Aggregate Demand I: Building
the IS-LM Model
Chapter 11 of Macroeconomics, 8th
edition, by N. Gregory Mankiw
ECO62 Udayan Roy
THE GOODS MARKET IN THE SHORT
RUN
Recap: Long-Run Theory of Output
• As before, let Y denote total real GDP
• Recall that, in the long run, total real GDP is
calculated as Y = F(K, L)
– The economy produces as much as it can
• Total real GDP in the long run is also called:
– Natural GDP, or
– Potential GDP
• From now on, total long-run real GDP will be
denoted 𝒀 = F(K, L)
Actual Output ≠ Potential Output
• In the short run, total real GDP is not
necessarily equal to natural GDP, or potential
GDP
• Y≠𝒀
• We need a new theory of Y, because the longrun theory—𝑌 = F(K, L)—no longer works
Short-Run Theory of Output: it’s all
about demand
• The short-run theory of total real GDP is also
called
– Keynesian theory, after the economist John
Maynard Keynes, or
– Aggregate Demand Theory
• This theory assumes that, in the short run,
output is determined by aggregate demand:
the economy will produce as much output as
there is demand for
The simplest theory of short-run equilibrium in the goods market
THE KEYNESIAN CROSS
Planned Expenditure
• Assumption: The economy is a closed
economy
• Planned Expenditure (PE) is the total desired
expenditure of the three sectors of the
economy:
– Households (C)
– Businesses (I) and
– Government (G)
• PE = C + I + G
Consumption Expenditure
• PE = C + I + G
• What determines the planned expenditure of
households (C)?
– We did this before in chapter 3
Consumption, C
• Net Taxes = Tax Revenue – Transfer Payments
– Denoted T and always assumed exogenous: 𝑻 = 𝑻
• Recall that GDP is defined as the market value of all final
goods and services produced in an economy during a given
period of time
• But this is also actual total expenditure,
• which is also actual total income
• Therefore, Y also represents actual total income
• Disposable income (or, after-tax income) is total income
minus total net taxes: Y – T.
• Assumption: planned consumption expenditure (C) is directly
related to disposable income (Y – T)
Consumption, C
• Assumption: Planned expenditure by households is
directly related to disposable income
• Consumption function: C = C (Y – T )
Consumption Function: algebra
• Consumption function: C = C (Y – T )
• Specifically, C = Co + Cy✕(Y – T)
• Co represents all other exogenous variables that
affect consumption, such as asset prices, consumer
optimism, etc.
• Cy is the marginal propensity to consume (MPC), the
fraction of every additional dollar of income that is
consumed
Consumption Function: graph
C
C (Y –T) = Co + Cy✕(Y – T)
MPC
1
The slope of the
consumption function
is the MPC.
Co
Y–T
Marginal propensity to consume (MPC) is the
increase in consumption (C) when disposable
income (Y – T) increases by one dollar. It is also Cy.
Consumption Function: shifts
C
C = Co2 + Cy✕(Y – T)
C = Co1 + Cy✕(Y – T)
Consumption shift factor: higher
consumer optimism, higher asset prices
(Co↑).
Y
Consumption Function: shifts
C
C = Co + Cy✕(Y – T2)
C = Co + Cy✕(Y – T1)
The same shift can also be caused by
lower taxes. (T2 < T1)
Y
Consumption Function: example
•
•
•
•
Suppose Y = 30.85 and T = 0.85.
Therefore, disposable income is Y – T = 30.
Now, suppose C = 2 + 0.8 ✕ (Y – T).
Then, C = 2 + 0.8 ✕ 30 = 26
Private Saving is defined
as disposable income –
consumption, which is Y –
T – C = 30 – 26 = 4.
Y
C
C(Y – T), T
Income and Private Saving
• The marginal propensity to consume is a
positive fraction (0 < MPC < 1)
• That is, when income (Y) increases,
consumption (C) also increases, but by only a
fraction of the increase in income.
• Therefore, Y↑⇒ C↑ and Y – C↑ and Y – T – C↑
• Similarly, Y↓⇒ C↓ and Y – C↓ and Y – T – C↓
Planned Investment
• PE = C + I + G
• Assumption: Planned investment spending by
businesses (I) is exogenous
• This assumption is a big deal.
