# Supply and demand by bwzPATb

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```									The IS-LM model

1
The model

   The IS-LM model was developed in
1937 by John R. Hicks in an attempt
to authentically interpret the “General
Theory of Employment, Interest and
Money”, the famous book published
by John Maynard Keynes in 1936.

2
The model

   The model tries to explain the movement of
output and interest rate in the short run.
   To this end, it uses two curves: the IS (short
for Investment and Saving) and the LM (short
for Liquidity and Money).
   The IS curve represents equilibrium in the
goods market.
   The LM curve represents equilibrium in the
financial markets.
3
The IS curve

   We will try to use the goods market to
establish a relationship between the interest
rate and output.
   We already know [from introductory macro…]
that output in a closed economy is the sum of
consumption (C), investment (I) and
government expenditures (G).

Y    =C+I+G
4
The IS curve (the Keynesian cross)

   We also know that output (Y) is by definition equal
to income and that it represents the amount of
spending undertaken by households, firms and the
government.
   But, how much do we want to spend? In other
words, what is our demand for goods and services?
   If we denote demand with Z, then:
Z=C+I+G
   So, demand (like output) is simply equal to the sum
of consumption, investment and government
expenditures.

5
The IS curve (the Keynesian cross)

   If we try to elaborate a bit more on the form
of consumption, we can say that consumption
must depend on our disposable income.
   Our disposable income must be equal to total
income (Y) minus the taxes that we pay to
the government (T).
   So, consumption is a function of our
disposable income C(Y-T).

6
The IS curve (the Keynesian cross)
   What if we want to be more specific about the functional form of the
consumption function.
   Let’s assume that we must cosume something anyway in order to
survive, like food. We call this amount autonomous consumption
and let’s denote it by c0.
   The rest of our consumption depends on our disposable income (Y-
T). It is reasonable to assume that we consume a percentage of our
disposable income and that we save the rest of it. We call this
percentage marginal propensity to consume (MPC) and let’s denote
it by c1. Since we consume less than our disposable income, c1
must be a number between 0 and 1. So, the non autonomous part of
consumption must look like that: c1(Y-T).
   Therefore, consumption in general must be equal to:
C = c0 + c1(Y-T)

7
The IS curve (the Keynesian cross)
   If this is the form of consumption, then demand in total must be equal
to:
Z = C + I + G =>
Z = c0 + c1(Y-T) + I + G =>
Z = (c0 - c1T + I + G) + c1Y
   This last equation tells us that demand is equal to a sum of some
variables that are exogenously given, namely:
c0 : the amount of autonomous consumption,
c1T: the amount of taxes times MPC,
I: investment, which for now we can assume that it is constant, and
G: government expenditures.
We will call this whole expression (c0 - c1T + I + G), autonomous
spending.
   It also tells us that demand is a positive function of income (Y) and,
moreover, that the slope of this positive function is c1, which is less than
one. So the slope of the demand is flatter than the 45o line (the slope of
which is 1).

8
The IS curve (the Keynesian cross)

   Now we have the first building block of the
Keynesian cross. We are going to graph the
demand as a function of income. We already
proved earlier that the demand is a positive
function of income and this is what we are
going to graph now.

9
The IS curve (the Keynesian cross)

Z
This is a picture of the demand
as a function of income. The
ZZ
vertical intercept of the line ZZ
which represents the demand, is
Slope: MPC       the autonomous spending and
1\$
its slope is the marginal
propensity to consume.

Vertical intercept:
autonomous
spending

Y

10
The IS curve (the Keynesian cross)

   Our economy is in equilibrium when actual
production is equal to the demand, i.e. Y = Z.
   The only place that generally satisfies this
equilibrium condition is the 45o line in our
previous graph. So, our equilibrium must be
on that line.

11
The IS curve (the Keynesian cross)

   If we assume further, that there is no
inventory investment, then output (= income)
must always be equal to the demand.
   So, in that case, not only are we always on
the 45o line, but also always on the
intersection of the demand function with the
45o line, which is our equilibrium point.

12
The IS curve (the Keynesian cross)

Actual
Z          Production        This is a picture of the
Y=Z
Keynesian cross. We observe
ZZ
that in equilibrium, demand is
equal to income and production
Y*                           along the 45o line. In our model,
since there are no inventories,
we are always in equilibrium.

