0. Building the IS-LM Model
Macroeconomics
Chapter 10:
Aggregate Demand I:
Building the IS-LM Model

1. In this chapter, you will learn…
The “IS curve”, and its relation to the goods market
The “LM curve”, and its relation to the money market
How the IS-LM model determines income and the interest rate in the short run.

2. Context
Chapter 9 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

3. 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, Short Run Aggegate Supply curve is horizontal).
This chapter (and chapter 11) focus on the closed-economy case.

4. Building Blocks: The Keynesian “Cross” Model
A simple closed economy model in which income is determined by expenditure. (due to J.M. Keynes, 1936)
Notation:
I = planned investment
E = C + I + G = planned expenditure
Y = real GDP = actual expenditure (production)
Difference between actual & planned expenditure = unplanned inventory investment

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

6. Graphing planned expenditure
E =C +I +G
MPC 1
Why slope of E 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 E---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

7. Graphing the equilibrium condition
planned
expenditure
E =Y
45º
income, output, Y

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

9. An increase in government purchases/spendingY E
E =Y
At Y1, there is now an unplanned drop in inventory…
E =C +I +G2
E =C +I +G1 G
…so firms increase output, and income rises toward a new equilibrium.
Explain why the vertical distance of the shift in the E curve equals G:
At any value of Y, an increase in G by the amount G causes an increase in E by the same amount.
At Y1, there is now an unplanned depletion of inventories, because people are buying more than firms are producing (E > Y).
E1 = Y1 Y
E2 = Y2

10. 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 :

11. The government purchases 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!

12. 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
So the final impact on income is much bigger than the initial G.
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 Ford Explorers. Then, Ford sees its revenues increase by $80 million, all of which becomes income to somebody - either Ford’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).

13. An increase in taxes E C = MPC T Y Y E =C1 +I +G E =C2 +I +G
E =Y Y E
Initially, the tax increase reduces consumption, and therefore E:
E =C1 +I +G
E =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 E 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.
E2 = Y2 Y
E1 = Y1

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

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

16. 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.

17. Exercise:
Use a graph of the Keynesian cross to show the effects of an increase in planned investment on the equilibrium level of income/output.

18. 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:

19. Deriving the IS curve r  I  E  Y E =C +I (r2 )+G

20. 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 (E ).
To restore equilibrium in the goods market, output (a.k.a. actual expenditure, Y ) must increase.

21. The IS curve and the loanable funds model
(a) The L.F. model
(b) The IS curve
I (r )
S, I r r Y S2 S1 Y2 Y1 r2 r2 r1 r1
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.” IS

22. 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

23. Shifting the IS curve: G
E =Y Y E
E =C +I (r1 )+G2
At any value of r, G  E  Y
E =C +I (r1 )+G1
…so the IS curve shifts to the right.
The horizontal distance of the IS shift equals Y1 Y2 r Y r1 Y
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 E equation for both expenditure curves – to remind us that investment and the interest rate are not changing.
IS2
IS1 Y1 Y2

24. Exercise: Shifting the IS curve
Use the diagram of the Keynesian cross or loanable funds model to show how an increase in taxes shifts the IS curve.

25. 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.

26. Money supply The supply of real money balances is fixed: r M/P
interest
rate
The supply of real money balances is fixed:
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

27. 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

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

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

30. 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:

31. 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

32. 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.

33. 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
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.)

34. Exercise: 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 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.

35. 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
Equilibrium
interest
rate
Equilibrium
level of
income

36. 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 10-15, p.300.
This schematic diagram shows how the different pieces of the theory of short-run fluctuations fit together.
Agg. supply curve

37. 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.

38. 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

39. 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

40. 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.