1. aggregate demand II IS-LM model
Macroeconomics ECO 110/1, AAU
Lecture 7
aggregate demand II IS-LM model
Eva Hromádková,

2. Overview of Lecture 7 IS-LM model of AD curve:
Model for AD curve => analysis of stabilization policies
IS curve – goods market
Fiscal policy – expenditures and taxes
LM curve – money market
Monetary policy – money supply
Equilibrium – interest rates

3. IS-LM model Context
We have already introduced the model of aggregate demand (QTM) 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 is negatively related to output

4. IS-LM model Context II
Today we will develop IS-LM model, the theory that explains the aggregate demand curve
First, we focus on the short run and assume hat price level is fixed
Then, we allow price to be flexible, and derive AD curve
Finally, we analyze the effect of fiscal and monetary policy on the most important macroeconomic aggregates – output and unemployment

5. IS curve Keynesian cross
A simple closed economy model in which income is determined by expenditure. (due to J.M. Keynes)
Notation:
I = planned investment
E = C + I + G = planned expenditure
Y = real GDP = actual expenditure
Difference between actual & planned expenditure: unplanned inventory investment

6. IS curve Elements of the Keynesian cross
Consumption function: C = MPC*(Y-T) Govt. policy variables: G, T Investment: I = I(r) Planned expenditure: E = C(Y-T) + I(r) + G Equilibrium: Y = E

7. IS curve Graphing planned expenditure
E =C +I +G
Slope is MPC
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.
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

8. IS curve Graphing the equilibrium condition
planned
expenditure
E =Y
45º
income, output, Y

9. IS curve Equilibrium value of income
planned
expenditure
E =Y
E<Y
E>Y
income, output, Y
E>Y: depleting inventories => produce more E<Y: accumulating inventories=> produce less

10. IS curve Fiscal policy Fiscal stimulus: Fiscal restraint:
Increase in government expenditures
Cut taxes
Increase transfer payments
Fiscal restraint:
Decrease in government expenditures
Increased taxes
Decreased transfer payments

11. IS curve Increase in government purchasesY E
E =Y
E =C +I +G2
E =C +I +G1 G
Looks like Y>G
E1 = Y1 Y
E2 = Y2

12. IS curve Why is change in Y > change in G?
Def: Government purchases multiplier:
Initially, the increase in G causes an equal increase in Y: Y = G.
But Y  C (Y-T)
 further Y
 further C
So the government purchases multiplier will be greater than one.
What is the effect of the increase in the government purchases
At any value of Y, an increase in G by the amount G causes an increase in E by the same amount.
- So we are in the same situation as on the previous slide
At Y1, there is now an unplanned depletion of inventories, because people are buying more than firms are producing (E > Y) = > firms decide to produce more.
+ it seems that increase in output is bigger than increase in government spending

13. IS curve Change in G - Sum up changes in expenditure
Back to our example:
Delta G = 100
MPC = 0.8
Government expenditure multiplier = 5 and increase in Y = 5 * 100 = 500

14. IS curve Increase in taxes
E =Y Y 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
E2 = Y2 Y
E1 = Y1

15. IS curve Change in T - Sum up changes in expenditure
equilibrium condition in changes
I and G exogenous
Solving for Y :
Final result:

16. IS curve Tax multiplier
Question: how is this different from the government spending multiplier considered previously? The tax multiplier: …is negative: An increase in taxes reduces consumer spending, which reduces equilibrium income. …is smaller than the govt spending multiplier: (in absolute value) 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. IS curve How to derive the IS curve I
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: Y = C(Y-T) + I(r) + G 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 (E ). To restore equilibrium in the goods market, output (a.k.a. actual expenditure, Y ) must increase.

18. IS curve How to derive the IS curve II
E =Y Y E
E =C +I (r2 )+G
r  I
E =C +I (r1 )+G
 E I
 Y Y1 Y2 r Y r1
How to draw it
Take a value of r
Compute the value of investment (remember that higher the r, lower the investment)
Compute the value of planned expenditures
Compute Y r2 Y1 Y2 IS

19. IS curve Fiscal policy and IS curve – ex. of increase in G
E =C +I (r1 )+G2
E =Y Y E
At given 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
IS2
IS1 Y1 Y2

20. LM curve How to build the LM curve
The theory of liquidity preference:
Developed by John Maynard Keynes.
A simple theory in which the interest rate is determined by money supply and money demand.

21. LM curve Money supply The supply of real money balances is fixed.
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 chosen by CB.
M/P
real money balances

22. LM curve Money demand r
interest
rate
The demand for real money balances is negatively dependent on interest rate.
L (r,Y )
The nominal interest rate is the opportunity cost of holding money (instead of putting them into bank or buying bonds and earning interest).
In the Money lecture, (M/P)d = L(r +pi)
Here, we are assuming the price level is fixed, so  = 0 and r = i.
We forget for a while on Y (it is important determinant of our decision to hold money!)
M/P
real money balances

23. LM curve Equilibrium r
interest
rate
The interest rate adjusts to equate the supply and demand for money r1
L (r,Y )
M/P
real money balances

24. LM curve Monetary policy

25. LM curve Monetary policy – How can CB affect the interest rate?
To reduce r, central bank reduces M.
In reality, this is hardly he case.
More used technique = change of discount rate. r2 r1
L (r ,Y)
M/P
real money balances

26. LM curve How to derive LM curve?
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:
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. The interest rate must rise to restore equilibrium in the money market.
What is the relation between M/P and Y?
POSITIVE – more goods are there, more you want to hold money (to buy them, of course ).

