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Chapter 4
Strong and Weak Policy Effects
in the IS-LM Model

Chapter Outline
4-1 Introduction: The Power of Monetary and Fiscal Policy
4-2 Income, the Interest Rate, and the Demand for Money
a. Income and the Demand for Money
b. The Interest Rate and the Demand for Money
c. Other Factors That Shift the Demand for Money Schedule
4-3 The LM Curve
a. How to Derive the LM Curve
Box: Learning About Diagrams: The LM Curve
b. What the LM Curve Shows
4-4 The IS Curve Meets the LM Curve
Global Economic Crisis Focus: Causes of a Leftward Shift in the IS Curve
4-5 Monetary Policy in Action
a. Normal Effects of an Increase in the Money Supply
b. The LM Curve Can Also Be Shifted by Changes in the Demand for Money
4-6 How Fiscal Expansion Can “Crowd Out” Private Investment
a. Expansionary Fiscal Policy Shifts the IS Curve
b. The Crowding-Out Effect
c. Can Crowding Out Be Avoided?
Global Economic Crisis Focus: How Monetary Policy Can Be Ineffective in the IS-LM Model
4-7 Strong and Weak Effects of Monetary Policy
a. Strong Effects of Monetary Expansion
b. Weak Effects of Monetary Policy
Understanding the Global Economic Crisis: How Easy Money Helped to Create the Housing
Bubble and Bust
©2012 Pearson Education, Inc. Publishing as Addison Wesley
Chapter Overview
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4-8 Strong and Weak Effects of Fiscal Policy
a. Summary of Crowding Out
4-9 Using Fiscal and Monetary Policy Together
a. The Fiscal Multiplier Depends on the Monetary Response
b. The Monetary-Fiscal Mix and Economic Growth
Box: International Perspective
(Monetary Policy Hits the Zero Lower Bound in Japan and in the United States)
c. Summary of Monetary-Fiscal Interactions
Summary
Appendix: The Elementary Algebra of the IS-LM Model
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Chapter Overview
Because the material covered in this chapter is essential in comprehending the policy analysis of
later chapters, careful coverage of this chapter is strongly recommended. This chapter provides a
complete and straightforward presentation of the IS-LM model, which continues to be an important
tool of macroeconomic analysis. The IS-LM model is used to analyze the implications of different
macroeconomic policies. It is also for the development and application of the static and dynamic
theory of aggregate demand and aggregate supply as discussed in detail in Chapters 7 and 8. Having
presented the IS curve in Chapter 3, Gordon explains in the introduction to Chapter 4 that the LM
curve is the second important relationship needed to determine real GDP and the interest rate
simultaneously.
Section 4-2 provides the “missing relation” that is needed to determine the equilibrium levels of
income and the interest rate. The money supply consists of currency and transactions accounts. He
discusses in detail that the amount of money that people demand in real terms depends both on
income and on the interest rate. It follows from the essential role of money as a medium of
exchange, store of value, and unit of account. In Section 4-2, Gordon discusses the role of income
and in Section 4-3, he discusses the role of interest rate for determining the demand for real
balances. The term “demand for money” sometimes confuses students. Emphasize that money
demand refers to holding money, either physically or in checking accounts, rather than holding
interest-bearing assets such as stocks, bonds, or saving accounts. Interest rates are simply the cost
of holding money rather than interest-yielding assets. Figure 4-1 shows that money demand is
negatively related to the interest rate and Figure 4-2 shows that a decrease in income implies a
leftward shift of the money-demand function. This occurs because the demand for money is directly
related to income, but income is not a variable on either of the axes. It also discusses the role of
other factors such as wealth of the household, expected future inflation, and payments.
Technologies may also affect the position of the demand for money curve.
Section 4-3 explains in detail how to derive the LM curve, which shows the combinations of
interest rates and real income levels which keep money market in equilibrium always. The analysis
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Chapter 4
Strong and Weak Policy Effects in the IS-LM Model
assumes that the real money supply is an exogenous variable determined by the Fed because the
Fed directly controls Ms and the price level, P, is assumed to be fixed. The equilibrium interest rate
is determined by the intersection of the money-demand curve and the vertical money-supply curve
in the graph of the interest rate against real money balances. Thus, changes in money supply affect
the equilibrium interest rate. From here, the graphical derivation of the LM curve in Figure 4-3 is
straightforward. It simply shows that a higher income level shifts the money-demand function and
raises the equilibrium rate of interest. Therefore, the LM curve represents every combination of
interest rate and income consistent with money-market equilibrium. Although the graphical
explanation of why the LM curve is upward sloping is clear, the intuition behind the diagram is a
bit more difficult to explain. The demand for money is covered in greater detail in Chapter 13. It
might be helpful, however, to supplement the text by combining the money-market equilibrium
equation, Equation (4.1), with a distinction between the transactions and asset-holding motives for
holding money. Explain that as income increases, the demand for money rises to finance more
transactions. Because of a fixed money supply, however, the quantity of money demanded exceeds
the quantity supplied. Thus, Equation (4.1) no longer holds, and the economy is to the right of the
LM curve as at Point D in Figure 4-3. Money-market equilibrium requires an increase in the interest
rate. This would entice asset holders to switch from money to interest-yielding assets. This process
continues until Equation (4.1) is satisfied and money demand is again equal to money supply. Be
sure students can distinguish between movements along the LM curve (caused by changes in Y and
r) and shifts in the LM curve (caused by changes in the real money supply (Ms/P)). This is covered
in the “Learning About Diagrams” box in Section 4-4. Also, be sure students understand why
points above and below the LM curve are not points of money-market equilibrium. You might wish
to relate the velocity of money to movements along the LM curve.
Section 4-4 combines the IS and LM schedules to establish a general equilibrium income and
interest rate for this economy. Explain that the IS and LM curves represent combinations of the
interest rate and income level consistent with equilibrium in the commodity market and money
market, respectively. Neither of the schedules alone can determine both the interest rate and
income, just as no single equation can be solved for two unknowns. General equilibrium is the
simultaneous equilibrium of the commodity and money markets. Thus, the general-equilibrium
income and interest rate are those consistent with the simultaneous equilibrium of the commodity
and money markets. This equilibrium occurs at the intersection of the IS and LM curves in Figure
4-4. Students may have difficulty remembering what is true of points off both the IS and LM curves
in Figure 4-4. It would be helpful if the instructor labeled what is true in each of the four quadrants
of the diagram (see Figure 4-A in this manual). The Appendix to Chapter 4 provides an algebraic
treatment of the IS-LM model; it is covered in this manual directly following Chapter 4. Consider
teaching the algebra and graphs simultaneously so that students can see how each equation
corresponds to the graphs.
In the Global Recession Focus, Gordon has explained how IS-LM model helps to sort out the
causes of business cycles and sources of Global Recession of 2008-09.
