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Lecture

# Introduction to Macroeconomics: Math App - Lecture 010

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University of Toronto Scarborough

Economics for Management Studies

MGEA06H3

Iris Au

Winter

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6 February 2013
CHAPTER 23: FISCAL POLICY AND AGGREGATED SUPPLY TO DEMAND MODEL [CONT’D]
The Size of the Government and the Size of the Multiplier
It turns out the size of the government/public sector would affect the fluctuations of Y* when the
economy experiences exogenous shocks.
CASE 1: A SMALLER GOVERNMENT
The Initial Model (Week 4) A Smaller Government (After)
C = 20 + (7/8)DI C = 20 + (7/8)DI
T = (2/7)Y – 20 T = (3/28)Y
TR = 220 – (1/7)Y TR = 80 – (1/28)Y
I = 100 I = 100
G = 250 G = 110
X = 120 X = 120
IM = (1/8)Y IM = (1/8)Y
A smaller government has lower tax rate, lower (transfer) benefit reduction rate, and smaller
government spending. We want to see what happens to the equilibrium output and multiplier.
The Initial Model (Week 4) A Smaller Government (After)
DI = Y – T + TR DI = Y – T + TR
DI = 240 + (4/7)Y DI = Y – 3/28Y + (80 – 1/28Y)
DI = 80 + (6/7)Y
C = C(Y) C = C(Y)
C = 230 + 1/2Y C = 20 + 7/8 (80 + 6/7Y)
C = 90 + 3/4Y
AE = C + I + G + X – IM AE = C + I + G + X – IM
AE = 700 + 3/8Y AE = (90 + 3/4Y) + 100 + 110 + 120 – (1/8)Y
AE = 420 + 5/8Y
Y* = 1120 Y = 420 + 5/8Y
Y* = 1120
Multiplier, M Multiplier, M
M = 1 / (1 - Y ) = 1.6 M = 1 / (1 – Y ) = 2.67
When the government goes smaller, the multiplier becomes bigger.
CASE 2: A LARGER GOVERNMENT
The Initial Model (Week 4) A Larger Government (After)
C = 20 + (7/8)DI C = 20 + (7/8)DI
T = (2/7)Y – 20 T = (4/7)Y TR = 220 – (1/7)Y TR = 320 – (3/14)Y
I = 100 I = 100
G = 250 G = 530
X = 120 X = 120
IM = (1/8)Y IM = (1/8)Y
A larger government has higher tax rate, higher (transfer) benefit reduction rate, and larger government
spending.
The Initial Model (Week 4) A Larger Government (After)
DI = Y – T + TR DI = Y – T + TR
DI = 240 + (4/7)Y DI = 320 + (3/14)Y
C = C(Y) C = C(Y)
C = 230 + 1/2Y C = 300 + (3/16)Y
AE = C + I + G + X – IM AE = C + I + G + X – IM
AE = 700 + 3/8Y AE = 1050 + (1/16)Y
Y* = 1120 Y* = 1120
Multiplier, M Multiplier, M
M = 1 / (1 - CY) = 1.6 M = 1 / (1 – CY) = 1.067
When the government becomes larger, the multiplier becomes smaller.
Bigger government means a smaller multiplier. This implies that if the economy is less prone to external
shocks (output fluctuates by smaller amount for a given change in autonomous expenditure). Smaller
government means a larger multiplier. This implies that the economy is more prone, vulnerable; to
external shocks (output fluctuates by larger amount for a given change in autonomous expenditure).
The effectiveness of the automatic stabilizer depends on the size of the government.
Develop the AS-AD Model: Bringing Price into the Model
We need to include prices in the model which had been absent so far. In fact, so far, all we have had is a
demand side model (the Keynesian cross and the AE function focus on the demand side only).
How do we get prices into the model? We need to look at both supply

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