ECON2123 (Spring 2012)
22 & 23.2.2012 (Tutorial 3)
Chapter 3: The Goods Market
Composition of GDP
 GDP = Y = C + I + G + X – IM
 Consumption (C): purchases of goods and services by consumers
 Investment (I): purchases of new capital goods (residential and nonresidential investment)
 Government spending (G): purchases of goods and services by the government.
(Government transfers are not included)
 Export (X): purchases of domestic good and services by foreigners
 Import (IM): purchases of foreign good and services
 Inventory investment: difference between production and sales
Consumption function
 The consumption function shows the relationship between consumption and disposable
income
 Disposable income: YD = Y – T ( T = taxes – transfers)
 C = C (YD)
 C = c0 + c1YD
 c0: Autonomous consumption: the amount of consumption which is independent of Y
 Example: Y = 0, C = 200, then 200 is the autonomous consumption

c1: Marginal propensity to consume (MPC): the effect of an additional dollar of
disposable income on consumption
 Example: Y =1000, C = 800, then MPC = 0.8
Graphical representation of consumption function
Suppose a = 0, MPC = 1, then C = Y (Consume all income)
Suppose a = 0, MPC = 0.8, then C = 0.8Y (Consume 80% of income)
Suppose a = 200, MPC = 0.8, then C = 200 + 0.8Y
C
C
C = Y (45)
C = 200 + 0.8Y
C = 0.8Y
C = 0.8Y
200
Y




Slope = MPC = 0.8
Y
The consumption function is a linear function.
The consumption function is upward sloping, meaning that Y and C are positively related
The slope of the consumption function is MPC and it is constant at different level of Y.
When MPC changes, the slope of the consumption function will change.
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Saving function
 The saving function shows the relationship between the amount of saving and disposable
income.
 Y=C+S
 S = Y – C – T = YD – C
 S = S(YD)
 S = –c0 + (1 –c1) YD

(1 –c1): Marginal propensity to save (MPS): the effect of an additional dollar of
disposable income on saving
The determination of equilibrium output
 Assumption: price is fixed (SR assumption), which implies supply responds to demand
passively, i.e. any quantity demanded would be supplied.

The equilibrium GDP is achieved when Production = Demand, i.e. Y = Z
 Aggregate demand : Z = C + I + G  (c0  I  G  c1T )  c1Y
 Y-intercept of the demand curve is  (c0  I  G  c1T ) and slope is c1
Algebraic representation
 The equilibrium GDP is achieved when Y = Z
 Y  c0  c1 (Y  T )  I  G
 Y  c0  c1Y  c1T  I  G
 (1  c1 )Y  c0  I  G  c1T
1
1
[c0  I  G  c1T ] where
 Y
is the multiplier
1  c1
1  c1
Graphical representation
 The equilibrium GDP is achieved when. Y = Z (point E)
ZZ / Y
45 (Production)
Y2
Excess Supply
AD2
ZZ = C + I + G
E
AD1
Excess Demand
Y1
Y
Y1
Y*
Y2
2
 Suppose Y = Y1
 Excess demand (AD1 > Y1)
 The price is fixed and the producer would response to the demand and increases
production
 Y increases and then AD increases
 This process continues until point E is reached.





Suppose Y = Y2
Excess supply (Y2 > AD2)
The price is fixed and the producer would response to the demand and reduces production
Y falls and AD falls
This process continues until point E is reached.
The Multiplier effect
(1) Change in autonomous spending
 An increase in autonomous demand (autonomous G, I or C) would rise Y by more than
the original increase in demand.

Multiplier: the ratio of the change in Y to a change in the government expenditure, i.e.
Y
G
Period 1
Period 2
Period 3
Period 4

Period N
G  by 200
Y  by 200
Y  by (200 MPC)
Y  by (200 MPC2)

Y  by (200 MPCn-2)
AD  by 200
C  by (200  MPC)
C  by (200 MPC2)
C  by (200 MPC3)

 C  by (200 MPCn-1)




Y  by 200
AD and Y  by (200 MPC)
AD and Y  by (200 MPC2)
AD and Y  by (200 MPC3)

 AD and Y  by (200 MPC n-1)




 Y  G  (G  MPC )  (G  MPC 2 )    (G  MPC n1 )
1
 Y  G 
1  MPC
Y
1
 Multiplier 

G 1  MPC

The size of the multiplier (i.e. Y/G) depends on the size of MPC: the higher (lower)
the value of MPC, the larger (smaller) the multiplier effect.
(2) Change in Tax (assuming lump-sum tax)
 Y  (T  MPC )  (T  MPC 2 )    (T  MPC n1 )
MPC
 Y  T 
1  MPC
Y
MPC