27. LM curve How to derive LM curve II
(b) The LM curve
(a) The market for real money balances
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 central bank reduces M, the vertical distance of the shift tells us what happens to the equilibrium interest rate associated with a given value of income.

28. IS-LM model EquilibriumY r
The short-run equilibrium is the combination of r and Y that simultaneously satisfies the equilibrium conditions in the goods & money markets: LM IS
Model takes fiscal (G,T) and monetary (M) policy as exogenous. Short run – prices are fixed.
Equilibrium
interest
rate
Equilibrium
level of
income

29. IS-LM model Fiscal policy: An increase in government purchases
1. IS curve shifts right
IS1 r2
causing output & income to rise. Y2 r1 Y1 2. 1.
2. This raises money demand, causing the interest rate to rise…
Topic 10 showed that an increase in G causes the IS curve to shift to the right by (G)/(1-MPC).
Higher G => higher E (planned expenditures) => higher Y Y = 1/(1-MPC)* G. This all happens at a constant level of r => IS shifts by Y
Get partial crowding out of investment. Was complete under neoclassical model (i.e. by what G increase, I had to decrease); here only partial, since Y rises to allow G+I to be bigger
3. …which reduces investment, so the final increase in Y 3.

30. IS-LM model Fiscal policy: A tax cutr
Because consumers save (1MPC) of the tax cut, the initial boost in spending is smaller for T than for an equal G…
and the IS curve shifts by LM
IS2
IS1 r2 2. Y2 r1 Y1 1. 1.
Topic 10 used the Keynesian Cross to show that a decrease in T causes the IS curve to shift to the right by (-MPCT)/(1-MPC).
Again, it is due to fact that if T is smaller => Y-T is higher => people have more money to spend (although they only spend MPC share of it) => C is increasing => E is increasing => Y is increasing 2.
…so the effects on r and Y are smaller for a T than for an equal G. 2.

31. IS-LM model Monetary Policy: an increase in M
1. M > 0 shifts the LM curve down (or to the right) Y r
LM1
LM2 IS r1 Y1
2. …causing the interest rate to fall r2 Y2
3. …which increases investment, causing output & income to rise.
Topic 10 showed increase M shifts LM right.
Here is a richer explanation:
- The increase in M (shift of money supply curve) causes interest rate to fall.
- The fall in the interest rate induces an increase in investment demand, which causes output and income to increase (through planned expenditures).
The increase in income causes money demand to increase, which increases interest rate (though doesn’t increase it all the way back to its initial value; instead, this effect simply reduces the total decrease interest rate).
- is called the “monetary transmission mechanism.”
REMEMBER, THIS IS STILL UNDER FIXED PRICE ASSUMPTION!

32. IS-LM model Shocks I
LM shocks: exogenous changes in the demand for money.
Examples:
a wave of credit card fraud increases demand for money
more ATMs or the Internet banking reduce money demand

33. IS-LM model Shocks II
IS shocks: exogenous changes in the demand for goods & services.
Examples:
stock market boom or crash  change in households’ wealth  C
change in business or consumer confidence or expectations  I and/or C

34. Aggregate demand How to get from IS-LM to AD
So far, we’ve been using the IS-LM model to analyze the short run, when the price level is assumed fixed.
However, a change in P would shift the LM curve and therefore affect Y.
The aggregate demand curve (introduced in chap. 9 ) captures this relationship between P and Y

35. Aggregate demand How to get from IS-LM to AD II
Intuition for slope of AD curve:
P  (M/P )
 LM shifts left
 r
 I
 Y Y r
LM(P2) IS
LM(P1) r2 r1 Y2 Y1 Y P
Upper panel: IS-LM model (r and Y)
Lower panel: AD curve (P and Y)
For given P1 – equilibrium valued from IS-LM model
If P2>P1 => real money balances in the economy are lower (M/P lower) => r is higher =>LM shifts upwards
Higher r => lower investment => lower Y in the new equilibrium
Altogether higher P => lower Y == AD curve P2 P1 AD Y2 Y1

36. Aggregate demand Effect of monetary policy
LM(M1/P1)
The Fed can increase aggregate demand:
M  LM shifts right IS
LM(M2/P1) r1 Y1 r2 Y2
 r
 I
 Y at each value of P Y P
AD2
AD1
Just the opposite mechanism as on the other slide
We see only part of the picture – aggregate demand at given price level. It’s worth taking a moment to explain why we are holding P fixed at P1:
To find out whether the AD curve shifts to the left or right, we need to find out what happens to the value of Y associated with any given value of P. This is not to say that the equilibrium value of P will remain fixed after the policy change (though, in fact, we are assuming P is fixed in the short run). We just want to see what happens to the AD curve.
Once we know how the AD curve shifts, we can then add the AS curves (short- or long-run) to find out what, if anything, happens to P (in the short- or long-run). P1

37. Aggregate demand Effect of fiscal policyLM
IS2
Expansionary fiscal policy (G and/or T ) increases agg. demand:
T  C
 IS shifts right
 Y at each value of P Y2 r2
IS1 Y1 r1 Y P
AD2
AD1 P1

38. Aggregate demand When is fiscal policy more effective?
Fiscal policy is effective (Y will rise much) when:
LM flatter LM Y1
IS1 r 1 Y2
IS2 2
As the rise in G raises Y,
the increase in money demand does not raise r much:
so investment is not crowded out as much.
LM’
Y2’ 2’
When is LM flatter?

