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Chapter 3
Income and Interest Rates: The Keynesian
Cross Model and the IS Curve

Chapter Outline
3-1 Business Cycles and the Theory of Income Determination
a. The Volatile Business Cycle: The Global Crisis Follows the Great Moderation
Global Economic Crisis Focus: What Were the Shocks That made the 2008-09 Economic
Crisis So Severe?
3-2 Income Determination, Unemployment, and the Price Level
a. Income Determination and the Price Level
b. What We Explain and What We Take as Given
3-3 Planned Expenditure
a. The Consumption Function
b. Induced Saving and the Marginal Propensity to Save
c. Autonomous Consumption, the Interest Rate, the Asset Values, and Financial Markets
Global Economic Crisis Focus: Financial Market Instability as the
Main Cause of the Global Economic Crisis
3-4 The Economy In and Out of Equilibrium
a. Autonomous Planned Spending
b. When Is the Economy in Equilibrium?
c. The “Keynesian Cross” Model In and Out of Equilibrium
d. What Happens out of Equilibrium?
e. Determining Equilibrium Real GDP
Understanding the Global Economic Crisis:
How Changes in Wealth Influence Consumer Spending
3-5 The Multiplier Effect
a. Calculating the Multiplier
b. Example of the Multiplier Effect in Action
©2012 Pearson Education, Inc. Publishing as Addison Wesley
Chapter Overview
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3-6 Sources of Shifts in Planned Spending
a. Government Spending and Taxation
b. Fiscal Expansion
c. The Government Budget Deficit and Its Financing
d. The Tax Multiplier
e. The Balanced Budget Multiplier
3-7 How Can Monetary Policy Affect Planned Saving?
a. Functions of Interest Rates
b. Types of Interest Rates
3-8 The Relation of Autonomous Planned Spending to the Interest Rate
a. The Demand for Autonomous Planned Spending
b. Shifts in the Ap Demand Schedule
Understanding the Global Economic Crisis: A Central Explanation of Business Cycles Is the
Volatility of Investment
3.9 The IS Curve
a. How to Derive the IS Curve
b. What the IS Curve Shows
3.10 Conclusion: The Missing Relation
Box: Learning About Diagrams: The IS Curve
Summary
Appendix: Allowing for Income Taxes and Income-Dependent Net Exports
a. Effect of Income Taxes
b. The Government Budget
c. Autonomous and Induced Net Exports
d. Full Equations for Equilibrium Income and the Multiplier
e. The Balanced Budget Multiplier

Chapter Overview
This Chapter begins with the example of current economic situation where moderate volatility of
the real GDP in the United States over the last couple of decades has been followed by a severe
economic downturn (named as great recession). Gordon introduces the concepts of aggregate
demand and aggregate supply and analysis of the macroeconomic issues in the short run, where the
price level is fixed. The main focus of the chapter is the development of a model of income
determination, which can explain the variations of real GDP over a period of time. Initially, both
the price level and the interest rate are held fixed in the model. Later in the chapter, Gordon relaxes
the assumptions (such as the price level is fixed, but the interest rate varies) and extends his
analysis. He explains that the interest rate will affect autonomous planned spending (Ap) through
©2012 Pearson Education, Inc. Publishing as Addison Wesley
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Chapter 3
Income and Interest Rates: The Keynesian Cross Model and the IS Curve
the effect of the interest rate on planned investment and autonomous consumption. Gordon
constructs the Ap demand schedule and shows how this can be used to construct the IS curve.
Because the material presented in Chapter 3 is an essential first step in developing the IS-LM model
discussed in Chapter 4, your lecture should provide detailed coverage of this chapter.
Gordon begins Chapter 3 by reviewing the distinction between short-run and long-run
macroeconomic issues. He tells us that Chapters 3 through 9 will deal with short-run issues, such as
business cycles and how monetary and fiscal policy might be used to dampen the severity of the
volatility of business cycles. In Section 3-1, Gordon begins by reviewing the essential elements of
business cycles by drawing our attention to Figure 3-1, where he plots actual average real GDP
growth in the United States from 1950 to 2010 to exhibit such volatility. Possible reasons for the
higher volatility of actual real GDP growth before 1985, moderate volatility during 1985–2006 and
severe decline in the real GDP after that time, are discussed. He explains the volatility by
introducing the concept of aggregate demand, aggregate supply, and aggregate demand shocks
(which will be shown to have a multiplier effect later in Chapter 3). These shocks may have
become smaller during 1985–2006 because of wise use of monetary and fiscal policy to offset the
harshness of such shocks. However, as the economy experienced severe downturn after 2006,
Gordon tried to explain it by the sudden presence of substantial negative shocks.
