1. Chapter 11, 8th and 9th Editions Chapter 10 in the 7th Edition
The Economy in the Short-run
Aggregate Demand I: Building the IS-LM 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. Motivation
The Great Depression caused a rethinking of the Classical Theory of the macroeconomy. It could not explain:
Drop in output by 30% from 1929 to 1933
Rise in unemployment to 25%
In 1936, J.M. Keynes developed a theory to explain this phenomenon.
We will learn a version of this theory, called the ‘IS-LM’ model.

3. Growth rates of real GDP, consumption
Percent change from 4 quarters earlier
Real GDP growth rate
Consumption growth rate
Average growth rate about 3% - 3.5%
Over the long run, real GDP grows about 3 percent per year. Over the short run, though, there are substantial fluctuations in GDP, as this graph clearly shows.
The pink shaded vertical bars denote recessions.
This graph also shows the growth rate of consumption (from Figure 9-2(a) on p.260).
consumption is less volatile than income. (An exception occurs in the late 1990s, when consumption growth exceeded income growth – probably due to the stock market boom.) As Chapter 17 covers in more detail, consumers prefer smooth consumption, so they use saving as a buffer against income shocks.
Source of data: See Figure 9-1, p.259

4. Growth rates of real GDP, consumption, investment
Percent change from 4 quarters earlier
Investment growth rate
Real GDP growth rate
Consumption growth rate
This graph reproduces GDP and consumption growth using a larger scale. The scale accommodates the investment growth rate data.
The point: investment is much more volatile than consumption or GDP in the short run.
Source: See Figure 9-2, p.260

5. Unemployment Percent of labor force
The unemployment rate rises during recessions and falls during expansions.
The unemployment rate sometimes lags changes in GDP growth. For example, after the 1991 recession ended, unemployment continued to rise for about a year before falling. After the 2001 recession ended, unemployment did not begin to fall for a couple quarters.
people are looking for signs that the recession (which began December 2007) is ending. They shouldn’t look at the unemployment rate – it probably won’t start falling, and may continue rising, until a while after the recession ends.
Source: See Figure 9-3, p.261.

6. Change in unemployment rate
Okun’s Law
Percentage change in real GDP
1951
1966
1984
2003
1971
1987
2008
1975
A replica of Figure 9.4, p.262.
The boxed equation in the upper right is the Okun’s Law equation shown on the bottom of p In this equation, “u” denotes the unemployment rate.
2001
1991
1982
Change in unemployment rate

7. Time horizons in macroeconomics
Long run Prices are flexible, respond to changes in supply or demand.
Short run Many prices are “sticky” at a predetermined level. .
It might also be worth reminding them that they (and most adults) are already aware of the concept of sticky prices. If they have a favorite beverage at Starbucks, ask if they can remember when its price was last increased. If they work, ask how long they go between wage changes. Sticky prices are a fact of everyday life, even if most adults have not heard the term “sticky prices” or studied the implications of sticky prices for short-run economic fluctuations.
The economy behaves much differently when prices are sticky.

8. Chapter 11 In this chapter:
the IS curve, and its relation to:
the Keynesian cross
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
Continue to assume a closed economy 7

9. Context Short run Long run prices fixed
output determined by aggregate demand
unemployment negatively related to output
Demand oriented model
Long run
prices flexible
output determined by factors of production & technology
unemployment equals its natural rate
Supply oriented model

10. The Keynesian Cross (Simple Keynesian) Model – Econ 201 stuff
A simple closed economy model in which income is determined by spending.
Notation:
I = planned investment
PE = C + I + G = planned expenditure
(NOTE): Older edition uses E = C + I + G
Y = real GDP = actual expenditure
Difference between actual & planned expenditure = unplanned changes in inventory - (so sales at Nordstrom)

11. Elements of the Keynesian Cross Model
disposable income
consumption function:
govt policy variables:
for now, planned investment is exogenous:
planned expenditure:
Note: In equilibrium, there is no unplanned inventory investment. Firms are selling everything they had intended to sell.
equilibrium condition:
actual expenditure = planned expenditure

12. Planned Consumption Expenditure
C = a +mpc x (Y-T)
The Keynesian consumption function has a constant term and we assume its linear.
MPC 1 a
income, output, Y

13. Graphing planned expenditure: Remember I and G are exogenous.
PE =C +𝑰 +G
MPC 1
C = a +mpc x (Y-T)
MPC 1 a
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.
income, output, Y

14. 45O line - Graphing the equilibrium conditionPE
planned
expenditure
PE =Y
45º
income, output, Y

15. The equilibrium value of incomePE
planned
expenditure
PE =Y
PE =C +I +G
The equilibrium point is the value of income where the curves cross.
Equilibrium income
income, output, Y

16. Why this is the equilibrium value of incomePE
planned
expenditure
PE =Y
PE =C +I +G
E<Y
E>Y
income, output, Y
PE > Y: Unplanned reduction in inventories: must produce more.
PE < Y: unplanned increase in inventories: must produce less.