45o

Y*            Y

13
The IS curve (the multiplier)

   If we combine the equilibrium condition Y = Z,
with the expression for the demand that we
derived earlier, Z = c0 + c1(Y-T) + I + G, we get:
Y = c0 + c1(Y-T) + I + G =>
Y = c0 + c1Y - c1T + I + G =>
Y - c1Y = c0 - c1T + I + G =>
Y(1 - c1) = c0 - c1T + I + G =>
Y = [1/(1 - c1)] (c0 - c1T + I + G)

14
The IS curve (the multiplier)

   We have already called the (c0 - c1T + I + G)
part of the above equation, autonomous
spending.
   Now, we will give a name to the 1/(1 - c1) part
and we will call it the multiplier. The reason
for that name is that this fraction is greater
than one (remember that 0<c1<1).

15
The IS curve (the multiplier)

   Therefore, whatever the change is in any of the
parts of autonomous spending, the change in
output is a multiple of that change.
   So, if the government, e.g., decides to increase
G by an amount x, this will result in an increase
of Y by x times the multiplier.
   Graphically, the demand will shift up by as much
as the change in autonomous spending (the
vertical intercept) but output will increase by
more than that.

16
The IS curve (the multiplier)

   The size of the multiplier obviously depends on c1,
the marginal propensity to consume. The larger the
MPC, the smaller the denominator and the larger the
multiplier.
   Graphically, a large MPC corresponds to a steeply
sloped demand curve. Shifts of a steep demand
curve have large effects on income.
   A small MPC corresponds to a relatively flatter
demand curve. Shifts of a flatter demand curve have
relatively milder effects on income.
   We will now graph those two cases.

17
The IS curve (the multiplier)
The Keynesian cross                            The Keynesian cross
with a steep demand                            with a flat demand
(large MPC). The shift                         (small MPC). The shift
in demand has a large    Actual                in demand has a          Actual
effect on output.        Production            milder effect on         Production
Z                                               Z    output.
Y=Z        ZZ2                                 Y=Z
Y2
ZZ1

ZZ2

Y1                                              Y2
ZZ1

Y1

45o                                         45o

Y1               Y2      Y            Y1       Y2                        Y

18
Deriving the IS curve

   The Keynesian cross is an important building
block toward the IS curve but our mission is not
accomplished yet.
   However, from this point the derivation of the IS
curve is straightforward. It relies on the
relaxation of an assumption that we made
earlier, namely that the level of investment is
constant.

19
Deriving the IS curve
   Constant investment is a clear simplification of the Keynesian cross
model. We already know that investment is not constant but rather a
negative function of the interest rate.
   At this point we also add that investment is also positively related
with output. The line of reasoning is that as firms see their volume of
sales going up, they will undertake more investment to
accommodate this increase. But the level of sales is just proportional
to output, since if output is increasing, more goods are going to be
sold and if output is decreasing less goods are going to be sold. So,
the bottom line is that we observe a positive relationship between
the level of investment and the level of output.
   Therefore, investment is a negative function of the interest rate and
a positive function of output. In symbols we write:
I = I(Y,i)

20
Deriving the IS curve

   Focusing on the interest rate, we can say that
if the interest rate increases, this reduces the
level of investment, shifts down the demand
and consequently, through the multiplier,
reduces the level of income.
   On the other hand, if the interest rate
decreases, the level of investment increases,
the demand shifts up and the level of income
increases.

21
Deriving the IS curve

   We have therefore shown that there exists a
negative relationship between the interest rate and
income.
   This negative relationship is what is known as the IS
curve.
   The mathematical form of the IS curve is called the IS
relation and it is simply:
Y = C(Y-T) + I(Y,i) + G
   A more specific form of this equation is the already
familiar to us equation:
Y = [1/(1 - c1)] (c0 - c1T + I + G)
   This is the graphical derivation of the IS curve.

22
Deriving the IS curve
Z               Actual
A decrease in the interest rate                      Production
Y=Z
increases the level of investment                                  ZZ2
(Panel A), which shifts up the       Y2
demand and increases income                                              Panel B
ZZ1
(Panel B). The IS curve sums up
these movements in the goods         Y1
market (Panel C).
45o

Y1   Y2        Y
i                             i

i1
i1
Panel A                                                                     Panel C
i2
i2                   IS
I

I1         I2       I          Y1       Y2        Y

23
Shifts of the IS curve

 As always in economics, here too we
are interested in curve shifts.
 So, we are going to mix things up a
bit, shift the curves around and see
what happens.

24
Shifts of the IS curve

   So, what could possibly move the IS curve?
   First, let’s recall the IS relation, Y = C(Y-T) + I(Y,i) + G, the
general equation that describes the IS curve.
   Which part of this equation could move the IS curve?
   Maybe, it’s better if we start by what could by no means
move the IS curve: income (Y) and the interest rate (i).
   Why? Because, these are the endogenous variables of our
model. These are the variable that we are trying to explain.
They are the variables on the two axes of our graph (like
price and quantity in a supply and demand diagram). So, if
these two variables move, we move along the curve. We
don’t shift it.

