LM model.
Exercise 14
Answer the following questions according to the Mundell-Fleming model with perfect
capital mobility and flexible exchange rates seen in class (de Gregorio, chapter 20).
1. How does an increase in government spending affects output, interest rates and the
exchange rate? Explain using graphs and words.
2. How does an increase in the money supply affects output, interest rates and the
exchange rate? Explain using graphs and words.
3. How does an increase in the international interest rate affects output interest rates
and the exchange rate? Explain using graphs and words.
Macroeconomía II, 2018/2 8
4. Answer items 1, 2 and 3 again assuming a fixed exchange rate regime instead of
flexible exchange rate regime.
5. Still assuming a fixed exchange rate regime and perfect capital mobility, what hap-
pens when the central bank increases the fixed exchange rate? Explain using graphs
and words.
Macroeconomía II, 2018/2 9
Macroeconomía II – Solutions
TA Session 6
Professor: Caio Machado (caio.machado@uc.cl)
TA assigned: Wei Xiong (wxiong@uc.cl)
Exercise 1
Item 1
Equating demand and supply for goods:
Y = c0 + c1(Y − T ) +G+ I
Solving the equation above for Y we get the equilibrium level output:
Y = 11− c1
[
c0 +G+ I − c1T
]
(1)
Item 2
Replacing T by G (since T = G) in (1):
Y = 11− c1
[
c0 +G+ I − c1G
]
= 11− c1
[
c0 + I
]
+G
The equation above clearly shows that the government can still increase the equilibrium
output by increasing G (and consequently T ). It happens, because as (1) shows, the nega-
tive impact of reducing taxes in one unit is smaller than the positive impact of increasing
expenditure in one unit.
Item 3
Equating demand and supply for goods and solving for Y :
Y = c0 + c1 [Y − (t0 + t1Y )] +G+ I
Macroeconomía II, 2018/2 1
Y = 11− c1(1− t1)
[
c0 +G+ I − c1t0
]
The government spending multiplier here is 11−c1(1−t1) , while in item 1 it was
1
1−c1 , and thus
the latter is larger. The intuition for the smaller multiplier with taxes that increase with
output is that part of the increase in income after an increase in government spending
translate into larger taxes, reducing the increase in available income.
Exercise 2
Item 1
Equating demand and supply (and assuming and later veryfing that the equilibrium in-
terest rate is larger than zero):
100(0.25− i) = 20
i = 5%
Note that if i = 0, the demand would be 0.25 × 100 = 25 dollars, which is larger than
supply.
Item 2
Equating demand and supply (and guess and later veryfing that the equilibrium interest
rate is larger than zero):
100(0.25− i) = 30⇒ i = −5%
Our guess failed since we found a negative solution for i. The equilibrium interest is
i = 0%, since when it happens agents will be willing to demand any amount larger than
0.25× 100 = 25 dollars, and therefore they may as well demand $30, clearing the market.
Item 3
Nothing happens. The interest rate remains at zero.
Item 4
Yes, the interest rate will increase. You can easily see drawing the demand and supply
before and after the increase in output, as in the graph below.
Macroeconomía II, 2018/2 2
money demand
(Md) with $Y = 200
money demand
(Md) with $Y = 100
money supply
25 50
12.5%
0
A
B
i
M
Exercise 3
Item 1
False. Equilibrium output is given by
Y = c0 + c1(Y − T ) + I +G
Y = 11− c1
(c0 − c1T + I +G) (*)
Thus an increase in G of 500 increases Y in 11−c1 500, while a reduction of 500 in taxes
increases output in c11−c1 500. Thus, the decrease in taxes have a lower effect. Intuition:
part of the decrease in taxes is saved, not spent.
Item 2
False. Suppose initially we have Y = 1000 and G = 50 and c1 = 0.5. Using (*), an
increase of 5 units in G (10%), leads to an increase of 11−0.5 ∗ 5 = 10 in GDP, an increase
of 1% in GDP.
Item 3
True. The marginal increase in GDP after a marginal decrease in taxes is given by
f(c1) ≡
c1
1− c1
Macroeconomía II, 2018/2 3
Note that
f ′(c1) =
c1
(1− c1)2
+ 11− c1
= c1 + 1−c1(1− c1)2
= 1(1− c1)2
> 0 ∀c1 ∈ (0, 1)
Item 4
False. Now equilibrium output is:
Y = c0 + c1(Y − τY ) + I +G
Y = c0 + c1(1− τ)Y + I +G
Y = 11− c1(1− τ)
[c0 + I +G]
The multiplier is now 11−c1(1−τ) , which is lower than
1
1−c1 .
