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08金融 梁剑雄
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Outline
Overview of Macroeconomics
National Income Accounting
Economic Growth (I)
Overview of Macroeconomics
 About macroeconomics
Two main themes of macroeconomics:
Economic growth and economic fluctuation
 Macroeconomics versus microeconomics
Microeconomics is the study of how households and
firms make decisions and how these decisionmakers
interact in the marketplace.
Macroeconomics is the study of the economy as a
whole—including growth in incomes, changes in
prices, and the rate of unemployment.
The AS-AD Model
P
AS
AD
Y*
Y
How Can We Measure Y & P?
P
AS
AD
Y*
Y
National Income Accounting
 GDP
 Other measures of income:
GNP, NNP, NDP, National Income…
 Price indexes:
CPI, PPI
GDP deflator
GDP: Definition
 Gross domestic product (GDP) is the market value
of all final goods and services produced within a
country in a given period of time.
Three Methods to Calculate GDP
 Production approach: value added
 Income approach
 Expenditure approach
Production Approach: Example
A farmer grows a bushel of wheat and sells it to a
miller for $1.00. The miller turns the wheat into
flour and then sells the flour to a baker for $3.00.
The baker uses the flour to make bread and sells
the bread to an engineer for $6.00.The engineer
eats the bread. What is the value added by each
person? What is GDP?
the value added by the farmer is $1.00 ($1 – 0 = $1)
The value added by the miller is $2 ($3 – 1 = $2)
The value added by the baker is $3 ($6 – 3 = $3)
GDP is the total value added, or $1 + $2 + $3 = $6.
Income Approach
& Expenditure Approach: a simple example
GDP is the total income:
Wages plus profit
Expenditure($)
GDP is the total expenditure:
Payment to firms for goods
Expenditure Approach:
A Closed Economy
Y  C  I G
C (Consumption): the goods and services bought by households.
I(Investment ): goods bought for future use.
G(Government): purchases are the goods and services bought
by federal, state, and local governments.
Expenditure Approach:
An Open Economy
Y  C  I  G  EX
d
d
d
Where
C d stands for consumption of domestic goods and services
I d stands for investment in domestic goods and services
d
G stands for government purchases of domestic goods and services
EX stands for exports of domestic goods and services.
f
C
Denote consumption of foreign goods and services as
f
investment in foreign goods and services as I
government purchases of foreign goods and services as G f
And
d
f
C  C C
total consumption
d
f
total investment
I I I
total government purchases
G  Gd  G f
Y
 C d  I d  G d  EX
 (C  C )  ( I  I )  (G  G )  EX  (C  I  G )
d
f
d
f
d
f
 C  I  G  EX  (C  I  G )
 C  I  G  ( EX  IM )
f
 C  I  G  NX
f
f
f
f
Expenditure on IMPORT
f
Other Measures of National Income
 GNP(Gross National Product)
GNP = GDP + Factor Payments From Abroad − Factor
Payments to Abroad
 NDP(Net Domestic Product) & NNP(Net National
Product)
NDP = GDP − Depreciation
NNP = GNP − Depreciation
Note: GDP≈GNP, NDP ≈NNP
 NI (National Income) = NNP − Indirect Business Taxes
Other Measures of National Income
(continued)
 PI (Personal Income)=National Income− Corporate Profits−
Social Insurance Contributions− Net Interest+ Dividends+
Government Transfers to Individuals+ Personal Interest
Income
You are not required to remember this formula. We have a
simplified version:
PI=National Income + Government Transfers to Individuals(TR)
 Disposable Personal Income= Personal Income − Personal Tax
and Nontax Payments.
or just this simplified version:
YD( Disposable Income)=PI-TA
Saving & Investment
A two-sector economy
Y CI
Y CS
I S
Saving & Investment
A Closed Economy
Saving & Investment
A Closed Economy
Y  C  I G
I  Y C G
I  (Y  TR  TA  C )  (TA  TR  G )
I  (YD  C )  (TA  TR  G )
I  S  (TA  TR  G )
An Important Identity
(An Open Economy)
YD  Y  TR  TA  C  S
Y  C  I  G  NX
Y  TR  TA  C  I  (G  TR  TA)  NX
YD  C  I  (G  TR  TA)  NX
S  I  (G  TR  TA)  NX
Note: We have assumed depreciation and indirect taxes are both zero here!!
A Complicated Example
Gross domestic product
Gross investment
Net investment
Consumption
Government purchase of
goods and services
Government budget surplus
$6000
$800
$200
$4000
$1100
$30
Calculate a) NDP
Depr.=Ig – In=600
NDP=GDP – Depr.=5,400
A Complicated Example
Gross domestic product
Gross investment
Net investment
Consumption
Government purchase of
goods and services
Government budget surplus
Calculate b) Net exports
NX=GDP – Ig – C – G=100
$6000
$800
$200
$4000
$1100
$30
A Complicated Example
Gross domestic product
Gross investment
Net investment
Consumption
Government purchase of
goods and services
Government budget surplus
$6000
$800
$200
$4000
$1100
$30
Calculate c) Government taxes minus transfers
BS= TA – TR – G 
TA – TR=BS+G=1,130
A Complicated Example
Gross domestic product
Gross investment
Net investment
Consumption
Government purchase of
goods and services
Government budget surplus
$6000
$800
$200
$4000
$1100
$30
Calculate d) Disposable income
YD=GDP – Depr. – TA+TR=4,270
A Complicated Example
Gross domestic product
Gross investment
Net investment
Consumption
Government purchase of
goods and services
Government budget surplus
$6000
$800
$200
$4000
$1100
Calculate e) Personal saving rate
S=YD – C=270
s=S/YD=6.32%
$30
Be Careful!
 If depreciation and indirect taxes can’t be neglected,
don’t apply this formula
S  I  (G  TR  TA)  NX
 Actually I don’t suggest you apply it directly…
 More precisely, Solve
 GDP  C  I  G  NX
 NDP  GDP  Depr.


