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Aggregate Demand II:

Applying the IS-LM Model

Readings: Chapter 12, Mankiw

MACROECONOMICS

N. Gregory Mankiw

PowerPoint ® Slides by Ron Cronovich

Fall 2014 update

Context

Chapter 10 introduced the model of aggregate demand and supply.

Chapter 11 developed the IS-LM model, the basis of the aggregate demand curve.

If you wish, delete this slide and give students this information orally.

IN THIS CHAPTER, YOU WILL LEARN:

how to use the IS-LM model to analyze the effects of shocks, fiscal policy, and monetary policy

how to derive the aggregate demand curve from the IS-LM model

several theories about what caused the Great Depression

The intersection determines the unique combination of Y and r that satisfies equilibrium in both markets.

The LM curve represents money market equilibrium.

Equilibrium in the IS -LM model

The IS curve represents equilibrium in the goods market.

Review/recap of Chapter 11.

Policy analysis with the IS -LM model

We can use the IS-LM model to analyze the effects of

fiscal policy: G and/or T

monetary policy: M or i

A lil` more recap

AD= C + I + G + NX => Equilibrium output or IS curve:

causing output & income to rise.

IS1

Fiscal policy example: An increase in government purchases

1. IS curve shifts right

IS2

2. This raises money demand, causing the interest rate to rise…

3. …which reduces investment, so the final increase in Y

Chapter 11 (both DFS and Mankiw) showed that an increase in G causes the IS curve to shift to the right by (G)/(1-MPC).

An increase in tax rate

IS: Y = (Ao - bi)

= [1/(1 - c + ct)](Ao - bi

Rearrange it for i:

i = (1/b)Ao - (1/b)Y

= (1/b)Ao – [(1 - c + ct)/b]Y.

This is just also the equation for IS.

A rise in t would increase the slope of IS given by: [(1 - c + ct)/b] => IS2 => fall in i and Y

What’s the economics intuition behind the fall in interest rate and output? When tax rate increases, people cut back on their consumption. So aggregate demand falls. That leads to a fall in output. As a response, firms cut back in their investments too. So demand for borrowing declines and interest rate falls.

2. …causing the interest rate to fall

Monetary policy: An increase in M

1. ΔM > 0 shifts the LM curve down (or to the right)

LM1

LM2

3. …which increases investment, causing output & income to rise.

Chapter 11 showed that an increase in M shifts the LM curve to the right.

Here is a richer explanation for the LM shift if you already know how bonds are priced:

The increase in M causes the interest rate to fall. [People like to keep optimal proportions of money and bonds in their portfolios; if money is increased, then people try to re-attain their optimal proportions by “exchanging” some of the money for bonds: they use some of the extra money to buy bonds. This increase in the demand for bonds drives up the price of bonds -- and causes interest rates to fall (since interest rates are inversely related to bond prices).

The fall in the interest rate induces an increase in investment demand, which causes output and income to increase.

The increase in income causes money demand to increase, which increases the interest rate (though doesn’t increase it all the way back to its initial value; instead, this effect simply reduces the total decrease in the interest rate).

Interaction between monetary & fiscal policy

Model:

Monetary & fiscal policy variables (M, G, and T ) are exogenous.

Real world:

Monetary policymakers may adjust M in response to changes in fiscal policy, or vice versa.

Such interactions may alter the impact of the original policy change.

The Fed’s response to ΔG > 0

Suppose Congress increases G.

Possible Fed responses:

1. hold M constant

2. hold r constant

3. hold Y constant

In each case, the effects of the ΔG are different…

If Congress raises G, the IS curve shifts right.

IS1

Response 1: Hold M constant

LM1

IS2

If Fed holds M constant, then LM curve doesn’t shift.

Results:

If Congress raises G, the IS curve shifts right.

IS1

Response 2: Hold r constant

LM1

IS2

To keep r constant, Fed increases M to shift LM curve right.

LM2

Results:

IS1

Response 3: Hold Y constant

LM1

IS2

To keep Y constant, Fed reduces M to shift LM curve left.

LM2

Results:

If Congress raises G, the IS curve shifts right.

Shocks in the IS -LM model

IS shocks: exogenous changes in the demand for goods & services.

Examples:

stock market boom or crash g change in households’ wealth g ΔC

change in business or consumer confidence or expectations g ΔI and/or ΔC

Shocks in the IS -LM model

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 reduce money demand.

