Midterm Exam
Introduction to Macroeconomics
Uni Wien
Solutions
Question 1 Short Questions: (30 Points)
Part 1.1 (4 Points) Over the last year nominal GDP in Fantasia grew by 6%. Unemployment was at 4%. Inflation was measured to be 8%. Can you say what happened to real
GDP? If yes, do so. If not, explain why not?
We know that nominal GDP can increase either because prices or because quantities
increase. Let γ denote growth rates. In class we showed that the growth rate of
nominal GDP is approximately the growth rate of real GDP plus the growth rate of
the price level, i.e.: γnom GDP = γnom GDP + γP . Therefore to find the growth rate
of real GDP, just subtract the growth rate of prices (inflation) from the growth rate
of nominal GDP and we obtain that real GDP ‘grew’ by −2%. The information on
the unemployment rate is not necessary to answer the question.
Part 1.2 (4 Points) Consider an economy with M1 = 1000 and a money multiplier of 8.
After a long day of classes you go to a bar and meet a guy who claims to be a Central Banker.
He tells you that reserves of commercial banks at the Central Bank in this economy are 200.
Does this make sense? If yes, explain why, if not, explain that, too.
Clearly the guy has no idea what he is talking about! A money multiplier of 8
implies that high powered money must be 125. However, high powered money is
the sum of currency and reserves. If reserves were really 200 then currency would
have to be negative, which is not possible.
Part 1.3 (10 Points) Consider the following information on the Euro area (in billion e):
Year
2000
2007
2008
2009
nominal GDP
676.3
896.3
918.2
889.6
real GDP
676.3
785.5
809.0
788.7
GDP Defl.
100.0
114.1
113.5
112.8
GDP Infl.
CPI Infl.
-0.5%
-0.6%
3.3%
0.3%
CPI
100.0
116.4
120.3
120.6
1. Explain how the CPI is constructed.
2. Provide at least two arguments why GDP-inflation and CPI-inflation differ.
The key question when trying to measure price changes is how to handle changing
quantities. The consumer price index is based on a regularly (roughly every 5–10
years) updated consumption basket of a representative household. Every month
statistical agencies collect price data on each good in the basket. The important
point is that prices are aggregated using the weights of the consumption basket, i.e.
CPIt =
∑i Pit Qi0
∑i Pi0 Qi0
Solutions: Midterm Exam
— 2—
Winter Semester 2010/2011
where i is an index over all the goods in the basket. The period in which the quantities of the basket is determined is often referred to as the base year. An index number that uses weights determined in some past period is referred to as Laspeyres
Index.
One key difference between GDP-deflator and CPI is the basket of goods concerned. Whereas the GDP-deflator by construction only measures goods that enter
GDP, the CPI considers everything that is consumed by households. The key differences are imported goods.
The second key difference is in the choice of the weighting scheme. We already
discussed that the quantities for the CPI are for some base period in the past. This
has the tendency to overestimate by how much consumers are affected by price increases. Normally, consumers reduce the consumption of goods that have become
relatively more expensive. However, this change in consumption behavior is not
taken into account in a Laspeyres type index as the CPI.
The GDP-deflator, on the other hand, is the ratio of nominal over real GDP, i.e.
GDPde f =
GDPnom
∑ Pit Qit
= i
GDPreal
∑i Pi0 Qit
and we notice immediately that the weight of price i in period t is the current quantity. It will therefore not suffer from the problem of the CPI when prices increase
because it takes into account how quantities adjust.
Part 1.4 (12 Points) Consider two economies that are almost identical. They only differ
along two dimensions that both affect the slope of the IS-curve:
A: Country A has a very high marginal propensity to consume of cA1 = 0.8 and taxes are
independent of income.
B: Country B has a low marginal propensity to consume of cB1 = 0.3 and the marginal
tax rate is 50%, i.e. of every additional e of income half is taxed.
i (6 Points) Consider the two Short run equilibria depicted in the IS-LM diagrams
below. Which diagram belongs to which country? Explain!
ii (6 Points) If the government in each country increases government spending by
e100 million, will the increase in GDP be the same for both countries? If yes, explain
why. If not, explain where the increase will be stronger, and why.
Solutions: Midterm Exam
— 3—
Winter Semester 2010/2011
IS-LM: Case Flat
0.5
Nominal Interest Rate, i
0.4
0.3
0.2
0.1
0
IS-curve
LM-curve
-0.1
1000
1500
2000
2500
3000
3500
4000
4500
5000
Output, Y
IS-LM: Case Steep
0.5
Nominal Interest Rate, i
0.4
0.3
0.2
0.1
0
IS-curve
LM-curve
-0.1
1000
1500
2000
2500
3000
3500
4000
4500
5000
Output, Y
A high marginal propensity to consume or a low marginal income tax both imply
a flat IS-curve. This is easy to check when you derive an expression for the slope
of the IS-curve. Therefore country A’s IS-curve is the flat curve and country B’s
IS-curve is the steep curve.