• Recall that business investment was
endogenous in long-run analysis of chapters 3,
8 and 9.
Government Spending
• PE = C + I + G
• Assumption: government spending (G) is
exogenous
• Public Saving is defined as the net tax revenue
of the government minus government
spending, which is T – G
– This is also called the budget surplus
Planned Expenditure
• PE = C + I + G
• Therefore, PE = C(Y – T) + I + G
• Or, more specifically, PE = Co + Cy✕(Y – T) + I +
G
Equilibrium
• Assumption: The goods market will be in
equilibrium. That is, actual expenditure will
be equal to planned expenditure.
Actual and planned expenditure
• Actual and planned expenditure do not have
to be equal in all circumstances
• Actual expenditure = planned expenditure +
unplanned increase in inventory
– When unplanned increase in inventory > 0, more
is bought than was intended.
– When unplanned increase in inventory < 0, less is
bought than was intended.
Equilibrium
• When unplanned increase in inventory > 0,
more is bought than was intended.
• So, actual expenditure > planned expenditure
• In this case, output will shrink
• In other words, the current output level
cannot represent equilibrium
Equilibrium
• When unplanned increase in inventory < 0,
less is bought than was intended.
• So, actual expenditure < planned expenditure
• In this case, output will increase
• In other words, the current output level
cannot represent equilibrium
Equilibrium
• For an economy to be in equilibrium,
unplanned increase in inventory must be zero
• Therefore, actual expenditure = planned
expenditure + unplanned increase in
inventory = planned expenditure
• But recall that actual expenditure is actual
GDP or Y, and planned expenditure is C + I + G
• Therefore, in equilibrium, Y = C + I + G
Short-Run GDP: calculation
•
•
•
•
We just saw that in equilibrium Y = C + I + G
Therefore, Y = Co + Cy ✕ (Y – T) + I + G
This is one equation with one unknown, Y
So, this equation can be used to solve for Y
– Example: C = 2 + 0.8✕(Y – T), T = 0.85, G = 3, and I
= 1.85
– Then, Y = 2 + 0.8✕(Y – 0.85) + 1.85 + 3
– Check that Y = 30.85
Short-Run GDP: calculation
• In equilibrium, Y = C + I + G
Y  Co  C y  (Y  T )  I  G
Y  Co  C yY  C yT  I  G
Y  C yY  Co  C yT  I  G
(1  C y )  Y  Co  C yT  I  G
Y
Co  C yT  I  G
1 Cy
At this point, you should be
able to do problems 2 and 4
on pages 325-26 of the
textbook. Please try them.
Every variable on the right hand-side
of the equation is exogenous. So, this
equation tells us everything we can say
about Y in the Keynesian Cross model.
Short-Run GDP: predictions
Y
Co  C yT  I  G
1 Cy
Every variable on the right hand-side
of the equation is exogenous. So, this
equation tells us everything we can say
about Y in the Keynesian Cross model.
Important: Note that there is
absolutely no reason why this shortrun equilibrium GDP has to be equal to
the long-run equilibrium GDP (𝒀).
Predictions Grid
Y
Co
+
T
−
I
+
G
+
In other words, the Keynesian Cross
model is able to explain why
recessions and booms happen.
The Keynesian Cross Equation
Y
Co  C y T  I  G
1 Cy
Cy
1

 (Co  I  G ) 
T
1 Cy
1 Cy
The Spending Multiplier
Cy
1
Y
 (Co  I  G ) 
T
1 Cy
1 Cy
• Note that for every $1.00 increase in Co + I + G,
Y increases by $1/(1 – Cy).
• As Cy is the marginal propensity to consume,
1/(1 – Cy) may be written as 1/(1 – MPC).
• This is called the spending multiplier.
The Spending Multiplier
Cy
1
Y
 (Co  I  G ) 
T
1 Cy
1 Cy
• As the marginal propensity to consume is a
positive fraction (0 < MPC < 1), 1 – MPC is also
a positive fraction.