 Multiplier 
T 1  MPC
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Examples and Problems
Question 1
Consider an economy in which tax collections are always $200
GDP
480
540
600
660
720
Taxes
200
200
200
200
200
DI
C
210
255
300
345
390
I
100
100
100
100
100
G
215
215
215
215
215
I
100
100
100
100
100
G
215
215
215
215
215
(a) Fill in the column for DI, disposable income
GDP
480
540
600
660
720
Taxes
200
200
200
200
200
DI
280
340
400
460
520
C
210
255
300
345
390
AD
525
570
615
660
705
(b) Find the equilibrium level of GDP for this economy
Equilibrium = 660 when Y = AD
(c) What is the marginal propensity to consume?
MPC = ¾
(d) What is the simple multiplier for the economy?
Multiplier = 1/(1-MPC) = 4
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Question 2
Giving the consumption function, C = 200 + 0.8Y
(a) Derive the saving function.
Y=C+S
S = Y – C  S = Y – 200 – 0.8Y  S = – 200 + 0.2Y
(b) Graph the saving function (Try to derive it from the consumption function!). How much
is saving/ dissaving when Y = 400 and Y = 2000
C
45
2000
1800
Saving = 200
C = 200 + 0.8Y
520
400
200
Dissaving = 120
Y
400
1000
2000
S
S
200
Y
–120
1000
2000
–200
At Y = 0, C = 200, which means S = –200
At Y = 400, C = 520, which means S = –120
At Y = 1000, C = 1000, which means S = 0
At Y = 2000, C = 1800, which means S = 200
The saving function is a linear function.
The saving function is upward sloping, meaning that Y and S are positively related.
The slope of the saving function is MPS and it is constant at different level of Y.
When MPS changes, the slope of the saving function will change
(c) Identify the autonomous saving and the marginal propensity to save (MPS). What is the
relationship between MPS and MPC?
Autonomous saving = –200 (borrowing) and MPS = 0.2 (MPS = S/Y).
MPC + MPS = 1
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Question 3
Suppose the economy is characterized by the following equations:
C = 160 + 0.6 YD
I = 150
G = 150
T = 100
Solve for the following questions and put your answers in a graph.
45
(a) Equilibrium output (Y)
AD’’
ZZ/ Y
AD
Y = 160 + 0.6 (Y – 100) + 150 +150
Y* = 1000
E
AD’
E
(b) Disposable income (YD)
YD = Y – T = 1000 – 100 = 900
E
440
400
360
(c) Consumption spending
C = 160 + 0.6 (900) = 700
Y**=900
(d) Suppose now G falls to 110. Solve for the new equilibrium.
’
’Y
Y**=1100
’
Y*=1000
1
1

 2.5
1  MPC 1  0.6
G = 40, Y = -40  Multiplier = -40  2.5 = -100
Y** = Y* + Y = 900
Multiplier 
(e) Suppose the government increases taxes and government expenditure by 100 at the same
time. Solve for the new equilibrium.
Y = 160 + 0.6 (Y – 100-100) + 150 +250
Y*** = 1100
Alternatively,
Y = 100  [1/(1 – MPC) – C1 /(1– MPC)] = 100
Y*** = Y* + Y = 1100
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Example 4: Taxes and Transfers
Recall that we define T as net of transfers. In other words, T = taxes – transfer payments.
(a) Suppose that the government increases transfer payments to private households, but
these transfer payments are not financed by tax increases. Instead, the government
borrows to pay for the transfer payments. Show in the diagram (like Figure 3-2) how this
policy affects equilibrium output. Explain.
AD
45 (Production)
ZZ’
Y*
ZZ
E’
Y’
Disposable income and hence consumption both
increases for any level of Y, so the ZZ curve
shifts up, and equilibrium output increases.
E
Y
Y*
Y’
(b) Suppose instead that the government pays for the increase in transfer payments with an
equivalent increase in taxes. How does the increase in transfer payments affect
equilibrium output in this case?
There is no effect on equilibrium output, since T does not change.
(c) Now suppose that the population includes two kinds of people, those with high
propensity to consume and those with low propensity to consume. Suppose that transfer
policy increases taxes on those with low propensity to consume to pay for the transfers
to people with high propensity to consume. How does this policy affect equilibrium
output?
The ZZ line shifts up and output increases. The reduction in demand due to the tax
increase on low MPC group is smaller than the increase in demand due to the increase in
transfers on high MPC group. Therefore, this policy increases equilibrium output.
Effectively the income transfers increases the propensity to consume for the economy as
a whole.
(d) The propensity to consume is likely to be higher for low-income taxpayers. Do you
think tax cuts will be more effective at stimulating output when they are directed toward
high-income or toward low-income taxpayers?
People with high wealth probably have a lower propensity to consume than people with
low wealth. At the extreme, those in poverty may spend most of any additional dollar on
basic needs.
Since wealth and income are usually related, people with high income probably have a
lower propensity to consume than people with low income. Therefore, tax cuts are likely
to be more effective at stimulating output when they are directed toward people with low
income, who are likely to spend more of the extra disposable income.
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