Item 5
True. Using (*), the equilibrium real output is:
Y = 11− c1
(c0 − c1G+ I +G)
Y = 11− c1
(c0 + (1− c1)G+ I)
Y = 11− c1
(c0 + I) +G
Item 6
True. Let A denote the group with high propensity to consume and B the group with low
propensity to consume.
Y = CA + CB +G+ I
Y = cA0 + cA1
(
Y
2 − T
A
)
+ cB0 + cB1
(
Y
2 − T
B
)
+G+ I(
1− c
A
1
2 −
cB1
2
)
Y = cA0 − cA1 TA + cB0 − cB1 TB +G+ I
Y = 1
1− c
A
1
2 −
cB1
2
[
cA0 − cA1 TA + cB0 − cB1 TB +G+ I
]
Macroeconomía II, 2018/2 4
Since cA1 > cB1 , a decrease in TB followed by the same increase in TAincreases output.
Exercise 4
Item 1
As shown in item 3 below, output increases.
Item 2
Nominal interest rate, i
Real money balances, M/P
Money demand before the policy
Money demand after the policy
0
Because of the policy, bonds become more attractive and money less attractive. The
money demand shifts down. Moreover, when the interest rate is 0%, a decrease in interest
rates will still cause the demand for money to increase (now, when the nominal interest
rate is 0%, bonds still pay a interest rate higher than money, and therefore a reduction in
i will make people substitute bonds for money). Nominal interest rates can go negative
after the policy, but they certainly can’t go below -10% (otherwise no one would demand
bonds).
Macroeconomía II, 2018/2 5
Item 3
The IS curve does not shift after the policy. Consumption is still a function of available
income, and that did not change. For a given level of Y and i, firms will be willing to
invest the same as before. G did not change as well. Thus, the only thing that shifts is
the LM curve. Take some interest rate i > 0. For that interest rate, the level of output
Y consistent with equilibrium in the money market will have to be higher after the policy
to make people demand a given quantity of money (to see that, go back to item 2 and
draw the equilibrium in the money market for different values of Y before and after the
policy, assuming a constant money supply). Obs: one could always say that the IS shifts
for reasons that are not in the model. Here, you are asked to analyze this policy through
the lens of the basic IS-LM model.
In the new equilibrium output will be higher. The economy can leave the liquidity
trap, or enter a new liquidity trap with negative interest rates (depending on how much
the LM curve shifts). The two cases are represented below, but in both cases, output
increases (note where the origin is positioned).
0
LM(before policy)
IS
Output, Y
Interest
rate, i
Equilibrium
(before policy)
LM(after policy)
Equilibrium
(after policy)
0
LM (before policy)
IS
Output, Y
Interest
rate, i
Equilibrium
(before policy)
LM (after policy)
Equilibrium
(after policy)
Exercise 5
Item 1
Let’s start with the new equilibrium. The shock in G shifts the IS curve to the right, and
the equilibrium goes from point A to point A′ in the graph below.
Macroeconomía II, 2018/2 6
LM
IS
IS ′
i
Y
A
A′
∆G > 0
Now we look at the transition. Since we are assuming that money market is always in
equilibrium during the transition, we must never leave the LM curve (remember that the
LM curve gives us all combinations of i and Y such that the demand for money equals
the supply of money). Hence, we must move on the LM curve, as represented below.
LM
IS
IS ′
i
Y
A
A′
∆G > 0
i
time
Y
time
In words what happens is the following. The increase in government spending increases
demand, which increases firms production and income. The higher income make people
demand more money. Since the money supply fixed, as income increases, interest rates
increase to ensure equilibrium in money markets, until production fully adjusts and we
reach the new equilibrium.
Item 2
Again we start with new equilibrium. The increase in M shifts the LM curve to the right
and the equilibrium goes from point A to A′.