• Therefore, 1/(1 – MPC) > 1.
• So, for every $1.00 increase in Co + I + G, Y
increases by more than $1.00!
The Spending Multiplier
Cy
1
Y
 (Co  I  G ) 
T
1 Cy
1 Cy
• The spending multiplier is 1/(1 – MPC).
• Example: If MPC = 0.2, the spending multiplier = 1/(1 – 0.2)
= 1.25. Therefore, if the government spends $3 billion on a
new highway, real GDP will increase by $3.75 billion
• Example: If MPC = 0.8, the spending multiplier = 1/(1 – 0.8)
= 5. Therefore, if the government spends $3 billion on a new
highway, real GDP will increase by $15 billion
• The bigger MPC is, the bigger the spending multiplier will
be. Why???
The Tax-Cut Multiplier
Cy
1
Y
 (Co  I  G ) 
T
1 Cy
1 Cy
• Note that for every $1.00 decrease in T, Y
increases by $Cy/(1 – Cy).
• As Cy is the marginal propensity to consume, Cy
/(1 – Cy) may be written as MPC/(1 – MPC).
• This is the tax-cut multiplier.
The Tax-Cut Multiplier
Cy
1
Y
 (Co  I  G ) 
T
1 Cy
1 Cy
• As the marginal propensity to consume is a
positive fraction (0 < MPC < 1), At this point, you should
be able to do problem 1
on page 325 of the
textbook. Please try it.
– MPC/(1 – MPC) < 1/(1 – MPC)
– Tax-cut multiplier < spending multiplier
– That is, a $1.00 tax cut provides a smaller boost to
the economy than a $1.00 increase in
government spending. Why??
The Tax-Cut Multiplier
Cy
1
Y
 (Co  I  G ) 
T
1 Cy
1 Cy
• The tax-cut multiplier is MPC/(1 – MPC).
• Example: If MPC = 0.2, the tax-cut multiplier = 0.2/(1 –
0.2) = 0.25 < 1. Therefore, if the government cuts taxes
by $3 billion, real GDP will increase by $0.75 billion
• Example: If MPC = 0.8, the tax-cut multiplier = 0.8/(1 –
0.8) = 4. Therefore, if the government cuts taxes by $3
billion, real GDP will increase by $12 billion
Fiscal Policy
• The practice of changing the levels of
government spending (G) and/or taxes (T) in
order to affect the macroeconomic outcome is
called fiscal policy
– Spending more (G↑) and/or cutting taxes (T↓) is
called expansionary fiscal policy
– Spending less (G↓) and/or raising taxes (T↑) is
called contractionary fiscal policy
Fiscal Policy
• The consequences of expansionary and
contractionary fiscal policy in the Keynesian
Cross model were analyzed in previous slides
• In any case, they can be easily seen from the
Keynesian Cross model’s equation:
Cy
1
Y
 (Co  I  G ) 
T
1 Cy
1 Cy
K.C. Spending
multiplier
K.C. Tax-cut
multiplier
Fiscal Policy: balanced budget
multiplier
• Note that expansionary fiscal policy (G↑
and/or T↓) leads to lower public saving (T –
G↓)
– This could mean a rise in the budget deficit or a
fall in the budget surplus
• Is there no way to stimulate an economy in a
recession while keeping the budget balanced?
• There is!
Fiscal Policy: balanced budget
multiplier
• What happens if both G and T increase by $1?
• The $1 increase in G increases Y by 1/(1 –
MPC)
• The $1 increase in T decreases Y by MPC/(1 –
MPC)
• Therefore, the total change in Y is
𝐶𝑦
1 − 𝐶𝑦
1
∆𝑌 =
−
=
=1
1 − 𝐶𝑦 1 − 𝐶𝑦 1 − 𝐶𝑦
• This is the balanced budget multiplier
Fiscal Policy: balanced budget
multiplier
• The balanced budget multiplier shows that if
both government spending and taxes are
increased by the same amount—thereby
keeping the budget balanced—then output
will increase by the same amount.
