The IS-LM model

1
The IS-LM model
2
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.

3
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.

4
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

5
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.

6
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).

7
The IS curve (the Keynesian cross)

• What if we want to be more specific about the
  functional form of the consumption function.
• Lets assume that we must cosume something anyway
  in order to survive, like food. We call this
  amount autonomous consumption and lets 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 lets 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)

8
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 gt
• Z c0 c1(Y-T) I G gt
• 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).

9
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.

10
The IS curve (the Keynesian cross)
Z
This is a picture of the demand as a function of
income. The vertical intercept of the line ZZ
which represents the demand, is the autonomous
spending and its slope is the marginal propensity
to consume.
ZZ
Slope MPC
1
Vertical intercept autonomous spending
Y
11
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.

12
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.

13
The IS curve (the Keynesian cross)
Actual Production YZ
Z
This is a picture of the Keynesian cross. We
observe that in equilibrium, demand is equal to
income and production along the 45o line. In our
model, since there are no inventories, we are
always in equilibrium.
ZZ
Y
45o
Y
Y
14
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 gt
• Y c0 c1Y - c1T I G gt
• Y - c1Y c0 - c1T I G gt
• Y(1 - c1) c0 - c1T I G gt
• Y 1/(1 - c1) (c0 - c1T I G)

15
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 0ltc1lt1).

16
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.

17
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.

18
The IS curve (the multiplier)
The Keynesian cross with a flat demand (small
MPC). The shift in demand has a milder effect on
output.
The Keynesian cross with a steep demand (large
MPC). The shift in demand has a large effect on
output.
Actual Production YZ
Actual Production YZ
Z
Z
ZZ2
Y2
ZZ1
ZZ2
Y2
Y1
ZZ1
Y1
45o
45o
Y
Y1
Y
Y1
Y2
Y2
19
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.

20
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)

21
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.

22
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.

23
Deriving the IS curve
Actual Production YZ
Z
A decrease in the interest rate increases the
level of investment (Panel A), which shifts up
the demand and increases income (Panel B). The IS
curve sums up these movements in the goods market
(Panel C).
ZZ2
Y2
Panel B
ZZ1
Y1
45o
Y1
Y2
Y
i
i
i1
i1
Panel A
Panel C
i2
IS
i2
I
Y
I
Y1
Y2
I1
I2
24
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.

25
Shifts of the IS curve

• So, what could possibly move the IS curve?
• First, lets 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, its 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 dont
  shift it.

26
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
• G, government expenditures (variable controlled
  by the government),
• T, taxes (variable controlled by the government),
• 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
• 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).

27
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.

28
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, lets 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 ?G), then it is obvious that the
  demand curve would shift up by an amount equal to
  ?G. The vertical intercept would move up by ?G
  but the slope would remain the same.

29
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 ?G times
  the multiplier 1/(1 - c1), so by more than ?G.
• So, it looks like its 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.

30
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.
• Lets look at this effect graphically.

31
The effects of G?
Z
Actual Production YZ
ZZ2
Y2
?G
An initial increase in G shifts up the demand by
?G, which increases income by ?G/(1 - c1) in
Panel A. This means that for a given level of
interest rate, the IS curve in Panel B must shift
to the right by ?G/(1 - c1).
Panel A
ZZ1
Y1
?Y?G1/(1 - c1)
45o
Y1
Y2
Y
i
?Y?G1/(1 - c1)
Panel B
i
IS1
IS2
Y
Y1
Y2
32
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 ?G), then it is obvious that the
  demand curve would shift down by an amount equal
  to ?G. The vertical intercept would move down by
  ?G but the slope would remain the same.

33
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 ?G
  times the multiplier 1/(1 - c1), so by more than
  ?G.
• 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.

34
The effects of G?
Z
Actual Production YZ
ZZ1
Y1
?G
An initial decrease in G shifts down the demand
by ?G, which decreases income by ?G/(1 - c1) in
Panel A. This means that for a given level of
interest rate, the IS curve in Panel B must shift
to the left by ?G/(1 - c1).
Panel A
ZZ2
Y2
?Y?G1/(1 - c1)
45o
Y1
Y2
Y
i
?Y?G1/(1 - c1)
Panel B
i
IS1
IS2
Y
Y1
Y2
35
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 ?T (so ?T is negative), then it is
  obvious that the demand curve would shift up by
  an amount equal to -c1?T. The vertical intercept
  would move up by -c1?T but the slope would remain
  the same.

36
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 ?T 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.

37
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.

