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EC201 Intermediate Macroeconomics
EC201 Intermediate Macroeconomics

Lecture 2: National Accounting

Lecture Outline:
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How to measure economic activity (GDP, Inflation rate, Unemployment rate,
etc
...
);

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Important identities in national accounting;

-

Issues in aggregate income distribution;

Essential reading:
Mankiw: Ch
...

In the previous lecture we have seen the series of real GDP per capita in the US
...

GDP (Gross Domestic Product): the value of final output produced during a given
period of time within the borders of a given country
...

There are three approaches to measuring GDP, and all give exactly the same measure
of GDP:
1) Product approach (or value-added);
2) Expenditure approach;
3) Income approach;
To see how all these approaches work we consider a simple example
...


1

The coconut producer: owns all the coconut trees, harvests the coconuts and in
current year produces 10 million coconuts which are sold for $2 each, yielding total
revenue of $20 million
...
5 million in interest on a loan to some
consumers and $1
...

The following table summarises those data:
Table 1

Coconut Producer

Total revenue

$20 million

Wages

$5 million

Interest on Loan

$0
...
5 million

The restaurant: of the 10 million coconuts produced, 6 million go to the restaurant
that uses them to produce meals that are sold to the consumers
...
All coconuts cost $2 therefore the total cost
for the restaurant from buying them is $12 million
...

The restaurant sells $30 million in meals during current year
...

The restaurant pays its workers $4 million and pays $3 million in taxes
...
Using the data from the previous tables we have:
After tax profits: 50 – 9 – 0
...
5 = $24 million
$24 million are the after tax profits of the two firms in the economy (the coconut
producer and the restaurant)
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2

Consumers: work for the producer of coconuts, the restaurant and the government
(notice that the owner of the restaurant and the producer of coconuts are consumers as
well)
...
5
million from the government
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5 million from interest on a loan to the
producer and $24 million of after tax profits
...

Furthermore, they pay $1 million in taxes
...
5 million

Profits distributed

$24 million

Interest Income

$0
...

It pays the army using the taxes collected
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5 million) is equal to total spending
...
5 million

Wages

$5
...

In this approach, to calculate the GDP: we add the value of all goods and services
produced and then subtract the value of all intermediate goods used in production
...

Using this approach the GDP is simply defined as the sum of value added to goods
and services across all productive units in the economy
...

For the restaurant, the value added is its total revenues minus its cost of intermediate
goods: $30 million – $12 million = $18 million
...
However, we have a problem here
...

The standard practice in this case is to evaluate the national security services at the

3

cost of the inputs to production
...
5 million
...
5 million
...
5 = $43
...

Notice: the word final in the definition implies that WE DO NOT COUNT spending
on intermediate goods
...
In some models we will see we shall consider the case of a closed
economy
...
We will do this because it is
simpler to analyse a closed economy than an open economy
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There is no investment in our example and no international trade
...
Government expenditure is $5
...

Therefore: GDP=C+I+G+NX=$43
...

Income includes the profits of firms
...
5 million in wages
...
5
million of income on the interest on a loan
...
Finally we need to include the taxes paid by the
producers since they are income for the government
...

Using this method: GDP = 14
...
5 + 24 + 4
...
5 million
Therefore, the GDP is equivalent to the total income in the economy
...

It is the basic identity in national accounting
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The different components of aggregate expenditure:
a) Consumption: the value of all goods and services bought by households
It includes:
durable goods: last a long time, ex: cars, home appliances
nondurable goods: last a short time, ex: food, clothing
services: work done for consumers, ex: dry cleaning, air travel
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residential fixed investment: Spending on housing units by consumers and landlords
...

c) Government spending: includes all government spending on goods and services
...
g
...

d) Net Exports: The value of total exports (X) minus the value of total imports (M)
...

Does this violate the expenditure = output identity?

5

The answer is NO, because unsold output adds to inventory, and thus counts as
inventory investment – whether intentional or unplanned
...
We have just seen the inventory enters
in the definition of Investment and therefore they counted as expenditure
...
However, there
are other measures of total income that can be used:
Gross National Product (GNP) = GDP + Net Factor Payments (NFP)
The GNP measures the value of output produced by domestic factors of production,
regardless of whether the production takes place
...

For example, if a UK firm is managed by Italian residents, then the profits created by
this firm will be counted in the Italian GNP but not in the Italian GDP
...

Another way to write the income-expenditure identity
The income-expenditure identity implies
Y = C + I + G + NX

Define with YD the disposable income of the private sector:
Y D = Y + NFP − T
where Y is the aggregate income, NFP are the net factor payments from abroad and T
are the taxes
...
etc
...