The LM curve is the same for both countries. The effectiveness of fiscal policy
hence mainly depends on the magnitude of the shift in the IS-curve. The shift is
driven by the government spending multiplier. High marginal propensity to consume is important for fueling the multiplier process and therefore the high multiplier of 5 in country A will lead to a stronger effect of fiscal policy than the low
multiplier in country B.
Solutions: Midterm Exam
— 4—
Winter Semester 2010/2011
Question 2 GDP and Prices (30 Points)
You are given the following information on prices and quantities for 3 products (A, B, and
C) in the years 2006 - 2008:
2006
2007
2008
Product A
200
220
210
Quantities
Product B Product C
300
70
350
80
350
90
Product A
9
10
11
Prices
Product B
8
8
9
Product C
5
4
3
Also assume that goods A and C are produced domestically, good B is imported and good C
is exported.
Part 2.1 (6 Points) Calculate nominal GDP for all three years.
Nominal GDP is simply the product of current price times quantity of each good
sold as final good in the economy within a year. Good B is imported and therefore
not relevant for GDP computations.
Part 2.2 (6 Points) Using 2006 as the base year, calculate real GDP for all three years.
Again, good B does not enter the calculation. So for 2007 we compute: 220 · 9 + 80 ·
5 = 2380.
Part 2.3 (6 Points) Calculate the GDP Deflator for all three years. Also calculate the
inflation rate implied by the GDP Deflator for 2007 and 2008.
GDP deflator is simply the ratio of nominal over real GDP (if you like you can
multiply by 100). GDP-inflation is then computed as the percentage growth rate of
the GDP deflator, i.e.
de f l
πGDP =
de f l
GDPt+1 − GDPt
de f l
GDPt
de f l
=
GDPt+1
de f l
GDPt
− 1.
Part 2.4 (6 Points) Calculate the CPI for all three years using a consumer basket consisting of the quantities consumed in 2006.
When computing the CPI it is now important to realize that product B is consumed
and enters the consumption basket. However, good C is exported and does not
affect the consumption basket. So for 2008 we obtain the value of the consumption
basket to be: CB2008 = 200 · 11 + 300 · 9 = 4900. Whether you simply compute the
growth rate of the value of the consumption basket or first normalize to compute
the CPI by dividing each year’s consumption basked value by the value of CB2006
does not matter for measured CPI - inflation.
Part 2.5 (6 Points) Deduce the inflation rates for 2007 and 2008 based on the CPI.
Year
2006
2007
2008
GDPN
2150
2520
2580
GDPR
2150
2380
2340
GDPde f
100.00
105.88
110.26
GDP-infl.
5.88%
4.13%
CB
4200
4400
4900
CPI
100.00
104.76
116.67
CPI-infl
4.76%
11.36%
Solutions: Midterm Exam
— 5—
Winter Semester 2010/2011
Question 3 IS–LM (40 Points)
Consider the following numerical version of the IS-LM model:
C = 400 + 0.6YD
I = 280 + 0.3Y − 2000i
= 0.25Y − 400
T
G = 580
d
M
= 0.3Y − 600i
P
s
M
= 1500
P
Part 3.1 (5 Points) Derive an equation for the IS curve.
Equilibrium condition on the goods market:
Y
= 400 + 0.6 (Y − 0.25Y + 400) + 280 + 0.3Y − 2000i + 580
Y
= 0.75Y − 2000i + 1500
0.25Y
= 1500 − 2000i
Y
= 6000 − 8000i
Part 3.2 (5 Points) Derive an equation for the LM curve.
Equilibrium condition on financial market:
1500 = 0.3Y − 600i
i = 0.0005Y − 2.5
or
Y = 2000i + 5000
Part 3.3 (5 Points) Solve for the equilibrium values of real GDP (Y ), the interest rate (i),
private consumption (C), investments (I) and of the tax returns (T ).
Equating IS and LM curve:
6000 − 8000i = 2000i + 5000
1000 = 10000i
i = 0.1 = 10%
Inserting this into IS or LM curve: Y = 5200.
C = 400 + 0.6 (5200 − 0.25 · 5200 + 400) = 2980
I = 280 + 0.3 · 5200 − 2000 · 0.1 = 1640
T = 0.25 · 5200 − 400 = 900
Part 3.4 (4 Points) Calculate the values of private saving and of public saving in the equilibrium. Is the government running a budget deficit or a budget surplus?
