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Chapter 3
Spending,
Income, and
Interest Rates
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Theory of Business Cycles: Outline
• Ch 3: Spending, Income, and Interest Rates
– Use the Keynesian Cross Model to derive the IS curve
• Ch 4: Monetary and Fiscal Policy in the IS/LM Model
– Use equilibrium in the money market to derive the LM curve
– Combine the IS and LM curves to determine Y and i
• Ch 5: The Government Budget, Foreign Borrowing,
and the Twin Deficits
• Ch 6: International Trade, Exchange Rates, and
Macroeconomic Policy
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The “Great Moderation”
• The goal of monetary and fiscal policy is to
dampen business cycle fluctuations and to
promote steady economic growth.
• Since 1985, business cycle fluctuations have
noticeably diminished.
• This data has caused debate among economists:
– Have there been fewer shocks since 1985?
– Or were monetary and fiscal policy more effective in
offsetting shocks?
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Figure 3-1 Real GDP Growth
in the United States, 1950–2007
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Aggregate Demand and Supply
•
Aggregate Demand (AD) is the total amount of desired
spending expressed in current (or nominal) dollars.
– A demand shock is a significant change in desired spending by
consumers, business firms, the government, or foreigners.
• Algebraically, any change in C, I, G or NX
•
Aggregate Supply (AS) is the amount that firms are
will to produce at any given price level.
– A supply shock is a significant change in costs of production for
business firms, including wages and the prices of raw materials,
like oil.
• AS and supply shocks will be considered in Chapters 7 and 8.
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Modeling Preliminaries
•
Simplifying assumption:
– The price level (P) is fixed in the short run.
• Implication: All changes in AD automatically cause changes in real
GDP by the same amount and in the same direction.
•
The variables that an economic theory tries to explain
are called endogenous variables.
– Examples: Output and interest rates
•
Exogenous variable are those that are relevant
but whose behavior the theory does not attempt
to explain; their values are taken as given.
– Examples: Money supply, government spending, tax rates
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Consumption and Savings
•
•
The consumption function is any relationship that
describes the determinants of consumption spending.
General linear form: C = Cα + c(Y – T) where…
– Cα = Autonomous consumption
– c = marginal propensity to consume
– c(Y – T) = induced consumption
•
Savings (S) = Y – T – C
Substituting in C from above yields:
S = Y – T – [Cα + c(Y – T)]
 S = – Cα + (1 – c)(Y – T)] where…
– (1 – c) = marginal propensity to save (s)
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Figure 3-2 A Simple Hypothesis
Regarding Consumption Behavior
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Figure 3-3 Consumption, Saving,
and Disposable Income, 1929–
2007
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Factors Affecting Cα
• Interest Rates (r): When r↓  borrowing is cheaper
for consumers  Cα↑
– Example: Low interest rates in 2001-04 stimulated consumption of
automobiles and other consumer products.
• Household Wealth (W) is the total net value of all
household assets (minus any debt), including the market
value of homes, possessions such as automobiles, and
financial assets such as stocks, bonds, and bank accounts.
– If W↑  household spending can rise even if income is fixed
 C α↑
– Example: The 1990s stock market boom raised consumption.
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Planned vs. Unplanned Expenditure
•
Recall the National Income Accounting Identity:
Y = C + I + G + NX
GDP or Output = Unplanned Expenditure
– Unplanned Expenditure always equals GDP because the equation
is an identity.
•
Planned Expenditure (EP) = C + IP + G + NX
– Only Investment has an unplanned spending component
• Goods that are produced but not sold are counted as unplanned
inventories.
– EP = GDP only at equilibrium (when unplanned spending = 0)
• Algebraically, EP = AP + c(Y – T) where…
– AP = Autonomous Spending = Cα – cTα + IP + G + NZ
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The Equilibrium of the Economy
• At equilibrium, Y = EP
Y = AP + cY (assuming T = 0)
To find equilibrium Y, solve the above equation for Y:
 (1 – c)Y = AP
 sY = Ap
 Y = (1/s) AP
• If the level of AP changes over time by ∆AP , then the
change in output, ∆Y, is given by:
∆Y = (1/s) ∆AP
• 1/s is called the multiplier because it shows how each
additional dollar of autonomous spending results in a
greater than $1 increase in equilibrium output.
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Table 3-1 Comparison of the
Economy’s “Always True” and
Equilibrium Situations
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Figure 3-4 How Equilibrium
Income Is Determined
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Figure 3-5 The Change in Equilibrium
Income Caused by a $500 Billion Increase in
Autonomous Planned Spending
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Shifts in Planned Spending
• Recall: EP = C + IP + G + NX = AP + cY
where AP = Cα – cTα + IP + G + NZ
• Any increase in AP will shift up EP on the
Keynesian Cross Diagram.
– Effect on Y: ∆Y = (1/s) ∆AP
• If c changes, the EP line will rotate
• If the effect on Y is negative, fiscal policy
can be used to offset the effect.
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Figure 3-6 Relation of the Various
Components of Autonomous Planned
Spending to the Interest Rate
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Figure 3-7 Relation of the IS Curve to
the Demand for Autonomous Spending
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Chapter Equations
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Chapter Equations
Changes in Aggregate Demand
Changes in Real GDP 
Fixed Price Level
E  C  I  G  NX
(3.1)
(3.2)
General Linear Form
C  Ca  c(Y  T )
(3.3)
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Chapter Equations
General Linear Form
S  Y  T  C  Y  T  Ca  c (Y  T )
 Ca  (1  c)(Y  T )
Numerical Example
S  Y  T  C  Y  t  500  0.75(Y  T )
 500  0.25(Y  T )
(3.4)
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Chapter Equations
E p  C  I p  G  NX
(3.5)
E p  Ca  c(Y  T )  I p  G  NX
(3.6)
General Linear Form
Ap  E p  cY  Ca  cTa  I p  G  NX
(3.7)
General Linear Form Numerical Example
E p  Ap  cY
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E p  1,500  0.75Y
(3.8)
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Chapter Equations
income(Y )  expenditure( E )
 Unplanned expenditure( E p ) 
unintended inventory investment( I u )
Y  Ep
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(3.9)
(3.10)
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Chapter Equations
(1  c)Y  Ap
(3.11)
General Linear Form Numerical Example
sY  Ap
0.25Y  1,500
(3.12)
General Linear Form Numerical Example
Ap
1,500
Y
Y
 6, 000 (3.13)
s
0.25
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Chapter Equations
General Linear Form Numerical Example
Ap1
2, 000
Take new situation
Y1 
Y1 
 8, 000
s
0.25
Ap 0
1,500
Subtract old situation
Y0 
Y0 
 6, 000
s
0.25
Ap
500
Equals change in income
Y 
Y 
 2, 000 (3.14)
s
0.25
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Chapter Equations
General Linear Form
Numerical Example
Y 1
multiplier (k ) 

Ap s
Y
1

 4.0
Ap 0.25
Ap  Ca  cTa  I p  G  NX
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(3.15)
(3.16)
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Chapter Equations
T  G  I  NX  S (3.17)
1 c 1  c
Balanced budget multiplier  

 1.0 (3.18)
s s
s
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Appendix Equations
(1)
(2)
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Appendix Equations
(3)
(4)
(5)
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Appendix Equations
(6)
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Appendix Equations
(7)
(8)
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Appendix Equations
(9)
(10)
(11)
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Appendix Equations
(12)
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