25
Shifts of the IS curve

    So, what could move the IS curve is any of the other
variables that are exogenous, i.e. they are taken as given
outside the model, namely:
a)   G, government expenditures (variable controlled by the
government),
b)   T, taxes (variable controlled by the government),
c)   C, consumption patterns that are independent of disposable
income, if for example, the households decide to consume
more because an asteroid is going to hit the earth (variable
controlled by household preferences), and
d)   I, investment patterns that are independent of the interest
rate and income, if for example firms go into an unexplained
investing spree (variable controlled by the animal spirits of
the investors).
26
Shifts of the IS curve

   Out of those four parameters, we are mostly
interested in the first two (G and T), because it is
only those that policy makers can control. The other
two cannot be affected directly by government
policies.
   So, our analysis will be primarily focused on
government expenditures and taxes.
   However, just bear in mind that changes in
consumption and investment patterns affect the IS
curve in exactly the same way as changes in
government expenditures.

27
What happens if the government decides to increase
government expenditures (G↑)?

   We will use the Keynesian cross to explore the
effects of such a move.
   First, let’s recall the equation for the demand that we
derived earlier:
Z = (c0 - c1T + I + G) + c1Y
   If, ceteris paribus, the government decides to
increase G (by ΔG), then it is obvious that the
demand curve would shift up by an amount equal to
ΔG. The vertical intercept would move up by ΔG but
the slope would remain the same.

28
What happens if the government decides to increase
government expenditures (G↑)?

   But would happen to income after this shift of the
demand curve?
   Now, we have to recall the IS relation in the specific
form that we also mentioned earlier:
Y = [1/(1 - c1)] (c0 - c1T + I + G)
   If G↑, then Y would go up by as much as ΔG times the
multiplier 1/(1 - c1), so by more than ΔG.
   So, it looks like it’s a good deal for the government to
increase G, since with an initial amount of increase, it
can get income to increase more through the
multiplier.
29
What happens if the government decides to increase
government expenditures (G↑)?

   But, what does this mean for the IS curve?
   It means that the increase in government
expenditures caused an increase in income
for a given level of interest rate. Remember
that the interest rate did not move at all.
   This corresponds to a shift of the IS curve to
the right. For a given level of interest rate
now we have more income.
   Let’s look at this effect graphically.
30
The effects of G↑
Z                  Actual
Production
Y=Z
ZZ2
Y2
Panel A                                ΔG               An initial increase in G shifts up
ZZ1
the demand by ΔG, which
Y1                                            increases income by ΔG/(1 - c1)
ΔY=ΔG[1/(1 - c1)]   in Panel A. This means that for a
o
45
given level of interest rate, the
Y1      Y2          Y           IS curve in Panel B must shift to
i
the right by ΔG/(1 - c1).
ΔY=ΔG[1/(1 - c1)]

Panel B       i*

IS1       IS2

Y1     Y2           Y

31
What happens if the government decides to decrease
government expenditures (G↓)?

   The process that we follow must be clear by
now.
   Again we use the demand equation:
Z = (c0 - c1T + I + G) + c1Y
   If, ceteris paribus, the government decides to
decrease G (by ΔG), then it is obvious that
the demand curve would shift down by an
amount equal to ΔG. The vertical intercept
would move down by ΔG but the slope would
remain the same.
32
What happens if the government decides to decrease
government expenditures (G↓)?

   Then we use the IS relation to see what happens to
income:
Y = [1/(1 - c1)] (c0 - c1T + I + G)
   If G↓, then Y would go down by as much as ΔG times
the multiplier 1/(1 - c1), so by more than ΔG.
   This means that the decrease in government
expenditures caused a decrease in income for a given
level of interest rate.
   This corresponds to a shift of the IS curve to the left.
For a given level of interest rate now we have less
income.
33
The effects of G↓
Z                  Actual
Production
Y=Z
ZZ1
Y1
Panel A                                ΔG               An initial decrease in G shifts
ZZ2
down the demand by ΔG, which
Y2                                            decreases income by ΔG/(1 - c1)
ΔY=ΔG[1/(1 - c1)]   in Panel A. This means that for a
o
45
given level of interest rate, the
Y2      Y1          Y           IS curve in Panel B must shift to
i
the left by ΔG/(1 - c1).
ΔY=ΔG[1/(1 - c1)]

Panel B       i*

IS2       IS1

Y2     Y1           Y

34
What happens if the government decides to decrease
taxes (T↓)?

   Again we use the demand equation:
Z = (c0 - c1T + I + G) + c1Y
   If, ceteris paribus, the government decides to
decrease T by ΔT (so ΔT is negative), then it
is obvious that the demand curve would shift
up by an amount equal to -c1ΔT. The vertical
intercept would move up by -c1ΔT but the
slope would remain the same.