The National Saving is then defined as:
S = S P + SG = Y D − C + T − G

1)

By the definition of Y D , we have that Y D + T = Y + NFP
Therefore, we can rewrite equation 1) as
S = Y + NFP − C − G

2)

Substitute into 2) the definition of Y given by the Income-Expenditure identity:
S = C + I + G + NX + NFP − C − G = I + NX + NFP

Thus, national saving must be equal investment plus net exports plus net factor
payments from abroad
...

Therefore, our income-expenditure identity can be written also as:
S = I + CA
In a closed economy, where NX = 0, and NFP = 0, the income-expenditure identity
implies: S = I
National saving must be equal to aggregate investment
...
nominal GDP
GDP is the value of all final goods and services produced
...

real GDP measure these values using the prices of a base year
...

changes in quantities of output produced
...

Real GDP is a better measure of the well-being of an economy
...
Then the GDP will double as well, however, quantities are the
same of before, therefore, the economy is not better-off even if the GDP has double
...
This is
because the price effect (inflation) has been taken out by using a base year for the
prices (2006)
...

For example, if we choose 2007 as the base year, the real GDP in 2007 is $51,400,
while in 2008 is $53,460
...

One measure of the price level is the GDP deflator, defined as:

GDP deflator = 100 ×

Nominal GDP
Real GDP

8

Using the same example as before:
Nominal GDP Real GDP

GDP

Inflation

deflator

rate

2006

$46,200

$46,200

100
...
a
...
8

2
...
1

9
...

Inflation rate is the rate of change of that index from one year to the following
...


 Qit
The weight 
 RGDP
t



 on each price reflects that good’s relative importance in GDP
...

CPI in any month equals:
100 ×

Cost of basket in that month
Cost of basket in base period

9

Example with 3 goods
For good i = 1, 2, 3
Ci = the amount of good i in the CPI’s basket
Pit = the price of good i in month t
Et = the cost of the CPI basket in month t
Eb = the cost of the basket in the base period

CPI in month t =

Et
P C + P2t C2 + P3t C3
= 1t 1
Eb
Eb

C 
C 
C 
=  1  P1t +  2  P2t +  3  P3t
 Eb 
 Eb 
 Eb 
The CPI is a weighted average of prices
...

Note that the weights remain fixed over time
...
GDP Deflator
prices of capital goods
included in GDP deflator (if produced domestically)
excluded from CPI
prices of imported consumer goods
included in CPI
excluded from GDP deflator
the basket of goods
CPI: fixed
GDP deflator: changes every year
In the following figure we plot the CPI and the GDP deflator for the US economy
from 1950 to 2005
...
Those differences are due to the elements we listed in the previous
page
...
This is
because it is based on the consumption of households and therefore is a better
measure of the cost of living in an economy
...

Unmeasured changes in quality: Quality improvements increase the value of the
dollar, but are often not fully measured
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U
...
adult population by group, June 2007

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Number employed

=

146
...
9 million

Adult population

231
...
1, U = 6
...
7
L = E +U = 146
...
9 = 153
...
7 – 153 = 78
...
9/153) x 100% = 4
...

A stock is a quantity measured at a point in time
...
g
...
S
...
”
A flow is a quantity measured per unit of time
...
g
...
S
...
5 trillion during 2006
...
Here are some examples:
Stock
↔
a person’s wealth
n
...
When we consider income distribution in a given
economy we may look at the personal distribution of income
...
For example, 50% of UK
population holds 93% of the total income of UK
...
In this case we want to know how the aggregate
income is divided among the factors of production, meaning, workers, owners of
capital (capitalists) and owners of land etc
...
Here we consider the issue of the
functional distribution of income
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It produces consumption goods, investment goods ect
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Now we ask: how we produce those goods
...
In economics the way inputs are transformed into outputs is
defined by a production function
...
So our problem is to find how aggregate income is divided between workers
and capitalists
...
K is for the level of Capital and L for Labour
...
The production
function reflects the available technology for turning capital and labour into output
...
When we talk about changing the scale we talk about the effects on output of
changing ALL the inputs of production (therefore, we may assume we are in the longrun)
...
A function f(X) is homogeneous of degree k if it’s true that:
f ( rX ) = r k f ( X )
where r is a constant
...
In terms of
homogeneity, constant returns to scale are equivalent to say that the
production function is homogeneous of degree 1;
b) Decreasing returns to scale: if we increase all the inputs by r, the total output
increases by an amount less than r;
c) Increasing returns to scale: if we increase all the inputs by r, the total output
increases by an amount larger than r;
Example: the Cobb-Douglas production function
Y = F ( K , L ) = K α Lβ
where α and β are two positive constants
...

Therefore, we have constant returns to scale when α + β = 1, decreasing returns when
α + β < 1 and increasing returns when α + β > 1
...
, x n ) homogenous of degree k, then it
is possible to show that:
kf ( x1 , x 2 ,
...
+ x n
∂ x1
∂x2
∂xn

The Euler’s theorem tells us that we can rewrite a homogenous function in terms of its
partial-derivatives
...

