Lecture 16: The IS-LM Model

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Fall Semester ’06-’07 Akila Weerapana

Lecture 16: The IS-LM Model

I. OVERVIEW

• In the last two lectures, we derived the IS-LM model, which is a short run model of the determination of output. The model has two main parts: an IS curve that summarizes all the combinations of Y and r consistent with goods market equilibrium and an LM curve that summarizes all the combinations of Y and r that are consistent with money market equilibrium.

• We also discussed why the IS curve slopes downward, while the LM curve slopes upward. We also discussed circumstances under which the IS curve or the LM curve would shift.

• Today’s lecture puts the two sides of the model together and shows how to find equilibrium output and the equilibrium interest rate for an economy. Furthermore, it will also examine what happens to the equilibrium output and interest rate when there is a change in monetary or fiscal policy.

II. THE SHORT RUN EQUILIBRIUM IN A CLOSED ECONOMY

• Since the IS curve summarizes all combinations of income and interest rates that clear the market for goods and services while the LM curve summarizes all combinations of income and interest rates that clear the money market, equilibrium income and the equilibrium interest rate are at the intersection of the two curves.

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@

@ r

Y IS

LM

Y

0

r

₀

A

B

• Anywhere other than the intersection, which we label r

₀

and Y

0

, we would expect there to be changes in Y or r that restore either goods market or money market equilibrium.

• Generally, we believe that the money market adjusts very quickly so the economy will rarely

be off the LM curve. However, it will not stay off the IS curve for very long either as firms

can adjust production to bring it in line with demand.

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is not (we are off the IS curve). At that low interest rate, Y is too low to clear the goods market so firms increase production and Y rises. As Y rises, r has to rise as well in order to maintain money market equilibrium so the economy moves towards the intersection point.

• Now consider a point like B. Once again, the money market is in equilibrium but the goods market is not (we are off the IS curve). At that high interest rate, Y is too high to clear the goods market so firms decrease production and Y falls. As Y falls, r has to fall as well in order to maintain money market equilibrium so the economy moves towards the intersection point.

III. USING THE IS-LM MODEL TO ANALYZE POLICY

Fiscal Policy (Government Spending)

• Expansionary fiscal policy in the form of government spending shifts the IS curve out by the full Keynesian multiplier effect, i.e. an increase in exogenous government purchases shifts the IS curve out by

_1−b(1−t)¹

(∆G). However, the presence of an upward sloping LM curve means that the increase in the equilibrium level of Y is less than in the Keynesian case. In other words, the spending multiplier in the IS-LM model is smaller than the spending multiplier in the Keynesian model.

• Graphically we can see that the increase in Y (from Y

₀

to Y

₁

, the IS-LM multiplier effect) is less than the shift out of the IS curve from Y

0

to ˜ Y , the Keynesian multiplier effect).

Increase in G

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@

@ r

Y IS

LM

IS

⁰

Y

₀

r

₀

Y

₁

r

₁

Y ˜ - -

Decrease in G

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@

@ r

Y IS LM

IS

⁰

Y

₁

r

₁

Y

₀

r

₀

Y ˜

• We can get intuition for why the multiplier effects are smaller by looking at what happens to

the various components of the IS curve and the LM curve when G increases (you should be

able to figure out what happens when G decreases).

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– C = ¯ C + b(1 − t)Y ↑ (since Y is higher) – I = ¯ I − βr ↓ (since r increased)

– G ↑ (G increased, according to the question) – NX ↔ (NX is exogenous and unchanged) – M

^s

↔ (Exogenous and unchanged)

– M

^d

↔ (↓ since r increased and ↑ since Y increased. We know that they must offset because M

^s

= M

^d

and M

^s

↔)

• Notice that the increase in exogenous government purchases increases r which in turn reduces I and reduces the overall positive impact of the increased government spending.

• The opposite would be true for contractionary fiscal policy in the form of lower government purchases. This shifts the IS curve in by the full multiplier effect, i.e. a decrease in exogenous government purchases shifts the IS curve in by

_1−b(1−t)¹

(∆G). However, the presence of an upward sloping LM curve means that the decrease in the equilibrium level of Y is less than the multiplier effect.

• Graphically we can see that the decrease in Y is less than the shift in of the IS curve (from Y

0

to Y

1

instead of to ˜ Y )

Fiscal Policy (Taxes)

• Expansionary fiscal policy can also take the form of tax cuts. Given an IS curve of the form Y =

_1−b(1−t)¹

[ ¯ C + ¯ I + ¯ G + ¯ N X] −

_1−b(1−t)¹

[βr], we can see that changes in the tax rate affects the slope of the IS curve.

