Problem Set 4 - Solutions
1. (Numerical Problem 3, p.207)
The information given in the question is the following.
In a small open economy, we have that:
Savings are given by the function:
S d = 10 + 100rw
Investment:
I d = 15 − 100rw
Output:
Y = 50
Government Purchases:
G = 10
World Interest Rate:
rw = 0.03
(Everything given in billion dollars)
Remember that a small open economy does not affect the interest rate in
the world, so this country takes the rw as given. This means that the interest
rate is going to be equal to 0.03 for us here.
a) In the first item, you are asked to draw the graph of S and I equilibrium and also to compute the economy’s national saving, investment, current
account surplus,net exports, desired consumption and absorption.
Let’s start with the graph. What we want is to plot the saving and
investment function in the plane (S/I, r). Note that to do this we need
to know the relationship between the level of saving or investment and the
interest rate. By the functions given above we can see that saving is positively
related to r and that investment is negatively related to r. Another way to
do this is to isolate the interest rate in each function:
rsaving = −0.1 + 0.01S d
rinvestment = 0.15 − 0.01I d
1
Therefore, we have a straight line with positive slope for saving and a
straight line with negative slope for investment. Plotting these functions we
get that:
Note that if we had a closed economy the equilibrium would be given by
the point in which the two curves cross, i.e., when S = I.However, since this
is a small open economy the equilibrium is given by the level of interest rate
that corresponds to the world interest rate. The equilibrium can occur either
above or below the closed economy equilibrium. To know which one is the
case, we have to compute the levels of saving and investment.
To find the levels of investment and saving we have to use the value given
by the world interest rate since this is the rate of equilibrium for an open
economy. Substituting r=0.03 in the saving and investment functions we get
that:
S d = 10 + (100)(0.03) = 13
I d = 15 − (100)(0.03) = 12
We have then that at the world interest rate S > I, therefore we are
at a point above the closed economy equilibrium. The equilibrium can be
represented by:
2
where r(w) is the world interest rate, I(eq) and S(eq) are the equilibrium
levels of investment and saving respectively.
We also know that in equilibrium:
S = I + CA → CA = S − I = 13 − 12 = 1 → CA = 1
Assuming that NF P = 0, we have that NX = CA = 1
To calculate the level of consumption, remember that:
Y = C + I + G + NX → C = Y − I − G − NX
Substituting the values found previously, we get that:
C = 50 − 12 − 10 − 1 = 27
The desired absorption is given by:
Absorption = C + I + G = 27 + 12 + 10 = 49
To sum up:
3
S
I
C
NX
Absorption
=
=
=
=
=
13
12
27
CA = 1
49
(b) In this item, you are asked to analyze the effects of an increase in the
level of investment by 2 billion for each level of interest rate.
This corresponds to an increase in the intercept of the investment function, which becomes:
I d = 17 − 100rw
Isolating r:
rinvestment = 0.17 − 0.01I
Therefore, in the graph of S-I there is a shift of the I curve to the right:
We see that the level of investment at the world interest rate will increase,
but we do not know yet by how much. In item a, we got that S > I. So,
now with the increase in I it could be the case that either saving still being
higher than investment or that investment becomes higher than saving. To
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assess what happens , we need to calculate the levels of S and I. Remember
that since the world interest rate has not changed the equilibrium will still
occur at the level rw = 0.03.
The level of saving does not change, since neither the intercept nor the
slope of the saving function changed. Then, S = 13. Investment is now:
I d = 17 − 100rw = 17 − 3 = 14
So, now S < I, implying that CA < 0.Representing the new equilibrium
in our diagram:
where r(w) is again the world interest rate, I(a) is the equilibrium level
of investment from item (a) and I(b) is the equilibrium level of investment
of item (b).
As the figure illustrates, the change in the investment curve caused the
balance of the current account to become negative.
We also know that in equilibrium:
S = I + CA → CA = S − I = 13 − 14 = −1 → CA = −1
Assuming that NF P = 0, we have that
NX = CA = −1
To calculate the level of consumption, remember that:
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Y = C + I + G + NX → C = Y − I − G − NX
Substituting the values found previously, we get that:
C = 50 − 14 − 10 + 1 = 27
The desired absorption is given by:
Absorption = C + I + G = 27 + 14 + 10 = 51
To sum up:
S
I
C
NX
Absorption
=
=
=
=
=
13
14
27
CA = −1
51
2. (Analytical Problem 1,p/208)
This question asks you to explain how each of the following transactions
would enter the US balance of payments accounts.
a) The U.S. government sells F-16 fighter planes to a foreign government.
This transaction corresponds to an increase(credit) in net exports which
also increases the current account balance. Remember that each time there
is an inflow of dollars this corresponds to a credit and has to enter with a
positive sign.
b)A London bank sells yen to, and buys dollars from, a Swiss bank.
This transaction does not affect any account of the balance of payments.
It is just a transaction between foreign banks and does not correspond to
any inflow or outflow of dollars in the U.S.
c) The Fed sells yen to, and buys dollars from, a Swiss bank.
This transaction corresponds to a decrease in the Fed official reserves in
the Financial Account and has to enter with a positive sign (credit) since
there is an inflow of dollars in the U.S. So, there is an increase in the balance
of the Financial Account.
d)A New York bank receives the interest on its loans to Brazil.