Graphing planned expenditure
PE
planned
expenditure
PE =C +I +G
MPC
1
income, output, Y
Graphing the equilibrium condition
PE
PE =Y
planned
expenditure
45º
income, output, Y
The equilibrium value of income
PE
planned
expenditure
PE =Y
PE =C +I +G
Output gap
Y
Equilibrium
income
𝒀, natural rate
of output
An increase in government purchases
PE
At Y1,
there is now an
unplanned drop
in inventory…
PE =C +I +G2
PE =C +I +G1
G
…so firms
increase output,
and income
rises toward a
new equilibrium.
Y
PE1 = Y1
Y
PE2 = Y2
Solving for Y
Y  C  I  G
equilibrium condition
Y  C  I  G
in changes

C
 G
 MPC  Y  G
Collect terms with Y
on the left side of the
equals sign:
(1  MPC)  Y  G
because I exogenous
because C = MPC Y
Solve for Y :


1
Y  
  G
 1  MPC 
The government purchases multiplier
Definition: the increase in income resulting from a $1
increase in G.
In this model, the govt
Y
1
purchases multiplier equals

G
1  MPC
Example: If MPC = 0.8, then
Y
1

 5
G
1  0.8
An increase in G
causes income to
increase 5 times
as much!
Why the multiplier is greater than 1
• Initially, the increase in G causes an equal increase in Y:
Y = G.
• But Y  C
 further Y
 further C
 further Y
• So the final impact on income is much bigger than the
initial G.
An increase in taxes
PE
Initially, the tax
increase reduces
consumption, and
therefore PE:
PE =C1 +I +G
PE =C2 +I +G
At Y1, there is now
an unplanned
inventory buildup…
C = MPC T
…so firms
reduce output,
and income falls
toward a new
equilibrium
Y
PE2 = Y2
Y
PE1 = Y1
Solving for Y
eq’m condition in
changes
Y  C  I  G
I and G exogenous
 C
 MPC   Y  T
Solving for Y :
Final result:

(1  MPC)  Y   MPC  T
  MPC 
Y  
  T
 1  MPC 
The tax multiplier
def: the change in income resulting from
a $1 increase in T :
Y
T
 MPC

1  MPC
If MPC = 0.8, then the tax multiplier equals
Y
T
 0.8
 0.8


 4
1  0.8
0.2
The tax multiplier
…is negative:
A tax increase reduces C,
which reduces income.
…is smaller than the spending
multiplier:
Consumers save the fraction
(1 – MPC) of a tax cut,
so the initial boost in
spending from a tax cut is
smaller than from an equal
increase in G (or Co or Io).
NOW YOU TRY:
Practice with the Keynesian Cross
• Use a graph of the Keynesian cross
to show the effects of an increase in planned
investment on the equilibrium level of
income/output.
Tax Cuts: JFK
• Kennedy cut personal and corporate income
taxes in 1964
• An economic boom followed.
– GDP grew 5.3% in 1964 and 6.0 in 1965.
– Unemployment fell from 5.7% in 1963 to 5.2% in 1964
to 4.5% in 1965.
• However, it is not easy to prove that the tax cuts
caused the boom
• Even when they agree that the tax cuts caused
the boom, economists can’t agree on the reason
Tax Cuts: JFK
• Keynesians argued that the tax cuts boosted
demand, which led to higher production and
falling unemployment
• Supply-siders argued that demand had
nothing to do with it. The tax cuts gave people
the incentive to work harder. So, L increased.
Therefore, Y = F(K, L) also increased.
– Personally, I feel this argument doesn’t explain
why the unemployment rate fell
Tax Cuts: GWB
• Bush cut taxes in 2001 and 2003
• After the second tax cut, a weak recovery from
the 2001 recession turned into a strong recovery
– GDP grew 4.4% in 2004
– Unemployment fell from its peak of 6.3% in June 2003
to 5.4% in December 2004
• In justifying his tax cut, Bush used the Keynesian
explanation:
– “When people have more money, they can spend it on
goods and services. … when they demand an
additional good or service, somebody will produce the
good or service.”