Sections 4-5 and 4-6 look at the “normal” effects of monetary and fiscal policy when the IS and LM
curves have their normal slopes. Section 4-5 shows that expansionary monetary policy shifts the
LM curve outward, lowering the interest rate and raising equilibrium income. A box in Section 4-5,
How Easy Money Helped to Create the Housing Bubble and Bust explains how easy monetary
©2012 Pearson Education, Inc. Publishing as Addison Wesley
Chapter Overview
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policy actually worked in the period 2001–2007 in creating the mortgage market problem. Thus this
box represents a chance to display the usefulness of the IS-LM model and affords the instructor
Figure 4-A
an opportunity to apply the model to current and practical real-world policy issues. Section 4-6
explains that expansionary fiscal policy shifts the IS curve outward, raising both equilibrium
income and the interest rate. “Crowding out” is explained and illustrated in Figure 4-6. Stress the
fact that interest rates must rise following an increase in government spending to keep the money
market in equilibrium. The crowding-out effect implies that equilibrium income will rise by less
than the full amount of the horizontal shift in the IS curve. It is important for students to understand
that because of this, the simple autonomous spending multipliers of the previous chapter, which
assumed constant interest rates, are now too large. The chapter emphasizes fiscal policy as a source
of crowding out. It should be clear to students, however, that an equal rise in any of the other
components of autonomous spending will have the same effect. As a final note, you might wish to
extend the material by introducing the notion of “crowding in,” which arises from an accelerator
specification of investment. You would explain that if investment depends on the change in GDP
and if an expansionary fiscal policy results in a large increase in GDP, investment could possibly be
crowded in through the increase of “induced investment.”
Now that the students have learned how the IS-LM model works, Sections 4-7, 4-8, and 4-9 use the
IS-LM model to analyze the factors that determine the effectiveness of monetary and fiscal policy,
and in particular those factors that make the effects of policy deviate from the “normal” outcomes
examined in previous sections. The issue of the strong and weak effects of monetary and fiscal
policy centers on how much real income and the interest rate change in response to given policy
actions. The text explains this intuitively and graphically in Sections 4-7 and 4-8. (An algebraic
approach to teaching the material is provided in the Appendix.) Stress the roles that the slopes of
the IS and LM curves play in determining the effectiveness of both monetary and fiscal policy. For
example, the stronger the expansionary monetary policy (has a larger effect on income) the steeper
the LM curve (see Figure 4-7). The LM curve becomes steeper as the interest responsiveness of the
demand for money declines. That this makes monetary policy more potent is explained in reference
to money-market equilibrium. If the money supply increases (exogenously), the demand for money
must increase (endogenously) as well, requiring some combination of a lower interest rate and a
higher income level. Explain to students that in the normal case, a lower interest rate causes
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Chapter 4
Strong and Weak Policy Effects in the IS-LM Model
autonomous planned spending and hence income to rise. The lower interest rate and the higher
income work jointly to increase the demand for money. However, a lower interest rate will have
less effect on the demand for money the lower its interest responsiveness. Thus, as the interest
responsiveness of the demand for money falls, a larger increase in income must occur to boost the
demand for money and maintain equilibrium in the money market. Figure 4-7 illustrates the
importance of the slope of the LM curve by comparing the case of a normally sloped LM curve with
the extreme case of a vertical LM curve representing a zero interest responsiveness of the demand
for money. If the LM curve is vertical, a given increase in the money supply produces a larger
decline in the interest rate. Although this has no direct effect on the demand for money, it generates
a sufficiently larger increase in autonomous planned spending and income that provides the
required increase in the demand for money.
Figure 4-8 shows that monetary policy will have weak effects if the LM curve is flat, caused by a
highly interest-responsive demand for money, or if the IS curve is vertical, reflecting a zero interestresponsiveness of autonomous planned spending. If a relatively small drop in the interest rate when
the money supply increases spawns a relatively large increase in the demand for money, the extent
to which the interest rate declines and autonomous planned spending and income rise is truncated.
And, if autonomous planned spending is totally unresponsive to the interest rate, income will be
unaffected no matter how much the interest rate falls.
Section 4-8 takes up the question of the strong and weak effects of fiscal policy, which hinge on the
extent of crowding out. This is shown to depend on the slope of the LM curve. The extreme cases
of no crowding out (strong fiscal policy) when the LM curve is horizontal and complete crowding
out (weak fiscal policy) when it is vertical are illustrated in Figure 4-9. The text argues that the
“normal” case illustrated in Figure 4-6, in which expansionary fiscal policy produces partial
crowding out, provides the most accurate description of the results of fiscal policy.
You might point out to your students the empirical nature of these issues. What effects should
policymakers expect to result from monetary and fiscal policy? Though theoretically possible, the
extreme cases of vertical IS and vertical or horizontal LM curves are unlikely; the real question
policymakers face is “How steep or flat are the IS and LM curves?” You might also point out that
this issue resurfaces later in the text, in conjunction with discussion of the effects of financial
deregulation on the slopes of the curves and of multiplier uncertainty in the context of stabilization
policy.
Section 4-9 takes up the fiscal–monetary policy mix. Three alternative monetary policies might
accompany a fiscal stimulus: leaving the money supply unchanged (a money supply target) and
creating a partial crowding-out effect, increasing the money supply to prevent a rise in the interest
rate (an interest rate target) thus no crowding-out effect at all, or decreasing the money supply to
avoid an increase in income (an income target) or a complete crowding-out effect. The effects of
the fiscal stimulus depend on which alternative the Fed chooses. Consideration of the zero real
GDP gap target leads to the general observation that the economy could achieve a given level of
income with a number of different combinations of fiscal and monetary policy. “Easy” (more
expansionary) fiscal policies would be accompanied by “tight” (less expansionary) monetary
policies and hence higher interest rates. Point out to students the implications of the policy mix for
the interest rate, the level of investment, and the future level of productivity growth. These long-run
macroeconomic concerns are treated at length in Chapters 10 through 12.
©2012 Pearson Education, Inc. Publishing as Addison Wesley
Changes in the Twelfth Edition
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An IP Box examines policy paralysis in Japan and in United States. The long economic slump in
Japan during the 1990s and in the United States in the 1930s and after 2009 is discussed with
attention to the paralysis confronting policymakers. Monetary policymakers are paralyzed because
they believe that with interest rates so close to zero that there is nothing left for them to do. With
short-term Japanese interest rates at extremely low levels, there is speculation that the Japanese
economy is experiencing a liquidity trap. Same is also true for the U.S. economy since 2008.