• Therefore lower income taxes will lead to a flatter slope of the IS curve resulting in a higher GDP because people have more money to spend on goods and services.

Lower Taxes

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@

@ Q

Q Q

Q Q r

Y IS

LM

IS

⁰

Y

₀

r

₀

Y

₁

r

₁

- -

Higher Taxes

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@

@ Q

Q Q

Q Q r

Y IS

⁰

LM

IS

Y

₁

r

₁

Y

₀

r

₀

• Conversely, contractionary fiscal policy in the form of tax increases will make the slope steeper.

The result is lower GDP in the economy because the higher taxes reduces consumer income

and therefore causes consumption to fall as well.

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happens to the various components of the IS curve and the LM curve. You should test yourself by figuring out what happens when there is a tax increase.

– C = ¯ C + b(1 − t)Y ↑ (since Y is higher AND because t is lower) – I = ¯ I − βr ↓ (since r increased)

– G ↔ (G is exogenous and unchanged) – NX ↔ (NX is exogenous and unchanged) – M

^s

↔ (Exogenous and unchanged)

– M

^d

↔ (↓ since r increased and ↑ since Y increased. We know that they must offset because M

^s

= M

^d

and M

^s

↔)

Monetary Policy

• We can also use the IS-LM model to think about monetary policy decisions. When the Fed pursues an expansionary monetary policy, i.e. it increases the money supply, we showed that this would cause the LM curve to shift to the right. From the graph below we see that this causes GDP to rise and interest rates to fall in the economy.

Expansionary Monetary Policy

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@

@ r

Y IS

LM LM

⁰

Y

₀

r

₀

Y

₁

r

₁

-

Contractionary Monetary Policy

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@

@ r

Y IS

LM

⁰

LM

Y

₁

r

₁

Y

₀

r

₀

• Intuitively, expansionary monetary policy has a positive impact on Y because the increase in real money supply over real money demand causes interest rates to fall in order to restore money market equilibrium. On the goods market side, the lower interest rates result in increased investment spending, which in turn increases Y .

• The opposite would be true for contractionary monetary policy. The decrease in real money supply over real money demand causes interest rates to rise in order to restore money market equilibrium. On the goods market side, the higher interest rates result in decreased investment spending, which in turn lowers Y .

• Once again, we can better understand the economic impact of expansionary monetary policy by looking at what happens to the various components of the IS curve and the LM curve.

You should try and figure out the corresponding impact of a contractionary monetary policy.

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– C = ¯ C + b(1 − t)Y ↑ (since Y is higher) – I = ¯ I − βr ↑ (since r decreased)

– G ↔ (G is exogenous and unchanged) – NX ↔ (NX is exogenous and unchanged) – M

^s

↑ (Increase in M

^s

)

– M

^d

↑ (Since r decreased and Y increased)

IV. POLICY INTERACTIONS

• The interaction between fiscal and monetary policy is very important. Suppose that there is a negative shock ot the economy, say in the form of a fall in consumer confidence. This will shift the IS curve back.

• We can show using the IS-LM model that the appropriate policy response to this shock is to use expansionary policy: fiscal, monetary or both. How much of expansionary fiscal policy (in the figures below, this is assumed to be in the form of higher G) for example depends greatly on what the Fed does with monetary policy, and how much expansionary monetary policy is needed depends on what the government does with fiscal policy.

OPTION 1: The Fed does nothing. The response is entirely from expansionary fiscal policy.

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@

@ r

Y IS

⁰

LM

IS

Y

₁

r

₁

Y

₀

= Y

₂

r

₀

= r

₂

- -

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monetary policy.

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@

@ r

Y IS

⁰

LM

IS LM

⁰

Y

1

r

1

r

0

r

2

Y

0

= Y

2

-

OPTION 3: The Fed and the government both use expansionary fiscal policy to move us back to the original leve of output. Less expansionary fiscal and less expansionary monetary policy is needed than in the absence of the other.

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@

@ r

Y IS

⁰

LM

IS LM

⁰

IS

⁰⁰

Y

1

r

1

= r

2

r

0

Y

0

= Y

2

-

- -

• A potential flaw in the IS-LM model seems to be the prediction that accommodation by the

Fed is always better: the Fed should increase M

^s

all the time because it only leads to higher

output and lower prices. This is not true in the real world where we think of the Fed as being

very cautious about expanding the money supply during booms. In order to inject realism

into the model we may need to expand it to endogenize the determination of prices.

Lecture 16: The IS-LM Model

Fall Semester ’06-’07 Akila Weerapana