Spending Stimulus: Barack Obama
• When President Obama took office in January
2009, the economy had suffered the worst
collapse since the Great Depression
• Obama helped enact an $800 billion (5% of
annual GDP) stimulus to be spent over a twoyear period
• About 40% was tax cuts, and 60% was
additional government spending
– White House economists had estimated the
spending multiplier to be 1.57 and the tax-cut
multiplier to be 0.99
Spending Stimulus: Barack Obama
• Much of the new spending was on
infrastructure projects
• These projects were fine for the long run, but
took a long time to be implemented, and were
therefore not ideal as a short-run boost
• Obama publicly justified his stimulus bill using
Keynesian demand-side reasoning
A slightly more complex theory of short-run equilibrium in the goods
market
THE IS CURVE
Planned Investment
• The Keynesian Cross model assumed that
planned expenditure by businesses (I) is
exogenous
• Recall that, in chapter 3, we had assumed that
investment spending is inversely related to the
real interest rate
• The IS Curve theory of the goods market
brings back the investment function I = I(r)
The Real Interest Rate
• Recall from chapter 3 that, the real interest
rate is the inflation-adjusted interest rate
• To adjust the nominal interest rate for
inflation, you simply subtract the inflation rate
from the nominal interest rate
– If the bank charges you 5% interest rate on a cash
loan, that’s the nominal interest rate (i = 0.05).
– If the inflation rate turns out to be 3% during the
loan period (π = 0.03), then you paid the real
interest rate of just 2% (r = i − π = 0.02)
The Real Interest Rate
• The problem is that when you are taking out a
loan you don’t quite know what the inflation
rate will be over the loan period
• So, economists distinguish between
– the ex post real interest rate: r = i − π
– and the ex ante real interest rate: r = i − Eπ,
where Eπ is the expected inflation rate over the
loan period
– We will use the ex ante interpretation of the real
interest rate
Investment and the real interest rate
• Assumption: investment spending is inversely
related to the real interest rate
• I = I(r), such that r↑⇒ I↓
r
I (r )
I
Investment and the real interest rate
• Specifically, I = Io − Irr
• Here Ir is the effect of r
on I and
• Io represents all other
factors that also affect
business investment
spending
– such as business
optimism, technological
progress, etc.
r
Io2 − Irr
Io1 − Irr
I
Investment: example
• Suppose I = 11.85 – 2r is the investment
function
• Then, if r = 5 percent, we get I = 11.85 – 2r =
1.85.
The IS Curve
• Recall that the goods market is in equilibrium
when Y = C + I + G
• The IS curve is a graph that shows all
combinations of r and Y for which the goods
market is in equilibrium
• Therefore, the basic equation underlying the
IS curve is Y = C(Y – T) + I(r) + G
Deriving the IS Curve: algebra
Y  C (Y  T )  I (r )  G
Y  Co  C y  (Y  T )  I o  I r  r  G
Y  Co  C y  Y  C y  T  I o  I r  r  G
Y  C y  Y  Co  C y  T  I o  I r  r  G
(1  C y )  Y  Co  C y  T  I o  I r  r  G
Cy
1
Ir
Y
 (Co  I o  G ) 
T 
r
1 Cy
1 Cy
1 Cy
K.C. Spending
multiplier
K.C. Tax-cut
multiplier
IS Interest
rate effect
Deriving the IS Curve: algebra
So, although the basic equation underlying the IS curve is …
Y  C (Y  T )  I (r )  G
… for my specific consumption and investment functions, the
equation underlying the IS curve can also be expressed as:
Cy
1
Ir
Y
 (Co  I o  G ) 
T 
r
1 Cy
1 Cy
1 Cy
The two equations are equivalent forms of the IS curve.
Comparing the Equations of the
Keynesian Cross and the IS Curve
Keynesian Cross
Cy
1
Y
 (Co  I o  G ) 
T
1 Cy
1 Cy
K.C. Spending
multiplier
K.C. Tax-cut
multiplier
This is the only
difference
IS Curve
Cy
1
Ir
Y
 (Co  I o  G ) 
T 
r
1 Cy
1 Cy
1 Cy
K.C. Spending
multiplier
K.C. Tax-cut
multiplier
IS Interest
rate effect
The IS Curve
Cy
1
Ir
Y
 (Co  I o  G ) 
T 
r
1 Cy
1 Cy
1 Cy
K.C. Spending
multiplier
K.C. Tax-cut
multiplier
r
IS Interest
rate effect
Any change in the real interest rate will cause
an opposite change in real total GDP by a
multiple determined by the size of the interest
rate effect.
r1
Δr
r2
This is why the IS curve is negatively sloped.