In Section 3-2, Gordon begins by reminding the reader that determining the level of real GDP is
important for determining the level of the unemployment rate (which is a mirror image of the GDP
gap), difference between actual and natural real GDP, which is the first of the three central
macroeconomic concepts in Chapter 1. He explains that the final central concept, productivity
growth, is discussed later in the book, while the second central concept, inflation, is to be discussed
in Chapters 7 through 9. Gordon then explains that, theoretically, aggregate demand shocks may
affect the price level as well as real GDP. The concept of aggregate supply is mentioned, but it
would be covered in detail in Chapters 7 and 8. He explains with practical examples why fixed
price level may be a reasonable assumption for short-run analysis. And fixed price level means that
changes in aggregate demand translate into proportional changes in real GDP (through Equation
3.1). Gordon next distinguishes between exogenous variables, which are variables taken as given,
and endogenous variables, which are variables that are determined by the given set of exogenous
variables through a known or theoretical relationship. To clarify the relationship between
exogenous and endogenous variables, you might want to give the simplest example of a oneindependent-variable equation, y = f(x). Explain that the dependent or endogenous variable y is
determined from the independent or exogenous variable x and that theory usually gives the
functional relationship. If you do use this approach, it will be helpful to give some simple physical
or economic examples of exogenous and endogenous variables. These concepts are then used to
make the point that the first simple model that will be developed will explain only consumption and
real GDP, and, specifically, the interest rate and price level will be exogenously fixed. This
assumption simplifies the analysis of the direct effects of changes in government spending,
investment, and autonomous net exports on equilibrium income.
Section 3-3 categorizes total expenditure into consumption, investment, government, and net
exports. This section also explains how households divide disposable income between consumption
and saving by introducing the concepts of consumption and saving functions. This allows the
distinction between the autonomous components of consumption and saving and the
©2012 Pearson Education, Inc. Publishing as Addison Wesley
Chapter Overview
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income-induced components of consumption and saving. The marginal propensities to consume
and save are also defined in terms of the consumption and saving functions. Emphasize that
“marginal” propensity pertains to the fraction of each additional dollar of income that is consumed
or saved and not necessarily the fraction of total income consumed or saved, that is, the average
propensity to consume. Figure 3-2 expresses the relationship between the consumption and saving
functions by showing that whenever total disposable income equals zero, saving is equal to the
negative of autonomous consumption; whenever consumption equals total disposable income,
saving is zero; and whenever consumption is less than total disposable income, saving is positive.
The figure shows that it is possible for consumption to be greater than income by noting that
individuals, especially students, often have to borrow money to finance their expenditures. In this
context, he explains how interest rate and household wealth can affect the autonomous
consumption expenditure.
After a brief discussion about the great recession of 2007–09, in a box Global Economic Crisis
Focus: Financial Market Instability as the Main Cause of the Global Economic Crisis, the chapter
turns, in Section 3-4, to the concept of macroeconomic equilibrium. Macroeconomic equilibrium
occurs where actual expenditures and planned expenditures ( E p ) coincide. The notion of
“autonomous planned spending” ( Ap  Ca  cTa  I p  G  NX a ) is introduced as a component of
planned expenditure distinct from induced consumption, so that E p  Ap  cY . (Equation 3.8) Point
out why you are using the subscript “a” on the right-hand side of the Ap equation (3.7). The
subscript stands for autonomous planned, which to economists describes a component that does not
depend on income Y. Total net taxes and total net exports are currently autonomous as well,
although these restrictive assumptions are relaxed in the Appendix to Chapter 3. But even in the
Appendix, only the autonomous components are on the right-hand side of the Ap equation. Explain
that it is not necessary to put the subscript “a” on I p or G. The text defines equilibrium income or
GDP as that level of income where planned expenditure equals total income ( E p  Y ). It explicitly
distinguishes between actual expenditure, E  C  I  G  NX , and planned expenditure, Ep = C + Ip +
G + NX. The difference between the two quantities is unplanned, or unintended, inventory
investment, I u . Explain that because a business firm does not desire unintended inventory
accumulation (corresponding to the case Iu  0) or decumulation (corresponding to the case Iu  0), it
will always adjust its level of production until there is no unintended inventory investment
(corresponding to the case Iu  0). This is precisely why the equation Y  E p is an equilibrium
condition: There is no pressure for change. Equilibrium and how and why the economy moves
toward it are explained diagrammatically (Keynesian Cross Model in Figure 3-3) and algebraically,
as well as verbally.
