ECON 2123: Macroeconomics
Problem Set #1
Due Date: September 26 (Thu), 2024, 10:00 pm
Instructions:
•
•
•
Please upload your answers on Canvas by 10:00 pm.
Late submissions will not be accepted.
Please put your name and student ID at the upper right corner of the first page.
110 points total
1. Real GDP and the GDP deflator:
In this exercise, you will generate a graph of nominal and real GDP in Hong Kong, calculate
the growth rate of real GDP, and compute the inflation rate based on the GDP deflator. This
exercise is designed to enhance your data-handling skills and to review the relationship
between major macroeconomic variables. In your report, you do not need to attach the
spreadsheet or a screen capture of it. Showing the results is enough.
(a) (10 points) Download data on nominal and real GDP in Hong Kong from the following
page
(https://www.censtatd.gov.hk/hkstat/sub/sp250.jsp?tableID=030&ID=0&productType=8).
You can click “Customise Table / More Data,” select “At current market prices HK$ million,” “In chained (2022) dollars - HK$ million,” “All” under Year, and “GDP”
for GDP expenditure components, press “Submit,” and use the download menu. Create a
chart similar to Figure 2-1 in our textbook using the downloaded data for Hong Kong.
(b) (5 points) Compute the growth rates of real GDP for each year. Express them in percent
by multiplying 100. What is the average of the growth rates during the period? (HINT: Use
‘average’ function in Excel.)
(c) (5 points) Calculate the GDP deflator, 𝑃𝑡 , and the inflation rate, 𝜋𝑡 , which is defined as
𝑃𝑡 −𝑃𝑡−1
𝑃𝑡−1
, for each year. Sometimes, economists use Δ ln(𝑃𝑡 ) = ln(𝑃𝑡 ) − ln(𝑃𝑡−1 ) to
compute the inflation rate, where ln(⋅) is a natural logarithm. Compute the inflation rates
using both methods. Draw the two series of inflation rates on the same chart and compare
the results. Do you find that they are similar?
1
"
a
b)
C
Average
Growth Rate :
5 321
.
Both methods yield similar inflation rates the first method
is
bit higher during certain peak periods. It is identified
that when In (1 + X) is close to X when x is around 0
.
,
a
2. The composition of HK GDP, 2022:
(a) (10 points) Using data provided by Census and Statistics Department, the Government of
the Hong Kong Special Administrative Region, fill in the following table. Specifically, you
may want to look at “Table 310-31002: GDP and its main expenditure components at
current
market
prices.”
(https://www.censtatd.gov.hk/hkstat/sub/sp250.jsp?tableID=031&ID=0&productType=8)
Millions of HKD, 2022
Percent of GDP
GDP (Y)
2,808,981
100.0
Consumption (C)
1,863,515
Investment (I)
451,397
66
16
Government spending (G)
402,722
14
Net Exports (NX)
114,940
4
Exports (X)
5,463,066
194.4
Imports (IM)
5,348,126
190.4
Inventory investment
-23,593
0
(b) (5 points) Among C, I, G, and NX, what is the largest component of GDP in Hong Kong?
(c) (5 points) A widely used measure of trade openness is the openness index, which is given
by
𝑋+𝐼𝑀
𝑌
. Calculate the index of the Hong Kong economy in 2022. Compare your answer
with that of the US economy in 2022, 25%.
(d) (5 points) (Industry-wise decomposition) Check out “Table 310-34101: Gross Domestic
Product (GDP) by major economic activity - percentage contribution to GDP.”
(https://www.censtatd.gov.hk/hkstat/sub/sp250.jsp?tableID=036&ID=0&productType=8)
What is the most important industry in Hong Kong among the five sectors listed in the
table?
2
b) Consumption (c)
1) AxM
5463066 = 5348126
=
2808981
=
=
3 85
.
385 %
385%) 25 %
%
Hong Kong
index
,
is
9) Services
.
has
economy
than
more
open
The
contribution
is
a
openness
high
economy
US
.
almost 93 4 %
.
3. The employment rate:
(10 points) First, see the following definition of the employment rate from the OECD.
