Multiplier

Closing the recessionary gapClosing the recessionary gap

Classical TheoryClassical Theory In the Classical Economics, a recessionary gap is In the Classical Economics, a recessionary gap is

only temporary. only temporary. Because the surplus in the labor market will Because the surplus in the labor market will

depress the wage ratedepress the wage rate Then cost of production fallsThen cost of production falls Price of products will also fall. Price of products will also fall. Through wealth effect, consumption will go up Through wealth effect, consumption will go up In the income-expenditure diagram, the AE In the income-expenditure diagram, the AE

schedule will shift up. schedule will shift up. Hence the recessionary gap will be closed Hence the recessionary gap will be closed

automatically at reasonable speed.automatically at reasonable speed.

Closing the recessionary gapClosing the recessionary gap

Keynesian TheoryKeynesian Theory Prices and wage rates are rigid to go Prices and wage rates are rigid to go

downwarddownward When the firms and consumers When the firms and consumers

remain pessimistic, even the wage remain pessimistic, even the wage rates and product prices fall, they do rates and product prices fall, they do not increase employment or not increase employment or consumptionconsumption

So the recessionary gap remains for So the recessionary gap remains for long time. Recession is prolonged long time. Recession is prolonged

Recessionary Gap

0 YY*

AE

AE=Y$

Yp

Recessionary gap

Close Recessionary Gap Close Recessionary Gap

Increase total spending AEIncrease total spending AE AE = C + I + G + (X - IM) AE = C + I + G + (X - IM) C, I and X-IM are not controllable C, I and X-IM are not controllable G can be controlled by the G can be controlled by the

governmentgovernment Keynes suggests to increase G thus Keynes suggests to increase G thus

AE to create more demandAE to create more demand

Closing the Recessionary Gap

0 YY*

AE

AE=Y

$

Yp

Recessionary gap

AE’

G

How much should G increase to How much should G increase to close the gap close the gap

A smaller increase in G leads to A smaller increase in G leads to larger increase in Y*larger increase in Y*

Graphically illustration Graphically illustration

Closing the Recessionary Gap

0 YY*

AE

AE=Y

$

Yp

Larger increase in Y*

AE’

Initial increase in G

Numerical illustrationNumerical illustration

The model economyThe model economyC = 100 + 0.9 DIC = 100 + 0.9 DIT = 0T = 0 I = 150I = 150G = 200G = 200X - IM = -50X - IM = -50

Solved: Y* = 4000Solved: Y* = 4000 Suppose: Yp = 5000Suppose: Yp = 5000

Numerical illustrationNumerical illustration

AE = 400 + 0.9 Y AE = 400 + 0.9 Y Equilibrium Y:Equilibrium Y:

Y* = 1/(1-0.9) X 400 Y* = 1/(1-0.9) X 400 = 10 X 400 = 10 X 400 = 4000= 4000

Potential GDP: Yp = 5000Potential GDP: Yp = 5000 The recessionary gapThe recessionary gap

Yp - Y* = 5000 - 4000 = 1000Yp - Y* = 5000 - 4000 = 1000

Numerical illustrationNumerical illustration

Suppose G rises by 100, from 200 to Suppose G rises by 100, from 200 to 300, what happens to Y*? 300, what happens to Y*?

AE = C + I + G + (X - IM)AE = C + I + G + (X - IM) = 500 + 0.9 Y= 500 + 0.9 Y The new equilibrium Y*The new equilibrium Y*

Y** = 1/(1-0.9) X 500 Y** = 1/(1-0.9) X 500 = 10 X 500 = 10 X 500 = 5000 = 5000

Numerical illustrationNumerical illustration

Increase in Y*Increase in Y* Y* = 5000 - 4000 = $1000 Y* = 5000 - 4000 = $1000 G = $100 G = $100 Y* = $1000 Y* = $1000 An increase in G by 100 leads to an An increase in G by 100 leads to an

increase in Y* by 1000. increase in Y* by 1000. Ten times large.Ten times large.

