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Aggregate Demand I:
Building the IS-LM Model
11
CHAPTER
CHAPTER 11 Aggregate Demand I
This chapter builds the IS-LM model, which Chapter 12 will use extensively to analyze the effects of policies and economic shocks.
This chapter also introduces students to the Keynesian cross and liquidity preference models, which underlie the IS curve and LM curve, respectively.
IN THIS CHAPTER, YOU WILL LEARN:
the IS curve and its relation to:
the Keynesian cross
the loanable funds model
the LM curve and its relation to:
the theory of liquidity preference
how the IS-LM model determines income and the interest rate in the short run when P is fixed
CHAPTER 11 Aggregate Demand I
Context
Chapter 10 introduced the model of aggregate demand and aggregate supply.
Long run:
prices flexible
output determined by factors of production & technology
unemployment equals its natural rate
Short run:
prices fixed
output determined by aggregate demand
unemployment negatively related to output
CHAPTER 11 Aggregate Demand I
Context
This chapter develops the IS-LM model,
the basis of the aggregate demand curve.
We focus on the short run and assume the price level is fixed (so the SRAS curve is horizontal).
Chapters 11 and 12 focus on the closed-economy case. Chapter 13 presents the open-economy case.
CHAPTER 11 Aggregate Demand I
The Keynesian cross
A simple closed-economy model in which income is determined by expenditure.
(due to J. M. Keynes)
Notation:
I = planned investment
PE = C + I + G = planned expenditure
Y = real GDP = actual expenditure
Difference between actual & planned expenditure = unplanned inventory investment
CHAPTER 11 Aggregate Demand I
Elements of the Keynesian cross
consumption function:
for now, planned
investment is exogenous:
planned expenditure:
equilibrium condition:
govt policy variables:
actual expenditure = planned expenditure
CHAPTER 11 Aggregate Demand I
Stress that much of this model is very familiar to students: same consumption function as in previous chapters, same treatment of fiscal policy variables.
In equilibrium, there is no unplanned inventory investment: Firms are selling everything they had intended to sell.
Graphing planned expenditure
income, output, Y
PE
planned
expenditure
PE =C +I +G
MPC
1
CHAPTER 11 Aggregate Demand I
Why slope of PE line equals the MPC:
With I and G exogenous, the only component of (C+I+G) that changes when income changes is consumption. A one-unit increase in income causes consumption—and therefore PE—to increase by the MPC.
Recall from Chapter 3: the marginal propensity to consume, MPC, equals the increase in consumption resulting from a one-unit increase in disposable income. Since T is exogenous here, a one-unit increase in Y causes a one-unit increase in disposable income.
Graphing the equilibrium condition
income, output, Y
PE
planned
expenditure
PE =Y
45º
CHAPTER 11 Aggregate Demand I
The equilibrium value of income
income, output, Y
PE =Y
PE =C +I +G
Equilibrium
income
PE
planned
expenditure
CHAPTER 11 Aggregate Demand I
The equilibrium point is the value of income at which the curves cross.
Be sure your students understand why the equilibrium income appears on both the horizontal and vertical axes.
Answer: In equilibrium, PE (which is measured on the vertical) equals Y (which is measured on the horizontal).
An increase in government purchases
Y
PE
PE =Y
PE =C +I +G1
PE1 = Y1
PE =C +I +G2
PE2 = Y2
ΔY
At Y1,
there is now an unplanned drop in inventory…
…so firms increase output, and income rises toward a new equilibrium.
ΔG
CHAPTER 11 Aggregate Demand I
Solving for ΔY
equilibrium condition
in changes
because I exogenous
because ΔC = MPC ΔY
Collect terms with ΔY on the left side of the equals sign:
Solve for ΔY :
CHAPTER 11 Aggregate Demand I
The government purchases multiplier
Example: If MPC = 0.8, then
Definition: the increase in income resulting from a $1 increase in G.
In this model, the govt
purchases multiplier equals
An increase in G causes income to increase 5 times
as much!
CHAPTER 11 Aggregate Demand I
The textbook defines the multiplier as the increase in income resulting from a $1 increase in G.
However, G is a real variable (as is Y ).
So, if you wish to be more precise, consider defining the multiplier as “the increase in income resulting from a one-unit increase in G.”
Why the multiplier is greater than 1
Initially, the increase in G causes an equal increase in Y: ΔY = ΔG.
But #Y g #C
g further #Y
g further #C
g further #Y
So the final impact on income is much bigger than the initial ΔG.
CHAPTER 11 Aggregate Demand I
Students are better able to understand this if given a more concrete example, which you can explain as you display the elements on this slide.
For instance, suppose the government spends an additional $100 million on defense.
Then, the revenues of defense firms increase by $100 million, all of which becomes income to various groups: some of it is paid to the workers and engineers and managers, the rest is profit paid as dividends to shareholders. Hence, total income rises $100 million (ΔY = $100 million = ΔG ).