38
The effects of T?
Z
Actual Production YZ
ZZ2
Y2
An initial decrease in T shifts up the demand by
-c1?T, which increases income by ?T-
c1/(1 - c1) in Panel A. This means that for a
given level of interest rate, the IS curve in
Panel B must shift to the right by ?T- c1/(1 -
c1).
Panel A
-c1?T
ZZ1
Y1
?Y?T- c1/(1 - c1)
45o
Y1
Y2
Y
i
?Y?T- c1/(1 - c1)
Panel B
i
IS1
IS2
Y
Y1
Y2
39
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 ?T (now ?T is positive), then it is
  obvious that the demand curve would shift down by
  an amount equal to -c1?T. The vertical intercept
  would move down by -c1?T but the slope would
  remain the same.

40
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 ?T
  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.

41
The effects of T?
Z
Actual Production YZ
ZZ1
Y1
-c1?T
An initial increase in T shifts down the demand
by -c1?T, which decreases income by ?T- c1/(1 -
c1) in Panel A. This means that for a given
level of interest rate, the IS curve in Panel B
must shift to the left by ?T- c1/(1 - c1).
Panel A
ZZ2
Y2
?Y?T- c1/(1 - c1)
45o
Y1
Y2
Y
i
?Y?T- c1/(1 - c1)
Panel B
i
IS1
IS2
Y
Y1
Y2
42
To sum up IS shifts
Initial Change Shift of IS
G? Right
G? Left
T? Right
T? Left
43
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.).

44
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.

45
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.

46
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.

47
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.

48
The LM curve (Money supply)
i
Since money supply (Ms) is 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.
Ms
M/P
49
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.

50
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)

51
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
52
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 gt
• (M/P)s (M/P)d gt
• (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.

53
The LM curve (Money supply and money demand in
equilibrium)
i
Therefore in equilibrium if we equate money
supply and money demand, we get the equilibrium
level of real money balances and the equilibrium
level of interest rate.
Ms
i
Md YL(i)
(M/P)
M/P
54
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

55
Deriving the LM curve
i
So, we notice that a higher level of income (Y2
gtY1), by shifting the money demand to the right,
is associated with a higher level of interest
rate.
Ms
i2
i1
Md Y2L(i)
Md Y1L(i)
(M/P)
M/P
56
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.

57
Deriving the LM curve
Panel A
Panel B
In Panel A, a higher level of income (Y2 gtY1)
shifts the money demand to the right and results
in a higher level of interest rate. In Panel B,
the LM curve sums up this positive relationship
between income and interest rate.
i
i
Ms
LM
i2
i2
Md Y2L(i)
i1
i1
Md Y1L(i)
Y2
Y1
(M/P)
Y
M/P
58
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 dont shift it.

59
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
• 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),
• P, the level of prices, and
• 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)).

60
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.

61
The effects of Ms?
Panel A
Panel B
In Panel A, the increase in money supply shifts
the money supply to the right and results in a
lower level of interest rate. In Panel B, the LM
curve shifts down since, for the same level of
income, now we have a lower level of interest
rate.
i
i
(Ms)1
(Ms)2
LM1
LM2
i1
i1
i2
i2
Md YL(i)
Y
(M/P)1
(M/P)2
Y
M/P
62
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.

63
The effects of Ms?
Panel A
Panel B
In Panel A, the decrease in money supply shifts
the money supply to the left and results in a
higher level of interest rate. In Panel B, the LM
curve shifts up since, for the same level of
income, now we have a higher level of interest
rate.
i
i
(Ms)1
(Ms)2
LM2
LM1
i2
i2
i1
i1
Md YL(i)
Y
(M/P)1
(M/P)2
Y
M/P
64
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.

65
The effects of P?
In Panel A, the decrease in prices (P2lt P1)
causes the money supply to increase and shift to
the right. This results in a lower level of
interest rate. In Panel B, the LM curve shifts
down since, for the same level of income, now we
have a lower level of interest rate.
Panel A
Panel B
i
i
(M/P1) s
(M/P2) s
LM1
LM2
i1
i1
i2
i2
Md YL(i)
Y
(M/P)1
(M/P)2
Y
M/P
66
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.

67
The effects of P?
In Panel A, the increase in prices (P2gtP1) causes
the money supply to decrease and shift to the
left. This results in a higher level of interest
rate. In Panel B, the LM curve shifts up since,
for the same level of income, now we have a
higher level of interest rate.
Panel A
Panel B
i
i
(M/P1) s
(M/P2) s
LM2
LM1
i2
i2
i1
i1
Md YL(i)
Y
(M/P)1
(M/P)2
Y
M/P
68
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.