Explain to your students that if this is the case, monetary policy is impotent to lower interest rates
and stimulate autonomous planned spending. Fiscal policymakers, on the other hand, believe that
there is little that they can do because public debt in Japan is now over 100 percent of GDP. The IP
Box starts by comparing the interest rate situation of Japan in the 1990s with the situation of the
United States in the 1930s and in the United States during 2000–2010. Graphs also exhibit the
same information. It is suggested that the Bank of Japan could “monetize” the debt—introduce a
fiscal stimulus, paid for by an issue of government bonds which the Bank of Japan then buys. Show
that a mix of easy fiscal and monetary policies would shift both the IS and LM curves to the right
and raise the level of income without the need to lower interest rates and without increasing the
level of publicly held debt.
The IP Box concludes by suggesting that in 2010–2011 the United States faced a similar dilemma,
as the economic recovery appeared to be too weak to achieve the swift decline in the
unemployment rate that was needed.
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Changes in the Twelfth Edition
Chapter 4 in the 12th edition begins with an introduction explaining that the LM curve is the second
relationship needed to determine real GDP and the interest rate simultaneously, just like the 11th
edition. However, this chapter has also gone through significant changes from the 10th edition. In
all equations and figures numerical references have been eliminated.
Section 4-1 has been severely shortened by deleting several paragraphs of discussion about LM
curve. Section 4-2 has been deleted and Section 4-3 has been changed to Section 4-2. And the
subsequent sections have been renumbered. New Section 4-2 discusses the relation between
income, interest rate, and the demand for money.
Section 4-3 has been modified significantly with a new discussion about how to derive the LM
curve. Questions on the self test has been changed. The title of the Box: “How Easy Money Created
a Boom and Bust in Housing” has been changed to How Easy Money helped to create Housing
Bubble and Bust.” It explains how Fed allowing the housing bubble and the bust later on indirectly
created the economic situation for Global Recession. An explanatory footnote has been added.
In Section 4-6, discussion about “Expansionary Fiscal Policy shifts the IS curve” has been changed
significantly. The table with numerical example for comparison of the equilibrium value has been
deleted. Similarly in the discussion about “crowding out” also numerical examples has been
eliminated.
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Chapter 4
Strong and Weak Policy Effects in the IS-LM Model
In Section 4-7, discussion about Strong and Weak Effects of Monetary policy has been rewritten.
For discussion about Weak Effects of Monetary Policy he added a new analysis regarding zero
lower bound of interest rate.
In Section 4-9, discussion about the subsection “The Fiscal Multiplier Depends on the Monetary
Response” has been shortened by deleting a paragraph about Japanese economic condition. He also
deleted a subsection (Infrastructure, Minneapolis, and the Monetary Policy Mix). The IP Box in
International Perspective has been changed from “Monetary and Fiscal Policy in Japan’s Lost
Decade” to “Monetary Policy Hits the Zero Lower Bound in Japan and in the United States” It has
a more detailed explanation about how monetary policy looses effectiveness in the United States
and in Japan. In the box, graphs haven updated and a new graph for U.S. economy has been added.
From the Concepts section four concepts such as Medium of Exchange, Store of Value, Unit of
Account, and Infrastructure have been deleted.
No change in the Questions or problems in the textbook. Self-test answers have been modified.

Answers to Questions in Textbook
1. When the economy is “off” the IS curve, planned expenditure will not equal output. If the economy is
to the “left” of the IS curve, Ep > Y, and there is a negative unplanned inventory change. Firms will
increase output until Ep = Y. As firms seek funds with which to increase inventory investment, they
will bid up the interest rate. Thus, the movement will tend to be upward and to the right. If the
economy is to the “right” of the IS curve, there is a positive unplanned inventory change and either
output, the interest rate, or both will decline.
2. When the economy is “off” the LM curve, the demand for real money balances will not equal the
supply of real balances in the economy. If the economy is to the left of the LM curve, the amount of
money demanded, given the interest rate and income level, is less than the money supplied. Then,
individuals will attempt to “get rid of” the excess money; this activity will cause bond prices to rise
and interest rates to fall. This process will continue until interest rates fall enough to cause equality
between the demand for real balances and the money supply. It is also possible that individuals will
“get rid of” their excess money balances by spending them on goods and services. Then, the
movement will be downward and to the right. The opposite movements will occur if the economy is to
the right of the LM curve.
3. The crowding-out effect comes through rising interest rates. Thus, autonomous expenditure sensitive
to the interest rate would decrease. Induced expenditure responds to changes in real output.
4. Some government expenditure, such as local bonding for school building construction and other state
and local expenditure for capital improvements, is sensitive to changes in the interest rate and could
be “crowded out” if the interest rate increases. The government debt seemed to encourage fiscal
responsibility in Congress during the 1980s and 1990s. In early 2011, Congress and President Obama
debated how to reduce the budget deficit over concerns about the size of the federal debt. These
occasions indicate when it is possible that the “normal” increase in government expenditure may be
reduced in response to the interest burden on the federal budget. Whether one thinks this is a likely
scenario, of course, depends on one’s view of the government budgetary process.
5. Along a given LM curve the money supply is unchanged. Thus, the velocity of money rises as income
rises and falls as income falls. Velocity behaves this way because of the effects of the interest rate and
©2012 Pearson Education, Inc. Publishing as Addison Wesley
Answers to Questions in Textbook
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income on the demand for money. A higher interest rate reduces the demand for real money balances
and requires higher income to keep the demand for money equal to the fixed money supply. At a lower
interest rate, a smaller income maintains equilibrium in the money market.
6. a. This situation is a point to the left of the IS and LM curves. Planned spending exceeds income at
any point to the left of the IS curve. There is an excess supply of money at any point to the left of
the LM curve. When planned spending exceeds income, firms have negative inventory investment,
so they step up production and income rises. When there is an excess supply of money, people
attempt to turn money into stock, bonds, and other income generating assets. These actions drive up
the prices of those assets and drive down the interest rate.
b. This situation is a point to the right of the IS curve and to the left of the LM curve. Unintended
inventory investment is positive at any point to the right of the IS curve. The real demand for
money is less than the supply of money at any point to the left of the LM curve. When unintended
inventory investment is positive, firms cut output and income falls. When the demand for money is
less than the supply of money, people attempt to turn money into stock, bonds, and other income
generating assets. These actions drive up the prices of those assets and drive down the interest rate.
c. This situation is a point to the left of the IS curve and to the right of the LM curve. Unintended
inventory investment is negative at any point to the left of the IS curve. This causes firms to step up
production and income rises. There is an excess demand for money at any point to the right of the
LM curve. People attempt to turn stock, bonds, and other income generating assets into money.
These actions drive down the prices of those assets and drive up the interest rate.
d. This situation is a point to the right of the IS and the LM curves. Planned spending is less than
income at any point to the right of the IS curve and firms have positive quantities of unwanted
inventories. Therefore, they cut production and income falls. The real demand for money exceeds
the supply of money at any point to the right of the LM curve. People attempt to turn stock, bonds,
and other income generating assets into money. These actions drive down the prices of those assets
and drive up the interest rate.