The people whose income just rose by $100 million are also consumers, and they will spend the fraction MPC of this extra income.
Suppose MPC = 0.8, so C rises by $80 million. To be concrete, suppose they buy $80 million worth of Ford Explorers. Then, Ford sees its revenues increase by $80 million, all of which becomes income to Ford’s workers and shareholders (ΔY = $80 million). These folks spend the fraction MPC (0.8) of it, causing ΔC = $64 million (8/10 of $80 million). Suppose they spend all $64 million on Hershey’s chocolate bars, the ones with the mint cookie bits inside. Then, Hershey Foods Corporation experiences a revenue increase of $64 million, which becomes income to Hershey’s owners and workers (ΔY = $64 million).
At this point in the story, the total impact on income is $100 million + $80 million + $64 million, which is much bigger than the government’s initial increase in spending. But this process continues, and the final impact on Y is $500 million (because the multiplier is 5).
An increase in taxes
Y
PE
PE =Y
PE =C2 +I +G
PE2 = Y2
PE =C1 +I +G
PE1 = Y1
ΔY
At Y1, there is now an unplanned
inventory buildup…
…so firms reduce output, and income falls toward a new equilibrium
ΔC = −MPC×ΔT
Initially, the tax increase reduces consumption and therefore PE:
CHAPTER 11 Aggregate Demand I
Experiment: An increase in taxes (note: the book does a decrease in taxes)
Suppose taxes are increased by ΔT. Because I and G are exogenous, they do not change. However, C depends on (Y – T). So, at the initial value of Y, a tax increase of ΔT causes disposable income to fall by ΔT, which causes consumption to fall by MPC x ΔT. Because consumption falls, the change in C is negative: ΔC = –MPC x ΔT
C is part of planned expenditure. The fall in C causes the PE line to shift down by the size of the initial drop in C.
At the initial value of output, there is now unplanned inventory investment: Sales have fallen below output, so the unsold output adds to inventory.
In this situation, firms will reduce production, causing total output, income, and expenditure to fall.
The new equilibrium is at Y2, where planned expenditure once again equals actual expenditure/output, and unplanned inventory investment is again equal to zero.
Solving for ΔY
eq’m condition in changes
I and G exogenous
Solving for ΔY :
Final result:
CHAPTER 11 Aggregate Demand I
The tax multiplier
def: the change in income resulting from
a $1 increase in T :
If MPC = 0.8, then the tax multiplier equals
CHAPTER 11 Aggregate Demand I
The tax multiplier
…is negative:
A tax increase reduces C,
which reduces income.
…is greater than one
(in absolute value):
A change in taxes has a
multiplier effect on income.
…is smaller than the govt 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.
CHAPTER 11 Aggregate Demand I
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.
CHAPTER 11 Aggregate Demand I
This in-class exercise not only gives students practice with the model, it also helps them understand the next topic: the derivation of the IS curve.
ANSWERS
Practice with the Keynesian cross
Y
PE
PE =Y
PE =C +I1 +G
PE1 = Y1
PE =C +I2 +G
PE2 = Y2
ΔY
At Y1,
there is now an unplanned drop in inventory…
…so firms increase output, and income rises toward a new equilibrium.
ΔI
CHAPTER 11 Aggregate Demand I
The IS curve
def: a graph of all combinations of r and Y that result in goods market equilibrium
i.e. actual expenditure (output)
= planned expenditure
The equation for the IS curve is:
CHAPTER 11 Aggregate Demand I
Y2
Y1
Y2
Y1
Deriving the IS curve
ir g hI
Y
PE
r
Y
PE =C +I (r1 )+G
PE =C +I (r2 )+G
r1
r2
PE =Y
IS
ΔI
g hPE
g hY
CHAPTER 11 Aggregate Demand I
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.
CHAPTER 11 Aggregate Demand I
This slide simply states the intuition behind the graphs on the preceding slide.
Suggestion: Omit this slide from your presentation, and just give the students this information orally as you present the preceding slide.
The IS curve and the loanable funds model
S, I
r
I (r )
r1
r2
r
Y
Y1
r1
r2
(a) The L.F. model
(b) The IS curve
Y2
S1
S2
IS
CHAPTER 11 Aggregate Demand I
***
This material was covered in previous editions of the textbook but was deleted to help make room for newer material in other chapters. I have “hidden” this slide rather than deleted it, since many professors still may wish to show their students how the IS curve is just another expression of the familiar loanable funds model from Chapter 3.
***
The IS curve can also be derived from the (hopefully now familiar) loanable funds model from chapter 3.
A decrease in income from Y1 to Y2 causes a fall in national saving.
(Recall, S = Y-C-G)
The fall in saving causes a reduction in the supply of loanable funds. The interest rate must rise to restore equilibrium to the loanable funds market.