35
What happens if the government decides to decrease
taxes (T↓)?

   Then we use the IS relation to see what happens to
income:
Y = [1/(1 - c1)] (c0 - c1T + I + G)
   If T↓, then Y would go up by as much as ΔT times [- c1/(1 -
c1)].
   The expression [- c1/(1 - c1)] is the version of the multiplier
when taxes are changed by the government.
   We observe that in the numerator of this expression there
is c1, which corresponds to a number that is less than one.
Therefore, if we compare this version of the multiplier with
the general version [1/(1 - c1)], we conclude that the
general version is larger. This means that expansionary
fiscal policy is normally more effective if conducted through
increases in government expenditures rather than
decreases in taxation.
36
What happens if the government decides to decrease
taxes (T↓)?

   So, in effect the decrease in taxes caused
an increase in income for a given level of
interest rate.
   This corresponds to a shift of the IS curve
to the right. For a given level of interest
rate now we have more income.

37
The effects of T↓
Z                  Actual
Production
Y=Z
ZZ2
Y2                                               An initial decrease in T shifts up
Panel A                               -c1ΔT
ZZ1        the demand by -c1ΔT, which
increases income by
Y1                                               ΔT[- c1/(1 - c1)] in Panel A. This
ΔY=ΔT[- c1/(1 - c1)]
o
45                                      means that for a given level of
Y1      Y2          Y              interest rate, the IS curve in
i
Panel B must shift to the right by
ΔT[- c1/(1 - c1)].
ΔY=ΔT[- c1/(1 - c1)]

Panel B       i*

IS1       IS2

Y1     Y2           Y

38
What happens if the government decides to increase
taxes (T↑)?

   Again we use the demand equation:
Z = (c0 - c1T + I + G) + c1Y
   If, ceteris paribus, the government decides to
increase T by ΔT (now ΔT is positive), then it
is obvious that the demand curve would shift
down by an amount equal to -c1ΔT. The
vertical intercept would move down by -c1ΔT
but the slope would remain the same.

39
What happens if the government decides to increase
taxes (T↑)?

   Then we use the IS relation to see what happens to
income:
Y = [1/(1 - c1)] (c0 - c1T + I + G)
   If T↑, then Y would go down by as much as ΔT times
[- c1/(1 - c1)].
   So, in effect the increase in taxes caused a
decrease in income for a given level of interest rate.
   This corresponds to a shift of the IS curve to the left.
For a given level of interest rate now we have less
income.

40
The effects of T↑
Z                  Actual
Production
Y=Z
ZZ1
Y1
Panel A                                -c1ΔT               An initial increase in T shifts
ZZ2        down the demand by -c1ΔT,
which decreases income by
Y2
ΔY=ΔT[- c1/(1 - c1)]   ΔT[- c1/(1 - c1)] in Panel A. This
o
45
means that for a given level of
i
Y2      Y1          Y              interest rate, the IS curve in
Panel B must shift to the left by
ΔT[- c1/(1 - c1)].
ΔY=ΔT[- c1/(1 - c1)]

Panel B       i*

IS2       IS1

Y2     Y1           Y

41
To sum up IS shifts…
Initial
Shift of IS
Change
G↑         Right

G↓          Left

T↓         Right

T↑          Left

42
The LM curve

   To get to the LM curve, we have to use financial
markets and go through the theory of liquidity
preference. We have to understand why people
decide to hold money in their pockets or in non-
interest bearing bank accounts (checking
accounts). In other words why we choose to
forgo the interest rate that the banks offer us
when we hold illiquid bank products (e.g. CDs,
etc.).

43
The LM curve

   The answer is very simple: convenience and
security.
   It is true that having highly liquid assets, such as
cash or immediately available, through an ATM,
checking accounts makes our life easier.
   Imagine if we had to go to the bank to liquidate
part of our investments every time we needed to
go to the grocery store. Also having liquid assets
provide us with a sense of security, that we will,
no matter what, have some money immediately
available in case an emergency (or a new
financial opportunity) occurs.

