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Lecture 4: Ch.5 The IS-LM Model
5.1 The Goods Market and the IS relation
• In practice, investment depends primarily on two factors: Y and i. Firms increase investment
as there is an increase in sales (Y) and reduce investment as there is an increase in the cost of
borrowing (i):
డூ
డ
> 0 and
డூ
డ
< 0.
Now the equilibrium condition in the goods market becomes
ܻ = ܥሺܻ − ܶሻ + ܫሺܻ, ݅ሻ + ܩ ∶ ࡵࡿ ܖܗܑܜ܉ܔ܍ܚ
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5.1.1 Determining Output
• Equilibrium in the Goods Market: ܻ = ܥሺܻ − ܶሻ + ܫሺܻ, ݅ሻ + ܩ
• One example: ܥ = ܿ + ܿଵሺܻ − ܶሻ; ܫ = ܾ + ܾଵܻ − ܾଶ݅ where ܿ, ܿଵ, ܾ, ܾଵ, ܾଶ > 0
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5.1.2 Deriving the IS curve
• At any level of output, .i I Z↑ ⇒ ↓ ⇒ ↓
As the demand curve ZZ shifts down to ZZ′,
& through the multiplier effect.Y C I↓ ⇒ ↓ ↓
• Equilibrium in the goods market implies that an
increase in the interest rate leads to a decrease
in output. The IS curve is therefore downward
sloping.
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5.1.3 Shifts of the IS curve
• Changes in either T or G, so called fiscal policy, shift the IS curve.
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5.2 Financial Markets and LM Relation
• Equilibrium condition in the financial market in nominal terms: ܯ = $ܻܮሺ݅ሻ
• In real terms (i.e., in terms of goods not dollars),
ܯ
ܲ
= ܻܮሺ݅ሻ ∶ ࡸࡹ ܖܗܑܜ܉ܔ܍ܚ
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5.2.1 Deriving the LM curve
• At a given interest rate, .d
Y M↑ ⇒ ↑ Given the money supply, as the d
M curve shifts to
the right, the equilibrium interest rate rises.
• Equilibrium in the financial markets implies that an increase in income leads to an increase
in the interest rate. The LM curve is therefore upward sloping.
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• Why do we think about shifts of the IS curve to the left or to the right, but about shifts of
the LM curve up or down?
5.3 Putting the IS and the LM Relations Together
• IS relation: ܻ = ܥሺܻ − ܶሻ + ܫሺܻ, ݅ሻ + ܩ
• LM relation:
ெ
= ܻܮሺ݅ሻ
• The IS-LM model shows the overall
equilibrium at which there is equilibrium
in both the goods market and the financial
market.
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• When doing a policy analysis, ask yourself the following three questions:
i) How does it (i.e., policy change) affect the IS and/or the LM curve?
ii) What does this do to equilibrium output and the equilibrium interest rate?
iii) Describe the effects in words.
5.3.1 Fiscal Policy and the IS-LM model
• Example 1: Fiscal Contraction
Suppose there is an increase in T. Show the effect using the IS-LM model. What happens to
investment?
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5.3.2 Monetary Policy and the IS-LM model
• Example 2: Monetary Expansion
Suppose there is an increase in M. Show the effect using the IS-LM model. What happens to
investment?
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• The Effects of Fiscal and Monetary Policy
• Remember that fiscal policy (changes in T or G) affects the IS curve, not the LM curve, and
monetary policy (changes in M) affects the LM curve, not the IS curve. The results in the
table above are under the assumption that the price level is fixed in the short run.
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5.4 Using a Policy Mix
The combination of monetary and fiscal policies is known as the monetary-fiscal policy mix,
or simply, the policy mix.
• Example 3: Suggest a policy mix to achieve each of the following objectives.
a. Increase Y while keeping i constant.
b. Decrease the fiscal deficit while keeping Y constant. What happens to the interest rate i?
What happens to investment I?
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• Case Study: The U.S. Recession of 2001
The U.S. Growth Rate The Federal Funds Rate
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• Case Study: The U.S. Recession of 2001 (con’t)
U.S. Gov’t Revenues and Spending Policy Responses in 2001
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Practice Problem 1
We have seen that fiscal contraction has an ambiguous effect on investment. We revisit this
issue here. Consider the following IS-LM model:
C = c0 + c1(Y – T); I = b0 + b1Y – b2i;
ெ
= d1Y – d2i
a. Solve for equilibrium output. Assume c1 + b1 < 1.
b. Solve for the equilibrium interest rate.
c. Solve for investment.
d. Under what conditions on the parameters of the model (i.e., c0, c1 and so on) will
investment increase when G decreases? (Hint: If G decreases by one unit, by how much
does I increase?)
e. Explain the condition you derived in part (e).
