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Chapter 30 Aggregate Expenditure - Keynesian Model/SR Macro Model
A. The Consumption Function and SR Macro Model
Recall: Classical Economists – this was the group of economists and economic ideas
that predominated from Adam Smith the Great Depression in the US.
They believed in:
- Lassiez Faire (or hands off approach)
-markets clear
-Saye’s Law – If you produce it…it will be purchased. So supply creates its own
demand.
- All income is eventually spent
The classical model/school dealt with LR growth and its components. It painted a very
rosy picture of how the economy should work. If we had our 3 assumptions of what
should occur in the LR occur then the economy should work out fine.
In the classical model unemployment was temporary and the result would be a short
lived.
-so due to the outcome of the Great Depression we realized that although markets will
self-correct in the LR, in the SR there can be huge swings in output that affect both GDP
and unemployment. So what should a nation do if their economy is in a trough,
recession, or slump?
This was answered by an economist named John Maynard Keynes in the 1930’s who
noted that fluctuations coincided with changes in spending and if we wanted to affect
overall output we could, as a government, change:
(a) Taxes
(b) Government Spending
(c) Alter interest rates
Each of these items could spur on private spending and help bring out of a recession.
With that the SR or Keynesian Model was formed.
1. SR Model Assumptions and Notes
a. The SR Model focuses on the role of spending in explaining fluctuations
b. We assume that spending affects output (which it does not do in the LR model due to
crowding out).
c. We look at spending or Aggregate Expenditure – AE - in the following sectors:
i. Consumption – done by HH
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ii. Investment (Planned) – done by business firms
iii. Government – done by Gov’t on G/S  so don’t include transfers
iv. NX – net spending on US G/S by citizens of other nations
2. Consumption and the Consumption Function
a. Disposable Income – YD = Y – T; It is how much money you actually have to spend as
a consumer. So we have to subtract taxes from your income. If we break up disposable
income into two components we find that it is part Consumption (C) and what is not
spent, or saving (S). We may also write:
YD = C + S
**A logical equivalent is S = YD - C
b. Determinants of Consumption Spending:
i. Interest Rates – r – (inverse relationship)
ii. Wealth (positive relationship)
iii. Expectations
iv. Price Level (inverse relationship)
v. Disposable Income  this is the most important, so when we look at the consumption
function we look at how C changes with YD
So C & YD are movers while r, W, and expectations are shifters.
c. Consumption Function – relationship between C and YD
mathematically: C = a + b* YD
graphically:
C
CF
MPC =
a
C
Y d
YD
d. Important Concepts in Consumption Function
(i) The consumption function shows the ideas of the marginal propensity to consume, or
MPC in its slope. As disposable income changes we get a change in consumption. This
is the concept of the marginal propensity to consume. It tells us how much C changes
with Yd (or as we labeled it DI). We should note that it must be between [0, 1]. If you
get $1 you can’t spend more than $1. So the MPC tells how much of each new dollar that
you actually spend.
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-note: what is not spent is saved. So we may note that 1 = MPC + MPS, where MPS is
the marginal propensity to save.
(ii) Autonomous consumption, a, is the consumption that is unaffected by disposable
income. It is the intercept on the consumption axis. Autonomous consumption is what
you would spend even if you had no income. It can be thought of the amount of spending
you need to do to just maintain a poverty level standard of living.
(iii) Marginal Propensity to Save- MPS – this is the change in saving over the change in
disposable income. As mentioned before we can find MPS by: 1 - MPC = MPS
(iv) Dissaving – when the amount that you purchase exceeds your disposable income.
Graph 1:
45o – Line: Reference Line
Consumption (C)
CF
Saving: C < Yd
Dissaving: C > Yd
Disposable Income
-If MPC changed we would get a change in the slope of the line b/c MPC is the slope of
the Consumption Function. It could be a negative or positive change. If the MPC
increases the slope increases. If the MPC decreases the slope decreases. In Graph 2
below we can see an increase in the MPC.
