1. Chapter 11- Part 2 The Economy in the Short-run
Aggregate Demand I: Building the IS-LM Model and
Variations of the Model
This chapter builds the IS-LM model, which chapter 11 then uses 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.
New to the 7th edition: the notation for planned expenditure is now “PE” rather than “E.” The notation for planned investment remains “I.”

2. The short-run IS-LM model: The IS curve
Up to this point we have held r constant and treated I as exogenous. We now add r.
The IS-curve: a graph of all combinations of r and Y that result in goods market equilibrium
i.e. actual expenditure Y(output) = planned expenditure
The equation for the IS curve is:
𝒀=𝑪(𝒀− 𝑻 )+𝑰 𝒓 + 𝑮
𝒀=𝑪(𝒀− 𝑻 )+𝑰(i-e)+ 𝑮

3. Deriving the IS curve: reduction in r, e = 0
PE =Y Y PE
PE =C +I (r2 )+G
45o diagram
PE =C +I (r1 )+G I
From Chapter 3 Y1 Y2 r I r Y r Y r1 r1 r2 r2 IS I1 I2 Y1 Y2

4. Understanding the IS curve’s slope
The IS curve is negatively sloped.
Intuition: A fall in the interest rate motivates firms to increase investment spending, which drives up total planned spending (PE )…
and output (Y ) increases.
r  = I  => PE  => Y

5. Fiscal Policy and the IS curve
We can use the IS-LM model to see how fiscal policy (G and T ) can affect aggregate demand and output.
Let’s start by using the Keynesian Cross to see how fiscal policy shifts the IS curve…

6. Shifting the IS curve: G
At any value of r, G  PE  Y
PE =Y Y PE
PE =C +I (r1 )+G2
PE =C +I (r1 )+G1
…so the IS curve shifts to the right.
The horizontal distance of the IS shift equals: or Y1 Y2 r Y r1
ΔY = 𝟏 (𝟏−𝐦𝐩𝐜) 𝚫𝐆
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. Y
IS2
IS1 Y1 Y2
ΔY = 𝟏 (𝟏−𝐦𝐩𝐜(𝟏−𝐭)) 𝚫𝐆

7. NOW YOU TRY: Shifting the IS curve: T
Suppose T is reduced.

8. Equation For the IS-Curve; the real side of the economy
Eq.No Equation Description
Y = C + I + G, Output equals aggregate demand, the equilibrium condition
(2) C = a + b(YD), Consumption function, b is the mpc.
(3) YD = Y – T, Definition of disposable income
(4) T = T0 + tY, Tax function; T0 is lump sum taxes, t is marginal tax rate.
(5) I = d – ei, Investment function ( if e = 0, i = r)
e = ΔI/Δi , Sensitivity of investment (I) to the interest rate (i).
(6) G = G0, Government spending on goods and services, exogenous

9. Equation For the IS-Curve; the real side of the economy
Substitute (2)-(6) into (1): yields:
(7) Y = a + b(YD )+ d – ei + G0
(8) Y= a +b(Y – (T0 + tY)) + d – ei + G0
Solve for Y as a function of i:
(9) Y =( 1 1−𝑏+𝑏𝑡 ) [ 𝑎−𝑏 𝑇 0 +𝑑+ 𝐺 0 −𝑒𝑖] IS-curve
This is what we had without i in the simple Keynesian model

10. Equation For the IS-Curve; the real side of the economy
Solve for i as a function of Y:
(10) i = ( 𝑎−𝑏 𝑇 0 +𝑑+ 𝐺 0 𝑒 ) − 1−𝑏+𝑏𝑡 𝑒 𝑌, IS - Curve
Observations:
(1) as e => slope  ∆𝑖 ∆𝑌  decreases. As the sensitivity of investment (I) to the interest rate (i) increases, the slope of the IS curve decreases.
(2) as: a, d, or G increase => IS shifts to the right. If T0 decreases => IS shifts to the right
Shift variables
Slope

11. The IS curve: Slopes matter: r = i ( 𝑎−𝑏 𝑇 0 +𝑑+ 𝐺 0 𝑒 )
( 𝑎−𝑏 𝑇 0 +𝑑+ 𝐺 0 𝑒 )
1−𝑏+𝑏𝑡 𝑒 = slope IS Y
Slopes matter:
As e => slope decreases. The response in Y to a given change in i increases.
As t  => slope increases. The response in Y to a given change in i decreases.
As b  => slope decreases. The response in Y to a given change in i increases.

12. 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.
Two financial assets – Money and bonds.