44
The LM curve

   Since we have answered why, now we have
to answer how much money we hold.
   To answer this question, first we have to
define what is money.
   Generally, for our purposes money is cash
and checking (non interest bearing) bank
accounts. This is known as M1.
   There are also other measures of money but
we are not really interested in them.
45
The LM curve

   Then we have to come up with a measure of
money. We call the measure of money with
the interesting name: real money balances or
real money stock (M/P).
   To determine how much money we hold, as
always in economics, we will look for an
equilibrium.
   The equilibrium between the supply of real
money balances and the demand for real
money balances.
46
The LM curve (Money supply)

   The supply of real money balances is easy
because it is exogenously given. It is
controlled by the central bank through the
ways that we learned in introductory macro
(open market operations, discount rate,
required reserves ratio). So the supply is just
a number decided by the central bank and we
do not need to worry about it.

47
The LM curve (Money supply)

i
Since money supply (Ms) is
Ms       independent of the interest rate,
it can be represented by a
vertical line. The amount of
money supplied only depends
on the decision of the central
bank and nothing else.

M/P

48
The LM curve (Money demand)
   The demand for real money balances is more complicated. The
amount of real money balances that we demand, depends on
what?
   Well, first it depends on income (Y). The more income in an
economy, the more transactions will occur and the more money
we will demand to effect these transactions. So, there is a
positive relationship between demand for real money balances
and income.
   But also, it depends on the interest rate. The higher the interest
rate on illiquid financial products (e.g. CDs), the less money we
will demand, since money pays no interest whereas these illiquid
products do. Because we do not want to lose a lot of interest, as
interest rates go up, we will hold less and less real money
balances. So, there is a negative relationship between demand
for real money balances and interest rate.

49
The LM curve (Money demand)

   If we wanted to write down in symbols what we
just said in words, we would write this
expression for money demand:
(M/P)d = L(i,Y)
   Demand for real money balances is a function
L of the interest rate and income.
   Or, if we want to assume that money demand
is exactly proportional to the level of income in
an economy, we can even more simply write:
(M/P)d = YL(i)
50
The LM curve (Money demand)

i
So, if we want to graph the
relationship between money
demand (Md) and the interest
rate, it must be represented by a
downward sloping curve. As we
just said, money demand
depends negatively on the
interest rate.

Md = YL(i)

M/P

51
The LM curve (Money supply and money
demand in equilibrium)
   So, now that we have all the pieces, we can equate money
demand and money supply and find the equilibrium in the money
market, i.e. the equilibrium amount of real money balances in our
economy and the equilibrium level of interest rate.
   Mathematically:
Ms = Md =>
(M/P)s = (M/P)d =>
(M/P)s = YL(i)
   This expression is what is called the LM relation. It is the
mathematical representation of the LM curve.
   Note that for the purposes of these notes, the symbols Ms and Md
refer to real money supply and real money demand, unless
otherwise specified.

52
The LM curve (Money supply and money
demand in equilibrium)
i
Therefore in equilibrium if we
s
M               equate money supply and
money demand, we get the
equilibrium level of real money
balances and the equilibrium
level of interest rate.
i*

Md = YL(i)

(M/P)*
M/P

53
Deriving the LM curve

   From here the crucial step in order to derive the LM
curve is to bring income (Y) into play.
   We have already said that money demand depends
positively on income.
   This means that for a given level of interest rate, a
higher income would result to a shift of the money
demand to the right. If income increases, for a given
level of interest rate, I engage in more transactions
and I demand more real money balances.
   The picture is as follows:

54
Deriving the LM curve

i
So, we notice that a higher level
s
M                of income (Y2 >Y1), by shifting
the money demand to the right,
i2
is associated with a higher level
of interest rate.

i1
Md = Y2L(i)

Md = Y1L(i)

(M/P)*
M/P

55
Deriving the LM curve

   Therefore we have proved that, through the
channel of financial markets and the liquidity
preference theory, there is a positive
relationship between the interest rate and
output.
   This positive relationship between interest
rate and output is represented by the LM
curve.

56
Deriving the LM curve

Panel A                          Panel B
In Panel A, a higher level of
i                                   i                           income (Y2 >Y1) shifts the
Ms
LM       money demand to the right
i2                                                          and results in a higher level
i2
of interest rate. In Panel B,
Md = Y2L(i)                               the LM curve sums up this
i1                                                          positive relationship between
i1
income and interest rate.
Md = Y1L(i)

(M/P)*                             Y1     Y2
M/P                                  Y

57
Shifts of the LM curve

   Now we will explore what shifts the LM curve.
   To this end, we have to recall the LM relation,
(M/P)s = YL(i), the equation that describes the LM
curve.
   Starting again by what could by no means
move the LM curve, it is now very easy to say:
income (Y) and the interest rate (i). Exactly like
in the IS case, if these two variables move, we
move along the curve. We don’t shift it.