IS
Y1
Y2
ΔY
Y
The IS Curve: effect of fiscal policy
Cy
1
Ir
Y
 (Co  I o  G ) 
T 
r
1 Cy
1 Cy
1 Cy
K.C. Spending
multiplier
Any increase in Co + Io + G causes the IS curve
to shift right by the amount of the increase
magnified by the Keynesian Cross spending
multiplier
That is, if the real interest rate is unchanged,
the Keynesian Cross model is the same as the
IS curve model.
K.C. Tax-cut
multiplier
IS Interest
rate effect
r
r1
Y
IS1
Y1
Y2
IS2
Y
The IS Curve: effect of fiscal policy
Cy
1
Ir
Y
 (Co  I o  G ) 
T 
r
1 Cy
1 Cy
1 Cy
K.C. Spending
multiplier
Any decrease in taxes (T) causes the IS curve
to shift right by the amount of the tax cut
magnified by the Keynesian Cross tax-cut
multiplier
K.C. Tax-cut
multiplier
IS Interest
rate effect
r
r1
Y
IS1
Y1
Y2
IS2
Y
The IS Curve: shifts
• To sum up the previous two slides:
• The IS curve shifts right if there is:
– an increase in Co + Io + G, or
– a decrease in T.
Deriving the IS curve: graphs
PE =Y PE =C +I (r )+G
2
PE
r
PE =C +I (r1 )+G
 I
 PE
I
 Y
Any change in the real interest
rate will cause an opposite
change in real total GDP by a
multiple determined by the size
of the interest rate effect.
r
Y1
Y
Y2
r1
r2
IS
Y1
Y2
Y
The natural rate of interest
• Recall chapter 3 gave
us a long-run theory
of the real interest
rate
• At the long-run
interest rate, both
– Y = C + I + G (or,
equivalently, S = I)
and
– Y=𝒀
– are true.
• Note that 𝒓 in the
diagram satisfies the
requirements of longrun equilibrium
• This is the natural
rate of interest
PE = Y
PE
PE = C + I(𝒓) + G
PE = C + I(r1) + G
r
Y1
Y
𝒀
r1
𝒓
IS
Y1
𝒀
Y
The natural rate of
interest will reappear in chapter
14. But there it will
be denoted ρ.
(Confused???)
Why the IS curve is negatively sloped
• A fall in the interest rate motivates firms to
increase investment spending, which drives up
total planned spending (PE).
• To restore equilibrium in the goods market,
output (a.k.a. actual expenditure, Y)
must increase.
Fiscal Policy and the IS curve
• We can use the IS-LM model to see
how fiscal policy (G and T) affects
aggregate demand and output.
• Let’s start by using the Keynesian cross
to see how fiscal policy shifts the IS curve…
Shifting the IS curve: G
At any value of r, G
 PE  Y
PE =Y PE =C +I (r )+G
1
2
PE
PE =C +I (r1 )+G1
…so the IS curve shifts
to the right.
The horizontal
distance of the
IS shift equals
r
Y1
Y
Y2
r1
1
Y 
G
1 MPC
Y
Y1
IS1
Y2
IS2
Y
NOW YOU TRY:
Shifting the IS curve: T
• Use the diagram of the Keynesian cross or
loanable funds model to show how an increase in
taxes shifts the IS curve.
