1. McGraw-Hill/Irwin
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2. The Multiplier Model
Think about the Super Bowl: why would a particular city want to host the big game?
The answer: the multiplier effect
An initial change in spending will set off a spending chain that is magnified in the economy
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3. The Multiplier Model
The multiplier model: an economic model that emphasizes the effect of fluctuations in aggregate demand on output
For small and moderate fluctuations in AD, most economists believe that the AS/AD model works best
For large fluctuations in AD, the multiplier model works best
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4. Example: Effects of Government Spending
If the government spends $5 million, will AD increase by the same amount?
No: AD will increase even more as government spending becomes income for consumers
Consumers will take that money and spend it, thus increasing AD
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5. Example: Effects of Government Spending
How much will AD increase?
It depends on how much of the new income consumers save
If they save a lot, spending and AD will increase less
If the save only a small amount, spending and AD will be increase more
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6. Aggregate Production
Aggregate production (AP): total amount of final goods and services produced in every industry in an economy
Center of the multiplier model
Production creates an equal amount of income so actual income and actual production are always equal
AP in the multiplier model is represented by a 45° line—we call this the aggregate production (or income) curve
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7. The Aggregate Production Curve
Real production
Aggregate production
Production = Income
Aggregate production is the total amount of goods and services produced in every industry in an economy
Production creates an equal amount of income
The 45° line shows that real production = real income C
$4,000 A
45°
Real income
$4,000
Potential Income
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8. Aggregate Expenditures
Aggregate expenditures are the total amount of spending on final goods and services
This amount consists of four main expenditure classifications:
Consumption
Investment
Government spending
Net exports
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9. Aggregate Expenditures
In the multiplier model we look at how each type of expenditure relates to income
Furthermore, expenditures are classified as autonomous expenditures or induced expenditures
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10. Autonomous Expenditures
Autonomous expenditures are expenditures that do not vary with income
They are unrelated to income
They remain constant at all levels of income
Examples: food, shelter, rent/mortgage, etc. (these expenditures would still exist at zero dollars of income)
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11. Induced Expenditures
Induced expenditures are expenditures that change as income changes
They are directly related to income
When income changes, they change by less than income
Examples: changes in consumer spending and business purchases of capital goods
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12. Aggregate Expenditures Curve (Textbook)
Aggregate expenditures are the sum of autonomous and induced expenditures
Real production
Aggregate expenditures
$6,500
$5,500
Induced expenditures
Slope = mpe = y/x = 0.5 y
$3,000 x
Autonomous expenditures
$5,000
$7,000
Real income
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13. The Aggregate Expenditures Function (Textbook)
The relationship between aggregate expenditures and income can be expressed mathematically as:
AE =
AE0 + mpeY
autonomous
induced
AE0 = C0 + I0 + G0 + (X0 – M0)
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14. Application: Graphing the Expenditures Function (Textbook)
Real production
C0 = 100 I0 = 40 G0 = 20 (X0 – M0) = 30 mpe = 0.6
Aggregate expenditures
Slope = mpe = 0.6
$430
$120
$310
$200
$190
AE = Y
$200
$400
Real income
AE0 = 190
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15. Autonomous Shifts in the Expenditures Function
Changes are usually classified by which of the 4 subcomponents of autonomous expenditures changed:
Autonomous consumption
Autonomous investment
Autonomous government spending
Autonomous net exports
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16. Autonomous Shifts in the Expenditures Function
All of these can change suddenly, and, when one or more do, the AE curve shifts up or down
Economists look at autonomous components as they develop their forecasts of the economy
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17. The Multiplier Equation (Textbook)
Multiplier equation: income equals the multiplier times autonomous expenditures
Y = Multiplier x Autonomous expenditures
(Y represents income)
Expenditures multiplier: tells us how much income will change in response to a change in autonomous expenditures
Multiplier =
____1____
(1 – mpe)
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18. Consumption and Saving
Keep this in mind: with every dollar we can either spend it or save it
Disposal Income= Gross Income – Taxes
With disposable income, households can either:
Consume (spend money on goods & services)
Save (not spend money on goods & services)
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19. Consumption Consumption is spending by households
The ability to consume is constrained by:
The amount of disposable income (DI)
The propensity to save
Do households consume if DI = 0?