7. The Fed’s low federal funds rate from 2002 to 2004 fueled the development of the housing bubble as:
(a) households found it easy to finance the purchase of houses and condos not only as residences but
in addition, as speculative investments; (b) made it easy for lenders to borrow short-term at low
interest rates and issue long-term mortgages at higher interest rates; (c) spawned the development of
the sub-prime mortgage market where too often little attention was paid to the ability of borrowers to
repay loans; and (d) caused many homeowners to refinance their homes, often with increases in the
amount borrowed.
When the Fed raised interest rates between 2004 and 2006, lenders found mortgage loans less
profitable and raised interest rates above what subprime borrowers could afford. As a result, the climb
in housing prices first slowed, and then was reversed. As housing prices fell, many homeowners could
no longer afford their mortgages, leading to defaults on loans. Those defaults resulted in banks taking
ownership of homes that they then attempted to sell. The attempt by banks to sell the foreclosed
homes added to the supply of houses on the market, which only contributed to the slide of house
prices.
8. a. Shift (for a given Y, (Ms/P) = (M/P)d at a lower r).
b. Rotate (the horizontal intercept is unchanged).
c. Shift and rotate (both horizontal intercept and slope change).
d. No effect on position or slope of LM curve.
e. Causes movement along LM curve, but does not affect its position or slope.
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Chapter 4
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f. Since the prices of goods and services and nominal amounts in checking accounts were adjusted in
proportion to the amount a unit of each currency could be converted into the Euro, there would be
no change in either the real demand for money or the real money supply. Therefore, there would be
neither a shift or nor a rotation of the LM curve.
g. The switch from using checks to using debit cards to buy goods and services has no effect on the
real demand for money. The switch from checks to debit cards merely affects how people access
the funds they have in checking accounts when they buy goods and services. Therefore, there
would be neither a shift or nor a rotation of the LM curve.
h. The switch from using checks to credit cards to buy goods and services has two effects on the real
demand for money. First, the switch reduces the real demand for money at each combination of real
income and the interest rate. That causes the LM curve to shift to the right since it will take a higher
level of real income to equate the real demand for and real supply of money, given the interest rate.
Second, the switch reduces how much the real demand for money increases as real income rises,
given the interest rate. That causes the LM curve to rotate and become flatter because if the demand
for money increases by a smaller amount when real income rises, it takes a smaller increase in the
interest rate to restore equilibrium in the money market.
9. If government spending becomes negatively sensitive to changes in the interest rate, then autonomous
spending declines by a larger amount for any given change in the interest rate. Therefore, the IS curve
becomes flatter and, other things being equal, any given fiscal expansion results in smaller increases in
output and the interest rate. However, because the fiscal expansion causes a smaller increase the
interest rate, it also means that less autonomous consumption and planned investment is crowded out
by the fiscal expansion.
Likewise, if autonomous taxes become positively sensitive to changes in the interest rate, then
disposable income declines when the interest rate rises. That means that autonomous spending
becomes more sensitive to the interest rate. Therefore, the IS curve becomes flatter and, other things
being equal, any given fiscal expansion results in smaller increases in output and the interest rate.
However, because the fiscal expansion causes a smaller increase the interest rate, it also means that
less autonomous consumption and planned investment is crowded out by the fiscal expansion.
10. If private sector spending is highly sensitive to a change in the interest rate, then the IS curve is
relatively flat. The main effect of a fiscal expansion will be a higher interest rate that reduces private
sector spending almost as much as the fiscal expansion increases autonomous spending. As a result,
the fiscal expansion causes very little increase in output. In the case of a fiscal contraction, the effect
of the lower interest rate on private sector spending almost offsets the effect of the fiscal contraction.
As a result, fiscal policy is unable to have much of an impact on output.
On the other hand, monetary policy is quite capable of changing output if private sector spending is
highly sensitive to a change in the interest rate. A policy of tight money will result in a sharp
contraction of private sector spending as the interest rate rises. Easy money will provide a large
stimulus to private sector spending as the interest rate falls.
11. If the demand for money is highly insensitive to a change in the interest rate, then as fiscal policy
changes income and therefore the demand for money, it will take a large change in the interest rate to
restore equilibrium in the money market. This results in a change in private sector spending that
offsets most of the expansion or contraction of output caused by fiscal policy.
On the other hand, monetary policy is very powerful when the demand for money is highly insensitive
to a change in the interest rate. Any excess supply or demand for money that is created by a change in
monetary policy must be absorbed by the way in which income affects the demand for money. This
leads to a relatively large change in the interest rate and results in relatively large increases in
autonomous spending and real output.
©2012 Pearson Education, Inc. Publishing as Addison Wesley
Answers to Questions in Textbook
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12. An increase in autonomous taxes shifts the IS curve to the left. To maintain equilibrium in the
commodity and money markets, both equilibrium income and the interest rate fall. Consumption falls
as a decline in induced consumption dominates any boost the lower interest rate gives autonomous
consumption. Planned investment rises because of the lower interest rate.
13. Smaller demand shocks mean that the shifts left and right of the IS curve become smaller, and for a
given LM curve, there is less variation in both real income and the interest rate. Therefore, if the
“Great Moderation” was due to smaller demand shocks, then the decline in the variation of real GDP
was accompanied by a decrease in the variation of the interest rate as well.
On the other hand, if the “Great Moderation” was due to a better response by monetary policymakers
to the same demand shocks as previously, then that means that they were responding more rapidly by
(a) reducing the real money supply when a shock adds to demand and (b) increasing the real money
supply when a shock reduces demand. In terms of the IS-LM model, the LM curve shifts left when the
IS curve shifts right and the LM curve shifts right when the IS curve shifts left. Therefore, if the “Great
Moderation” was due to a better response by monetary policymakers to the same demand shocks as
previously, then the decline in the variation of real GDP was accompanied by an increase in the
variation of the interest rate.
14. If the Fed is not worried about inflation but is concerned that unemployment is too high, it is likely to
take actions to ensure that the tax cut has its maximum impact on output. The Fed is likely to increase
the money supply to prevent any rise in the interest rate that would otherwise result from the tax cut.
The Fed’s actions are likely to resemble those shown in the top right frame of Figure 4-10.
15. If only the Fed is able to take action, then it will have to reduce the money supply and raise interest
rates in order to reduce actual real GDP relative to natural real GDP. If, however, monetary and fiscal
policymakers are able to agree on a “tight money, tight fiscal policy” mix, then it is possible to reduce
real GDP relative to natural real GDP without any increase in the interest rate. The “tight money, tight
fiscal policy” mix would have less of an impact on interest-rate sensitive private sector spending than
a monetary policy that relied solely on higher interest rates to reduce inflationary pressures.