58
Shifts of the LM curve
    So, what could move the LM curve is any of the other variables that are
exogenous, i.e. they are taken as given outside the model, namely:
a)   Ms, the money supply controlled by the central bank (note that the central
bank controls the nominal money supply, but given that we can assume
constant prices, effectively the central bank can control the real money
supply),
b)   P, the level of prices, and
c)   Md, the demand for real money balances, BUT only to the extent that this is
affected by factors other than the interest rate and income. So, if just like
that, for some weird reason, we start demanding more or less money for a
given level of interest rate and income. E.g. because an asteroid is going to
hit the earth and we want to engage in more transactions in the last days of
our earthly existence, we increase our demand for money.
    Since, out of those factors, the policy maker can directly control only the
money supply (case (a)) through monetary policy, we are mostly interested
in changes in this first factor. However, for reasons of completeness, we will
examine here the other two factors as well (cases (b) and (c)).

59
What happens if the central bank decides to increase the
money supply (Ms↑)?

   If the central bank decides to increase the
money supply, this would certainly mean that
the interest rate would decrease.
   So, for a given level of income, now we would
have a lower level of interest rate.
   This necessarily means that the LM curve
must shift down.

60
The effects of Ms↑

Panel A                                 Panel B
In Panel A, the increase in
i               s
(M )1        s
(M )2               i                                money supply shifts the
money supply to the right
LM1   LM2       and results in a lower level
of interest rate. In Panel B,
i1                                         i1
the LM curve shifts down
since, for the same level of
i2                                                                      income, now we have a
i2
Md = YL(i)                                    lower level of interest rate.

(M/P)1    (M/P)2                            Y*
M/P                                      Y

61
What happens if the central bank decides to decrease
the money supply (Ms↓)?

   If the central bank decides to decrease the
money supply, this would certainly mean that
the interest rate would increase.
   So, for a given level of income, now we would
have a higher level of interest rate.
   This necessarily means that the LM curve
must shift up.

62
The effects of Ms↓

Panel A                                 Panel B
In Panel A, the decrease in
i               s
(M )2        s
(M )1               i                            money supply shifts the
LM2
money supply to the left and
LM1   results in a higher level of
interest rate. In Panel B, the
i2                                         i2
LM curve shifts up since, for
the same level of income,
i1                                                                  now we have a higher level
i1
Md = YL(i)                                of interest rate.

(M/P)2    (M/P)1                            Y*
M/P                                  Y

63
What happens if the level of prices goes down (P↓)?

   Since we are interested in real money balances, a
decrease in the level of prices effectively means that
the supply of real money (M/P)s increases. The
supply of real money balances increases without the
intervention of the central bank but only due the
price change.
   Therefore, because of the increase in money
supply, the interest rate decreases.
   So, for a given level of income, now we would have
a lower level of interest rate.
   This necessarily means that the LM curve must shift
down.

64
The effects of P↓

In Panel A, the decrease in
Panel A                                Panel B
prices (P2< P1) causes the
i            (M/P1) s (M/P2) s            i                                money supply to increase
and shift to the right. This
LM1   LM2       results in a lower level of
interest rate. In Panel B, the
i1                                                                     LM curve shifts down since,
i1
for the same level of income,
i2                                                                     now we have a lower level of
i2                           interest rate.
Md = YL(i)

(M/P)1   (M/P)2                            Y*
M/P                                      Y

65
What happens if the level of prices goes up (P↑)?

   An increase in the level of prices effectively means
that the supply of real money (M/P)s decreases. The
supply of real money balances decreases without
the intervention of the central bank but only due the
price change.
   Therefore, because of the decrease in money
supply, the interest rate increases.
   So, for a given level of income, now we would have
a higher level of interest rate.
   This necessarily means that the LM curve must shift
up.

66
The effects of P↑

In Panel A, the increase in
Panel A                                Panel B
prices (P2>P1) causes the
i            (M/P2) s (M/P1) s            i                                money supply to decrease
and shift to the left. This
LM2   LM1       results in a higher level of
interest rate. In Panel B, the
i2                                                                     LM curve shifts up since, for
i2
the same level of income,
i1                                                                     now we have a higher level
i1                           of interest rate.
Md = YL(i)

(M/P)2   (M/P)1                            Y*
M/P                                      Y

67
What happens if money demand decreases (Md↓)?

   If money demand decreases for a given level
of income and interest rate (i.e. the asteroid
case), then the money demand curve shifts to
the left. This results in a lower interest rate.
   So, for a given level of income, now we would
have a lower level of interest rate.
   This necessarily means that the LM curve
must shift down.