The theory of short-run equilibrium in the money market
THE MONEY MARKET IN THE SHORT
RUN: THE LM CURVE
The Theory of Liquidity Preference
• The theory of short-run equilibrium in the
money market is exactly the same as the
theory of long-run equilibrium in the money
market that we saw in Chapter 5
– Please review Chapter 5
Review of Ch. 5
Money demand and the interest rate
• Liquid assets are assumed to earn no interest
• Illiquid assets are assumed to earn the
nominal interest rate i
• Therefore, an increase in i is assumed to
reduce the demand for money
• That is, money demand (Md) is assumed to be
inversely related to the nominal interest rate
(i)
Review of Ch. 5
Money demand and the price level
• We also hold some of our wealth in the form
of money—in liquid form—because money is
an excellent medium of exchange
Review of Ch. 5
Money demand and the price level
• Recall that nominal GDP is the market value of
all final goods and services
• It is also the total expenditure on all final
goods and services
• Therefore, the bigger our nominal GDP, the
bigger will be our need for money, as money is
a medium of exchange
• It is, therefore, assumed that money demand
is directly related to nominal GDP
Review of Ch. 5
Money demand and the price level
• Let P represent the overall level of prices, as
measured by the GDP Deflator
Nominal GDP
• From Chapter 2: GDP Deflator =
Real GDP
• Therefore, Nominal GDP = GDP Deflator × Real
GDP = 𝑷 × 𝒀
• It is, therefore, assumed that money demand
(Md) is directly related to nominal GDP (𝑷 × 𝒀)
Review of Ch. 5
Money Demand
• So, Md is
– inversely related to i, and
– directly related to PY
• 𝑴𝒅 = 𝑳(𝒊) × 𝑷 × 𝒀
– L(i) is the liquidity function
– It is inversely related to i, the nominal interest rate
Review of Ch. 5
Money Demand: example
• 𝑴𝒅 = 𝑳(𝒊) × 𝑷 × 𝒀
– L(i) is the liquidity function
– It is inversely related to i, the nominal interest rate
• Specific form of L(i):
– 𝑳(𝒊) = 𝑳𝟎/𝒊
– Lo represents all factors other than P, Y and i that
also affect money demand
Review of Ch. 5
Money Demand = Money Supply
• M denotes money supply
• 𝑴𝒅 = 𝑳(𝒊) ∙ 𝑷 ∙ 𝒀 denotes money demand
• Therefore, 𝑴 = 𝑳(𝒊) ∙ 𝑷 ∙ 𝒀 denotes
equilibrium in the money market
Review of Ch. 5
Money Demand = Money Supply
• 𝑴 = 𝑳(𝒊) ∙ 𝑷 ∙ 𝒀
• 𝑌=
𝑀
𝐿 𝑖 ∙𝑃
• For the specific form 𝑳(𝒊) = 𝑳𝟎/𝒊, the above
equation becomes
• 𝒀=
𝑴
𝑳𝟎 /𝒊 ∙𝑷
=
𝑴∙𝒊
𝑳𝟎 ∙𝑷
Money Demand = Money Supply
• 𝒀=
𝑴∙𝒊
𝑳𝟎 ∙𝑷
• Now, recall that the ex ante real interest rate
is the nominal interest rate minus the
expected inflation rate: r = i – Eπ
• Therefore, r + Eπ = i
• So, the money market equilibrium equation
becomes 𝒀 =
𝑴∙ 𝒓+𝑬𝝅
𝑳𝟎 ∙𝑷
At this point, you should be able to do problem 5 on
page 326 of the textbook. Please try it.
The LM Equation
• So, for the specific form 𝑳(𝒊) = 𝑳𝟎/𝒊, the money
market equilibrium equation then becomes
• 𝒀=
𝑴∙ 𝒓+𝑬𝝅
𝑳𝟎 ∙𝑷
• Traditionally, this equation is called the LM
equation
Money Demand = Money Supply
• 𝒀=
𝑴∙ 𝒓+𝑬𝝅
𝑳𝟎 ∙𝑷
• Assumption: As always, the money supply (M),
which is controlled by the central bank, is
exogenous
• Assumption: unlike the long-run analysis of
Chapter 5, expected inflation (Eπ) is exogenous.
• Assumption: unlike the long-run analysis of
Chapter 5, the overall price level (P) is
exogenous
Prices are sticky in the short run
• Recall that the long-run analysis of Chapter 5
assumed that P is endogenous.
– Recall also that in the long run P changes
proportionately with M.