16. The effect of the personal tax cut is to increase consumption expenditures, which results in an increase
in autonomous planned spending and therefore equilibrium income at each interest rate. The effect of
the tax cut is shown graphically as a shift right of the IS curve. Since the Fed wants to maintain real
GDP at its current level, it needs to reduce the real money supply. The reduction in the money supply
raises the interest rate. The higher interest rate reduces planned investment expenditures. Therefore,
since real GDP is left unchanged as a result of the combination of expansionary fiscal policy and tight
money, a larger percentage of real GDP is made up of consumption expenditures and a smaller
percentage of output is made up of planned investment expenditures. The reduction is planned
investment expenditures will leave future generations with less capital resources, which would reduce
future economic growth.
17. The argument is incorrect. High levels of consumer and business confidence shift both the Ap demand
schedule and the IS curve to the right. As a result, equilibrium occurs in the commodity and money
markets at a higher level of income and a higher interest rate. However, it does not follow from this
that raising the interest rate during a recession would increase either consumer and business
confidence or income. Ceteris paribus, a monetary policy that raised the interest rate would shift the
LM curve to the left and reduce income.
18. When the interest rate reaches the lower zero bound, any additional increase in the real money supply
by the Fed can have no impact on the interest rate. Therefore when the zero lower bound for the
interest rate is reached, monetary policy cannot be used on its own to increase real GDP. However,
when the zero lower bound is reached, a combination of expansionary fiscal policy and easy money
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policy can be used to increase output without any increase in the interest rate. Specifically, the Fed
can buy up the debt issued by the government to finance the expansionary fiscal policy.
The arguments presented against this mix of fiscal and monetary policy are that it will impose a burden
on future generations because of the interest payments that result from an increase in the national debt
and that it will be inflationary. However, if the Fed buys the securities issued by the government to
finance the expansionary fiscal policy, then there will be no additional interest to be paid by future
generations. As for inflation worries, the expansionary policies adopted by the Bush administration
failed to increase “core inflation” (inflation less the effect of food and energy prices) between 2001
and 2007, and with unemployment as high as it was in 2010-11, the mix would not likely add to
inflation if it were to be used to expand output.

Answers to Problems in Textbook
1. a. The real demand for money at each combination of the interest rate and income is given in the
following table:
Income
Interest rate
4.4
4.7
5.0
5.3
5.6
5.9
6.2
11,940
2,765
2,750
2,735
2,720
2,705
2,690
2,675
12,000
2,780
2,765
2,750
2,735
2,720
2,705
2,690
12,060
2,795
2,780
2,765
2.750
2.735
2.720
2,705
12,120
2,810
2,795
2,780
2,765
2,750
2,735
2,720
12,180
2,825
2,810
2,795
2,780
2,765
2,750
2,735
b. The horizontal axis of your graph should be labeled real money balances, and the vertical axis of
your graph should be labeled interest rate. The points on demand for money curve when income
equals 11,940 are: (2,675, 4.4); (2,750, 4.7); (2,735, 5.0); (2,720, 5.3); (2,705, 5.6); (2,690, 5.9);
and (2,675, 6.2). The points on demand for money curve when income equals 12,180 are: (2,825,
4.4); (2,810, 4.7); (2,795, 5.0); (2,780, 5.3); (2,765, 5.6); (2,750, 5.9); and (2,735, 6.2).
c. The table in Part a shows that given that the real money supply equals 2,750, the real demand for
money and the real supply of money are equal at the following combinations of real income and the
interest rate: (11,940, 4.7); (12,000, 5.0); (12,060, 5.3); (12,120, 5.6); and (12,180, 5.9). The
horizontal axis of your graph for the LM curve should be labeled real income, and the vertical axis
of your graph should be labeled interest rate. The five points on LM0 are listed in the first sentence
of this part of the problem.
d. The table in Part a shows that given that the real money supply equals 2,780, the real demand for
money and the real supply of money are equal at the following combinations of real income and the
interest rate: (12,000, 4.4); (12,060, 4.7); (12,120, 5.0); and (12,180, 5.3). The four points on LM1
are just listed in the previous sentence of this part of the problem.
e. The table in Part a shows that given that the real money supply equals 2,720, the real demand for
money and the real supply of money are equal at the following combinations of real income and the
interest rate: (11,940, 5.3); (12,000, 5.6); (12,060, 5.9); and (12,120, 6.2). The four points on LM2
are just listed in the previous sentence of this part of the problem.
©2012 Pearson Education, Inc. Publishing as Addison Wesley
Answers to Questions in Textbook
43
2. a. The marginal propensity to save, s, equals 1 – c = 1 – .6 = .4. The multiplier, k, equals the inverse
of the marginal propensity to save. Therefore, the multiplier equals 1/.4 = 2.5.
b. The equation for autonomous planned spending, Ap, equals 2,180 – 20r – .6(1,800) + 2,400 – 60r +
2,000 – 300 = 5,200 – 80r.
c. The equation for the IS curve is Y = kAp. Given the answers to Parts a and b of this problem, we
have that the equation for the IS curve is Y = 2.5(5,200 – 80r) = 13,000 – 200r. Given the interest
rate equals 4.7, equilibrium income in the commodity market equals 13,000 – 200(4.7) = 12,060.
©2012 Pearson Education, Inc. Publishing as Addison Wesley
Answers to Problems in Textbook
44
Given the interest rate equals 5.0, equilibrium income in the commodity market equals 13,000 –
200(5.0) = 12,000. Given the interest rate equals 5.3, equilibrium income in the commodity market
equals 13,000 – 200(5.3) = 11,940. Given the interest rate equals 5.6, equilibrium income in the
commodity market equals 13,000 – 200(5.6) = 11,880, and given the interest rate equals 5.9,
equilibrium income in the commodity market equals 13,000 – 200(5.9) = 11,820. Your graph of the
IS curve has the label of real income on the horizontal axis
and the label of interest rate on the vertical axis. The five points on your IS curve are: (12,060, 4.7);
(12,000, 5.0); (11,940, 5.3); (11,880, 5.6); and (11,820, 5.9).
d. The commodity and money markets are both in equilibrium where the IS and LM curves intersect.
At that point and only at that point, planned expenditure and income are equal, and the real demand
for money and the real supply of money are equal. The only combination of real income and the
interest rate that is on both the IS curve and LM0 is real income equal to 12,000 and the interest rate
equal to 5.
e. If the goal of monetary policymakers is to increase real income to 12,060, which is also natural real
GDP, then they must take steps to decrease the interest rate in order to increase equilibrium income
in the commodity market. Specifically, Part c of this problem shows that for the commodity market
to be in equilibrium at a real income of 12,060, the interest rate must be reduced to 4.7 percent.
That decrease in the interest rate would result from an increase in the real money supply. Part d of
Problem 1 shows that monetary policymakers must increase the money supply to 2,780 in order to
have both the commodity and money markets in equilibrium at the real income and interest rate
combination of 12,060 and 4.7, respectively.