-If we have a change in autonomous consumption we get a change in the intercept. Once
again, a positive change would shift the intercept upwards and a negative change would
shift it downwards. We can see below in Graph 3 that autonomous consumption
increased from a1 to a2.
Graph 2:
Consumption (C)
a
(+) Change in MPC
Disposable Income
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Graph 3:
Consumption (C)
a2 (+ ) Change in a
a1
Disposable Income
3. A Closer look at I, G, & NX
a. Investment – Consists of business spending on plant equipment, purchase of new
homes by HH, and accumulation of unsold inventories. We will take a closer look at how
investment is affected and how its demand changes due to its large effect on overall
spending.
b. We treat IP, G, & NX as given. So although we could also analyze each in similar
fashion as consumption, we will assume that all are given levels in the economy. Since C
is nearly 2/3 of total spending in the economy this is another reason we will focus less on
these 3 sectors. See marginal propensity to import below.
4. Investment and the Investment Demand Curve
a. Investment Demand Curve – this shows the demand for investments at all possible
rates of interest. Firms generally consider how much the investment’s expected return
when determining whether or not to invest in new equipment, capital, land, etc.
b. Properties of Investment:
-It is highly dependent upon expected profits, so it tends to be very volatile and can be
influenced by:
i) expectations (i.e. higher or lower profit)
ii) tax rates –includes both after sale taxes as well as subsidies and tax credits
iii) capacity – is there a lot of capacity or not.
iv) technology
c. Autonomous Investment Spending vs. Investment Demand
-if we note that some forms of investment are long run and short run we may note that
there are two types of I. In the SR since all the variables above can be seen as fixed we
get an autonomous amount of investment. This is investment that does not depend on
real interest rates, which is called autonomous investment. Then there is investment that
does depend on the previous variables.
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5. Aggregate Planned Expenditure (i.e. total spending) –AE – this is the sum of all
spending from all 4 sectors on final goods and services in the US.
a. mathematically: AE = C + I + G + NX
also, ΔAE = MPC * ΔY
b. AE-Line: This shows us the total spending that takes place in an economy. When we
look at this graphically we make use of a 45o line. This is just a reference line. It
perfectly bisects the X & Y space, so if we look at AE and GDP is shows us where they
are equal. So when the AE-line crossed the 45o line it is at SR equilibrium b/c it shows us
where total spending equals total output. This means that all the items that are being
produced are sold. Recall that this is our definition of equilibrium in the economy.
Note:
-autonomous expenditure – the sum of all spending components that does not change
with GDP
-induced expenditure – the sum of all spending components that change when real GDP
changes.
Graphically:
AE
45-degree line
AE2
AE-Line
Here spending is
insufficient to
purchase total output
and inventories are
rising.
AEEq
AE1
Here spending is
greater than output
and inventories are
falling.
GDP1
GDPEq GDP2
So change in inventories = GDP – AE. If it is (+) then inventories are increasing. If it is
a (-) value then inventories are decreasing.
If the economy were at a point above the equilibrium level of spending and GDP, then we
would have a point where spending was insufficient for that level of GDP. This would
cause inventories to go up b/c goods that were being produced would not be bought. This
would cause a decrease in production and bring us back to a point where GDP and
spending are at equilibrium.
c. Spending Multiplier - If the spending in the economy changed then overall output in
the economy changes by a greater factor than 1:1. We can see this in the following
summation. If we were given there was an MPC of .6 would get a change in GDP of:
$1 + $0.60 + $0.36 + $0.196 + …. The reason that this occurs is that if you change
spending by $1 this becomes someone’s income. So they will spend 60% of it based on
the MPC. When they spend 60 cents this becomes someone else’s income. They then
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spend 60% of this. This continues on. This overall sum is captured in the following
equation:
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i. Spending Multiplier =
1  MPC
ii. Δ GDP = Δ spending * exp multiplier = (1/ (1-.6)) = 2.5
What this 2.5 means is that for every $1 spent it creates $2.50 of GDP
Example: Suppose that we have Government increase spending by 100 Million, what
would the change in GDP be if MPC = 0.8?