Yes: Autonomous consumption
Leads to dissaving
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20. Saving The disposal income the household is NOT spending
The ability to save is constrained by:
The amount of disposable income
The propensity to consume
Do households save if DI = 0? NO
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21. Average Propensity to Consume and Save
Average propensity to consume (APC) is the fraction of total income that is consumed
APC= Consumption
Disposable Income
Average propensity to save (APS) is the fractional of total income that is saved
APS= Saving
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22. Average Propensity to Consume and Save
APC + APS = 1
1 – APC = APS
1 – APS = APC
APC > 1 means dissaving
-APS means dissaving
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23. The Marginal Propensity to Expend
Marginal propensity to expend (MPE) is the ratio of the change in aggregate expenditures to a change in income
The MPE, always between 0 and 1, is the slope of the aggregate expenditures curve
MPE=
Changes in expenditures
Changes in income
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24. The Marginal Propensity to Expend
Income taxes reduce people’s income which lowers their expenditures
Taxes reduce the MPE
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25. The Marginal Propensity to Consume (MPC)
The marginal propensity to consume (MPC) is the change in consumption (C) that occurs with a change in disposable income (DI)
This tells us how much people consume rather than save, when there is an change in income
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26. The Marginal Propensity to Consume (MPC)
The MPC is less than one because individuals consume only a portion of an increase in income (they tend to save some of their income)
It is always expressed as a decimal
MPC= Consumption
Disposable Income
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27. Marginal Propensity to Save
Marginal propensity to save (MPS) is the change in saving caused by a change in disposable income
It is always expressed as a decimal
MPS= Saving
 Disposable income
MPC + MPS =1
1 – MPC = MPS
1 – MPS = MPC
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28. The Spending Multiplier Effect
An initial change in spending (C, IG, G, XN) causes a larger change in aggregate spending, or AD
Multiplier = Change in AD (real GDP)
Change in Spending
Multiplier = Δ AD/Δ C, I, G, or X
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29. The Spending Multiplier Effect
Why does this happen?
Expenditures and income flow continuously which sets off a spending increase in the economy
For example: If the government increases defense spending by $1 billion, then defense contractors will hire and pay more workers, which will increase aggregate spending by more than the original $1 billion
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30. The Spending Multiplier Effect
The spending multiplier can be calculated from the MPC or the MPS
Multiplier = 1/1-MPC or 1/MPS
Multipliers are (+) when there is an increase in spending and (–) when there is a decrease
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31. How is Spending “Multiplied?”
Assume the MPC is .5 for everyone
Assume the Super Bowl comes to town and there is an increase of $100 in Ashley’s restaurant
Ashley now has $100 more income
She saves $50 and spends $50 at Karl’s Salon
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32. How is Spending “Multiplied?”
Karl now has $50 more income
He saves $25 and spends $25 at Dan’s fruit stand
Dan now has $25 more income
This continues until every penny is spent or saved
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33. How is Spending “Multiplied?”
Multiplier = Change in real GDP OR
Initial change in spending
Total change in GDP
Initial Change
in Spending
= Multiplier x
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34. Sample Question#1
Suppose that disposable income is $1,000. Consumption is $700, and the marginal propensity to consume is If disposable income then increases by $100, consumption and savings will equal which of the following?
Consumption Savings
$420 $280
$600 $400
$660 $320
$660 $440
$760 $340
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35. Sample Question#1: Answer
C+S=DI
100(0.6)=60 consumed
100-60=40 saved
C=700+60=760
S=300+40=340
Answer is E
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36. Sample Question#2
2. Suppose that autonomous consumption is $400 and that the marginal propensity to consume is 0.8, if disposable income increases by $1200, consumption and spending will increase by
$1,600
$1,360
$1,200
$960
$400
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37. Sample Question#2: Answer
1200(0.8)=960
You do not need the autonomous consumption to solve this problem
Answer is D
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38. Calculating the Tax Multiplier
When the government taxes, the multiplier works in reverse
Why?
Because now money is leaving the circular flow
Tax multiplier (note: it is negative)
= -MPC/1-MPC or -MPC/MPS
If there is a tax cut, then the multiplier is +, because there is now more money in the circular flow
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39. MPS, MPC, & Multipliers
Example: Assume U.S. citizens spend 90¢ for every extra $1 they earn. Further assume that the real interest rate (r%) decreases, causing a $50 billion increase in gross private investment. Calculate the effect of a $50 billion increase in IG on U.S. AD
Step 1: Calculate the MPC and MPS
MPC = ΔC/ΔDI = .9/1 = .9
MPS = 1 – MPC = .10
Step 2: Determine which multiplier to use, and whether it’s + or -
The problem mentions an increase in Δ IG .: use a (+) spending multiplier
Step 3: Calculate the Spending and/or Tax Multiplier
1/MPS = 1/.10 = 10
Step 4: Calculate the Change in AD
(Δ C, IG, G, or XN) * Spending Multiplier
($50 billion Δ IG) * (10) = $500 billion ΔAD

40. MPS, MPC, & Multipliers
Example: Assume Germany raises taxes on its citizens by €200 billion . Furthermore, assume that Germans save 25% of the change in their disposable income. Calculate the effect the €200 billion change in taxes on the German economy.
