EC201 Intermediate Macroeconomics
EC201 Intermediate Macroeconomics
Problem Set 1 Solution
1) Given the difference between Gross Domestic Product and Gross National Product
for a given economy:
a) Provide an interpretation for the numbers of the following Table:
(GNP – GDP) as a percentage of GDP
selected countries, 2005
Phillippines
Phillippines
Bangladesh
Bangladesh
U.K.
U.K.
U.S.A.
U.S.A.
Mexico
Mexico
Russia
Russia
El Salvador
El Salvador
Argentina
Argentina
Indonesia
Indonesia
Panama
Panama
9.2%
9.2%
5.1
5.1
2.2
2.2
0.3
0.3
-1.8
-1.8
-2.5
-2.5
-3.4
-3.4
-5.4
-5.4
-6.5
-6.5
-7.3
-7.3
b) In your country, which would you want to be bigger, GDP, or GNP? Why?
Solution
The difference between GDP and GNP is given by the Net factor payments.
GNP = GDP + Net Factor Payments (NFP)
Therefore: GNP – GDP= NFP
Where: NFP = factor payments from abroad – factor payments to abroad
GNP is greater than GDP if NFP are positive.
For example, in Mexico, GNP is 1.8% smaller than GDP. This sounds like a tiny
number, but it means that about 2% of all the income generated in Mexico is taken
away and paid to foreigners (NFP negative).
In Panama, about 7% of the value of domestic production is paid to foreigners.
In the Phillippines, GNP is 9.2% bigger than its GDP. This means that the income
earned by the citizens of the Phillippines is 9.2% larger than the value of production
occurring within the country’s borders (GDP).
Reasons why GNP may exceed GDP:
- Country has done a lot of lending or investment overseas and is earning lots of
income from these foreign investments (income on nationally-owned capital located
abroad).
- A significant number of citizens have left the country to work overseas (their income
is counted in GNP, not GDP). This is probably true for Philippines.
Reasons why GDP may exceed GNP:
- Country has done a lot of borrowing from abroad, or foreigners have done a lot of
investment in the country (income earned by foreign-owned domestically-located
capital). This is most likely why Mexico and Argentina’s GDP > GNP.
- Country has a large immigrant labor force
b) There is not a unique answer to that question. However, a possible good answer
could be: it’s better to have GNP > GDP, because it means our nation’s income is
greater than the value of what we are producing domestically. If, instead, GDP >
GNP, then a portion of the income generated in our country is going to people in other
countries, so there’s less income left over for us to enjoy.
2) Consider the following economy that is producing only oranges and apples. Prices
and quantities for the last three years are displayed in the following table:
Year
Apples
Oranges
Quantity
Prices
Quantity
Prices
2004
50
$1.00
100
$0.80
2005
60
$1.50
110
$1.40
2006
65
$2.00
110
$1.50
a) Calculate the Nominal GDP, the Real GDP (using 2004 prices) and the GDP
deflator in each year;
b) Calculate an index for the nominal GDP and the real GDP with base year
2004. Comment your results;
c) Calculate the CPI index using the year 2004 as the base year. Comment on the
differences between the CPI and the GDP deflator index;
Solution
a)
The Nominal GDP in each year is given by:
2004:
50 × 1 + 100 × 0.80 = $130
2005: 60 × 1.50 + 110 × 1.40 = $244
2006: 65 × 2 + 110 × 1.50 = $295
The Real GDP
2004: $130
2005: 60 × 1 + 110 × 0.80 = $148
2006: 65 × 1 + 110 × 0.80 = $153
The GDP Deflator:
2004: (Nominal GDP/Real GDP) 100 = 100
2005: (244/148)100 = 164.86
2006: (295/153)100 = 192.81
b)
The base year is 2004:
Nominal GDP index:
2004: 100
2005: (244/130) 100 = 187.7
2006: (295/130) 100 = 226.9
Real GDP
2004: 100
2005: (148/130) 100= 113.8
2006: (153/130) 100 = 117.7
The Nominal GDP in 2005 was 87.7 % larger than in 2004, but the real GDP was
only 13.8% larger than the 2004 level.
The Nominal GDP in 2006 was 126.9% larger than the level in 2004, but the real
GDP was only 17.7% larger than the level in 2004.
