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AGGREGATE DEMAND AGGREGATE
SUPPLY DIAGRAM
AD = C + I + G + X – M
If any element increases by 100, AD shifts
to the right by more than 100. The increase
is multiplied.
If any element decreases by 100, AD shifts
to the left by more than 100. The decrease is
multiplied.
CONSUMPTION DEPENDS ON
INCOME. WHEN INCOME RISES, C
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
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.
The change in consumption from each added
dollar in income plus the change in saving
from each added dollar in income equals the
change in income.
Again in algebra.
Divide this equation by YD to obtain,
C/YD + S/YD = YD/YD,
or
MPC + MPS = 1.
Because consumption increases as income
increases, total expenditures increase as
income increases.
But we have ignored imports:
Import Function
In the short run, Canadian imports are
influenced primarily by Canadian real GDP.
The marginal propensity to import is the
fraction of an increase in real GDP spent on
imports.
The Canadian marginal propensity to import
is probably about 0.3.
But imports reduce total expenditures
Consumption expenditure minus imports, which
varies with real GDP, is induced expenditure.
The sum of investment, government purchases,
and exports, which does not vary with GDP, is
autonomous expenditure.
Now when prices do not change, but income
changes, we see that aggregate expenditures
increase. As real GDP increases, we move up
along the AE curve by the amount that
consumption rises as GDP rises, less the amount
that imports rise as GDP rises.
Actual Expenditure, Planned
Expenditure, and Real GDP
Actual aggregate expenditure is always
equal to real GDP.
Aggregate planned expenditure may differ
from actual aggregate expenditure because
firms can have unplanned changes in
inventories.
Equilibrium expenditure is the level of
aggregate expenditure that occurs when
aggregate planned expenditure equals real
GDP.
Increases in inventory, planned or not is
INVESTMENT.
Decreases in inventory, planned or not is a
reduction in INVESTMENT.
So even if we are in the process of adjusting
to equilibrium, actual AE equals GDP,
although firms actual Investment may be
quite different from what it intended.
Now we get to the MULTIPLIER.
AGGREGATE EXPENDITURE DIAGRAM
A given change in autonomous spending
investment creates a multiplied change in GDP
because of the rise in induced expenditures.
A $50 billion increase in investment is
multiplied into a $200 billion increase in GDP.
The multiplier = ΔGDP/ ΔAE
ΔAE is the autonomous change or shift up in
AE.
The Algebra of the Multiplier
Multiplier = 1 ÷ (1 – Slope of AE curve)
AE = C + I + G + X – M
C = mpc * YD
M = mpm * GDP
YD = GDP – NT
C = mpc * (GDP – NT)
mpc = marginal propensity to consume
mpm = marginal propensity to import
YD = disposable income
NT = taxes less transfer payments (Take as a lump sum= 0
and ignore)
C
M
AE = mpc * (GDP) + I + G + X – mpm * GDP
C
M
AE = mpc * GDP – mpm * GDP + I + G + X
C- M
AE = [(mpc– mpm) * GDP ] + I + G + X
In equilibrium AE = GDP
GDP = [(mpc– mpm) * GDP ] + I + G + X
GDP - [(mpc– mpm) * GDP ] = I + G + X
GDP * ( 1 – (mpc – mpm)) = I + G + X
The Multiplier
GDP = 1/[1-(mpm-mpm)] * (I + G + X)
The slope of the AE function in this simple model is the
mpc less the mpm.
If we included net taxes (taxes less transfers) as a function
of GDP as well (Taxes rise as GDP rises, and transfer
payments fall as GDP rises, so NT has propensity to rise as
GDP rises.) NT reduces expenditures, so like imports they
tend to make the AE flatter and reduce the multiplier.
If there are no imports (mpm = 0) and no
taxes, the multiplier is 1/(1-mpc). If the mpc
= .75, the multiplier is 1/(1-.75) = 1/.25 = 4
If the marginal propensity to import and the
tendency to tax is also .25, the multiplier is
1/(1-(.75-.25)) = 1/(1-.5) = 1/.5 = 2