NOW YOU TRY Analyze shocks with the IS-LM model

Use the IS-LM model to analyze the effects of

1. a housing market crash that reduces consumers’ wealth

2. consumers using cash in transactions more frequently in response to an increase in identity theft

For each shock,

a. use the IS-LM diagram to determine the effects on Y and r.

b. figure out what happens to C, I, and the unemployment rate.

Earlier slides showed how to use the IS-LM model to analyze fiscal and monetary policy. Now is a good time for students to get some hands-on practice with the model. Also, note that part (b) shows that shocks and policies can potentially affect all of the model’s endogenous variables, not just the ones that are measured on the axes.

ANSWERS, PART 1 Housing market crash

IS1

LM1

IS2

IS shifts left, causing

r and Y to fall.

C falls due to lower wealth and lower income,

I rises because r is lower

u rises because Y is lower (Okun’s law)

1a. The IS curve shifts to the left, because consumers cut back on spending in response to the decrease in their wealth. This causes Y and r to fall.

1b. C falls for two reasons: the housing market crash, and the fall in income. In this simple model, I depends only on the interest rate, which falls, causing I to rise. u rises, because firms need less labor when they are producing less output (recall Okun’s Law).

ANSWERS, PART 2 Increase in money demand

IS1

LM1

LM2

LM shifts left, causing

r to rise and Y to fall.

C falls due to lower income,

I falls because r is higher

u rises because Y is lower (Okun’s law)

The increase in money demand shifts the LM curve to the left: We are assuming that all other exogenous variables, including M and P, remain unchanged, so an increase in money demand causes an increase in the value of r associated with each value of Y (this can be seen easily using the Liquidity Preference diagram). This translates to an upward (i.e. leftward) shift in the LM curve. This shift causes Y to fall and r to rise.

2b. The fall in income causes a fall in C. The increase in r causes a fall in I. The fall in Y causes an increase in u.

What is the Fed’s policy instrument?

The news media commonly report the Fed’s policy changes as interest rate changes, as if the Fed has direct control over market interest rates.

In fact, the Fed targets the federal funds rate—the interest rate banks charge one another on overnight loans.

The Fed changes the money supply and shifts the LM curve to achieve its target.

Other short-term rates typically move with the federal funds rate.

What is the Fed’s policy instrument?

Why does the Fed target interest rates instead of the money supply? One of the reasons

-They are easier to measure than the money supply.

IS-LM and aggregate demand

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 LM and therefore affect Y.

The aggregate demand curve (introduced in Chap. 10) captures this relationship between P and Y.

Deriving the AD curve

LM(P1)

LM(P2)

Intuition for slope of AD curve:

hP g i(M/P )

g LM shifts left

g hr

g iI

g iY

It might be useful to explain the reason why we draw P1 before drawing the LM curve:

The position of the LM curve depends on the value of M/P. M is an exogenous policy variable. So, if P is low (like P1 in the lower panel of the diagram), then M/P is relatively high, so the LM curve is over toward the right in the upper diagram. If P is high, like P2, then M/P is relatively low, so the LM curve is more toward the left.

Because the value of P affects the position of the LM curve, we label the LM curves in the upper panel as LM(P1) and LM(P2).

Monetary policy and the AD curve

LM(M2/P1)

LM(M1/P1)

AD1

The Fed can increase aggregate demand:

hM g LM shifts right

AD2

g ir

g hI

g hY at each value of P

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).

Fiscal policy and the AD curve

IS1

AD1

Expansionary fiscal policy (hG and/or iT ) increases agg. demand:

iT g hC

g IS shifts right

g hY at each value of P

AD2

IS2

IS-LM and AD-AS in the short run & long run

Recall from Chapter 10: The force that moves the economy from the short run to the long run is the gradual adjustment of prices.

rise

fall

remain constant

In the short-run equilibrium, if

then over time, the price level will

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 10.

The SR and LR effects of an IS shock

A negative IS shock shifts IS and AD left, causing Y to fall.

LRAS

IS1

SRAS1

LM(P1)

IS2

AD2

AD1

Abbreviation:

SR = short run, LR = long run

The analysis that begins on this slide continues on the following slides.