Step 1: Calculate the MPC and MPS
MPS = 25%(given in the problem) = .25
MPC = 1 – MPS = = .75
Step 2: Determine which multiplier to use, and whether it’s + or -
The problem mentions an increase in T .: use (-) tax multiplier
Step 3: Calculate the Spending and/or Tax Multiplier
-MPC/MPS = -.75/.25 = -3
Step 4: Calculate the Change in AD
(Δ Tax) * Tax Multiplier
(€200 billion Δ T) * (-3) = -€600 billion Δ in AD

41. MPS, MPC, & Multipliers
Example: Assume the Japanese spend 4/5 of their disposable income. Furthermore, assume that the Japanese government increases its spending by ¥50 trillion and in order to maintain a balanced budget simultaneously increases taxes by ¥50 trillion. Calculate the effect the ¥50 trillion change in government spending and ¥50 trillion change in taxes on Japanese Aggregate Demand.
Step 1: Calculate the MPC and MPS
MPC = 4/5 (given in the problem) = .80
MPS = 1 – MPC = = .20
Step 2: Determine which multiplier to use, and whether it’s + or -
The problem mentions an increase in G and an increase in T .: combine a (+) spending with a (–) tax multiplier
Step 3: Calculate the Spending and Tax Multipliers
Spending Multiplier = 1/MPS = 1/.20 = 5
Tax Multiplier = -MPC/MPS = -.80/.20 = -4
Step 4: Calculate the Change in AD
[ Δ G * Spending Multiplier] + [ Δ T * Tax Multiplier]
[(¥50 trillion Δ G) * 5] + [(¥50 trillion Δ T) * -4]
[ ¥250 trillion ] + [ ¥200 trillion ] = ¥50 trillion Δ AD

42. The Balanced Budget Multiplier
Remember when government spending increases are matched with an equal size increase in taxes, that the change ends up being equal to the change in government spending
Why?
1/MPS + -MPC/MPS = 1- MPC/MPS = MPS/MPS = 1
The balanced budget multiplier always = 1
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43. Sample Question#3
Assume that current real gross domestic product falls short of full-employment output by $500 billion and the marginal propensity to consume is 0.8.
(i) Calculate the minimum increase in government spending that could bring about full employment.
(ii) Assume that instead of increasing government spending, the government decides to reduce personal income taxes. Will the reduction in personal income taxes required to achieve full employment be larger than or smaller than the government spending change you calculated in part (i) ? Explain why.
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44. Sample Question#3: Answer
i) billion = x (1/1-MPC)
= x (1/1-0.8)
=x(5)
X=$100 billion of spending
Recessionary Gap/Multiplier
500/5=$100 billion of spending
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45. Sample Question#3: Answer
ii). A larger reduction in personal income taxes is required than the $100 billion increase in government spending.
Households do not spend all of the initial increase in disposable income caused by a tax reduction, or that the tax multiplier is smaller than the government spending multiplier.
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46. Limitations of the Multiplier Model
It is not a complete model of the economy
Shifts are sometimes not as great as the model suggests
Fluctuations can sometimes be greater than the model suggests
The price level will often change in response to shifts in demand
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47. Limitations of the Multiplier Model
People’s forward-looking expectations make the adjustment process much more complicated
Shifts in expenditures might reflect desired shifts in S or D
Expenditures depend on much more than current income
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48. Chapter Summary
The multiplier model focuses on the induced effect that a change in production has on expenditures, which affects production, and so on
In equilibrium in the multiplier model, aggregate production (income) must equal planned aggregate expenditures (AE)
AE = C + I + G + (X – M)
The MPE tells us the change in expenditures that occurs with a change in income
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49. Y = multiplier x autonomous expenditures
Chapter Summary
Equilibrium output can be calculated using the multiplier equation:
Y = multiplier x autonomous expenditures
The multiplier tells us how much a change in autonomous expenditures will change equilibrium income
The multiplier equals 1/(1- MPE)
Expansionary fiscal policy, increasing government expenditures or decreasing taxes, is represented as an upward shift of the AE curve or a rightward shift in the AD curve
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50. Chapter Summary
Contractionary fiscal policy, decreasing government spending or increasing taxes, is represented as a downward shift of the AE curve or a leftward shift of the AD curve
The multiplier model has limitations:
It is incomplete, it overemphasizes shifts in AE, it assumes that the price level is fixed, it doesn’t take expectations into account, it ignores the possibility that shifts in expenditures are desired, and it ignores the possibility that consumption is based on lifetime income, not current income
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