68
Effects of Md↓

Panel A                     Panel B
LM1       In Panel A, a decrease in the
i                              i                            demand for money shifts the
Ms                                LM2
money demand to the left
i1                                                      and results in a lower level
i1
of interest rate. In Panel B,
(Md)1
the LM curve shifts down
i2                             i2                       since, for the same level of
income, now we have a
(Md)2                                 lower level of interest rate.

(M/P)*                        Y*
M/P                              Y

69
What happens if money demand increases (Md↑)?

   If money demand increases for a given level
of income and interest rate (again the
asteroid case), then the money demand shifts
to the right. This results in a higher interest
rate.
   So, for a given level of income, now we would
have a higher level of interest rate.
   This necessarily means that the LM curve
must shift up.
70
Effects of Md↑

Panel A                     Panel B
LM2       In Panel A, an increase in
i                              i                            the demand for money shifts
Ms                                LM1
the money demand to the
i2                                                      right and results in a higher
i2
level of interest rate. In
(Md)2
Panel B, the LM curve shifts
i1                                                      up since, for the same level
i1
of income, now we have a
(Md)1                                 higher level of interest rate.

(M/P)*                        Y*
M/P                              Y

71
To sum up LM shifts…
Initial change   Shift of LM
M s↑          Down
Ms↓             Up
P↓            Down
P↑              Up
Md↓            Down
Md↑              Up

72
The IS-LM model in all its glory…

i
LM            If we put the IS and the LM curves
together in a diagram we are able
to determine the equilibrium level
of output and interest rate in a
i*                           closed economy.

IS

Y*             Y

73
So, what happens if we shift the curves in
the full scale model?
   Now it’s time to use our model to see what
happens when we use fiscal or monetary
policy in order to affect different macro
variables.
   We will examine in turn fiscal expansion and
contraction and monetary expansion and
contraction.

74
Fiscal expansion

   As we already know, a fiscal expansion is a
situation where the government increases
government expenditures (G) or reduces
taxes (T).
   As we have mentioned, this corresponds to a
shift of the IS curve to the right.
   The result is a higher a level of output and a
higher level of interest rate.

75
Fiscal expansion

i

LM              If the government engages in a
fiscal expansion, the IS curve
shifts to the right. The LM stays
i2                     B                   still. The equilibrium moves from A
to B indicating a higher level of
i1
output and a higher level of
A
interest rate.

IS1       IS2

Y1       Y2
Y

76
Fiscal expansion elaborated…
   Now, let’s ask ourselves why did this happen?
   The first move was made by the government that chose to
embark on a fiscal expansion (by raising G or cutting T).
What’s the result?
   Either way (G↑ or T↓), the demand (Z) increases and
therefore output (= income) increases (remember the
Keynesian cross). What’s next?
   The increase in income, through the LM relation, increases
the demand for money leading to a higher interest rate
(remember the money supply and demand graph). What’s
next?
   The higher interest rate, by reducing private investment,
reduces demand and output but not enough to offset the
positive effect of the fiscal expansion on them.

77
Fiscal expansion elaborated…
    So now, we have a clear picture of how all our variables moved:
a)   C: consumption is positively affected either the fiscal expansion
was effected by an increase in G or through a reduction in T
(disposable income increases in both cases).
b)   I: the movement of investment is ambiguous because on the one
hand output went up and we know that this boosts I, but on the
other hand the interest rate increased and we also know that this
shrinks investment. So the net effect is ambiguous.
c)   G: government expenditures went up if the fiscal expansion was
effected by an increase in G or were unaffected if the fiscal
expansion was effected by a decrease in T.
d)   T: taxes went down if the fiscal expansion was effected by a
decrease in T or were unaffected if the fiscal expansion was
effected by an increase in G.

78
Aggregate effects of a fiscal expansion
conducted by G↑

Y     i     C     I     G     T

↑     ↑     ↑     ?     ↑     0

79
Aggregate effects of a fiscal expansion
conducted by T↓

Y     i     C     I     G     T

↑     ↑     ↑     ?     0     ↓

80
Fiscal contraction

   As we already know, a fiscal contraction is a
situation where the government decreases
government expenditures (G) or increases
taxes (T).
   This corresponds to a shift of the IS curve to
the left.
   The result is a lower level of output and a
lower level of interest rate.

81
Fiscal contraction

i

LM              If the government engages in a
fiscal contraction, the IS curve
shifts to the left. The LM stays
i1                      A               still. The equilibrium moves from A
to B indicating a lower level of
i2             B                        output and a lower level of
interest rate.