 NI  NDP  Indirect taxes
YD  NI  TR  TA  C  S
S  I  (G  TR  TA)  NX  Depr.  Indirect taxes
Measures of Price Level
 CPI (Consumer Price Index), PPI (Producer Price
Index)
Key: A basket of goods
 Nominal GDP vs. Real GDP
Key: Fix price
 The concept of GDP deflator
GDP Deflator 
 CPI vs. GDP Deflator
Nominal GDP
Real GDP
Inflation Rate
Pt  Pt 1

Pt 1
Price Level: An Example
Consider an economy that produces only apples. In the
following table are data for two different years.
Year 1
Year 2
Price of red apples
$1
$2
Price of green apples
$2
$1
Number of red apples produced
10
0
Number of green apples produced
0
10
Assume the only consumer in the economy Guy consumes all
the apples produced each year.
Price Level: An Example (continued)
a) Compute the nominal GDP for each year.
b) Compute the real GDP for each year. (Use Year 1 as the base
year.)
c) What’s the GDP deflator for each year? And compute the
inflation rate over Year 2 measured by GDP deflator.
d) Assume year 1 is the base year in which the consumer
basket is fixed. Calculate the CPI for each year, and the
inflation rate over Year 2 measured by CPI.
e) If it’s indifferent for Guy to consume red apples and green
apples, think of your answer of c) and d). What’s your
comment?
Now Turn Back to AS-AD
Framework
P
AS
AD
Y*
Y
The Classical Supply Curve
P
AS
Y*
Y
Shifts in Aggregate Supply:
Very Long Run
P
Y0 Y1 Y2
Y3
Y4
Y
Economic Growth:
Mathematical Preparation
 About growth rate
the growth rate of X can be calculated using the
following formula:
X X t  X t 1
g X (t , t  1)  % change in X 

X
X t 1
Actually, let t  1
X t  X t 1
g X (t , t  t ) 
X t 1
X t  X t 1 X t  X t t
t  (t  1)
t


X t 1
X t 1
Mathematical Preparation(continued)
 Note: X is the function of time t.(X is just a simplified
notation of X(t).) Most of the variables we are going to
talk about are functions of time t. REMEMBER THIS!
 Suppose X or X(t) is derivable (thus is continuous).

X
dX (t )

dt
Continuous Case of Growth Rate
 We have got
X t  X t t

t
g X (t , t  t ) 
X t 1
 Let

t  0
dX

X
dt
gX 

X
X
Continuous Case of Growth Rate (continued)

X
gX 
X
Notes:

 1)

X 1 dX d
gX  
 (ln X )  (ln X )
X X dt dt
So you can either calculate growth rate by differentiating
the natural logarithm or estimate the growth rate
through the difference of the natural logarithm
Continuous Case of Growth Rate (continued)

X
gX 
X
 2) If
gX
is constant from t=0 on, i.e.
gX  g
for t  [0, )
then we have (by solving the differential equation or
just doing some integrals)
X (t )  X (0)e  X 0e
gt
gt
Continuous Case of Growth Rate (continued)
X (t )  X (0)e  X 0e
gt
gt
 3) The average growth rate
ln X (t )  ln X (0)
ln X (t )  ln X (0)  gt  g 
t
ln( X (t ) / X (0))
or g 
t
ln 2
 The ”70” rule: If X (t ) / X (0)  2 then g 
t
 ln 2  0.69  0.7 (just for simplification)
70
t
100 g
70
100g 
t
Continuous Case of Growth Rate (continued)

X
gX 
X
 4) The linkage of discrete cases
 Average growth rate (discrete) (compound interest)
X (t )  X (0)(1  g )
g
t
t
X (t )
1
X (0)
g
e
 1 g
Linkage: think of Taylor’s formula
Continuous Case of Growth Rate (continued)

X d (ln X )
gX  
X
dt
 5) Be accustomed to the natural logarithm form of the
variables. In a graph, if the variable of the horizontal
axis is time, we usually use the natural logarithm form
of the variable in vertical axis. It’s easy to prove that
the slope of the tangent is the growth rate at that given
point. BE AWARE OF THIS WHEN YOU ARE
PREPARING YOUR PRESENTATION!
Mathematical Techniques: Some
Examples

