The Simple Keynesian Theory
• Some Basic Definitions
– Endogenous variables
The Simple Keynesian Theory of
Income Determination
• Output
• Consumer Spending
– To become endogenous variables
• Investment spending
• Net exports
• Interest rates
• Inflation
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The Simple Keynesian Theory
The Simple Keynesian Theory
• Some Basic Definitions (continued)
• Some Basic Definitions (continued)
– Exogenous variables
– Exogenous variables (continued)
• Policy instruments
• Demand shocks
– Money supply
– Government spending
– Tax rates
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– Unpredictable changes in
» Consumer spending
» Investment spending
» Net exports
† Foreign economic activity
– Abrupt changes in technology
– Changes in regulations
– Wars
– Political crises
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The Simple Keynesian Theory
The Simple Keynesian Theory
• Some Basic Definitions (continued)
• Determining Equilibrium Income
– Exogenous variables (continued)
– By definition
• Supply shocks
E = C + I + G + NX
– Large changes in oil prices
– Large changes in raw material prices
» Agricultural
» Industrial
– Now assume
• C, G and NX are always equal to planned
• Only I can differ from planned
I = I(p) + I(u)
• Parameters
• Therefore
E(p) = C + I(p) + G + NX
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Figure 3-1
A Simple Hypothesis Regarding Consumption Behavior
The Simple Keynesian Theory
• Determining Equilibrium Income (con’t)
– The Consumption Function
• Autonomous consumption
• Induced consumption
– marginal propensity to consume
• General linear form
C=a+c(Y-T)
» Figure 3-1
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Figure 3-3
Consumption, Saving, and Disposable Income, 1929–96
The Simple Keynesian Theory
• Determining Equilibrium Income (con’t)
– The Savings Function
• Autonomous saving
» Figure 3-3
• Induced saving
– marginal propensity to save
• General linear form
S=(Y-T)-C
=(Y-T)-a-c(Y-T)
= -a + (1 - c) ( Y - T) = -a + s ( Y - T )
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Figure 3-2
The Relation Between Induced Consumption, Induced Saving, and the Consumption Function
The Simple Keynesian Theory
• Determining Equilibrium Income (con’t)
– Consumption & Savings (Figure 3-2)
(Y-T)=C+S
= a + c ( Y - T ) -a + s ( Y - T )
=(c+s)(Y-T)
(c+s)=(Y-T)/(Y-T)
=1
so c + s = 1 ; c = 1 - s ; s = 1 - c
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Figure 3-4
Autonomous Planned Spending and the Level of Total Planned Expenditure
The Simple Keynesian Theory
• Determining Equilibrium Income (con’t)
– Equilibrium
• Equilibrium is a situation in which there is no
pressure for change
• Total Planned Expenditures
E(p) = C + I(p) + G + NX
= a + c ( Y - T ) + I(p) + G + NX
= a + cY - cT + I(p) + G + NX
» Figure 3-4
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The Simple Keynesian Theory
The Simple Keynesian Theory
• Determining Equilibrium Income (con’t)
• Determining Equilibrium Income (con’t)
– Equilibrium (continued)
– Equilibrium (continued)
• It is always true that
Y=E
Y = E(p) + I(u)
• Autonomous Planned Spending
A(p) = a - cT + I(p) + G + NX
– where I(u) is unintended inventory investment
• Total Planned Expenditures
• Equilibrium exists only when
E(p) = A(p) + cY
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Y = E(p)
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or
I(u) = 0
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Figure 3-5
How Equilibrium Income is Determined
The Simple Keynesian Theory
• Determining Equilibrium Income (con’t)
– Disequilibrium Dynamics (continued)
• Example
» Figure 3-5
• Does I(u) need to be reversed?
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The Simple Keynesian Theory
The Simple Keynesian Theory
• Determining Equilibrium Income (con’t)
• Determining Equilibrium Income (con’t)
– Equilibrium (continued)
– Equilibrium (continued)
• Autonomous planned spending equals induced
saving in equilibrium
• Autonomous planned spending equals induced
saving in equilibrium (continued)
Y = E(p)
Y - cY = E(p) - cY
( 1 - c ) Y = A(p)
sY = A(p)
– Induced saving = autonomous spending
– Leakages = injections
– remember
s=1-c
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Y(e) = A(p) / s
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The Simple Keynesian Theory
The Simple Keynesian Theory
• The Multiplier Effect
• The Multiplier (continued)
k = Change in Y / Change in A(p)
– An example
• from
– Calculating the Multiplier
Change in Y = Change in A(p) / s
• How much does income change?
Y(1) = A(p)(1) / s
Y(0) = A(p)(0) / s
Change in Y = Change in A(p) / s
k = Change in A(p) / s / Change in A(p)
k=1/s
• Relationship between leakages and the multiplier?