3. a. Under Party A’s proposal, the new equation for autonomous planned spending, Ap, equals 2,180 –
20r – .6(1,920) + 2,400 – 60r + 2,120 – 300 = 5,248 – 80r. The equation for the IS curve is Y = kAp.
Given the answers to Parts a and b of this problem, we have that the equation for the new IS curve
is Y = 2.5(5,248 – 80r) = 13,120 – 200r. Given the interest rate equals 4.7, equilibrium income in
the commodity market equals 13,120 – 200(4.7) = 12,180. Given the interest rate equals 5.0,
equilibrium income in the commodity market equals 13,120 – 200(5.0) = 12,120. Given the interest
rate equals 5.3, equilibrium income in the commodity market equals 13,120 – 200(5.3) = 12,060.
Given the interest rate equals 5.6, equilibrium income in the commodity market equals 13,120 –
200(5.6) = 12,000, and given the interest rate equals 5.9, equilibrium income in the commodity
market equals 13,120 – 200(5.9) = 11,940. Your graph of the new IS curve has the label of real
income on the horizontal axis and the label of interest rate on the vertical axis. The five points on
your IS curve are: (12,180, 4.7); (12,120, 5.0); (12,060, 5.3); (12,000, 5.6); and (11,940, 5.9).
b. Again, the commodity and money markets are both in equilibrium where the new IS and LM curves
intersect. The only combination of real income and the interest rate that is on both the new IS curve
and LM0 is real income equal to 12,060 and the interest rate equal to 5.3.
c. Under Party B’s proposal, the new equation for autonomous planned spending, Ap, equals 2,180 –
20r – .6(1,720) + 2,400 – 60r + 2,000 – 300 = 5,248 – 80r. Since the equation for autonomous
planned spending under Party B’s proposal is the same as for Party A’s proposal, the IS curves
under the two proposals are the same.
d. Since the IS curve for Party B’s proposal is the same as the for Party A’s proposal, the equilibrium
level of income and the equilibrium interest rate are the same under the two proposals.
e. The overall level of output and the interest rate are the same under the two proposals. Furthermore,
the amount of planned investment is the same under the two proposals, since they do not differ in
terms of their effects on the interest rate. The two proposals differ in the amounts of consumption
expenditures and government spending. Since taxes are higher under Party A’s proposal when
compared to Party B’s proposal and real income is the same under two proposals, disposable
©2012 Pearson Education, Inc. Publishing as Addison Wesley
Answers to Problems in Textbook
45
income, Y – T, is less under Party A’s proposal, resulting in a lower level of consumption as well.
On the other hand, government spending is higher under Party A’s proposal when compared to
Party B’s proposal.
4. a. The new equation for autonomous planned spending, Ap, equals 2,180 – 20r – .6(1,800) + 2,400 –
60r + 2,048 – 300 = 5,248 – 80r, given the 48 billion dollar increase in energy spending. Since this
is the same equation for autonomous planned spending as in Parts a and c of Problem 3, the new IS
equation and points on the new IS curve are the same as in Parts a and c of Problem 3.
b. Because the new IS curve in the problem is the same as those in Parts a and c of Problem 3, the
commodity and money markets are both in equilibrium at real income equal to 12,060 and the
interest rate equal to 5.3.
c. If there were no rise in the interest rate as a result of the increase in energy spending, the
commodity market would be in equilibrium at real income equal to 12,120. Therefore,
12,120 – 12,060 equals 60 billion of real income crowded out by the increase in energy spending. The increase in energy spending causes the interest rate to rise by .3 of a percentage point.
Since private sector spending decreases by 80 billion for every one percentage point increase in
the interest rate, the amount of private sector spending crowded out by the increase in energy
spending equals .3(80) = 24 billion.
d. In order to prevent any crowding out from the increase in energy spending, the Fed would have to
takes steps to prevent a rise in the interest rate when energy spending increases. That would require
the Fed to increase the real money supply to 2,780, since Part d of Problem 1 shows that real
income equal to 12,120 and the interest rate equal to 5.3 is a point on LM1. For the Fed to be
willing to do this without risking a rise in the inflation rate, natural real GDP would have to be at
least 12,060. If natural real GDP were less than 12,060 and if the Fed were to increase the real
money supply enough to allow both the commodity and money markets to be in equilibrium at
12,060, then real GDP would exceed natural real GDP, which we know from Chapter 1 would put
upward pressure on the inflation rate.
e. If natural real GDP equals 12,000 and the Fed does not want the increase in energy spending to
cause an increase in the inflation rate, then it would take action to prevent a rise in real income
when energy spending increases. In particular, the Fed would reduce the real money supply when
energy spending rises. From Part e of Problem 1, we know that the Fed would reduce money supply
to 2,720, so that the new IS curve would intersect LM2 where equilibrium real income equals
12,000 and the interest rate equals 5.6.
5. Ca = 260 – 10r,
a. From the Appendix of Chapter 3, we know that the multiplier equals the inverse of the marginal
leakage rate, where the marginal leakage rate equals s(1 – t) + t + nx. In this problem, s = 0.15,
t = 0.2, and nx = 0.08, so that the marginal leakage rate equals 0.15(1 – 0.2) + 0.2 + 0.08 = 0.12 +
0.2 + 0.08 = 0.4. Therefore, the multiplier, k, equals 1/0.4 = 2.5.
b. Ap = Ca – cTa + Ip + G + NXa = 260 – 10r – 0.85(200) + 1,500 – 30r + 1,700 + 500 = 3,790 – 40r.
c. The equation of the IS curve is Y = kAp. Therefore, the equation of the IS curve is Y = 2.5 (3,790 –
40r) = 9,475 – 100r.
d. The slope of the IS curve is r/Y. The equation for the IS curve tells us that Y/r = –100. Therefore,
r/Y = –1/100 = –0.01.
e. To obtain the equation for the LM curve, use either Equation (5) on page 126 in the Appendix (a) or
set the real demand for money equal to the real supply of money to get 0.25Y – 25r = 2,125. Adding
25r to both sides yields 0.25Y = 2,125 + 25r. Dividing both sides by 0.25 provides us with the LM
equation Y = 8,500 + 100r.
©2012 Pearson Education, Inc. Publishing as Addison Wesley
46
Chapter 4
Strong and Weak Policy Effects in the IS-LM Model
f. The slope of the LM curve is r/Y. The equation for the LM curve tells us that Y/r = 100. Therefore,
r/Y = 1/100 = 0.01.
g. To compute the equilibrium interest rate, set the equation for the IS curve equal to the equation for
the LM curve to get 9,475 – 100r = 8,500 + 100r. Adding 100r to and subtracting 8,500 from both
sides yields 200r = 975. Dividing both sides by 200 yields the equilibrium interest rate
r = 4.875.
h. To compute equilibrium real output, substitute the equilibrium interest rate into the equations for
the IS and LM curves to get Y = 9,475 – 100(4.875) = 8,500 + 100(4.875) = 8,987.5.