Now we can see where the IS curve gets its name:
When the loanable funds market is in equilibrium, investment = saving. The IS curve shows all combinations of r and Y such that investment (I) equals saving (S). Hence, IS curve.
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…
CHAPTER 11 Aggregate Demand I
Y2
Y1
Y2
Y1
Shifting the IS curve: ΔG
At any value of r, hG g hPE g hY
Y
PE
r
Y
PE =C +I (r1 )+G1
PE =C +I (r1 )+G2
r1
PE =Y
IS1
The horizontal distance of the
IS shift equals
IS2
…so the IS curve shifts to the right.
ΔY
CHAPTER 11 Aggregate Demand I
This slide has two purposes. First, to show which way the IS curve shifts when G changes. Second, to actually measure the distance of the shift.
We can measure either the horizontal or vertical distance of the shift. The horizontal distance of the IS curve shift is the change in Y required to restore goods market equilibrium AT THE INITIAL INTEREST RATE when G is raised.
Since the interest rate is unchanged at r1, investment will also be unchanged. This is why, in the upper panel, we write “I(r1)” in the PE equation for both expenditure curves – to remind us that investment and the interest rate are not changing.
NOW YOU TRY
Shifting the IS curve: ΔT
Use the diagram of the Keynesian cross or loanable funds model to show how an increase in taxes shifts the IS curve.
If you can, determine the size of the shift.
CHAPTER 11 Aggregate Demand I
One could also demonstrate the shift using the loanable funds model.
ANSWERS
Shifting the IS curve: ΔT
Y2
Y2
At any value of r,
hT g iC g iPE
PE =C2 +I (r1 )+G
IS2
The horizontal distance of the
IS shift equals
Y
PE
r
Y
PE =Y
Y1
Y1
PE =C1 +I (r1 )+G
r1
IS1
…so the IS curve shifts to the left.
ΔY
CHAPTER 11 Aggregate Demand I
To demonstrate the shift using the loanable funds model, note that the tax increase would increase national saving at each level of Y, causing a fall in the interest rate at each level of Y.
The theory of liquidity preference
Due to John Maynard Keynes.
A simple theory in which the interest rate
is determined by money supply and
money demand.
CHAPTER 11 Aggregate Demand I
Money supply
The supply of
real money
balances
is fixed:
M/P
real money balances
r
interest
rate
CHAPTER 11 Aggregate Demand I
We are assuming a fixed supply of real money balances because
P is fixed by assumption (short-run), and M is an exogenous policy variable.
Money demand
Demand for
real money
balances:
M/P
real money balances
r
interest
rate
L (r )
CHAPTER 11 Aggregate Demand I
As we learned in Chapter 5, the nominal interest rate is the opportunity cost of holding money (instead of bonds), so money demand depends negatively on the nominal interest rate.
Here, we are assuming the price level is fixed, so π = 0 and r = i.
Equilibrium
The interest rate adjusts
to equate the supply and demand for money:
M/P
real money balances
r
interest
rate
L (r )
r1
CHAPTER 11 Aggregate Demand I
How the Fed raises the interest rate
To increase r, Fed reduces M
M/P
real money balances
r
interest
rate
L (r )
r1
r2
CHAPTER 11 Aggregate Demand I
CASE STUDY:
Monetary Tightening & Interest Rates
Late 1970s: π > 10%
Oct 1979: Fed Chairman Paul Volcker announces that monetary policy
would aim to reduce inflation
Aug 1979–April 1980:
Fed reduces M/P 8.0%
Jan 1983: π = 3.7%
How do you think this policy change
would affect nominal interest rates?
CHAPTER 11 Aggregate Demand I
This and the next slide summarize the case study on p.330. The data source is given on the next slide.
At this point, students have now learned two theories about the effects of monetary policy on interest rates. This case study shows them that both theories are relevant, using a real-world example to remind students that the classical theory of Chapter 5 applies in the long run while the liquidity preference theory applies in the short run.
Monetary Tightening & Interest Rates, cont.
Δi < 0
Δi > 0
8/1979: i = 10.4%
1/1983: i = 8.2%
8/1979: i = 10.4%
4/1980: i = 15.8%
flexible
sticky
Quantity theory, Fisher effect
(Classical)
liquidity preference
(Keynesian)
prediction
actual
outcome
The effects of a monetary tightening
on nominal interest rates
prices
model
long run
short run
CHAPTER 11 Aggregate Demand I
Since prices are sticky in the short run, the liquidity preference theory predicts that both the nominal and real interest rates will rise in the short run. And in fact, both did. (However, the inflation rate was not zero, and in fact it increased, so the real interest rate didn’t rise as much as the nominal interest rate did during the period shown.)
