What does this equation mean: Y = Yad = C + I + G +
NX?
Why is this equation important?
What is the equation for C and why is it important?
What is the Keynesian cross diagram and what does it help us to
do?
Developed in 1937 by economist and
Keynes disciple John Hicks, the IS-LM model is still used today to
model aggregate output (gross domestic product [GDP], gross
national product [GNP], etc.) and interest rates in the short
run.en.Wikipedia.org/wiki/John_Hicks
It begins with John Maynard Keynes’s recognition that
Y = Y a d = C + I + G + N X
where:
Y = aggregate output (supplied)
Yad = aggregate demand
C = consumer expenditure
I = investment (on new physical capital
like computers and factories, and planned inventory)
G = government spending
NX = net exports (exports minus
imports)
Keynes further explained that C = a
+ (mpc × Yd)
where:
Yd = disposable income, all
that income above a
a = autonomous consumer expenditure
(food, clothing, shelter, and other necessaries)
mpc = marginal propensity to consume
(change in consumer expenditure from an extra dollar of income or
“disposable income;” it is a constant bounded by 0 and 1)
Practice calculating C in Exercise
1.
exercise
1. Calculate consumer expenditure using the formula C = a + (mpc
× Yd).
Autonomous Consumer Expenditure
Marginal Propensity to Consume
Disposable Income
Answer: C
200
0.5
0
200
400
0.5
0
400
200
0.5
200
300
200
0.5
300
350
300
0.5
300
450
300
0.75
300
525
300
0.25
300
375
300
0.01
300
303
300
1
300
600
100
0.5
1000
600
100
0.75
1000
850
You can plot aconsumption functionby drawing a graph, as in Figure 21.1 , with consumer
expenditure on the vertical axis and disposable income on the
horizontal. (Autonomous consumer expenditure a will be the
intercept and mpc × Yd will be the slope.)
Investment is composed of so-called fixed investment on
equipment and structures and planned inventory investment in raw
materials, parts, or finished goods.
For the present, we will ignore G and NX and, following Keynes,
changes in the price level. (Remember, we are talking about the
short term here. Remember, too, that Keynes wrote in the context of
the gold standard, not an inflationary free floating regime, so he
was not concerned with price level changes.) The simple model
that results, called a Keynesian cross diagram, looks like the
diagram in Figure 21.2 .
The 45-degree line simply represents the equilibrium Y =
Yad. The other line, the aggregate demand function,
is the consumption function line plus planned investment spending
I. Equilibrium is reached via inventories (part of I). If Y
> Yad, inventory levels will be higher than firms
want, so they’ll cut production. If Y < Yad,
inventories will shrink below desired levels and firms will
increase production. We can now predict changes in aggregate output
given changes in the level of I and C and the marginal propensity
to consume (the slope of the C component of Yad).
Suppose I increases. Due to the upward
slope of Yad, aggregate output will increase more than
the increase in I. This is called the expenditure multiplier
and it is summed up by the following equation:
Y = ( a + I ) × 1 / ( 1 - m p c )
So if a is 200 billion,
I is 400 billion, and mpc is .5, Y will
be
Y = 600 × 1 / .5 = 600 × 2 = $ 1,200 billion
If I increases to 600 billion, Y = 800
× 2 = $1,600 billion.
If the marginal propensity to consume
were to increase to .75, Y would increase to
Y = 800 × 1/.25 = 800 × 4 = $3,200
billion because Yad would have a much steeper slope. A
decline in mpc to .25, by contrast, would flatten Yad
and lead to a lower equilibrium:
Practice calculating aggregate output
in Exercise 2.
exercise
1. Calculate aggregate output with the formula: Y = (a + I) ×
1/(1 ? mpc)
Autonomous Spending
Marginal Propensity to Consume
Investment
Answer: Aggregate Output
200
0.5
500
1400
300
0.5
500
1600
400
0.5
500
1800
500
0.5
500
2000
500
0.6
500
2500
200
0.7
500
2333.33
200
0.8
500
3500
200
0.4
500
1166.67
200
0.3
500
1000
200
0.5
600
1600
200
0.5
700
1800
200
0.5
800
2000
200
0.5
400
1200
200
0.5
300
1000
200
0.5
200
800
Stop and Think Box
During the Great Depression, investment
(I) fell from $232 billion to $38 billion (in 2000 USD). What
happened to aggregate output? How do you know?
Aggregate output fell by more than $232
billion − $38 billion = $194 billion. We know that because
investment fell and the marginal propensity to consume was > 0,
so the fall was more than $194 billion, as expressed by the
equation Y = (a + I) × 1/(1 − mpc).
To make the model more realistic, we can easily add NX to
the equation. An increase in exports over imports will
increase aggregate output Y by the increase in NX times the
expenditure multiplier. Likewise, an increase in imports over
exports (a decrease in NX) will decrease Y by the decrease in NX
times the multiplier.
Government spending (G) also
increases Y. We must realize, however, that some government
spending comes from taxes, which consumers view as a reduction in
income. With taxation, the consumption function becomes the
following:
C = a + m p c × ( Y d - T )
T means taxes. The effect of G is always larger than that of T
because G expands by the multiplier, which is always > 1, while
T is multiplied by MPC, which never exceeds 1. So increasing G,
even if it is totally funded by T, will increase Y. (Remember, this
is a short-run analysis.) Nevertheless, Keynes argued that, to
help a country out of recession, government should cut taxes
because that will cause Yd to rise, ceteris paribus. Or,
in more extreme cases, it should borrow and spend (rather than tax
and spend) so that it can increase G without increasing T and thus
decreasing C.
Stop and Think Box
Many governments, including that of the
United States, responded to the Great Depression by increasing
tariffs in what was called a beggar-thy-neighbor policy. Today we
know that such policies beggared everyone. What were policymakers
thinking?
They were thinking that tariffs would
decrease imports and thereby increase NX (exports minus imports)
and Y. That would make their trading partner’s NX decrease, thus
beggaring them by decreasing their Y. It was a simple idea on
paper, but in reality it was dead wrong. For starters, other
countries retaliated with tariffs of their own. But even if they
did not, it was a losing strategy because by making neighbors
(trading partners) poorer, the policy limited their ability to
import (i.e., decreased the first country’s exports) and thus led
to no significant long-term change in NX.
Figure 21.3 sums up the discussion
of aggregate demand.
key takeaways
The equation Y = Yad = C + I + G + NX tells us that
aggregate output (or aggregate income) is equal to aggregate
demand, which in turn is equal to consumer expenditure plus
investment (planned, physical stuff) plus government spending plus
net exports (exports – imports).
It is important because it allows economists to model aggregate
output (to discern why, for example, GDP changes).
In a taxless Eden, like the Gulf Cooperation Council countries,
consumer expenditure equals autonomous consumer expenditure
(spending on necessaries) (a) plus the marginal propensity to
consume (mpc) times disposable income (Yd), income above
a.
In the rest of the world, C = a + mpc × (Yd − T),
where T = taxes.
C, particularly the marginal propensity to consume variable, is
important because it gives the aggregate demand curve in a
Keynesian cross diagram its upward slope.
A Keynesian cross diagram is a graph with aggregate demand
(Yad) on the vertical axis and aggregate output (Y) on
the horizontal.
It consists of a 45-degree line where Y = Yad and a
Yad curve, which plots C + I + G + NX with the slope
given by the expenditure multiplier, which is the reciprocal of 1
minus the marginal propensity to consume: Y = (a + I + NX + G) ×
1/(1 − mpc).
The diagram helps us to see that aggregate output is directly
related to a, I, exports, G, and mpc and indirectly related to T
and imports.