This means that most of the change in the Nominal GDP is due to the increase in
prices, as we can see from the GDP deflator index. Between 2004 and 2005 the prices
rose by 64.9%.
(Notice that 64.9 + 13.8 = 78.7%. Approximately, the percentage change in Nominal
GDP between 2004 and 2005 (87.7%) should be equal to the percentage change of the
real GDP plus the percentage change of the GDP deflator during the same period. In
this case this approximation is not particularly good given the big variations in the
variables we are considering)
c)
CPI index with base year 2004:
The cost of the basket in the base year is $130 (that is exactly the GDP and the Real
GDP).
2004: 100
2005:
(50 × 1.50 + 100 × 1.40)100 = 165.4
2006:
(50 × 2 + 100 × 1.50)100 = 192.3
130
130
As we can see there is a very small difference between the GDP deflator index and the
CPI.
In this particular example, the difference is simply given by the basket we are taking
to calculate the CPI. For the CPI the basket is the consumption basket in 2004, while
for the GDP deflator the basket of goods is not fixed.
The CPI compares the cost of a fixed consumption bundle (50 apples and 100
oranges) in different years. According to this measure, the inflation rate between 2004
and 2005 was 65.4%, while using the GDP deflator the inflation rate in the same
period was 64.86%.
The inflation rate between 2005 and 2006 is:
According to CPI: (192.3/165.4 – 1) 100 = 16.2%
According to the GDP deflator: (192.81/164.86 – 1) 100 = 16.95%
3) Consider a closed economy described by the following equations
Y = 5000
G = 1000
T = 1000
C = 100 + 0.75(Y − T )
I = 1000 − 10r
where Y is total income (GDP), G is the government expenditure, T are the taxes, C is
aggregate consumption that depends on disposable income (Y-T) and I is the
investment function that we assume to be negatively related with the interest rate (r).
a) From this economy, calculate private, public and national saving;
b) Use the income expenditure identity to calculate the equilibrium interest rate;
c) Now suppose that G increases to 1500, everything else constant. Calculate the
private, public and national saving in this case;
d) Find the new equilibrium interest rate. Comment your result;
Solution
a)
Private saving is what is left to households after they paid for consumption and taxes.
It is therefore given by the difference between disposable income YD and
consumption:
S P = Y D − C = (5000 − 1000) − 100 − 0.75(5000 − 1000) = 900
Public saving: it is given by the difference between taxes and government expenditure
(if it is positive the government is running a budget surplus, if it is negative the
government is running a budget deficit). In this particular example the government is
running a balanced budget (T = G) and therefore the public saving is zero.
The national saving is the sum of private and public saving and therefore is given by
900.
b)
In a closed economy, the income expenditure identity implies that:
Y = C+ I +G
or alternatively:
where S is national saving.
Using the first identity, we have:
S=I
5000 = 100 + 0.75(5000 − 1000) + 1000 − 10r + 1000
⇒ 10r = 100 + 3000 + 1000 + 1000 − 5000
100
⇒r=
= 10
10
Or using the second identity:
900 = 1000 − 10r
100
⇒r=
= 10
10
therefore, the equilibrium interest rate the equalises aggregate income and aggregate
expenditure is 10%.
c)
Now the government expenditure has increased everything else constant.
The first effect of this increase is a budget deficit for the government (1000 – 1500) =
500. therefore, the public saving in this case becomes negative (this means that
government is borrowing money).
The private saving is the same as before, since total income is still 5000 and taxes are
the same as before. Therefore private saving is 900.
National saving is therefore 900 – 500 = 400.
Since the national saving is reduced (because the government is borrowing money),
aggregate investments must decrease. In order for the investment expenditure to
decrease, the interest rate must increase.
The equilibrium interest rate is now given by:
400 = 1000 − 10r
600
⇒r=
= 60
10
Since the aggregate output is fixed in this example, an increase in government
expenditure (an example of fiscal policy) has the effect of increasing the equilibrium
interest rate and reducing aggregate investment (by reducing national saving).
This is an example of what is called crowding-out. Increasing government
expenditure may crowd out private investment expenditure because it raises interest
rate. However, how relevant is the crowding-out effect is still a debated issue in
macroecnomics.