Macroeconomía II, 2018/2 7
LM
IS
i
Y
A
LM ′
A′
∆M > 0
Again, we must always be on the LM curve. Hence, the representation in the graph
below. Initially, the economy jumps to point B and then slowly converges to A′. Interest
rate fall at point B, which makes output increase gradually, since the much lower interest
rate increases demand for goods. As output increases, the demand for money increases,
which forces interest to go up a bit to reduce the demand for money.
i
time
Y
time
LM
IS
i
Y
A
LM ′
A′
∆M > 0
B
Exercise 6
Item 1
If investment does not depend on the interest rate, the IS curve is vertical. To see that,
notice that equilibrium in the goods markets is not affected by an increase in the interest
rate (the demand curve Z of the model of equilibrium in the goods markets seen in class
does not change when we change i). If the IS curve is vertical, fiscal policy still affects
output and interest rates, but monetary policy only affects interest rates, as illustrated
below.
Macroeconomía II, 2018/2 8
LM
ISi
Y
A
∆G > 0
IS ′
A′
LM
ISi
Y
A
∆M > 0
A′
LM ′
Item 2
If the money demand does not depend on i (but still depends on Y ), the LM curve is
vertical. This is so because, for a given money supply, there is an unique Y that clears
the money markets. But notice that when M s/P increases, the level of Y that clears the
money market increases (since now people need to demand more money), and hence the
LM curve shifts to the right. Hence, fiscal policy is not effective to increase output, but it
increases interest rates. Expansive monetary policy, on the other hand, increases output
and lowers interest rates.
LM
IS
i
Y
A
∆G > 0
IS ′
A′
LM
IS
i
Y
A
A′
LM ′
∆M > 0
Item 3
If the demand for real balances does not depend on Y then, the interest rate that clears
money markets is the same for any Y . Hence, we get an horizontal LM curve. When
M s/P increases, the interest rate that clears money markets decreases, shifting LM down.
Expansive monetary leads to lower i and higher Y , while expansive fiscal policy increases
output without raising i.
Macroeconomía II, 2018/2 9
LM
IS
i
Y
A
∆G > 0
IS ′
A′
LM
IS
i
Y
A
LM ′
A′
∆M > 0
Item 4
Since the LM curve does not depend we know that the LM is vertical at some Y ∗ such
that:
M
P
= aY ∗ ⇒ Y ∗ = 1
a
M
P
Hence, as a → ∞, Y ∗ → 0, implying the LM curve becomes vertical at the origin.
Intuitively, since the LM curve does not depend on i, the income is entirely determined by
the equilibrium in the money markets. As the demand for money explodes for a given level
output, the only way to reach an equilibrium in money markets is to have an extremely
low income.
Exercise 7
Item 1
There are (at least) two ways to do it. First, the country could reduce government spending
(or increase taxes) and then expand the money supply. The IS would shift to the left and
the LM to the right. By choosing the right amount of monetary expansion one can ensure
output will not change. This is represented in the graph below.
Macroeconomía II, 2018/2 10
IS′
IS
A
i
Y
LM ′
LM
A′
Another way to achieve that is to increase both taxes and government spending. Re-
member that equilibrium in the goods markets (the IS curve) requires (I am assuming a
linear consumption function just to simplify, this is not needed for the argument, see the
next item)
Y = 11− c1
[c0 − c1T +G+ I (i, Y )]
Hence, if taxes increases in ∆T > 0, spending must increase only increase only ∆G =
c1∆T to keep the IS relation identical. Hence, since c1 ∈ (0, 1), ∆T > ∆G and therefore
the fiscal deficit improves, without changing the IS curve.
Item 2
The IS relation is given by:
Y = C(Y − T ) +G+ I(i, Y )
Therefore an equal and infinitesimal increase in T and G changes the RHS in dRHS =
−C ′(Y − T ) + 1. Since the marginal propensity to consume C ′(Y − T ) is smallerthan
one, dRHS > 0 and thefefore the IS shifts to the right.
Macroeconomía II, 2018/2 11
IS
IS′
A′
i
Y
LM
A
Item 3
We start with new equilibrium. The increase in M shifts the LM curve to the right and
the equilibrium goes from point A to A′.
LM
IS
i
Y
A
LM ′
A′
∆M > 0
Given that money markets are always in equilibrium, we must always be on the LM
curve. Hence, the representation in the graph below. Initially, the economy jumps to
point B and then slowly converges to A′. Interest rate fall at point B, which makes
output increase gradually, since the much lower interest rate increases demand for goods.