There are several possible sources of confusion that students may encounter, on which you may
wish to focus in your lecture.
1. Students who have never seen 45-degree line diagrams may find them a bit peculiar. When first
presenting these diagrams, explain that the 45-degree line represents equality between the quantity on
the horizontal axis and the quantity on the vertical axis. In Figure 3-4, show that the level of income
on the vertical axis corresponding to each level of income on the horizontal axis is always determined
from the 45-degree line (since they must be equal), and the level of total expenditure corresponding to
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Chapter 3
Income and Interest Rates: The Keynesian Cross Model and the IS Curve
each level of income is always determined from the planned-expenditure line. This makes it easier to
see why the intersection of the two lines determines the equilibrium level of income.
2. Students may be tempted to draw conclusions from the comparisons of Figures 3-2 and 3-3 that the
text is not making. Stress that Figure 3-2 simply establishes a relationship between consumption and
saving and does not attempt to model equilibrium in an economy (especially since even the simplest
economy must have both a business and a household sector). The intersection of the 45-degree totaldisposable-income line with the consumption function at Point F in Figure 3-2 is analogous to the
equilibrium Point B in Figure 3-3 only because, without investment, government spending, and net
exports, consumption would be the only source of expenditure. Note that the horizontal axis of Figure
3-2 is “disposable” income rather than “total” income and that there are no equilibrating forces (such
as unintended inventory accumulation or decumulation) that would determine an equilibrium position.
3. It is very important that students can distinguish between what is true by definition (i.e., what’s an
identity) and what’s true only in equilibrium. Table 3-1 of the text summarizes these concepts, and it
would be very helpful to review it in your lecture.
Section 3-5 analyzes the multiplier effect. The text derives the simple multiplier (1/s) directly from
Equation 3.12, sY = Ap by assuming two different levels of planned autonomous spending. The
difference between the corresponding equilibrium income levels is divided by the difference in the
autonomous spending levels(Y/ Ap = 1/S). Students must understand that the multiplier is the
change in equilibrium income arising from each dollar change in planned autonomous spending.
This is illustrated in Figure 3-4. Changes in government spending, planned autonomous investment,
autonomous consumption, or autonomous net exports will have the same multiplier effect on
equilibrium income.
In Section 3-6, it is explained that the change in Ap may arise because of possible changes in any
one of its five components. It has computed the government expenditure multiplier, tax multiplier,
and balanced budget multiplier in detail. Another important concept of how to finance a tax cut is
also analyzed.
Section 3-7 briefly describes why monetary policies can affect the planned spending. It explains
that interest rates are important to consumption and investment decisions. Because
macroeconomics is concerned with the average level of interest rates, the standard textbook
assumption of a single interest rate is used in our models.
Section 3-8 establishes the negative relationship between the interest rate and autonomous planned
spending via investment expenditures. The reasoning behind this relationship is that business firms
will only invest in projects that yield a rate of return greater than (or equal to) the rate of interest.
