Aggregate Expenditures
• The four expenditure components of
national income accounting were
developed around the multiplier model.
AE = C + I + G + (X - IM)
Expenditures Function
• AE = C + I + G + (X - IM)
• AEo = autonomous expenditures that don’t
change as income changes.
•  AE/  Y = those expenditures that change as
income changes
• We simplify the model for Econ 100: we pretend
that only consumption changes when income
changes.
The Marginal Propensity to
Consume
• The mpc is the fraction spent from an
additional dollar of income.
change in consumption C
mpc 

change in income
Y
Consumption and Income
• Consumption depends on income. When
income rises, consumption increases.
• The marginal propensity to consume is the
change in c divided by the change in y.
– YD = C + S
– MPC = C/YD
– MPS = S/YD
Consumption and Saving
• The MPC plus the MPS equals one.
• To see why, note that, if you receive an
additional $100 in disposable income, you
will spend part of the income or not spend
part of the income, that is save it.
• In algebra:
• C + S = YD.
Consumption Function
Aggregate Expenditure Diagram
Aggregate Expenditure Diagram
The Marginal Propensity to
Consume and AE
• Since only consumption expenditures
depend on income, in our simple model:
C AE

Y
Y
Expenditures Function

The expenditures function is expressed
as a mathematical function:
AE = AEo + mpcY
AE = aggregate
expenditures
AEo = autonomous
expenditures
mpc = marginal propensity to
consume
Y = income
The Multiplier Equation
• The multiplier is a number that reveals
how much income will change in response
to a change in autonomous expenditures.
Multiplier = 1/(1 – mpc)
Alternative Equation
• By definition:
mpc + mps = 1
• Alternatively expressed:
mps = 1 - mpc
multiplier = 1/mps
The two equations
Multiplier = 1/(1 – mpc)
multiplier = 1/mps
Because 1-mpc = mps
What you don’t consume is what you
save.
An Upward Shift of AE, Fig. 10-8a, p 248
Real
expenditures
$4,210
AE1
30
AE0
Y 
4,090
1,052.5
 4 AE0   120
30
1,022.5
0
1
AE0 
1 - 0.75
$120
$4,090
$4,210
Real income
An Downward Shift of AE, Fig. 10-8b, p
248
Real
expenditures
$4,152
Aggregate production
AE0
30 AE1
Y 
4,062
1,412
 3 AE0   90
30
1,382
0
1
AE0 
1 - 0.66
$90
$4,062
$4,152
Real income
An Example of the Multiplier
• Suppose Investment rises by $ 100 million
• the mpc is .8 so the mps is .2
• Multiplier = 1/(1 – mpc) = 1/(1-.8) = 1/.2 = 5
• multiplier = 1/mps = 1/.2 = 10/2 = 5
• Rise in Equilibrium Income 5 * $100 = $500
Realistic Multipliers
• Our simple model pretends that no one
pays taxes and no one buys imports
• We also assume that Investment and
government spending don’t change when
income changes.
• The real multiplier is closer to 2 than to 5.
Realistic Multipliers
• Observe that the multiplier is calculated
assuming prices are not changing.
• The multiplier tells us how much the AD
curve shifts to the right.
• When AD shifts, prices change so the
change in equilibrium income is even less
than an accurate multiplier predicts.