Notesale: Turn your study into money

Document Preview

Extracts from the notes are below, to see the PDF you'll receive please use the links above

---

EC201 Intermediate Macroeconomics

EC201 Intermediate Macroeconomics

Lecture 5: The Goods Market in the short-run: the
IS curve
Lecture Outline:
- The Keynesian cross and the IS curve;
Essential reading:
Mankiw: Ch
...
1
The Neoclassical Synthesis
In this lecture we build the first block of the IS-LM model
...

The IS-LM model is a formalization of the economic ideas that John Maynard Keynes
developed in his influential treaty: “The General Theory of Employment, Interest and
Money” in 1936
...

In his General Theory, Keynes explained his view on how an aggregate economic
system should work
...

The IS-LM is thus a model where the main Keynes’ ideas have been formalised in a
simple mathematical structure
...
1
The IS-LM model is also known as the “neoclassical synthesis” of Keynes’ theory
(neoclassical: economists that used general equilibrium analysis to study economics
(while Keynes used mainly partial equilibrium analysis in his book) and believed that
all it was needed for the economy to work perfectly was price flexibility
...


1

Hicks, John R
...

5, No
...


1

In order to build a model that explains how an entire economy works we need to
analysed some different important markets in that economy and the way those
markets interact (general equilibrium)
...
When we talked about national accounting we made a difference between
consumption and capital (or investment) goods
...
Therefore, the goods market
will be the market where all the goods (consumption and capital goods) and services
are traded
...

The second market that must be considered is the Money Market, where the nominal
interest rate is determined
...

In general we can say that those 3 markets represent the main markets in a given
economy
...

To justify that, we can use the Walras’ law (Leon Walras was the first economist that
tried to define and to prove the existence of a general economic equilibrium in an
economic system with different markets
...

The Walras’ law says that: “given an economy with n markets, if (n-1) markets are in
equilibrium, then, also the nth market must be in equilibrium”
So in our economy we are focusing on 3 markets, however, if two of them are in
equilibrium then also the 3rd one must be in equilibrium
...
If we can identify the conditions under which the goods market and the
money market are in equilibrium, then by the Walras’ law also the labour market will
be in equilibrium (this under the assumption that there are only 3 main markets in the
economy)
...
However, we have two markets and 3 unknowns
...
This means that our analysis will focus on the short-run
...
We will focus on a
closed economy
...

So the main ingredients of the IS-LM model are:
a) Two markets: the Goods Market and the Money Market;
b) The aggregate price level is fixed = short-run analysis;
c) Closed economy;
The Keynesian Cross
In order to derive the IS curve, we start with the basic Keynesian analysis on how
output is determined in a closed economy
...
Here we are going to use this property to determine the level
of output
...
We need to define the following functions:
Consumption function

C = C (Y − T )
where C is the aggregate consumption level, Y is aggregate income and T is the level
of taxation
...

Taxes here are going to be lump sum, meaning they do not depend on any other
variable
...
etc
...

The consumption function tells us that aggregate consumption depends through a
function C on disposable income
...
However, we do
not really need this distinction, since the price level is fixed, and we can normalise it
to 1 without affecting the analysis
...

We assume that:

G = G and T = T

3

Meaning: the government expenditure and the tax level are exogenous and equal to
some fixed amount

G

and

T

respectively
...
However,
according to Keynes, investments are not very sensitive to the interest rate, since what
determines an investment decision is what Keynes called “animal spirits”
...
Using the functions we have
defined so far into that expression we have:

E = C(Y − T ) + I + G
The equilibrium in this particular goods market is given by the condition that: actual
expenditure = planned expenditure, or Y

=E
...

The main ingredients of the Keynesian Cross model:
Consumption function C

= C (Y − T )

Policy Variables

G=G,

Investment function

I=I

Planned Expenditure

E = C (Y − T ) + I + G

Equilibrium condition Y

T =T

=E

We can see the equilibrium of the Keynesian Cross model in a graph, where on the
vertical axes we put E and on the horizontal axes we put Y (the only two endogenous
variables in the model, everything else is exogenous)
...

The planned expenditure function depends on Y only trough the consumption function
C(Y-T)
...
Let’s assume that the consumption function is linear
...


4

Therefore we need to know

dE
dY

According to the planned expenditure function we have:
dE dC
=
dY dY

Since only the function C depends on Y
...
It says:
dY

what the increase in consumption is if we increase income by $1
...

dY

That means that the marginal propensity to consume is positive but less than 1
...
Given the assumption that MPC<1, and the
fact that the cost function is linear, then the planned expenditure function will look
like:

The other line we need to put in the graph is the equilibrium condition that tells us
that Y=E
...
2

2

A word of caution: the Keynesian Cross as presented here and in many macro books is a “very”
simplified analysis based on Keynes writing on income determination (Ch
...


6

We can use the simple model just derived to see what happens to the equilibrium
when some of the variables in the model change
...
Furthermore,
we can comment about the transition from the initial equilibrium to the new one
...