 1)If
Z  XY
then
 3)If
ZX
then


Z X Y
 
Z X Z



Z X Y
 
then
Z X Y

X
 2)If Z 
Y


Z
X

Z
X
 Optional approach: total differential
About Economic Models
Neoclassical Model: Solow Model
 Production function
Y (t )  F ( K (t ), A(t ) L(t ))
 To simplify our discussion, ignore the technological
progress. Let A(t )  1 .
 The production function becomes
Y (t )  F ( K (t ), L(t ))
 Note: Time doesn’t enter the production function directly,
but only through K and L. That is, output changes over
time only if the inputs to production change.
Assumptions Concerning the
Production Function
 1) Constant Return to Scale
F (cK , cL)  cF ( K , L) For all c  0
 2) Positive and diminishing returns to single input
F
 0 ( MPK  0)
K
2 F
 0 ( MPK is diminishing)
2
K
F
 0 ( MPL  0)
L
2 F
 0 ( MPL is diminishing)
2
L
Consider Cobb-Douglas Production Function
 1)
(0    1)
Y  F ( K , L)  K  L
You can prove that C-D production function well satisfies
all the assumption we have just talked about. Finish it
as an exercise.
 2) We may concern more about output per capita.
Y K  L1 K  L1
K 

y 
    ( )  k
L
L
LL
L
y  f (k )  k

where y is output per capita and k is capital per capita.
More Assumptions
 1) No government and no international trade:
Y CI
 2) Saving rate is exogenous:
0  s 1
Y  C  S , S  sY , C  (1  s )Y
 3) Constant growth rate of labor (population)

L
n
L
Capital Accumulation Equation
 1) The concept of stock and flow
 2) The (total) capital accumulation equation

K  I  dK
The Key Equation of Solow Model
 1) Equilibrium of saving and investment
I  S  sY  sF ( K , L)
 2) Deriving the per capita capital accumulation
equation:


dk d K
K  L  L K
k
 ( ) 
dt dt L
L2


K
sY  dK
  nk 
 nk
L
L
 sy  (n  d )k

 k  sy  (n  d )k
 Optional approach: use the logarithm techniques.
Solow Diagram and Steady State
Break-even investment
Investment per
labor
y
(n  d )k
f (k )
*
sf (k )
Actual investment
k
*
k
Solve the Steady State Equilibrium

k  sy  (n  d )k  sk  (n  d )k  0
 Solve
 We get
s
k (
)
nd
*
1
1
s
y (
)
nd
*
and

1
 At steady state


y k
 0
y k



K k L
   n
K k L



Y y L
  n
Y y L
Solow Model: Comparative Statics
( n ' d ) k
Investment per
labor
(n  d )k
f (k )
*
y
**
y
sf (k )
A permanent increase in
growth rate of labor
k
**
k
*
Solow Model: Comparative Statics
Investment per
labor
(n  d )k
f (k )
**
y*
y
s ' f (k )
sf (k )
A permanent
increase in
saving rate
k
*
k
**
Adjustment Dynamic Process
Convergence: Some Data
Convergence across
OECD countries
Convergence: Some Data
Convergence
across U.S states
Convergence: Some Data
However….
Hence, absolute
convergence does not apply
for abroad cross section of
Countries.
Convergence: Two Concepts
 Absolute Convergence: There only exist the
differences of initial endowments between two distinct
economies, then they will reach to the same steady
state.
 Conditional Convergence: Besides the initial
endowments, there exist other differences between
two distinct economies, then they will reach distinct
steady states.
Some Challenging Problems
 1) Suppose there’s a permanent increase in saving rate
just as we have just discussed and we have already got a
description of the adjustment dynamic process: a y-t
graph and a ΔY/Y-t graph. Can you sketch a graph to
explain the adjustment of Investment ?
(Sketch a Per Capita Investment-Time graph.)
Some Challenging Problems (continued)
 2)Consider an economy with only depreciation but
without population growth and it’s at the steady state.
Now suppose there’s a one-time jump in the numbers of
workers. At the time of jump, what happens to output
per capita? Once the economy has again reached the
steady state, is output per capita higher, lower or the
same as it was before the new workers appeared? Sketch
an appropriate graph to describe this.
Some Challenging Problems (continued)
 3) Look back to our example of the adjustment dynamic
process.
Why is the curve concave nearby t1?
Study the shape of the ΔY/Y-t graph or other cases of
adjustment dynamic process if you are interested.
Reference
 王志伟译著，Rudiger Dornbusch, Stanley Fischer and
Richard Startz, Macroeconomics , Tenth Edition (东北
财经大学出版社,2008)
 N. Gregory Mankiw, Macroeconomics, Fifth Edition
(Worth Publishers,2003)
 David Romer, Advanced Macroeconomics, Second
Edition (McGraw-Hill, 2001)
 徐现祥编著，图解宏观经济学，第一版（中国人民大
学出版社，2008）