If we use our previous formula we get: Δ GDP = Δ spending * exp multiplier
=100 Million * (1/ (1-0.8)) = 100 Million * 5 = 500 Million.
If it were the case that Government decreased spending by this same amount the value
would be (-)
iii. Marginal Propensity to Import – the fraction of real GDP increase spent on imports.
Mathematically: MP to Import =
 Im ports
 Re alGDP
6. Inflationary and Recessionary Gaps
a. Recessionary Gap- This is when the current level of AE is below what is required to
be at FE. Graphically it can be seen below.
Agg.
Spending
or AE
45-degree line
AE-Line
AEEq
Recessionary
Gap
GDP
GDPEq GDPFE
To get to FE we need to increase AE. In this instance we would need to increase AE
enough to where the equilibrium would then be at GDPFE.
Example: Given a recessionary GAP of 500 Billion dollars with a MPC of 0.75,
calculate the increase in spending needed to achieve FE-GDP.
Δ GDP = Δ spending * exp multiplier  500 Billion = Δ spending * (1/ (1-0.75)) 
500 Billion = Δ spending * 4  500 B / 4 = Δ spending or we need about an increase of
125 Billion dollars to get to FE-GDP.
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Note: To get the same result with taxes you use the following formula:
Δ Taxes = Δ spending required /MPC
Example: So to get the same result as above but, doing it by taxes we would need a tax
cut of:
Δ Taxes = Δ spending required /MPC = 125 B / 0.75 = 168.9 Billion dollar tax cut to get
an increase in GDP overall of 500 Billion dollars.
b. Inflationary Gap – this is the amount that AE is higher than the amount needed for
FE-GDP. Graphically it can be seen below.
Agg.
Spending
or AE
45-degree line
AEEq
AE-Line
Inflationary
Gap
GDP
GDPFE GDPEq
Note: in order to find out how much to reduce spending you use the same process as
before, but now instead of increasing spending you decrease it. Likewise, in order to
decrease the inflationary gap you increase taxes instead of reducing them.
7. Employment and GDP in the SR Model
-We now may ask ourselves…if we have found what equilibrium GDP is in the economy
is it an efficient level? For this to be the case it must be a FE value. So to check this we
will introduce an APF and compare our value of FE.
Note: To make a comparison you must be given what FE is. This will always be given
to you in order for you to compare. It provides a reference point in which you can then
go and determine if the economy is operating at potential or not.
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Graphically:
45-degree line
Agg.
Spending
or AE
AE-Line
AEEq
GDP
GDPEq
L
APF
FE
LE
GDP
Note: that the APF is inverted here. We do this so we can use the same method that we used
before in just dropping down from the previous graph. Since we have GDP on the horizontal axis
we must invert the APF to have GDP line up.
We can see that if FE is above LE then we are not at LR equilibrium. But recall that FE was
given (or imposed) so it might just as well have been below LE or equal to LE. If it were equal to
LE, then our SR values and LR values would be the same. If we go back to our typical graph of
GDP when A.GDP and P. GDP are the same that is when LE
equals FE. The case above is that FE > LE, so we are less than full-employment so this is like a
recession or trough shown below.
Real
GDP
Potential GDP
Actual GDP
A
Time (t)
This is a recession or
trough which is what
we would have when
FE > LE
Note: if we had potential and actual GDP equal to one another we are at FE, so FE would also be
our SR equilibrium. An example is like point A above. We now see that we can show
fluctuations in GDP. They are now caused by changes in spending. In this case we can now
show that our current yr GDP (or actual GDP) is not guaranteed to be at our potential value, and
we are therefore not at FE levels.
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