Assume that the government expenditure, Taxes and the Investment are not fixed any
more, so they can change value
...

From equation 3), written with changes in the variables, we have that total change in
income is given by:

∆Y = c∆Y − c∆T + ∆G + ∆I

4)

So the total change in income is equal to the sum of the changes in the variables on
the right-hand side
...
The term
is called the Multiplier of the government
1− c
1− c

expenditure and it depends on the Marginal Propensity to Consume c
...
Why the multiplier is greater than
1? Answ
...
Suppose the government
spends an additional $100 million on defense
...
Hence, income rises $100 million (∆Y = $100 million = ∆G)
...
Suppose MPC = 0
...
To be concrete, suppose they buy $80
million worth of Ford Explorers
...
And what do these folks do with this extra income?
They spend the fraction MPC (0
...
Suppose they spend all $64 million on Hershey’s chocolate bars, the ones
with the bits of mint cookie inside
...
(∆Y =
$64 million)
...
But
this process continues, and the final impact on Y is $500 million (because the
multiplier is 5)
...

So we can write the change in Y given by a change in G as:

8

∆ Y = (1 + c + c 2 + c 3 +
...
) ∆ G
The terms in the brackets form a geometric series with geometric ratio given by c and
the first element given by 1
...
The effect of an increase in government expenditure, everything else
1− c

constant, can be seen graphically:

Suppose that G increases from G1 to G2
...
This change in
G will increase the planned expenditure by the same amount, therefore, the line
describing E will shift upwards by the amount ∆G
...

b) The effect of a change in Taxes
We now ask the following question: what is the effect of the change in the taxes
on total income, everything else constant (meaning

∆G = ∆I = 0 ) ?

From equation 4) we have:

∆ Y = c∆ Y − c∆ T
Therefore:

9

∆T

∆Y = −

c
∆T
1− c

If taxes increases buy 1%, total income decreases by

The term

−

c
1− c

−

c
%
...


It is negative because an increase in taxes (∆T positive) will decrease disposable
income
...
On the other hand a decrease in taxes (∆T negative) will
have the opposite effect
...

It is greater than one (in absolute value) if the marginal propensity to consume is
greater than 0
...

It is always smaller than the govt spending multiplier in absolute values: for example
if MPC=0
...

The IS Curve and the Keynesian Cross
Here we need to modify the analysis done so far by introducing a new variable, the
interest rate
...
In particular, we introduce the

interest rate r into the investment function
...
The idea is: the interest rate is the price of money, and it is also the price
of credit
...
Since most of investments are finance through credit, the
interest rate will affect the level of investments
...
On the
other hand, if the interest rate is very low, it is not so costly to borrow money and to
finance investment, and therefore we expect the investment expenditure to increase
...

dr

10

IS curve definition: a graph of all combinations of r and Y that result in goods
market equilibrium
...
From lecture 2 we know that another way to say the same thing
is

I = S , national saving equal to aggregate investment
...
The equation for the IS curve is

Y = C ( − T ) + I (r ) + G
Y
How to derive the IS curve from the Keynesian cross

Suppose you start at the equilibrium Y1 in the Keynesian Cross graph
...
Suppose that at the equilibrium Y1 the interest rate is r1
...
To restore equilibrium in the goods market, output (a
...
a
...
Therefore, in the graph the IS curve is downward
sloping
...
This negative relationship comes from the investment function
...


11

Mathematical Appendix
Total Differential of a function of several variables
...

We want to see what is the change in y if we change at the same time x1 and x 2 by
very small amounts: dx1 and dx 2
...

∂x1

For example suppose a function: y = 3x1 + 5 x2
Suppose that x1 = 1 and x 2 = 2 , then y = 13
...
2 and dx 2 = 0
...
The new
values

for

the

two

variables

are:

x1 = x1 + dx1 = 1 + 0
...
2
*

and

x 2 = x 2 + dx 2 = 2 + 0
...
5
...
2 + 5 × 2
...
6 + 12
...
1
Therefore the change in y induced by those changes in the x’s is given by:

dy = 16
...
1
...

You can see the same effect by applying the total differential approach
...
2 + 5 × 0
...
6 + 2
...
1
In writing equation 4) in the lecture note we are implicitly using the idea of total
differential
...


Therefore the total differential of Y is:

dY =

Since

C = C0 + c(Y − T )

∂E
∂E
∂E
dI A1)
dC +
dG +
∂C
∂G
∂I
and it depends on two variables (Y and Y), its total

differential is:

dC =
where

∂C
=c
∂Y

and

∂C
∂C
dY +
dT
∂Y
∂T

A2)

∂C
= −c
...


Substituting those facts and A3) into A1) we have:

dY = cdY − cdT + dG + dI

A4)

Equation A4) is the same as equation 4) in the lecture note with the only difference
that in equation 4) the changes in the variables are discrete and written with the
symbol ∆ instead of d

---