39. Aggregate demand When is monetary policy more effective?
Monetary policy is effective (Y will rise much) when:
IS flatter r
As a rise in M lowers the interest rate (r),
investment rises more in response to the fall in r,
so output rises more. IS
LM1
LM2 1
Y2’ 2’ 2
IS’ Y1 Y2

40. IS-LM and AD-AS model combination of short & long run
In the short-run equilibrium, if
then over time, the price level will
rise
fall
The next few slides put our IS-LM-AD in the context of the bigger picture - the AD-AS model in the short-run and long-run, which was introduced in Chapter 9.
remain constant

41. IS-LM and AD-AS model short & long run effect of IS shock IY r
LRAS
LM(P1)
IS1
IS2
AD2
A negative IS shock shifts IS and AD left, causing Y to fall.
LRAS
AD1 Y P
SRAS1 P1
Abbreviation:
SR = short run, LR = long run

42. IS-LM and AD-AS model short & long run effect of IS shock IIY r
In the new short-run equilibrium,
LRAS
LM(P1)
IS2
IS1 Y P
LRAS
AD2
SRAS1 P1
AD1

43. IS-LM and AD-AS model short & long run effect of IS shock IIY r
In the new short-run equilibrium,
LRAS
LM(P1)
IS2
IS1
Over time, P gradually falls, which causes
SRAS to move down
M/P to increase, which causes LM to move down Y P
LRAS
AD2
Pressure on prices from the real economy - decrease in prices, effect on two margins:
LM curve shifts downwards
Short run AS shifts downwards
SRAS1 P1
AD1

44. IS-LM and AD-AS model short & long run effect of IS shock IIIY r
LRAS
LM(P1)
SRAS2 P2
LM(P2)
IS2
IS1
Over time, P gradually falls, which causes
SRAS to move down
M/P to increase, which causes LM to move down Y P
LRAS
AD2
SRAS1 P1
AD1

45. IS-LM and AD-AS model short & long run effect of IS shock IVY r
LRAS
LM(P1)
This process continues until economy reaches a long-run equilibrium with
SRAS2 P2
LM(P2)
IS2
IS1 Y P
LRAS
AD2
SRAS1
A good thing to do: Go back through this experiment again, and see if your students can figure out what is happening to the other endogenous variables (C, I, u) in the short run and long run. P1
AD1

46. The Great Depression CASE STUDY
Unemployment (right scale)
Real GNP (left scale)
This was original motivation by Keynes – What caused the Great Depression
This chart presents data from Table 11-2 on p.296 of the text. For data sources, see notes accompanying that table.
Note the very strong negative correlation between output and unemployment.

47. Real side of economy:
Every measure hit the bottom in 1933

48. The Great Depression CASE STUDY
Real side of economy:
Output: falling
Consumption: falling
Investment: falling much
Gov. purchases: fall (with a delay)

49. Nominal side of economy

50. The Great Depression CASE STUDY
Nominal side:
Nominal interest rate: falling
Money supply (nominal): falling
Price level: falling (deflation)

51. The Great Depression CASE STUDY
The Spending Hypothesis: Shocks to the IS Curve
asserts that the Depression was largely due to an exogenous fall in the demand for goods & services -- a leftward shift of the IS curve
evidence: output and interest rates both fell, which is what a leftward IS shift would cause

52. The Spending Hypothesis: Reasons for the IS shift
Stock market crash  exogenous C
Oct-Dec 1929: S&P 500 fell 17%
Oct 1929-Dec 1933: S&P 500 fell 71%
Drop in investment
“correction” after overbuilding in the 1920s
widespread bank failures made it harder to obtain financing for investment
Contractionary fiscal policy
in the face of falling tax revenues and increasing deficits, politicians raised tax rates and cut spending
+ lower immigration

53. The Money Hypothesis: A Shock to the LM Curve
asserts that the Depression was largely due to huge fall in the money supply
evidence: M1 fell 25% during
But, two problems with this hypothesis:
P fell even more, so M/P actually rose slightly during
nominal interest rates fell, which is the opposite of what would result from a leftward LM shift.

54. The Money Hypothesis: Revision
There was a big deflation: P fell 25%
A sudden fall in expected inflation means the ex-ante real interest rate rises for any given nominal rate (i)
ex ante real interest rate = i – e
This could have discouraged the investment expenditure and helped cause the depression.
Since the deflation likely was caused by fall in M, monetary policy may have played a role here.