6. a. The only combination of real income and the interest rate that is on both the IS curve and LM0 is
real income currently equal to 8,987.5 and the interest rate equal to 4.875 (as we got in 5g and 5h).
If government spending increases by 160, new equilibrium GDP is 9,187.5 and r is 6.875. Thus,
change in GDP is 200, whereas IS curve shifts by 2.5(160) = 400. Thus, crowding out =
(400 – 200)/2.5 (2.5 is the multiplier we got in 5a) = 80 decline in autonomous expenditure when
Government expenditure increases by 160.
b. If money supply increases by 100, but G remains same at 1,700, then new LM curve is
Y = 8,900 + 100r instead of Y = 8,500 + 100r. New equilibrium GDP is 9,187.5 and interest
rate is 2.875.
7. To avoid the crowding out of the expansionary fiscal policy described in Part a of Problem 6, the Fed
would have to increase the money supply enough to (a) keep the interest rate at 5 along the new IS
curve, Y = 13,400 – 200r and (b) ensure that the money market is in equilibrium at this combination of
the interest rate and real output. First, let us compute what the equilibrium level of income is in terms
of the new IS curve by substituting 5 for r to obtain Y = 12,400. Now let’s compute the demand for
money at Y = 12,400 and r = 5 to obtain (M/P)d = 0.25(12,400) – 50(5) = 2,850. Therefore, the Fed
must increase the money supply by 100 from 2,750 to 2,850 to avoid crowding out.
8. Suppose that the real demand for money in the economy changes to (M/P)d = 0.25Y – 75r and the real
money supply changes to Ms/P = 1,875, but that the structure of the commodity market is the same as
in Problem 4.
a. To obtain the equation for the new LM curve, again use either Equation (5) on page 126 in the
Appendix or set the real demand for money equal to the real supply of money to get 0.2Y – 75r =
1,431.9. Adding 75r to both sides yields 0.2Y = 1,431.9 + 75r. Dividing both sides by 0.2 provides
us with the LM equation Y = 7,159.5 + 375r. To compute the equilibrium interest rate, set the
equation for the IS curve equal to the equation for the new LM curve to get 9,475 – 100r = 7,159.5
+ 375r. Adding 100r to and subtracting 7,159.5 from both sides yields 475r = 2,315.5. Dividing
both sides by 475 yields the equilibrium interest rate r = 4.875. To compute equilibrium real
output, substitute the equilibrium interest rate into the equations for the IS and LM curves to get
Y = 9,475 – 100(4.875) = 7,159.5 + 375(4.875) = 8,987.5. They are same as we got in Problems
5g and 5h.
b. The slope of the LM curve is r/Y. The equation for the LM curve tells us that Y/r = 375. Therefore,
r/Y = 1/375 = 0.00267.
c. When compared to the money-demand curve listed in Problem 5, the demand for money has
become more sensitive to a change in the interest rate. Each one percentage point rise in the interest
rate now results in a decrease in the demand for money of 75 billion as opposed to 25 billion in
Problem 1. The slope of the new LM curve is 0.00267, which is less than 0.01, the slope of Problem
5’s LM curve. This means that the new LM curve is flatter than that of Problem 5.
A fiscal expansion results in an increase in income and therefore the demand for money. Since the
demand for money is more responsive to a change in the interest rate, it takes less of an increase in
©2012 Pearson Education, Inc. Publishing as Addison Wesley
Answers to Problems in Textbook
47
the interest rate to restore equilibrium in the money market. Since there is a smaller increase in the
interest rate, less real output and autonomous spending is crowded out by the fiscal expansion. So
in terms of its effect on output, fiscal policy should be stronger in this problem than it was in
Problem 5.
On the other hand, monetary policy should be weaker than it was in Problem 5. Since the demand
for money is more responsive to a change in the interest rate, it takes less of a drop in the interest
rate to restore equilibrium in the money market when there is an increase in the money supply.
Since there is less of a decrease in the interest rate, there is a smaller increase in autonomous
spending, and therefore real output, for any given increase in the money supply.
d. The new IS curve is Y = 9,875 – 100r. (See Problem 5a for the derivation.) To compute the
equilibrium interest rate, set the equation for the new IS curve equal to the equation for the LM
curve to get 9,875 – 100r = 7,159.5 + 375r. Adding 100r to and subtracting 9,375 from both sides
yields 475r = 2,715.5. Dividing both sides by 475 yields the equilibrium interest rate r = 5.7168. To
compute equilibrium real output, substitute the equilibrium interest rate into the equations for the
IS and LM curves to get Y = 9,875 – 100(5.7168) = 7,159.5 + 375(5.7168) = 9,303.3.
e. The real money supply now equals 1,431.9 + 100 = 1,531.9. To obtain the equation for the new LM
curve, set the real demand for money equal to the new real supply of money to get 0.2Y – 75r =
1,531.9. Adding 75r to both sides yields 0.2Y = 1,531.9 + 75r. Dividing both sides by 0.2 provides
us with the new LM equation Y = 7,659.5 + 375r. To compute the equilibrium interest rate, set the
equation for the IS curve equal to the equation for the new LM curve to get 9,475 –
100r = 7,659.5 + 375r. Adding 100r to and subtracting 7,659.5 from both sides yields 475r =
1,815.5. Dividing both sides by 475 yields the equilibrium interest rate r = 3.822. To compute
equilibrium real output, substitute the equilibrium interest rate into the equations for the IS and LM
curves to get Y = 9,475 – 100(3.822) = 7,659.5 + 375(3.822) = 9,092.8.
f. The same fiscal expansion results in a larger increase in income and a smaller rise in the interest
rate in Part d than in Problem 6a. The same increase in the money supply results in a smaller
increase in output and a smaller decrease in the interest rate in Part e than in Problem 6b. These are
the exact predictions in Part c.
9. Suppose that autonomous consumption and planned investment in the economy described in Problem 4
change to Ca = 470 – 40r and Ip = 1,700 – 80r. All other aspects of the structure of the commodity and
the money markets are as described in Problem 4.
a. The new autonomous spending equation is Ap = 470 – 15r – 0.85(200) + 1,700 – 60r + 1,700 + 500
= 4,200 – 75r. The equation of the IS curve is Y = 2.5(4,200 – 60r) = 10,500 – 187.5r. To compute
the equilibrium interest rate, set the equation for the new IS curve equal to the equation for the LM
curve to get 10,500 – 187.5r = 8,500 + 100r. Adding 187.5r to and subtracting 8,500 from both
sides yields 287.5r = 2,000. Dividing both sides by 287.5 yields the equilibrium interest rate r =
6.9565. To compute equilibrium real output, substitute the equilibrium interest rate into the
equations for the IS and LM curves to get Y = 10,500 – 187.5(6.9565) = 8,500 + 100(6.9565) =
9,195.65.
b. The slope of the IS curve is r/Y. The equation for the IS curve tells us that Y/r = –187.5. Therefore,
r/Y = –1/187.5 = –0.0053.
c. When compared to Problem 4, autonomous consumption and planned investment have become
more responsive to a change in the interest rate. In this problem, a one percentage point increase in
the interest rate results in a 75 billion decrease in autonomous consumption and planned
investment, as opposed to only a 40 billion decrease in Problem 1. The slope of the new IS curve is
–0.0053, which is less in absolute value than –0.01, the slope of Problem 4’s IS curve. This means
that the new IS curve is flatter than that of Problem 4.