• The short-run analysis in the IS-LM model
assumes that P is exogenous: it is what it is, it
is historically determined
– That is, the overall price level is “sticky”: what it
was last week, it will be this week too
Prices are sticky in the short run
• This sticky-prices assumption is the crucial
distinction between long-run and short-run
macroeconomic analysis
• Except this assumption, all assumptions made
in short-run analysis are also assumed in longrun analysis
• So, the differences between long-run and
short-run theories are caused by this stickyprices assumption
Money Demand = Money Supply
• LM equation: 𝒀 =
𝑴∙ 𝒓+𝑬𝝅
𝑳𝟎 ∙𝑷
• Note that if the real interest rate (r) increases,
the real GDP (Y) must increase too, in order to
keep money demand equal to money supply
The LM Curve: algebra to graph
• The LM curve shows all
combinations of r and Y
for which the money
market is in equilibrium
• Note that the LM curve
is upward rising
𝑴 ∙ 𝒓 + 𝑬𝝅
𝒀=
𝑳𝟎 ∙ 𝑷
r
LM
r2
r1
Y1
Y2
Y
The LM Curve: algebra to graph
𝑴 ∙ 𝒓 + 𝑬𝝅
𝒀=
𝑳𝟎 ∙ 𝑷
• The LM curve shifts
(down) right if:
– M/P or Eπ increases
– Lo decreases
• Moreover, if Eπ
increases
(decreases), the LM
curve shifts down
(up) by the exact
same amount!
r
LM1
LM2
r1
r2
Y0
Y
NOW YOU TRY:
Shifting the LM curve
• Suppose a wave of credit card fraud causes
consumers to use cash more frequently in
transactions.
• Use the liquidity preference model
to show how these events shift the
LM curve.
Both the goods market and the money market need to be in equilibrium
SHORT-RUN EQUILIBRIUM IN THE
IS-LM MODEL
Short-run equilibrium
The short-run equilibrium is the
combination of r and Y that
simultaneously satisfies the
equilibrium conditions in both
the goods and money markets:
Y  C (Y  T )  I (r )  G
r
LM
IS
M  L(r  E )  P  Y
Equilibrium
interest
rate
Y
Equilibrium
level of
income
Short-run equilibrium
By insisting that both the goods
market and the money market
need to be in equilibrium, we
have managed to find a way to
pinpoint both r and Y
simultaneously!
r
LM
IS
Y  C (Y  T )  I (r )  G
M  L(r  E )  P  Y Equilibrium
interest
rate
Y
Equilibrium
level of
income
Short-run equilibrium
Note that the short-run
equilibrium GDP does not have
to be equal to the long-run
equilibrium GDP (𝑌, also called
potential GDP and natural GDP)
r
LM
Thus, like the Keynesian Cross
model, the IS-LM model can
explain recessions and booms.
But, the Keynesian Cross
model could determine
only equilibrium GDP. The
IS-LM model determines
the equilibrium interest
rate as well.
Equilibrium
interest
rate
IS
𝒀
Equilibrium
level of
income
Y
The IS-LM Model: summary
• Short-run equilibrium in the goods market is represented
by a downward-sloping IS curve linking Y and r.
• Short-run equilibrium in the money market is represented
by an upward-sloping LM curve linking Y and r.
• The intersection of the IS and LM curves determine the
short-run equilibrium values of Y and r.
• The IS curve shifts right if there is: r
– an increase in Co + Io + G, or
LM
– a decrease in T.
• The LM curve shifts right if:
– M/P or Eπ increases, or
– Lo decreases
IS
Y
The Big Picture
Keynesian
Cross
Theory of
Liquidity
Preference
IS
curve
LM
curve
IS-LM
model
Agg.
demand
curve
Agg.
supply
curve
Explanation
of short-run
fluctuations
Model of
Agg.
Demand
and Agg.
Supply
Preview of Chapter 12
In Chapter 12, we will
– use the IS-LM model to analyze the impact of
policies and shocks.
– learn how the aggregate demand curve comes
from IS-LM.
– use the IS-LM and AD-AS models together to
analyze the short-run and long-run effects of
shocks.
– use our models to learn about the
Great Depression.