IS1
IS2

Y2       Y1
Y

82
Fiscal contraction elaborated…
   Now, let’s ask again ourselves why did this happen?
   The first move was made by the government that chose to
embark on a fiscal contraction (by reducing G or increasing
T). What’s the result?
   Either way (G↓ or T↑), the demand (Z) decreases and
therefore output (= income) decreases (remember the
Keynesian cross). What’s next?
   The decrease in income, through the LM relation, decreases
the demand for money leading to a lower interest rate
(remember the money supply and demand graph). What’s
next?
   The lower interest rate, by increasing private investment,
increases demand and output but not enough to offset the
negative effect of the fiscal expansion on them.

83
Fiscal contraction elaborated…
    So now, we have a clear picture of how all the variables moved:
a)   C: consumption is negatively affected either the fiscal contraction
was effected by a decrease in G or through an increase in T
(disposable income decreases in both cases).
b)   I: the movement of investment is ambiguous because on the one
hand output went down and this decreases I, but on the other
hand the interest rate decreased and this boosts investment. So
the net effect is ambiguous.
c)   G: government expenditures went down if the fiscal contraction
was effected by a decrease in G or were unaffected if the fiscal
contraction was effected by an increase in T.
d)   T: taxes went up if the fiscal expansion was effected by an
increase in T or were unaffected if the fiscal expansion was
effected by a decrease in G.

84
Aggregate effects of a fiscal contraction
conducted by G↓

Y     i     C      I    G     T

↓     ↓     ↓     ?     ↓     0

85
Aggregate effects of a fiscal contraction
conducted by T↑

Y     i     C      I    G     T

↓     ↓     ↓     ?     0     ↑

86
Monetary expansion

   We already know that a monetary expansion
is a situation where the central bank
increases the money supply.
   We also know that this shifts the LM curve
down.
   The result is a higher a level of output and a
lower level of interest rate.

87
Monetary expansion

i
LM1           LM2       If the central bank engages in a
monetary expansion, the LM
curve shifts down. The IS stays
A                            still. The equilibrium moves from A
i1
to B indicating a higher level of
i2              B                  output and a lower level of
interest rate.
IS

Y1   Y2                  Y

88
Monetary expansion elaborated…

   Now we have to tell the story again.
   The first move was made by the central bank that
chose to expand the money supply. What’s the
result?
   By remembering the money supply and money
demand graph, we conclude that this leads to a
lower interest rate. What’s next?
   The lower interest rate in turn leads to higher
investment and thus, higher demand and output
(remember the Keynesian cross).
89
Monetary expansion elaborated…
    So now, we have a clear picture of how all our
variables moved:
a)   C: consumption increases since income went up and
so our disposable income (Y-T) went up.
b)   I: investment unambiguously increased because we
saw that the interest rate went down (this increases
investment) and also income went up (this also
increases investment). So a monetary expansion
gives a twofold boost to investment (compare that to
the fiscal expansion which had an ambiguous effect
on investment).
c)   G: government expenditures are unchanged.
d)   T: taxes are unchanged.

90
Aggregate effects of a monetary expansion

Y      i    C     I    G     T

↑    ↓     ↑    ↑     0     0

91
Monetary contraction

   We already know that a monetary contraction
is a situation where the central bank
decreases the money supply.
   We also know that this shifts the LM curve
up.
   The result is a lower level of output and a
higher level of interest rate.

92
Monetary contraction

i
LM2
LM1       If the central bank engages in a
monetary contraction, the LM
curve shifts up. The IS stays still.
B                            The equilibrium moves from A to
i2
B indicating a lower level of output
i1               A                  and a higher level of interest rate.

IS

Y2   Y1                  Y

93
Monetary contraction elaborated…

   Let’s tell the story for one last time.
   The first move was made by the central bank that
chose to contract the money supply. What’s the
result?
   By remembering the money supply and money
demand graph, we conclude that this leads to a
higher interest rate. What’s next?
   The higher interest rate in turn leads to lower
investment and thus, lower demand and output
(remember the Keynesian cross).
94
Monetary contraction elaborated…

    So now, we have a clear picture of how all our
variables moved:
a)   C: consumption decreases since income went down
and so our disposable income (Y-T) went down.
b)   I: investment unambiguously decreased because we
saw that the interest rate went up (this decreases
investment) and also income went down (this also
decreases investment). So a monetary contraction
gives a twofold blow to investment.
c)   G: government expenditures are unchanged.
d)   T: taxes are unchanged.

95
Aggregate effects of a monetary
contraction

Y     i    C     I    G     T

↓    ↑     ↓     ↓    0     0

96

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