» Figure 3-6
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Figure 3-6 The Change in Equilibrium Income Caused by a $250 Billion Increase in
Autonomous Planned Spending
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The Simple Keynesian Theory
• Fiscal Policy
– Fiscal Policy Definitions
• Changes in government spending
• Changes in autonomous tax revenues
• Changes in tax rates
– Now
A(p) = a - cT + I(p) + G + NX
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The Simple Keynesian Theory
The Simple Keynesian Theory
• Government Spending Multiplier
• Government Spending Multiplier (con’t)
– If
– The Government Budget Deficit
Change in Y = Change in A(p) / s
( G - T ) = S - I - NX
Change in G - Change in T =
Change in S - Change in I - Change in NX
– then
Change in A(p) = Change in G
Change in Y = Change in G / s
k = Change in G / s / Change in G
=1/s
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• but
Changes in T, I, and NX = 0
• therefore,
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The Simple Keynesian Theory
The Simple Keynesian Theory
• Government Spending Multiplier (con’t)
• The Tax Multiplier
– The Government Budget Deficit (continued)
– Autonomous Taxes
Change in G = Change in S
Change in A(p) = -c ( Change in T )
• or
Change in G = s ( change in Y)
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The Simple Keynesian Theory
The Simple Keynesian Theory
• The Tax Multiplier (continued)
• Balanced Budget Multiplier
k(G) = 1 / s & k(T) = -c / s
– Autonomous Tax Multiplier
k(T) = Change in Y / Change in T
– therefore,
• Remember
k(G) + k(T) = [ 1 / s ] + [ -c / s]
=[1-c]/s
=s/s
=1
Change in Y = Change in A(p) / s
= [-c ( Change in T )] / s
• therefore
k(T) = -c ( Change in T ) / s ( Change in T )
= -c / s
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» Figure 3-7
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Figure 3-7 Effect on Income of a $250 Billion Increase in Government Spending Followed
by a $250 Billion Increase in Autonomous Tax Revenue
The Simple Keynesian Theory
• The Tax Multiplier (continued)
– Effect of Income Taxes
• Autonomous taxes
• Induced taxes
• General linear form
• Now
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T = T(a) + tY
YD = Y - T
= Y - T(a) - tY
= ( 1 - t ) Y - T(a)
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The Simple Keynesian Theory
The Simple Keynesian Theory
• The Tax Multiplier (continued)
• The Tax Multiplier (continued)
– Effect of Income Taxes (continued)
– Effect of Income Taxes (continued)
• Induced consumption
• Induced saving
C=a+c(Y-T)
= a + c ( Y - T(a) - tY )
=a+c(1-t)Y
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S=(Y-T)-C
= Y - T(a) - tY -a - c ( 1 - t ) Y
= -a + ( 1 - t ) Y - c ( 1 - t ) Y
= -a + ( 1 - c ) ( 1 - t ) Y
= -a + s ( 1 - t ) Y
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The Simple Keynesian Theory
The Simple Keynesian Theory
• The Tax Multiplier (continued)
• The Tax Multiplier (continued)
– Effect of Income Taxes (continued)
– Effect of Income Taxes (continued)
• Induced income tax revenues
• Total induced changes
T = T(a) + tY
c(1-t)+s(1-t)+t
(c+s)(1-t)+t
(1 - t ) + t
1
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The Simple Keynesian Theory
The Simple Keynesian Theory
• The Tax Multiplier (continued)
• The Tax Multiplier (continued)
– Equilibrium Income with Income Taxes
– Income Taxes and the Multiplier
Change in Y = Change in A(p) / [ s ( 1 - t ) + t ]
Y = E(p)
Y - c ( 1 - t ) Y = E(p) - c ( 1 - t ) Y
[ 1 - c ( 1 - t ) ] Y = A(p)
• so
k=1/[s(1-t)+t]
• or
• so
= 1/ marginal leakage rate
Y(e) = A(p) / [ 1 - c ( 1 - t ) ]
= A(p) / [ s ( 1 - t ) + t ]
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The Simple Keynesian Theory
The Simple Keynesian Theory
• The Tax Multiplier (continued)
• The Tax Multiplier (continued)
– Income Taxes, the Multiplier and Stabilization
Policy
– Income Taxes and the Gov’t Budget Deficit
• Income taxes reduce the size of the multiplier
G - T = G - T(a) - tY
– A smaller multiplier means business cycles are dampened
– Income taxes are an automatic stabilizer.
• Y(e) changes when tax rates change
• Induced taxes makes the deficit cyclical
– Y(e) increases when tax rates are reduced
– Y(e) decreases when tax rates are increased
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– actual deficit
– structural deficit
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The Simple Keynesian Theory
The Simple Keynesian Theory
• The International Trade Multiplier
• The International Trade Multiplier
– Autonomous net exports
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– The multiplier now becomes
• exports
• autonomous imports
k = 1 / [ s ( 1- t ) + t + nx ]
– Induced net exports
• imports
– The multiplier becomes smaller the larger is the
economy’s elasticity to import.
– General linear form
NX = NX(a) - nxY
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The Simple Keynesian Theory
• Summarizing the Multiplier
k = 1 / marginal leakage rate
Types of leakages
Saving only
Saving and income tax
Saving, income tax, and imports
Marginal leakage rate
s
s(1-t)+t
s ( 1 - t ) + t + nx
– Implications for business cycles
– Implications for stabilization policy
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