The SR and LR effects of an IS shock

LRAS

IS1

SRAS1

LM(P1)

IS2

AD2

AD1

In the new short-run equilibrium,

The SR and LR effects of an IS shock

LRAS

IS1

SRAS1

LM(P1)

IS2

AD2

AD1

In the new short-run equilibrium,

Over time, P gradually falls, causing:

SRAS to move down

M/P to increase, which causes LM to move down

AD2

The SR and LR effects of an IS shock

LRAS

IS1

SRAS1

LM(P1)

IS2

AD1

SRAS2

LM(P2)

Over time, P gradually falls, causing:

SRAS to move down

M/P to increase, which causes LM to move down

AD2

SRAS2

LM(P2)

The SR and LR effects of an IS shock

LRAS

IS1

SRAS1

LM(P1)

IS2

AD1

This process continues until economy reaches a long-run equilibrium with

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.

NOW YOU TRY Analyze SR & LR effects of ΔM

Draw the IS-LM and AD-AS diagrams as shown here.

Suppose Fed increases M. Show the short-run effects on your graphs.

Show what happens in the transition from the short run to the long run.

How do the new long-run equilibrium values of the endogenous variables compare to their initial values?

LRAS

SRAS1

LM(M1/P1)

AD1

This exercise has two objectives:

1. To give students immediate reinforcement of the preceding concepts.

2. To show them that money is neutral in the long run, just like in Chapter 5.

You might have your students try other exercises using this framework:

* the short-run and long-run effects of expansionary fiscal policy. Have them compare the long-run results in this framework with the results they obtained when doing the same experiment in Chapter 3 (the loanable funds model).

* Immediately after a negative shock pushes output below its natural rate, show how monetary or fiscal policy can be used to restore full-employment immediately (i.e., without waiting for prices to adjust).

ANSWERS, PART 1 Short-run effects of ΔM

LM and AD shift right.

r falls, Y rises above

LRAS

SRAS

LM(M1/P1)

AD1

LM(M2/P1)

AD2

ANSWERS, PART 2 Transition from short run to long run

Over time,

P rises

SRAS moves upward

M/P falls

LM moves leftward

New long-run eq’m

P higher

all real variables back at their initial values

Money is neutral in the long run.

LRAS

SRAS

LM(M1/P1)

AD1

LM(M2/P1)

AD2

LM(M2/P3)

SRAS

r3 =

The Great Depression

Unemployment (right scale)

Real GNP (left scale)

120

140

160

180

200

220

240

1929

1931

1933

1935

1937

1939

billions of 1958 dollars

percent of labor force

This chart presents data from Table 12-2 on pp.342–343 of the text. For data sources, see the notes accompanying that table.

Things to note:

1. The magnitude of the fall in output and increase in unemployment. In 1933, the unemployment rate is over 25%!!

2. There’s a very strong negative correlation between output and unemployment.

THE SPENDING HYPOTHESIS: Shocks to the IS curve

Asserts 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.

THE SPENDING HYPOTHESIS: Reasons for the IS shift

Stock market crash reduced consumption

Oct 1929–Dec 1929: S&P 500 fell 17%

Oct 1929–Dec 1933: S&P 500 fell 71%

Drop in investment

Housing price correction after overbuilding in the 1920s => Loss of wealth in the 1930s

Widespread bank failures made it harder to obtain financing for investment.

Contractionary fiscal policy

Politicians raised tax rates and cut spending to combat increasing deficits.

In item 2, I’m using the term correction in the stock market sense.

THE MONEY HYPOTHESIS: A shock to the LM curve

Asserts that the Depression was largely due to huge fall in the money supply => LM shifted left.

Evidence: M1 fell 25% during 1929–33.

But, two problems with this hypothesis:

P fell even more, so M/P actually rose slightly during 1929–31 => LM must have shifted right.

nominal interest rates fell, which is the opposite of what a leftward LM shift would cause.

THE MONEY HYPOTHESIS AGAIN: The effects of falling prices

Asserts that the severity of the Depression was due to a huge deflation: P fell 25% during 1929–33.

This deflation was probably caused by the fall in M, so perhaps money played an important role after all.

In what ways does a deflation affect the economy?