13. Money supply The supply of real money balances is fixed:
interest
rate
The supply of real money balances is fixed:
M and P are exogenous.
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.
M/P
real money balances

14. Money demand Demand for real money balances: L (r ) i = r M/P interest
rate
Demand for real money balances:
L (r )
As we learned in chapter 4, 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  = 0 and r = i.
M/P
real money balances

15. Equilibrium
i=r
interest
rate
The interest rate adjusts to equate the supply and demand for money: r1
L (r )
M/P
real money balances

16. Equilibrium
The interest rate adjusts to equate the supply and demand for money.
Excess supply of money creates an excess demand for other assets – bonds in the Keynesian model.
Excess demand for money creates an excess supply of other assets – bonds in the Keynesian model.
i= r
interest
rate
Excess supply of money r2 r1 r3
L (r )
Excess demand for money
M/P
real money balances

17. How the Fed increases and decreases the interest rate
To decrease r, Fed increases M, creating an excess supply of money.
The demand for bonds increase and interest rates decrease. r
interest
rate r1 r2
L (r )
M/P
real money balances

18. CASE STUDY: Monetary Tightening & Interest Rates
Late 1970s:  > 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:  = 3.7%
This and the next slide summarize the case study on pp 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 that both theories are relevant, using a real-world example to remind us that the classical theory of chapter 4 applies in the long-run while the liquidity preference theory applies in the short run.
How do you think this policy change would affect nominal interest rates?

19. Monetary Tightening & Interest Rates, cont.
prediction
actual outcome
The effects of a monetary tightening on nominal interest rates
prices
model
long run
short run
Liquidity preference
(Keynesian)
Quantity theory, Fisher effect
(Classical)
sticky
flexible
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  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
i > 0 Why?
i < 0 Why?
8/1979: i = 10.4%
4/1980: i = 15.8%
8/1979: i = 10.4%
1/1983: i = 8.2%

20. The LM curve 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.
Equating M/P to Md, the equation for the LM curve is:

21. Deriving the LM curve L (r , Y2 ) L (r , Y1 ) r r LM Y1 Y2 r2 r2 r1 r1
(a) The market for real money balances
(b) The LM curve
L (r , Y1 )
M/P r r Y LM Y1 Y2 r2 r2 r1 r1

22. Understanding the LM curve’s slope
The LM curve is positively sloped.
Intuition: 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.
Sell bonds, the interest rate rises to restore equilibrium in the money market.

23. How M shifts the LM curve
(a) The market for real money balances
(b) The LM curve
L (r , Y1 )
M/P r r Y
LM2 Y1
LM1 r2 r2 r1 r1

24. Equation For the LM-Curve; the financial side of the economy
(1) M0/ 𝑃 = L(r,Y), Equilibrium condition
(2) M0 = nominal money supply
(3) (M/P)d = f + gY - hi, money demand
Substitute (2) and (3) into (1) and solve for Y:
Y = 1 𝑔 ( 𝑀 0 𝑃 )−( 𝑓 𝑔 )+( ℎ 𝑔 )𝑖 LM-curve
Solve for i (remember r = i):
i = ( 𝑓 ℎ )+( 𝑔 ℎ )𝑌−( 1 ℎ )( 𝑀 0 𝑃 ) LM-curve

25. Graph the LM curve: remember r = i
Slope = (g/h) Y
(f/h) - (1/h)(M/P)
A steep LM curve (g/h large) means that a rise in output implies a big rise in interest rate to maintain equilibrium.
Causes of this:
Money demand is not very responsive to interest rate (h is small)
Money demand is very responsive to output (g large)

26. 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.
Answer:
This causes an increase in money demand. In the Liquidity Preference diagram, the money demand curve shifts up. 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.

27. 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 LM IS
Remember:e = 0:
Equilibrium
interest
rate
𝒀=𝑪(𝒀− 𝑻 )+𝑰(i-e)+ 𝑮
Equilibrium
level of
income
M/𝑷 = L(i,Y),

28. The short-run equilibriumY r
𝑎−𝑏 𝑇 0 +𝑑+ 𝐺 0 𝑒 IS LM
Slope = g/h
Slope =
1−𝑏+𝑏𝑡 𝑒
( 𝑓 ℎ )−( 1 ℎ )( 𝑀 0 𝑃 )

29. The Big Picture Keynesian Cross IS curve IS-LM model
Explanation of short-run fluctuations
Theory of Liquidity Preference
LM curve
Agg. demand curve
Model of Agg. Demand and Agg. Supply
Figure 10-14, p.307.
This schematic diagram shows how the different pieces of the theory of short-run fluctuations fit together.
Agg. supply curve

30. Preview of Chapter 11 In Chapter 11, 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.
This slide serves as a bridge between this chapter and the next one.

31. Chapter Summary basic model of income determination
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 30

32. Chapter Summary basic model of interest rate determination
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 31

33. 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. 32