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# Macroeconomics by yurtgc548

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```									  Macroeconomics

Lecture 3
The Keynesian Cross Model
Outline of this lecture

• The national accounting identity.
• Planned and unplanned expenditure.
• Demand-side equilibrium in the
Keynesian Cross model.
• The Keynesian Multiplier.
• How to pay for the War?
(R,,Y)

Labour market
(AS)
Goods market
Keynesian
(R,P,Y)
Cross (IS)
IS-LM
(R, Y)
Financial
markets (LM)
Foreign
exchange
(R*,Y,e, CA)
markets
The national accounting identity

Y  C  I G X Z
Total income
Total expenditure

What guarantees this?
Investments may include an undesired component.

I I
P       U

Planned               Unplanned
Example
Suppose there is a boycott of exports.

Before: Y  AE0  Y  AE0  0
After: gap  Y  AE1  X
For unchanged spending plans and taxes,
the gap is filled by firms being forced to invest
in the form of unplanned inventory build-up

Y  AE1  I U
Demand-side equilibrium
An equilibrium is a situation in which no agent
would want to change behavior and the behavior
of all agents is consistent.
The economy is at equilibrium when there are
no unplanned expenditures (investments), that is
when

Planned expenditure

=
Actual expenditure    =   Income (output)
Only holds in equilibrium!

Actual                    Income Y =     Planned expenditure
expenditure              = Output
C                                        C
Consumption                               Consumption
+ Ip                                      + Ip
Planned investment                        Planned investment
+ IU
Unplanned investment

+G                                        +G
Government expenditure                    Government expenditure
+ X-Z                                     + X-Z
net exports                               net exports
Income determination
Assume that all prices (P, R, e) are fixed
(and that P=e=P*=1).
(1) Y  C  I  G  X  Z
(2) C  c0  c1 (1  t )Y  T 
(3) I P  i0  i1 R                 Planned demand
(4) Z  z0  z1Y                   Behavioral relations
(5) X   0  1Y f

(6) G  G, T  T , 0  t  1       Government behavior
Planned aggregate expenditure
AE  C  I P  G  X  Z

 c0  c1 (1  t )Y  T   i0  i1R   G
  0  1Y f   z0  z1Y 

 c1 (1  t )  z1 Y  A

A  G  i0  i1R  0  0Yf  z0  c0  c1T 
AE  c1 (1  t )  z1 Y  A
Planned expenditure, AE

AE
(1-t)      c1(1-t)
1
z1            C                          Flat if
• z1 large
• c1 small
c1 (1  t )  z1        • t large
B
slope less than 1
£1
A
income
output, Y
AE         Equilibrium: Y*=AE(Y*)

Actual Expenditure=Y
AEa
Expenditure
exceeds output                            AE
AE 0
AE1                                           I 0
u

AE 2
AE *                Output exceeds
expenditure
A

*                                         income
Y            Y2   Y1       Y0                 output, Y
Equilibrating mechanism
Actual demand > planned demand
Unplanned inventory build up
Firms want to change their production
plans to avoid this

Reduction in output and income (actual demand)

Reduction in planned demand, but

Gap between planned and actual reduced.
Equilibrium
Y  AE c1 (1  t )  z1 Y  A
1
Y   *
A
1  c1 (1  t )  z1 

The Keynesian
Autonomous               multiplier
expenditures
The Keynesian Multiplier
The effect on an endogenous variable of
a one unit change in an exogenous variable
CETERIS PARIBUS

The change in equilibrium income (Y*) when
autonomous expenditure (A) increases by £1
(keeping all prices fixed)

Why is this important?
• Determines the impact of economic policy
• Determines the impact of shocks
Import leakage
Initial impact

z1
Planned
expenditure
Y

Large multiplier                       Tax
if leakages are small          t     leakage

C                              Yd
c1
Savings leakage
z1=0

A             Yd                  C                      Y
1   1                                                             1

2                1 t               c1 (1  t )            c1 (1  t )

3          c1 (1  t )       2
c1 (1  t ) 2
2
c (1  t )
2
1
2

4          c1 (1  t ) 3
2
c1 (1  t ) 3 c1 (1  t ) 3
3             3



 Y
i 1
i    1  c1 (1  t )  c1 (1  t ) 2  c1 (1  t ) 3  ....
2               3

1
                 1           for   c1 (1  t )  1
1  c1 (1  t )
AE                        Actual expenditure=Y

AE1

A        AE0

A
1  c1 (1  t )  z1 
 Y
A1
A
Y
A0

Y0   Y2                            income
Y1                      output, Y
How large is it?
1
MP 
1  c1 (1  t )  z1 

“Back of the envelope”      Empirical estimates

z1=0.22
t=0.3      MP=2.7               MP=1.5-3
c1=0.8-0.9
How to Pay for the War?
(Keynes, 1940)

Question: How can Great Britain meet the economic efforts required by
the Second World War without generating inflation?

Y1938  £5520
Y  £825
Y  £6345
How much can government spending be raised?     G  £825????
G               z1  0       c1    C
   4380
 0.79
Y                                                 Y       5520

1  c1 (1  t )  z1    tT 
Y
770
5520    0.14
G
825                                      G  £265
1  0.79 (1  0.14 ) 
What is next?

• Fiscal policy in the Keynesian model
– The balanced budget
– Automatic stabilisers

• Comparison between Classical and Keynesian
model

• The IS curve
Leakages

Y                    Y T                Y T  S  C         CZ
Taxes                                 imports
Savings

Government

Rest of the
Income                         T               S                        X
sector

world
Expenditure                    G               I                        Z

Government
Investments         Exports
expenditure
C  I G X  Z      CI  X Z          C X Z              CZ
Injections

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