69
Effects of Md?
Panel A
Panel B
In Panel A, a decrease in the demand for money
shifts the money demand to the left and results
in a lower level of interest rate. In Panel B,
the LM curve shifts down since, for the same
level of income, now we have a lower level of
interest rate.
LM1
i
i
Ms
LM2
i1
i1
(Md)1
i2
i2
(Md)2
Y
(M/P)
Y
M/P
70
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.

71
Effects of Md?
Panel A
Panel B
In Panel A, an increase in the demand for money
shifts the money demand to the right and results
in a higher level of interest rate. In Panel B,
the LM curve shifts up since, for the same level
of income, now we have a higher level of interest
rate.
LM2
i
i
Ms
LM1
i2
i2
(Md)2
i1
i1
(Md)1
Y
(M/P)
Y
M/P
72
To sum up LM shifts
Initial change Shift of LM
Ms? Down
Ms? Up
P? Down
P? Up
Md? Down
Md? Up
73
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 closed
economy.
i
IS
Y
Y
74
So, what happens if we shift the curves in the
full scale model?

• Now its 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.

75
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.

76
Fiscal expansion
i
If the government engages in a fiscal expansion,
the IS curve shifts to the right. The LM stays
still. The equilibrium moves from A to B
indicating a higher level of output and a higher
level of interest rate.
LM
B
B
i2
A
A
i1
IS2
IS1
Y2
Y1
Y
77
Fiscal expansion elaborated

• Now, lets 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). Whats the result?
• Either way (G? or T?), the demand (Z) increases
  and therefore output ( income) increases
  (remember the Keynesian cross). Whats 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). Whats 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.

78
Fiscal expansion elaborated

• So now, we have a clear picture of how all our
  variables moved
• 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).
• 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.
• 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.
• 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.

79
Aggregate effects of a fiscal expansion conducted
by G?
Y i C I G T
? ? ? ? ? 0
80
Aggregate effects of a fiscal expansion conducted
by T?
Y i C I G T
? ? ? ? 0 ?
81
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.

82
Fiscal contraction
i
If the government engages in a fiscal
contraction, the IS curve shifts to the left. The
LM stays still. The equilibrium moves from A to B
indicating a lower level of output and a lower
level of interest rate.
LM
A
i1
B
i2
IS1
IS2
Y2
Y1
Y
83
Fiscal contraction elaborated

• Now, lets 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). Whats the result?
• Either way (G? or T?), the demand (Z) decreases
  and therefore output ( income) decreases
  (remember the Keynesian cross). Whats 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). Whats 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.

84
Fiscal contraction elaborated

• So now, we have a clear picture of how all the
  variables moved
• 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).
• 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.
• 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.
• 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.

85
Aggregate effects of a fiscal contraction
conducted by G?
Y i C I G T
? ? ? ? ? 0
86
Aggregate effects of a fiscal contraction
conducted by T?
Y i C I G T
? ? ? ? 0 ?
87
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.

88
Monetary expansion
i
LM1
LM2
If the central bank engages in a monetary
expansion, the LM curve shifts down. The IS stays
still. The equilibrium moves from A to B
indicating a higher level of output and a lower
level of interest rate.
A
i1
B
B
B
i2
IS
Y2
Y
Y1
89
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. Whats the
  result?
• By remembering the money supply and money demand
  graph, we conclude that this leads to a lower
  interest rate. Whats next?
• The lower interest rate in turn leads to higher
  investment and thus, higher demand and output
  (remember the Keynesian cross).

90
Monetary expansion elaborated

• So now, we have a clear picture of how all our
  variables moved
• C consumption increases since income went up and
  so our disposable income (Y-T) went up.
• 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).
• G government expenditures are unchanged.
• T taxes are unchanged.

91
Aggregate effects of a monetary expansion
Y i C I G T
? ? ? ? 0 0
92
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.

93
Monetary contraction
i
LM2
LM1
If the central bank engages in a monetary
contraction, the LM curve shifts up. The IS stays
still. The equilibrium moves from A to B
indicating a lower level of output and a higher
level of interest rate.
B
i2
A
i1
IS
Y2
Y1
Y
94
Monetary contraction elaborated

• Lets tell the story for one last time.
• The first move was made by the central bank that
  chose to contract the money supply. Whats the
  result?
• By remembering the money supply and money demand
  graph, we conclude that this leads to a higher
  interest rate. Whats next?
• The higher interest rate in turn leads to lower
  investment and thus, lower demand and output
  (remember the Keynesian cross).

95
Monetary contraction elaborated

• So now, we have a clear picture of how all our
  variables moved
• C consumption decreases since income went down
  and so our disposable income (Y-T) went down.
• 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.
• G government expenditures are unchanged.
• T taxes are unchanged.

96
Aggregate effects of a monetary contraction
Y i C I G T
? ? ? ? 0 0