As output increases, the demand for money increases, which forces interest to go up a bit
to reduce the demand for money.
Macroeconomía II, 2018/2 12
i
time
Y
time
LM
IS
i
Y
A
LM ′
A′
∆M > 0
B
Exercise 8
Item 1
Equilibrium in the goods markets is given by
Y = c0 + c1 (Y − T ) + d0 + d1Y +G+ x1Y ∗ −m1Y
Y = 11− c1 − d1 +m1
[c0 − c1T + x1Y ∗ + d0 +G]
Item 2
The government spending multiplier is
1
1− c1 − d1 +m1
Item 3
Let NX = X − IM = x1Y ∗ −m1Y (remember that the real exchange rate is one). The,
since output increases in 11−c1−d1+m1 when government spending increases in one unit, the
change in NX is
∆NX = −m1︸ ︷︷ ︸
dNX/dY
 11− c1 − d1 +m1︸ ︷︷ ︸
dY/dG

Item 4
The equilibrium condition becomes
Y = c0 + c1 (Y − T ) + d0 + d1Y +G
Macroeconomía II, 2018/2 13
And therefore
Y = 11− c1 − d1
[c0 − c1T + d0 +G]
And then the multiplier is 11−c1−d1 . Since m0 > 0, it is larger than the multiplier in item
2. The reason is that in the open economy part of the increase in demand caused by
the increase in G (and the subsequent increases in income) do not become demand for
domestic goods, but demand for foreign goods.
Exercise 9
Item 1
The monetary base is the same. When the central spends $100 buying bonds, it initially
increases the monetary base, putting pressure to lower domestic interest rates. Hence
domestic investors start to exchange domestic currency for foreign currency to invest
abroad. This forces the central bank to sell its reserves, decreasing the monetary base back
again. He keeps selling reserves until the pressure on interest rates are totally offset, which
happens when the monetary base return to its previous level. Since all this adjustment is
quick and happens between t and t+ 1, the monetary base does not change between those
dates.
Item 2
It changed. Now the central bank has less reserves and more bonds.
Exercise 10
Item 1
The idea here is the following: you do expansive monetary policy and then you cancel the
change in net exports with fiscal policy (since with perfect capital mobility and flexible
exchange rate ∆G = −∆XN). Below we explain it in more detail.
Let’s start looking first to the effect of increasing the money supply alone. An increase
in M shifts the LM to the right. Since interest rates must be equal i∗, domestic residents
have too much money and they start to buy foreign bonds. This leads the exchange rate to
depreciate, shifting the IS curve to the right (IS ′). The economy would move from point
A to point B. At point B, net exports may be have changed, since e increased (which
causes an increase in net exports) and Y increased (which causes a fall in net exports).
Macroeconomía II, 2018/2 14
Denote by ∆B the impact on net exports of the increase in the money supply (it does not
matter if it is positive or negative).
LM
IS
IS′
A
LM∗
B
A
i
Y
e
Y
IS∗
i∗
LM ′
B,A′
LM∗
′
IS∗
′
A′
IS′′
Now consider we are at point B and let’s see what happens when the government
does fiscal policy. Say the government increases G (which would shift IS ′ to IS ′′). The
higher demand for goods, increases the demand for money. As residents sell their domestic
bonds, foreign capital enters, appreciating the exchange rate, pushing the IS curve back to
IS ′. The exchanges rate keeps appreciating, until the change in demand is offset, that is,
∆G = −∆XN . Hence, by changing government spending in ∆G = ∆B the government
ensures net exports will not change.
Item 2
The effects are identical to the ones of an increase in G. This higher demand for exports
will shift the IS and IS∗, as illustrated below. The initial increase in demand, makes
domestic residents demand more money. They sell their bonds to foreign investors, who
exchange foreign currency by domestic currency. Since exchange rates are fixed, this forces
the central bank to buy reserves, which increases the money supply, shifting the LM curve
as well. This is illustrated in the graph below. In the end, the central bank will have more
reserves.
Macroeconomía II, 2018/2 15
LM
IS
IS′
A
LM∗
A
i
Y
e
Y
IS∗
i∗
LM ′
A′
LM∗
′
IS∗
′
A′
e
Macroeconomía II, 2018/2 16