Verify that your solution in (3.3) constitutes an equilibrium by showing that at your solution investment equals total saving.
Solutions: Midterm Exam
— 6—
Winter Semester 2010/2011
S = Y − T −C
= 5200 − 900 − 2980
= 1320
Public saving is T − G = 900 − 580 = 320 > 0 ⇒ budget surplus
Total saving is 1320 + 320 = 1640 = I
Part 3.5 (10
s Points) Suppose that the central bank decides to decrease the real money supply to M
= 900.
P
Solve again for the equilibrium values of Y , i, C, I and T . Additionally, solve for the new
value of public saving in equilibrium. Is the government running a budget deficit or a budget surplus?
Moreover, use a diagram to show the effects of this policy on Y and i and give an explanation
for all the observed changes (i.e. of the effects of the policy on Y , i, C, I and T ).
new LM-curve:
900 = 0.3Y − 600i
Y
= 3000 + 2000i
Equating this with IS-curve from (a):
6000 − 8000i = 3000 + 2000i
3000 = 10000i
i = 0.3 = 30%
Inserting this into IS or LM curve: Y = 3600
C = 400 + 0.6 (3600 − 0.25 · 3600 + 400) = 2260
I = 280 + 0.3 · 3600 − 2000 · 0.3 = 760
T = 0.25 · 3600 − 400 = 500
Public saving = T − G = 580 − 500 = −80 < 0 ⇒ Budget deficit
Solutions: Midterm Exam
— 7—
Winter Semester 2010/2011
Explanation: central bank must sell bonds in order to reduce the money supply,
given Y this creates an excess supply of bonds, bond price goes down, interest rate
goes up ⇒ LM curve shifts upwards, new money market equilibrium at point B
At point B the interest rate is higher meaning that I decreases ⇒ Z ↓ ⇒ Y ↓ ⇒ C ↓
, I ↓⇒ Z ↓⇒ . . . (multiplier process on the goods market, results in lower Y )
this decrease in Y means that money demand decreases as well, people buy bonds,
bond price goes up again, interest rate decreases a little bit to keep money market
in equilibrium ⇒ movement along new LM-curve from B to the new equilibrium
A’
Overall effects: Y decreases, i increases, because disposable income is lower C decreases, I decreases both because of lower production and higher interest rate, T
decreases because of lower income
Part 3.6 (11 Points) Suppose that the central bank still sets a real money supply of 900,
but that additionally the government pursues the goal of a balanced budget. Does this
require contractionary or expansionary fiscal policy? (Why?)
Suppose that the government wants to obtain a balanced budget solely through changes in
government consumption. Calculate the value of G which is needed to implement a balanced
budget in an equilibrium. Which values of Y , i, C and I does this imply?
Moreover, use a diagram to show the effects of this policy on Y and i and give an explanation
for all the observed changes (i.e. of the effects of the policy on Y , i, C, I and T ).
To achieve a balanced budget, government must reduce the budget deficit found in
(e) ⇒ use contractionary fiscal policy
IS curve for G = T = 0.25Y − 400:
Y
= 400 + 0.6 (Y − 0.25Y + 400) + 280 + 0.3Y − 2000i + 0.25Y − 400
Y
= Y + 520 − 2000i
i = 0.26 = 26%
Inserting this into the LM curve from (e):
Y = 3000 + 2000 · 0.26 = 3520
G = T = 0.25 · 3520 − 400 = 480
C = 400 + 0.6 (3520 − 480) = 2224
I = 280 + 0.3 · 3520 − 2000 · 0.26 = 816
Solutions: Midterm Exam
— 8—
Winter Semester 2010/2011
Explanation: In order to reduce the budget deficit, the government must decrease G ⇒ given i, Z ↓ ⇒ Y ↓ ⇒ C ↓, I ↓ ⇒ Z ↓ ⇒ Y ↓ ⇒ . . . (multiplier process on the
goods market results in lower Y ) ⇒ shift of IS curve to the left, new goods market
equilibrium at B
at B Y is lower, thus money demand decreases as well (lower need for transactions),
people want to buy bonds ⇒ excess demand for bonds ⇒ bond price ↑ ⇒ i ↓
a lower i leads to higher I ⇒ Z ↑ ⇒ Y ↑ ⇒ C, I ↑ ⇒ Y ↑ ⇒ . . . (multiplier process on
goods market results in slight increase in Y again to keep goods market in equilibrium) ⇒ movement along new IS curve from point B to new equilibrium A’
Overall effects: Y decreases, i decreases, C decreases because of lower disposable
income, two effects on I: on the one hand I should decrease because of lower production, on the other hand I should increase because of lower interest rate (in this
example the first effect is dominating and I increases), T decreases because of lower
income