Ayudantia 5

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Macroeconomía II – Problem Set
TA Session 5
Professor: Caio Machado (caio.machado@uc.cl)
TA assigned: Soledad Alegria Palma (salegria3@uc.cl)
Some of those exercises will be solved on the ayudantia of October 17, 2018.
Exchange rates
Exercise 1
[Adapted from de Gregorio] Assume a small open economy economy with perfect capital
mobility and full employment, and hence you can assume that the real interest rate equals
the international real interest rate (which is exogenous).
1. In a diagram plot a relationship between domestic savings (denote it by SD ) and
real interest rates and investment and real interest rates in a way you think makes
sense. In that diagram, explain what happens to the current account balance when
there is a temporary and exogenous reduction in domestic output.
2. Suppose now that there an increase in consumption and investment of domestic
goods (but output is constant at its full employment level). Explain what happens
with the current account balance in that case.
3. Which of the previous cases do you think is more damaging in terms of inflation?
4. What happens in item 2 with the equilibrium real exchange rate q?
Exercise 2
[Adapted from de Gregorio] Suppose an economy with three countries, A, B and C. The
value of imports in countries A and B are given by
qAMA = 250 − 2qA + 0.4Y A
qBMB = 260 − 2qB + 0.4Y B
Macroeconomía II, 2018/2 1
where Y j denote output in country j and qj is the real exchange rate between country j
and country C. Exports in each country are given by
XA = 1200 + 3qA
XB = 100 + 2qB
I am implicitly assuming that A and B only export to and import from country C, not
between each other (that is why they only care about the real exchange related to country
C). Assume that Y A = 3000 and Y B = 300 are exogenously given. Investment in each
country is given by
IA = 1000 − 2rA
IB = 150 − rB
Domestic savings in each country is given by
SAD = 350 + rA + 0.2Y A
SBD = 10 + rB + 0.2Y B
where rj denotes the real interest rate in each country.
1. Suppose these countries (A, B and C) live in financial autarky (they do not borrow
to or lend from the rest of the world). Find the equilibrium real exchange rate and
real interest rate in country A and B.
2. Suppose the barriers that do not allow country A and B to borrow or lend between
each other are removed (but country C is still in financial autarky). Compute the
equilibrium real exchange rates in each country.
3. Suppose now that there was also in change in tariffs after the financial openness, so
that the value of imports in country B fell 16 units (the function that determined
qBMB changed, changing the equilibrium MB). What will happen with qB?
Exercise 3
1. Show that qt = 1+r
∗
t
1+rt q
e
t+1 (the notation is the standard one).
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2. Express the Marshall-Lerner condition in terms of elasticities. You may assume that
the country has a zero trade deficit (X = qM).
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Proposed exercises
Exercise 4
Suppose that at date t you can buy or sell USD in future markets at a price ft+1. In other
words, agents agree at t that they will buy/sell dollars at t + 1 at the agreed price ft+1.
1. Suppose all agents in the economy are risk neutral. Show that 1 + it = (1 + i∗) ft+1et .
2. Do you expect that equation to hold in practice?
Exercise 5
Suppose inflation in the US is always 3%, while inflation in Chile is always 2%. Suppose
also that the nominal exchange rate between CLP and USD is fixed. What do you expect
to happen to the nominal interest rate in Chile?
Exercise 6
Explain (using a graph) what you expect to happen to the real exchange rate in each of
the scenarios below.
1. The government increases expenditure without increasing taxes. Assume the increase
in government purchases only increase demand for domestic goods.
2. The government reduces import tariffs. Suppose first it does not affect other taxes
and then that the government compensates the reduction by increasing other taxes.
3. The productivity increases because the government found a lot of oil.
Macroeconomía II, 2018/2 4
Macroeconomía II – Solutions
TA Session 5
Professor: Caio Machado (caio.machado@uc.cl)
TA assigned: Soledad Alegria Palma (salegria3@uc.cl)
Exercise 1
Item 1
First of all, it makes sense to think that when real interest rates go down investment
goes up, since it makes cheaper for firms to borrow to finance projects that increase their
capital. Second, it makes sense to think that a higher real interest rate will induce more
savings, since it increases savings returns. Hence, we assume the SD and I curves are
upward and downward sloping, respectively.
The shock is temporary, so the consumption keeps equal (we are assuming that agents
smooth consumption). The saving curve moves because the income falls, so the saving is
lower for each level of interest rate. Now notice that (the notation is the same used in
class and SD = SG + SP ):
Y = C + I +G+XN
Y − F − T = C + I +G+XN − F − T
YD = I + (G− T ) + CC
YD − C = I + (G− T ) + CC
CC = SP + SG − I = SD − I
Hence, if the economy initially had CC = 0, this produce a deficit in the current account.