(https://data.oecd.org/emp/employment-rate.htm)
Employment rates are defined as a measure of the extent to which available labour resources
(people available to work) are being used. They are calculated as the ratio of the employed to
the working age population.
Suppose that the participation and unemployment rates are 80% and 10% in an economy,
respectively. What is the employment rate in this economy?
4. (Blanchard (2017), #2-5 on p.85)
The following equations refer to the goods market of an economy in billions of euros:
𝐶 = 480 + 0.5𝑌𝐷
𝐼 = 110
𝑇 = 70
𝐺 = 250
(a) (10 points) Solve for the goods market equilibrium.
(b) (5 points) Find equilibrium disposable income (𝑌𝐷 ).
(c) (5 points) Find equilibrium consumption (𝐶).
(d) (5 points) Calculate the private savings, public savings, and investment spending.
(e) Calculate the multipliers in the following cases.
Δ𝑌
(i)
(5 points) The government increases 𝐺 by one unit, while 𝑇 does not change (Δ𝐺).
(ii)
(5 points) The government increases 𝑇 by one unit, while 𝐺 does not change (Δ𝑇).
(iii)
(5 points) The government increases 𝐺 and 𝑇 by one unit (Δ𝐺 |Δ𝐺=Δ𝑇 ).
Δ𝑌
Δ𝑌
(f) (10 points) Now, suppose that taxes depend on the level of income. Specifically, consider
the following equation for taxes:
𝑇 = −252 + 0.2𝑌.
Recalculate the government spending multiplier.
(g) (5 points) Why is fiscal policy in this case called an automatic stabilizer?
3
Participation Rate
=
Unemployment Rate
93) Employment Rate
80%
=
=
Participation Rate
=
=
gn)a)
Y=
c + I + G
(480
y=
+
0
.
10%
0 8 x(1
0 72
YD
y =
180 + 0 5(y
y
1
=
-
Y
=
+
0
.
1
-
T
250
70) + 110 + 250
(480
I-0 3
-
35 + 110 + 250)
.
Y
b)
1610
=
Disposable
YD
=
Yp
=
YD
400
Y
income
-
=
YD
T
1610
-
70
1540
=
+0 5
.
(1-Unemploymento
72 %
=
.
54p) + 110
.
-
.
x
(Y-120) + 110 + 250
c) Equilibrium Consumption (C)
c = 480 +
0 5 YD
.
YD = 1540
c = 480 + 0
.
5(1540
C = 1250
d) Private Savings
1540
-
:
70 - 250
110
=
1250 =
Public Saving
Investment Spending
S
:
Yp
>
290
T
G
=
- 180
-
-
Private Savings + Public
=
=
290
-
180
Savings
e) (i)
G
increases
the same
by
one
# =5
o
(i)
T
increases
change
unit while
=
Tremains
2
.
by one unit
but
h doesn't
=
(ii)
G
&
T
increase
by
one
unit
= /
(
+
I
+ 3
-
xi)
T
f)
y
=
y =
=
Y
=
.
6
+
(480 + 0 5yx)
.
=
Yx
Y
252 + 0 24
c+ 1
=
Yp
-
Y
=
T
-
y
( 252 + 0 24)
-
-
.
(480 + 0 5 (y + 252
.
(480 + 0 Sy + 126
.
-
-
0
.
24) + 110 + 250
0
.
14) + 110 + 250
Y = (480 + 0 4y + 126 + 110 + 250
.
Y
=
ou
(480 + 126 + 110 +250)
y = 1610
New
Multiplier
=
Fon =
=
1 67
.
&
Fiscal
policies
form
in the
and welfare benefits
state of the economy
people earn
amount
progressive taxes
change automatically based
.
more , the
of
When
progressive tax systems that the
of tax
increases.
they
pay
rate would be low the
,
welfare benefits
However,
the
economy is doing and
unemployment
less
on
As the
government pays
economy is struggling the
welfare benefits
help the unemployed people in meeting
the
when
,
and
their
basic
needs
less
well
and , hence
This
as
helps
in
surviving
they
.
People earn
pay lower
taxes
keeping the economy steady.
.