Expenditure MultiplierExpenditure Multiplier Expenditure multiplierExpenditure multiplier Also called “income multiplier”Also called “income multiplier”

Increase in Y*Increase in Y* Expenditure Multiplier = ------------------Expenditure Multiplier = ------------------

Increase in GIncrease in G

Y*Y* EE = ---------- = ----------

GG

Expenditure MultiplierExpenditure Multiplier

Y*Y* 1000 1000

EE = ---------- = -------- = 10 = ---------- = -------- = 10

GG 100 100

Expenditure MultiplierExpenditure Multiplier

Y* Y* Y* Y* Y* Y* Y*Y*

EE = ----- = ---- = ---- = ----- = ----- = ---- = ---- = -----

GG C C I I X-IMX-IM

Economic insight of the multiplier Economic insight of the multiplier

The trickling down effectThe trickling down effect– The multiplier is greater than 1 because The multiplier is greater than 1 because

one person’s spending is another one person’s spending is another person’s income.person’s income.

spending spending income income– A portion of the increase in income is A portion of the increase in income is

spent on consumption, creating more spent on consumption, creating more income, which in turn creates more income, which in turn creates more consumption spending, and so on consumption spending, and so on

Insight of multiplierInsight of multiplier Suppose the government increases G by Suppose the government increases G by

100 (b$)100 (b$) 1st round, government spending:1st round, government spending:

G = G = AE = 100AE = 100 2nd round, contracted firms:2nd round, contracted firms:

C = C = AE = AE = DI X 0.9 = 100 X MPC DI X 0.9 = 100 X MPC = 100 X 0.9 = 90= 100 X 0.9 = 90

3rd round, the shopkeepers,3rd round, the shopkeepers,C = C = AE = AE = DI X 0.9 = 90 X MPC DI X 0.9 = 90 X MPC = 90 X 0.9 = 81= 90 X 0.9 = 81

How the Multiplier Builds

Copyright © 2003 South-Western/Thomson Learning. All rights reserved.

Spending Round

20 15 10 8 6 4 2

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2.0

3.0

1.0

0

Insight of Multiplier

Round Number

Increase in Spending in this round (b$)

Cumulative total(b$)

1 100 100

2 90 190

3 81 271

4 72.9 343.9

5 65.61 409.51

... ... ... ... ... ...

Infinity 0 1,000

Insight of multiplierInsight of multiplier Cumulative increase in Y*:Cumulative increase in Y*:

100 + 90 + 81 + 72.9 + 65.61 + ...100 + 90 + 81 + 72.9 + 65.61 + ...= 100 + 100 X 0.9 + 100 X (0.9)= 100 + 100 X 0.9 + 100 X (0.9)22 + 100 X + 100 X

(0.9)(0.9)33 + 100 X (0.9) + 100 X (0.9)44 +... +...

= 100 X ( 1+0.9+0.9= 100 X ( 1+0.9+0.922+ 0.9+ 0.933 + 0.9 + 0.944 + ... ) + ... ) 11

= 100 X ---------= 100 X --------- 1 - 0.91 - 0.9

= 100 X 10= 100 X 10= 1000= 1000

Geometric Progression and Geometric Progression and solutionsolution

1 + x + x1 + x + x22 + x + x33 + x + x44 + ... + ...

11

= ---------- ( x < 1 )= ---------- ( x < 1 )

1 - x1 - x

Expenditure multiplierExpenditure multiplier

11

EE = ---------- = ----------

1 – MPC1 – MPC

"oversimplified multiplier" formula"oversimplified multiplier" formula

Larger MPC, larger Larger MPC, larger EE

Autonomous changes in AEAutonomous changes in AE

Autonomous increase in C, I, or X-IMAutonomous increase in C, I, or X-IM

refers to an increase in C, I, or X refers to an increase in C, I, or X - IM, which is independent of income - IM, which is independent of income Y. Y.

In graph, an autonomous increase In graph, an autonomous increase shifts the AE schedule up.shifts the AE schedule up.

Any autonomous increase generates Any autonomous increase generates a multiplier effect on Y*a multiplier effect on Y*

Induced changes in AEInduced changes in AE

Induced increase in C, I, or X – IMInduced increase in C, I, or X – IM refers to an increase in C, I or X - IM refers to an increase in C, I or X - IM

due to an increase in income Y. due to an increase in income Y. In graph, an induced increase In graph, an induced increase

produces a movement along the AE produces a movement along the AE schedule. schedule.

Autonomous and induced changes

0 YY*

AE

AE=Y

$

Yp

Autonomous change

AE’Induced change

The Paradox of ThriftThe Paradox of Thrift

If everyone tries to save more in If everyone tries to save more in recessionrecession

Then C fallsThen C falls Then causes a multiple decrease in Then causes a multiple decrease in

Y* Y* Then each individual ends up with Then each individual ends up with

less saving in absolute term. less saving in absolute term.

The Paradox of Thrift

Saving

GDP before recession

GDP in recession