Macroeconomía II, 2018/2 1
S ′D(r)
SD(r)
I(r)
r
I, SD
r∗
CC deficit
Item 2
The increase in consumption is exogenous and decrease savings for each level of interest
rate, because the income has not changed. The saving curve moves like the case before. At
the same time investment increase, moving that curve to the right, pushing the demand
of resources of the economy. The deficit of the current account increase.
S ′D(r)
SD(r)
I(r)
r
I, SD
r∗
I ′(r)
CC deficit
Item 3
In the first case, the lower income generate a deficit but it does not push the production
capabilities, so it does not push inflation. In the second one, the increase in consumption
pushes inflation by increasing aggregate demand (since output it is already at its full
employment level).
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Item 4
Remember that CC = −SE. Hence, on item 2, the −SE curve shifts to the left, so the
real exchange rate fall. Remember that we assumed that the higher demand for C and I
consisted only of domestic goods, so that exports and imports are not directly affected.
CC
q
−SE−S ′E
q∗
q∗
′
[Remark: sometimes in this exercise we had to think a bit outside the model, which imply
that there may be more than one answer that makes sense to some of the items.]
Exercise 2
Item 1
Financial autarky in both countries implies that exports must be equal to imports (in
local currency): Xj = qjM j. Hence:
250 − 2qA + 0.4 × 3000 = 1200 + 3qA
260 − 2qB + 0.4 × 300 = 100 + 2qB
Which implies qA = 50 and qB = 70. Since they live in financial autarky we must have
SA = IA and SB = IB
350 + rA + 0.2 × 3000 = 1000 − 2rA
10 + rB + 0.2 × 300 = 150 − rB
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Which implies rA = 16, 6 and rB = 40 .
Item 2
When the financial account is opened, these countries will have the same real interest rate:
rA = rB = r∗. We find r∗ by imposing IA + IB = SAD + SBD :
[1000 − 2r∗] + [150 − r∗] = [350 + r∗ + 0.2 × 3000] + [10 + r∗ + 0.2 × 300]
This implies r∗ = 26 Therefore, IA = 948 IB = 124, SAD = 976 and SBD = 96.
When the financial account is released, the real exchange rates fluctuates, so that the
difference between exports and imports adjusts to the availability of resources given by
supply and demand of capital. Remember that CCj = SjD − Ij = −S
j
E, for j = A,B .
Hence SAE = −28 and SBE = 28. The equilibrium exchange rate in each country must then
be such that Xj − qjM j = −SjE:[
1200 + 3qA
]
−
[
250 − 2qA + 0.4Y A
]
= 28
[
100 + 2qB
]
−
[
260 − 2qB + 0.4Y B
]
= −28
Solving this we have that qA = 55.6 and qB = 63. Therefore, since one country needs
external savings, this appreciates real exchange rate because of the entry of capital. The
opposite happens to the country with excess savings.
Item 3
SAE and SBE will remain unaffected (think about it). Hence, applying differences to XB −
qBMB= −SBE we get:
∆XB = ∆
(
qBMB
)
− ∆SBE = −16
Since XB = 100 + 2qB, we need qB to decrease 8 units.
Exercise 3
Item 1
Start from the interest rate parity
(1 + it) = (1 + i∗t )
eet+1
et
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Using the Fisher equation for the domestic and foreign countries:
(1 + rt) =
(1 + it)
(1 + πet+1)
(1 + r∗t ) =
(1 + i∗t )
(1 + π∗et+1)
Eliminate nominal interest rates in the interest parity condition:
(1 + rt) = (1 + r∗t )
(
1 + π∗et+1
)
(1 + πet+1)
eet+1
et
Rearranging:
(1 + rt) = (1 + r∗t )
P ∗et+1/P
∗
t
P et+1/Pt
eet+1
et
(1 + rt) = (1 + r∗t )
qet+1
qt
(1 + rt) = (1 + r∗t )
qt
qet+1
qt =
1 + r∗t
1 + rt
qet+1
Remark: note that we implicitly assumed that Et
[
P ∗t+1et+1
]
= Et
[
P ∗t+1
]
Et [et+1] in the
derivation, which is only an approximation if these random variables are not independent.
Item 2
The M-L condition states that dXN
dq
> 0. Hence:
dXN
dq
= dX
dq
−M − qdM
dq
> 0
Multiplying both sides by q/X:
dX
dq
q
X
− qM
X
− q
2
X
dM
dq
> 0
Using X = qM and denoting elasticities by �’s:
�X,q − 1 −
q2
qM
dM
dq
> 0
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�X,q − 1 −
q
M
dM
dq
> 0
�X,q − 1 − �M,q > 0
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