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This corresponds to an increase in the Net Income from Abroad(NFP).
Since this corresponds to an inflow of dollars in the U.S. it is a credit and
has to enter with a positive sign, increasing the current account balance.
e) A U.S. collector buys some ancient artifacts from a collection in Egypt.
This corresponds to the import of goods. There is an outflow of dollars
from the U.S., so there is a decrease in the Net Exports of Goods and Services
Account(NX) in the current account. This reduces the balance of the current
account.
f) A U.S. oil company buys insurance from a Canadian insurance company
to insure its rigs in the Gulf of Mexico.
Since there is an outflow of dollars this is a debit and has to enter with a
negative sign in the Financial Account reducing this balance.
g) A U.S. company borrows from a British bank.
This corresponds to an inflow of dollars in the U.S. in the form of a loan.
So, there is an increase in balance of the Financial Account.
3. (Analytical Problem 3, p.208)
In this problem we have the following situation.
There is a large country that decides to impose capital controls that
prohibit foreign borrowing and lending.
This means that the Financial Account has to be equal to zero. (KF A =
0).
Another information is the assumption that before the controls were imposed the country was running a capital and financial account surplus, i.e.,
KF A > 0.
Then, before the controls, we had that KF A > 0,which since CA +
KF A = 0, implies that we had CA < 0.
Remember also that S = I + CA. So, we get that S < I.(the country
wants to invest more than is saving at the interest rate level, so it has to
borrow from abroad to able to finance this additional investment).
When the capital controls are imposed the country is not anymore able to
borrow from abroad. So, the initial equilibrium is not going to hold anymore.
Since it is a large country the world interest rate depends on what happens
in this country. So, after the introduction of the controls another interest
rate level will correspond to the equilibrium.
To analyze this problem think of the world as being composed by this
large country and the rest of the world, as if all the other countries were
aggregated in ROW.
Representing the equilibrium before the controls in a diagram we get that:
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(assume that r(eq) in each graph corresponds to the same level, it is the
interest rate of equilibrium).
So, in the equilibrium before the controls(r(eq)) our Large country was
running a current account deficit with S < I. When the controls are introduced what is going to happen is that this country will become a closed
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economy and there will be the case that S = I and CA = 0. From the first
figure presented , the one corresponding to the large country, we see that the
interest rate in which S and I curves cross is above the r(eq). Therefore, after
the controls the interest rate in our large country will increase.
It is also possible to see that the level of Saving will increase,the level
of Investment will decrease and the current account balance will equal zero
corresponding to an increase in its balance.
At the same time, the Rest of the World will also become closed. From
the second figure presented we see that the level of interest at which S equals
I occurs at a level lower than r(eq). Therefore, the interest rate of equilibrium
in this new situation in the Rest of the World will decrease.
Contrary to what occurs in the Large country, in the Rest of the World
the Saving decreases, Investment increases and current account balance(with
respect to the Large Country) equals zero.
4. According to Friedman and Schwartz, bank panics lead to macroeconomic contractions in part because they reduce the supply of money. Explain
in words or algebra:
a. For a given quantity of high-powered money, how a panic reduces the
money supply.
Remember that the money supply is given by the following expression:
cu + 1
)BASE
cu + res
where BASE corresponds to the Monetary Base, cu is the currencydeposits ratio and res is the reserve-deposit ratio. The term in brackets is
the money multiplier.
The monetary base is the sum of Currency hold by the public(CU) and
the Reserves of the banks at the Central Bank(RES). The money supply
can also be expressed as the sum of the Currency hold by the public(CU)
and the Deposits in the private banks(DEP ).
In a bank panics situation, there is a run to the banks and people want
to hold more currency and withdraw from their deposits. This corresponds
to an increase in the currency to deposits ratio.
Using the expression above, we can see that, with fixed levels of the
monetary base and res, an increase in cu will decrease M, since:
dM
res−1
= (cu+res)−(1+cu)
(BASE) = (cu+res)
2 BASE
dcu
(cu+res)2
because res < 1, we get that the derivative is negative which implies that
an increase in cu causes the money supply to decrease.
M =(
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The intuition for this comes from the fact that in a fractional banking
system, where res < 1, money is created from deposits, when the banks lend
part of the public deposits creating more deposits and so on. If the public
is holding too much currency the level of deposits decreases, reducing the
money multiplier.
A similar argument can be made with respect to the increase in the reserve
to deposit ratio. In panics situations, there occurs also an increase in res that
1+cu
decreases the money multiplier. (money multiplier= cu+res
, so an increase in
res causes the denominator to increase and the ratio to decrease, reducing
the multiplier). So, with a smaller multiplier, there is a decrease in the money
supply for a given level of monetary base.
b) Why, in a monetarist view of the determination of output, this would
lead to a macroeconomic contraction.
Remember that the expression for velocity is given by:
PY
Q
=
M
M
In the monetarist view, the velocity of money is constant. Then, given a
level of money supply and the value of velocity we can determine the level of
output in the economy, as we can see from the expression above.
If there is a decrease in the money supply, with constant velocity, the
level of output also decreases, i.e., there is a macroeconomic contraction.
V =
10