©2012 Pearson Education, Inc. Publishing as Addison Wesley
48
Chapter 4
d.
e.
f.
10. a.
b.
c.
d.
Strong and Weak Policy Effects in the IS-LM Model
A fiscal expansion results in an increase in income and therefore the demand for money.
That creates an excess demand for money and results in a rise in the interest rate. Since the
autonomous spending is more responsive to a change in the interest rate, the increase in the interest
rate needed to restore equilibrium in the money market results in a larger decrease in real output
and autonomous spending. So in terms of its effect on income, fiscal policy should be weaker in
this problem than it was in Problem 4.
On the other hand, monetary policy should be stronger than it was in Problem 4. Since autonomous
spending is more responsive to a decrease in the interest rate, the decrease in the interest rate
needed to restore equilibrium in the money market when there is an increase in the money supply
should result in larger increases in autonomous spending and real output.
The new autonomous spending equation is Ap = 4,200 – 75r + 160 = 4,360 – 75r. The equation of
the new IS curve is Y = 2.5(4,360 – 75r) = 10,900 – 187.5r. To compute the equilibrium interest
rate, set the equation for the new IS curve equal to the equation for the LM curve to get 10,900 –
187.5r = 8,500 + 100r. Adding 187.5r to and subtracting 8,500 from both sides yields 287.5r =
2,400. Dividing both sides by 287.5 yields the equilibrium interest rate r = 8.3478. To compute
equilibrium real output, substitute the equilibrium interest rate into the equations for the IS and LM
curves to get Y = 10,900 – 187.5(8.3478) = 8,500 + 100(8.3478) = 9,334.78.
The new LM equation is Y = 8,900 + 100r. (See Problem 5b for the derivation.) To compute the
equilibrium interest rate, set the equation for the IS curve equal to the equation for the new LM
curve to get 10,500 – 187.5r = 8,900 + 100r. Adding 187.5r to and subtracting 8,900 from both
sides yields 287.5r = 1,600. Dividing both sides by 287.5 yields the equilibrium interest rate
r = 5.5652. To compute equilibrium real output, substitute the equilibrium interest rate into the
equations for the IS and LM curves to get Y = 10,500 – 187.5(5.5652) = 8,900 + 100(5.5652) =
9,546.52.
The same fiscal expansion results in smaller increases in income and the interest rate in Part d than
in Problem 5a. The same increase in the money supply results in a larger increase in output and a
smaller decrease in the interest rate in Part e than in Problem 5b. These are the exact predictions in
Part c.
In this problem, s = 0.2, t = 0.2, and nx = 0.14, so that the marginal leakage rate equals
0.2(1 – 0.2) + 0.2 + 0.14 = 0.16 + 0.2 + 0.14 = 0.5. Therefore, the multiplier, k, equals 1/
0.5 = 2. The equation for autonomous spending is Ap = 260 – 10r – 0.8(200) + 1,900 – 40r + 1,800
+ 700 = 4,500 – 50r. The equation of the IS curve is Y = 2(4,500 – 50r) = 9,000 – 100r.
To obtain the equation for the LM curve use either Equation (5) on page 126 in the Appendix or set
the real demand for money equal to the real supply of money to get 0.25Y – 25r = 2,000. Adding
25r to both sides yields 0.25Y = 2,000 + 25r. Dividing both sides by 0.25 provides us with the LM
equation Y = 8,000 + 100r.
To compute the equilibrium interest rate, set the equation for the IS curve equal to the equation for
the LM curve to get 9,000 – 100r = 8,000 + 100r. Adding 100r to and subtracting 8,000 from both
sides yields 200r = 1,000. Dividing both sides by 200 yields the equilibrium interest rate
r = 5. To compute equilibrium real output, substitute the equilibrium interest rate into the equations
for the IS and LM curves to get Y = 9,000 – 100(5) = 8,000 + 100(5) = 8,500.
The new equation for autonomous spending is Ap = 4,500 – 50r – 40 – 60 = 4,400 – 50r. The
equation of the IS curve is Y = 2(4,400 – 50r) = 8,800 – 100r. To compute the new equilibrium
interest rate, set the equation for the new IS curve equal to the equation for the LM curve to get
8,800 – 100r = 8,000 + 100r. Adding 100r to and subtracting 8,000 from both sides yields
200r = 800. Dividing both sides by 200 yields the equilibrium interest rate r = 4. To compute
©2012 Pearson Education, Inc. Publishing as Addison Wesley
Answers to Problems in Textbook
49
equilibrium real output, substitute the equilibrium interest rate into the equations for the IS and LM
curves to get Y = 8,800 – 100(4) = 8,000 + 100(4) = 8,400.
e. In order to return output to natural real GDP, autonomous taxes would have to be cut enough to get
autonomous spending to rise by 100 billion, the amount that it fell due to the declines in consumer
and business confidence. Since 100 = Ap = –0.8 Ta, Ta = 100/(–0.8) = –125.
f. The money supply would have to be increased enough so that Y = 8,500 is now equilibrium output
in both the commodity and money markets, given the IS curve, Y = 8,800 – 100r, so that 8,500 =
8,800 – 100r. Adding 100r to and subtracting 8,500 from both sides yields 100r = 300 or r = 3.
That is, the Fed would have to increase the money supply enough to reduce the interest rate to 3
percent to offset the effects of declines in consumer and business confidence on autonomous
spending. To compute how much the money supply needs to be increased, let’s compute the
demand for money at Y = 8,500 and r = 3. The demand for money equals 0.25(8,500) – 25(3) =
2,125 – 75 = 2,050. Therefore, for both the commodity and money markets to be in equilibrium at Y
= 8,500 and r = 3, the Fed would have to increase the money supply by 50 billion from 2,000 to
2,050.
g. At r = 5, autonomous consumption equals 220 – 10(5) = 170, and planned investment equals
1,840 – 40(5) = 1,640. At r = 3, autonomous consumption equals 220 – 10(3) = 190, and planned
investment equals 1,840 – 40(3) = 1,720. Note that planned investment is much larger if monetary
policy as opposed to fiscal policy is used to restore real output to natural real GDP. That higher
level of planned investment contributes to a more rapid rate of productivity growth, and therefore a
higher rate of growth in real GDP over the long run.
©2012 Pearson Education, Inc. Publishing as Addison Wesley