In the long run, the quantity theory of money says that the monetary tightening should reduce inflation. The Fisher effect says that the fall in π should cause an equal fall in i. By January of 1983 (which is “the long run” from the viewpoint of 1979), inflation and nominal interest rates had fallen. (However, they did not fall by equal amounts. This doesn’t contradict the Fisher effect, though, as other economic changes caused movements in the real interest rate.)
About the data:
i = 3-month rate on commercial paper
% change in M/P from previous slide: I computed M1/CPI (the measure used in the case study), then computed the percentage change in M1/CPI over the 8-month period beginning with the month in which Volcker became the Fed chairman, August 1979.
Source: FRED database, Federal Reserve Bank of St. Louis.
The LM curve
Now let’s put Y back into the money demand function:
The LM curve is a graph of all combinations of r and Y that equate the supply and demand for real money balances.
The equation for the LM curve is:
CHAPTER 11 Aggregate Demand I
Deriving the LM curve
M/P
r
L (r , Y1 )
r1
r2
r
Y
Y1
r1
L (r , Y2 )
r2
Y2
LM
(a) The market for
real money balances
(b) The LM curve
CHAPTER 11 Aggregate Demand I
Why the LM curve is upward sloping
An increase in income raises money demand.
Since the supply of real balances is fixed, there is now excess demand in the money market at the initial interest rate.
The interest rate must rise to restore equilibrium in the money market.
CHAPTER 11 Aggregate Demand I
This slide simply states the intuition behind the graphs on the preceding slide. Suggestion: Omit this slide from your presentation, and just give the students this information orally as you present the preceding slide.
How ΔM shifts the LM curve
M/P
r
L (r , Y1 )
r1
r2
r
Y
Y1
r1
r2
LM1
(a) The market for
real money balances
(b) The LM curve
LM2
CHAPTER 11 Aggregate Demand I
If you’re as anal as I am, you might consider helping your students understand the analytical difference between looking at a shift as a horizontal shift and looking at it as a vertical shift.
We can think of the LM curve shift as a vertical shift:
When the Fed reduces M, the vertical distance of the shift tells us what happens to the equilibrium interest rate associated with a given value of income.
Or, we can think of the LM curve shifting horizontally:
When the Fed reduces M, the horizontal distance of the shift tells us what would have to happen to income to restore money market equilibrium at the initial interest rate. (The graphical analysis would be a little different than what’s depicted on this slide.)
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.
CHAPTER 11 Aggregate Demand I
ANSWERS
Shifting the LM curve
M/P
r
L (r , Y1 )
r1
r2
r
Y
Y1
r1
r2
LM1
(a) The market for
real money balances
(b) The LM curve
LM2
L (r , Y1 )
CHAPTER 11 Aggregate Demand I
If consumers desire to use cash more frequently, money demand will exogenously increase – that is, each (r, Y) pair will be associated with higher money demand than before. In the liquidity preference model, the money demand curve shifts upward/rightward.
Hence, at the initial value of income, the interest rate must rise to restore equilibrium in the money market. As a result, the LM curve shifts up: each value of income (such as the initial income) is associated with a higher interest rate than before.
The short-run equilibrium
The short-run equilibrium is the combination of r and Y that simultaneously satisfies the equilibrium conditions in the goods & money markets:
Y
r
IS
LM
Equilibrium
interest
rate
Equilibrium
level of
income
CHAPTER 11 Aggregate Demand I
The Big Picture
Keynesian
cross
Theory of liquidity preference
IS
curve
LM curve
IS-LM
model
Agg. demand
curve
Agg. supply
curve
Model of Agg. Demand and Agg. Supply
Explanation of short-run fluctuations
CHAPTER 11 Aggregate Demand I
Similar to Figure 11-14, p.334.
This schematic diagram shows how the different pieces of the theory of short-run fluctuations fit together.
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.
CHAPTER 11 Aggregate Demand I
This slide serves as a bridge between this chapter and the next one.
CHAPTER SUMMARY
Keynesian cross
basic model of income determination
takes fiscal policy & investment as exogenous
fiscal policy has a multiplier effect on income
IS curve
comes from Keynesian cross when planned investment depends negatively on interest rate
shows all combinations of r and Y
that equate planned expenditure with
actual expenditure on goods & services
CHAPTER 11 Aggregate Demand I
CHAPTER SUMMARY
Theory of liquidity preference
basic model of interest rate determination
takes money supply & price level as exogenous
an increase in the money supply lowers the interest rate
LM curve
comes from liquidity preference theory when
money demand depends positively on income
shows all combinations of r and Y that equate demand for real money balances with supply
CHAPTER 11 Aggregate Demand I
CHAPTER SUMMARY
IS-LM model
Intersection of IS and LM curves shows the unique point (Y, r ) that satisfies equilibrium in both the goods and money markets.
CHAPTER 11 Aggregate Demand I
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