THE MONEY HYPOTHESIS AGAIN: The effects of falling prices

The stabilizing effects of deflation:

iP g h(M/P) g LM shifts right g hY

Pigou effect: Arthur Pigou pointed out consumers deem M/P as a part of their wealth

iP g h(M/P )

g consumers’ wealth h

g hC

g IS shifts right

g hY

THE MONEY HYPOTHESIS AGAIN: The effects of falling prices

The destabilizing effects of unexpected deflation: debt-deflation theory

iP (if unexpected)

g transfers purchasing power from borrowers to lenders

g borrowers spend less, lenders spend more

g Typically borrowers’ propensity to spend is larger than lenders’, then aggregate spending falls, the IS curve shifts left, and Y falls

Suppose you borrowed $1000. While your nominal debt is $1000, your real debt= $1000/P. Now if P falls, then your real debt increases. In other words, you become impoverished and the creditor is enriched as purchasing power is transferred from you to the creditor.

THE MONEY HYPOTHESIS AGAIN: The effects of falling prices

The destabilizing effects of expected deflation:

iE π

g r = (i - E π) h for each value of i

g I i because I = I (r )

g planned expenditure & agg. demand i

income & output i

Notice that now we have started differentiating between nominal interest rate i and real interest rate r. Previously r and i both meant nominal interest rate.

The textbook (starting p.345) uses an “extended” IS-LM model (next slide), which includes both the nominal interest rate (measured on the vertical axis) and the real interest rate (which equals the nominal rate less expected inflation). Because money demand depends on the nominal rate, which is measured on the vertical axis, the change in expected inflation doesn’t shift the LM curve. However, investment depends on the real interest rate, so the fall in expected inflation shifts the IS curve: each value of i is now associated with a higher value of r, which reduces investment and shifts the IS curve to the left. Results: income falls, i falls, and r rises—which is exactly what happened from 1929 to 1931 (see Table 12-2 on pp.342-343).

This slide gives the basic intuition, which students often can grasp more quickly and easily than the graphical analysis. After I cover this material in the lecture, it will be easier for you to grasp the analysis on pp.345-347.

Fed was guilty!

If destabilizing power is stronger than the stabilizing power of deflation, then Fed can be held responsible for the Depression’s severity.

i = Nominal interest rate

r = Real interest rate

Why another Depression is unlikely

Policymakers (or their advisers) now know much more about macroeconomics:

The Fed knows better than to let M fall so much, especially during a contraction.

Fiscal policymakers know better than to raise taxes or cut spending during a contraction.

Federal deposit insurance makes widespread bank failures very unlikely.

Automatic stabilizers make fiscal policy expansionary during an economic downturn.

Examples of automatic stabilizers:

* the income tax: people pay less taxes automatically if their income falls. Check out on iLearn the handwritten note on automatic stabilizer for details.

* unemployment insurance: prevents income—and hence spending—from falling as much during a downturn

CHAPTER SUMMARY

1. IS-LM model

a theory of aggregate demand

exogenous: M, G, T, P exogenous in short run, Y in long run

endogenous: r, Y endogenous in short run, P in long run

IS curve: goods market equilibrium

LM curve: money market equilibrium

CHAPTER SUMMARY

2. AD curve

shows relation between P and the IS-LM model’s equilibrium Y.

negative slope because hP g i(M/P) g hr g iI g iY

expansionary fiscal policy shifts IS curve right, raises income, and shifts AD curve right.

expansionary monetary policy shifts LM curve right, raises income, and shifts AD curve right.

IS or LM shocks shift the AD curve.

Y = AD =>Y = α(A−bi)

M P =kY −hi

=> i = 1 h kY −

M P

⎛

⎝ ⎜⎜

⎞

⎠ ⎟⎟

Y0 = 1

1−c(1− t) (A−bi)

=> ΔY0 = 1

1−c(1− t) (ΔA−bΔi)=α(ΔA−bΔi)

A = C −cTR+ I +G+ NX⎡⎣ ⎤⎦

1-c(1-t)

(A-bi)

=>DY

1-c(1-t)

(DA-bDi)=a(DA-bDi)

A=C-cTR+I+G+NX

AD =[A−bi]+c(1− t)Y

AD=[A-bi]+c(1-t)Y

by 1

1 − c(1−t) ΔG = α

G ΔG

is smaller than α G ΔG

i IS1 IS2 LM i1 i2 0 Y2 Y1 Y

i IS

YYY

D=-

rrr

D=-

YYY

D=-

rrr

D=-