Why is this important for us?
The partial derivatives of the production function we are considering have a nice
economic interpretation:
∂F ( K , L )
= Marginal productivity of Capital (MPK)
∂K

∂F ( K , L )
= Marginal productivity of Labour (MPL)
∂L
In competitive markets, from profit maximisation conditions, it is true that:
MPK =

r
W
and MPL =
P
P

where r is the cost of renting capital, W is the nominal wage and P is the aggregate
price level
...

Those two conditions simply say that in competitive markets the inputs of production
are paid at their marginal productivity
...
Assume that the
production function defining the total output is homogenous of degree 1 (= constant
returns to scale)
...

Then P × F ( K , L) is the VALUE of total production (the GDP of our economy),
while we must notice that MPK × P = r and P × MPL = W
...


14

Using those facts we can rewrite the above equation as:
PY = K × r + L × W

3)

Equation 3) says that the total income in the economy is equal to the sum of factors
payments
...

Therefore, if there are:
a) Constant returns to scale;
b) Competitive markets;
Total output is divided between the payments to capital and the payments to labour,
depending on their marginal productivities
...

Denote with Yt the value of Y in period t (so Yt+1 denotes the value of Y in period t+1
and so on)
...

Therefore, the percentage change of Y between period t and period t+1 can be written
as:

∆Y
× 100
Yt

If we let the difference between Yt +1 − Yt to be really small, that is if we take the
following limit:
lim
∆ →0

∆Y dY
=
Y
Y

where dY is an infinitesimal change in Y, we obtain the expression

dY
that is called
Y

the instantaneous growth rate of Y
...

The term

∂f ( X , Y )
indicates the partial derivative of the function with respect the
∂X

variable X
...

Expression A1) says that the growth rate of XY is equal to the growth rate of X plus
the growth rate of Y
...
However, when we consider discrete changes (when we
use ∆ instead of d) expression A1) still hold approximately
...

Example: suppose that the real GDP has increased by 2% from 2005 to 2006
...

What is the growth rate of nominal GDP between 2005 and 2006?
We know that:
Nominal GDP = Real GDP

× GDP Deflator

Therefore:
Percentage change in Nominal GDP ≈ 2 + 3 ≈ 5%
...
Suppose that population has increased by 1% between 2005 and 2006,
while real GDP has increased by 2% during the same period
...


17

2) Index Numbers
In statistics index numbers are used to describe the behaviour over time of some
interesting variables
...
They are also useful to
compare series of numbers of different size
...
For example, consider the following series for GDP in UK from 1997 to
2002 (values are in million of pounds)
...
For example, use the first
year of the GDP series as the base year
...
11

1999

106

2000

110

2001

112
...
29

Some of the calculations are:
GDP index 1997 =

GDP value 1997
864710
× 100 =
100 = 100
GDP value 1997
864710

18

GDP index 1999 =

GDP value 1999
916639
× 100 =
100 = 106
GDP value 1997
864710

Notice that the index number is a pure number (it does not depend on any unit of
measure)
...
The
fact that the GDP index in 1998 is 103
...


What it is meaningful is that now we can easily compare the behaviour of the series
with respect the base year
...
11% higher than in
1997
...
3% higher than in 1997, and so on
...
We can calculate the year-to-year growth in the GDP
using the original series or using the index number series
...
77%
916639
GDP1999
or using the GDP index series
110 − 106
100 = 3
...

There are two main ways to calculate a price index:
1) Laspeyers Index:
Consider a set I of good and services, that is I={1,2,…i,…n}
Denote with:

p i , t the price of good i in period t
...
The denominator is the cost of the bundle in period 0 (the base year)
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The prices of a pizza and a compact disc are given by the
following table:
pizza

CDs

2002

$10

$15

2003

$11

$15

2004

$12

$16

2005

$13

$15

We can calculate the Laspeyres index with base year 2002
...
7
10 × 20 + 15 × 10

and so on
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The Laspeyers index of our basket of goods is summarised in the following table,
where we reported also the year-to-year inflation
...
0

n
...


2003

105
...
7%

2004

114
...
1%

2005

117
...
5%

2) Paasche Index
Differently from the Laspeyers index, here the basket of goods is changing over time
...

Notice that in order to calculate the Paasche index using the previous example we
should know the quantities sold in each year
...
Is this function
homogeneous? To see that: f (rx) = (rx) 2 = r 2 x 2 = r 2 f ( x)
You can see that f ( x) = x 2 is homogenous of degree 2 (k=2 using the notation in the
note)
...
Apply the Euler’s Theorem: 2 x 2 = x(2 x)
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