17. An increase in government purchasesY PE
PE =Y
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.
The vertical distance of the shift in the PE curve equals G:
At any value of Y, an increase in G by the amount G causes an increase in PE by the same amount.
At Y1, there is now an unplanned depletion of inventories, because people are buying more than firms are producing (PE > Y).
PE1 = Y1 Y
PE2 = Y2

18. Why the multiplier is greater than 1
Def: Government purchases multiplier:
Initially, the increase in G causes an equal increase in Y: Y = G.
But Y  C
 further Y
 further C
So the government purchases multiplier will be greater than one, i.e., Y >G
Students are better able to understand this if given a more concrete example. 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 somebody: some of it is paid to the workers and engineers and managers, the rest is profit paid as dividends to shareholders. Hence, income rises $100 million (Y = $100 million = G ). 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 Chevy Trailblazers. Then, General Motors sees its revenues increase by $80 million, all of which becomes income to somebody - either GM’s workers, or its shareholders (Y = $80 million). And what do these folks do with this extra income? They spend the fraction MPC (0.8) of it, causing C = $64 million (8/10 of $80 million). Suppose they spend all $64 million on Hershey’s chocolate bars, the ones with the bits of mint cookie inside. Then, Hershey Foods Corporation experiences a revenue increase of $64 million, which becomes income to somebody or other. (Y = $64 million). So far, 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).

19. Sum up changes in expenditure

20. Algebra example Suppose consumption function: C= a+b(Y-T)
where a and b are some numbers (MPC=b)
Use Goods market equilibrium condition:

21. Algebra example Solve for Y:
So if b=MPC=0.75, multiplier = 1/( ) = 4.

22. Solving for Y equilibrium condition in changes because I exogenous
because C = MPC Y
Collect terms with Y on the left side of the equals sign:
Solve for Y :

23. The simple government spending multiplier
Definition: the increase in income resulting from a $1 increase in G.
In this model, the govt purchases multiplier equals
Example: If MPC = 0.8, then
An increase in G causes income to increase 5 times as much!

24. An increase in lump-sum taxes
PE =Y Y 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
Experiment: An increase in taxes (note: the book does a decrease in taxes)
Suppose taxes are increased by T. 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 T causes disposable income to fall by T, which causes consumption to fall by MPC  T. Because consumption falls, the change in C is negative: C =  MPC  T
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.
PE2 = Y2 Y
PE1 = Y1

25. Algebra example Solve for Y:
So if b=MPC=0.75, multiplier = -0.75/( ) = -3.

26. Solving for Y eq’m condition in changes I and G exogenous
Final result:

27. The tax multiplier
def: the change in income resulting from a $1 increase in T :
If MPC = 0.8, then the tax multiplier equals

28. 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.

29. What is the formula for the Investment Multiplier?

30. The Math:
Deriving the Multipliers with Lump Sum Taxes

31. Tax Revenues Depend on Income: T = T0 +tY, t = tax rate
More realistic Model:
Tax Revenues Depend on Income: T = T0 +tY, t = tax rate
Through substitution we get
Solving for Y:

32. Lump Sum Tax Multiplier =
This means that a $1 increase in G or I (holding a and T0 constant) will increase the equilibrium level of Y by
Spending Multiplier =
Holding a, I, and G constant, a fixed or lump-sum tax cut (a cut in T0) will increase the equilibrium level of income by
Lump Sum Tax Multiplier =

33. Comparison of simple multiplier to more realistic multiplier.
Suppose MPC = 0.8 and t = .25.
Simple multiplier
Multiplier with t=.25:

34. Numerical Example: TAX REVENUES DEPEND ON INCOME

35. Solving for Y (Equilibrium):

36. Government spending multiplier is about 1.5 - not large!
A Warning on Multipliers
Government spending multiplier is about not large!
Changing G or T is not always easy.
Response in C or I (and imports in an open economy) are not certain
Anticipations are likely to matter
Budget deficits and public debt may have adverse implications in the long-run.

37. The short-run IS-LM model: The IS curve
Up to this point we have held r constant -
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

38. Deriving the IS curve: 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

39. 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

40. 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…

41. 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

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

43. 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

44. 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
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: as e => slope decreases
as: a, d, or G increase => IS shifts to the right.
Shift variables
Slope

45. The IS curve: r
( 𝑎−𝑏 𝑇 0 +𝑑+ 𝐺 0 𝑒 )
1−𝑏+𝑏𝑡 𝑒 = slope IS Y

46. 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.

47. 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

48. Money demand Demand for real money balances: L (r ) 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

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

50. Equilibrium r
interest
rate
The interest rate adjusts to equate the supply and demand for money:
Excess supply of money r2 r1 r3
L (r )
Excess demand for money
M/P
real money balances

51. How the Fed raises the interest rate
To increase r, Fed reduces M r2 r1
L (r )
M/P
real money balances

52. 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?

53. 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%

54. 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.
Equating M/P to Md, the equation for the LM curve is:

55. 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

56. 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.

57. 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

58. 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

59. 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)

60. 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.

61. 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),

62. 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 )

63. 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

64. 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.

65. 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 64

66. 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 65

67. 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. 66