1. Aggregate Expenditures
The four expenditure components of national income accounting were developed around the multiplier model.
AE = C + I + G + (X - IM)

2. 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.

3. The Marginal Propensity to Consume
The mpc is the fraction spent from an additional dollar of income.

4. 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

5. 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.

6. Consumption Function

7. Aggregate Expenditure Diagram

8. Aggregate Expenditure Diagram

9. The Marginal Propensity to Consume and AE
Since only consumption expenditures depend on income, in our simple model:

10. 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

11. 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)

12. Alternative Equation mpc + mps = 1 mps = 1 - mpc multiplier = 1/mps
By definition:
mpc + mps = 1
Alternatively expressed:
mps = 1 - mpc
multiplier = 1/mps

13. What you don’t consume is what you save.
The two equations
Multiplier = 1/(1 – mpc)
multiplier = 1/mps
Because 1-mpc = mps
What you don’t consume is what you save.

14. An Upward Shift of AE, Fig. 10-8a, p 248
Real expenditures
Real income
1,052.5
AE1
$4,210 30
1,022.5
AE0
4,090
$4,090
$120

15. An Downward Shift of AE, Fig. 10-8b, p 248
Real expenditures
Aggregate production
AE0
1,412
$4,152
AE1
1,382 30
$4,062
4,062
$90
Real income

16. 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

17. 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.

18. 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.