Stress that this condition holds true because a firm usually finances its projects by borrowing:
Projects with a rate of return lower than the interest rate will not have sufficient earnings to cover
the interest payment on the firm’s loan. Also point out that even if the firm had sufficient internal
funding, it would be more profitable to lend the funds out and earn the higher interest rate rather
than invest in the lower-yielding project. Thus, higher interest rates reduce the relative profitability
of investment projects. The text emphasizes that not only are investment decisions sensitive to the
interest rate, but so are autonomous consumption decisions. Students can readily identify with
examples of this, such as the decision to purchase an automobile, household appliance, or other
consumer durable. Therefore, higher interest rates will reduce planned autonomous spending by
discouraging both planned investment and autonomous consumption. When discussing the role of
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Chapter Overview
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business and consumer confidence in determining autonomous expenditure, emphasize that
movements along the rate-of-return line are due to changes in the interest rate while shifts in the
rate-of-return line are due to changes in business and consumer confidence. The rate-of-return line
for Ca + Ip is added horizontally to the other components of autonomous planned expenditure in
Figure 3-5 to obtain the Ap demand schedule. In the new topic box Understanding the Global
Economic Crisis: A Central Explanation of Business Cycles Is the Volatility of Investment, Gordon
examines the roles of the Volatility of Investment on the equilibrium real GDP.
Figure 3-6 in Section 3-9 connects the autonomous planned spending (Ap) demand schedule with
the IS curve. Note that this is consistent with the equilibrium concept developed in the simple
income-determination model. This is advantageous, because it shows students that the only
difference between the IS curve and the simple Keynesian model is that, instead of taking changes
in total planned spending as given, interest rates are now specified as the cause of these changes.
Since the relationship between autonomous planned spending and equilibrium income has already
been established, the link between interest rates and equilibrium income represented by the IS curve
is more easily understood. This equilibrium is termed the “goods” or “commodity-market”
equilibrium. Then clearly what the IS curve represents is income levels and interest rates that are
consistent with commodity-market equilibrium. Be sure the students are clear why the IS curve
slopes downward and why points above and below it are not commodity-market equilibrium points.
Also, be sure they know the difference between factors that cause movements along the curve and
those that cause shifts in the curve. The simplest and most direct approach is to explain that any
change in a variable plotted on the two axes will cause a movement along the curve, while any
change in the factors affecting the curve but not on either of the axes will shift the curve. This is
explained in the “Learning About Diagrams” box in Section 3-10. Your more mathematically
inclined students may notice that this “rule” of distinguishing between shifts and movements along
curves comes directly from the calculus concept of using “level curves” to graphically express
functions of more than one independent variable in two dimensions. Having explained this
important distinction, students more easily comprehend why shifts in Ap (i.e., changes in
autonomous planned spending resulting from factors such as consumer and business confidence)
will shift the IS curve. In explaining the role of the multiplier in the IS curve, you might note that
the value of the multiplier, k, determines how much the IS curve shifts horizontally in response to a
shift in the Ap line. The horizontal position of the IS curve depends on the parameter Ap , which
denotes the horizontal intercept of the Ap demand schedule (i.e., the zero-interest-rate level of Ap).
Because the horizontal intercept of the IS curve is kAp , shifts in Ap will shift the IS curve
horizontally by k Ap . Finally, you might want to discuss how changes in the interest responsiveness
of planned autonomous spending affect the IS curve. This can be facilitated by re-deriving the IS
curve graphically with different slopes for the Ap line.
At this point in the material, students may have gotten the impression that the only relationship
between the interest rate and income is the negative one represented by the IS curve. Point out that
there is no single relationship between interest rates and income and that the particular relationship
between the variables depends on which part of the economy is being examined. This is explained
in Section 3–10. Since most students are familiar with the graphical notion of supply and demand,
you may want to use that simple example to show that this is perfectly analogous to the idea that
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Chapter 3
Income and Interest Rates: The Keynesian Cross Model and the IS Curve
there is no one relationship between price and quantity. Be sure students understand that this
supply–demand analogy is strictly an example; Chapter 7 presents the macroeconomic
determination of the price level by aggregate demand and aggregate supply. Emphasize that the IS
curve represents the relationship between interest rates and income in the commodity market and
that, because the demand for money also depends on the interest rate and income, another
relationship between these variables exists.
The Appendix to this chapter expands the basic model by incorporating income taxes and letting
net exports depend on income. The introduction of income taxes into the model raises the marginal
leakage rate out of each additional dollar of income, reducing the multiplier’s value from 1/s to
1/[s(1 – t) + t], where t = the tax rate. Income taxes make the government’s budget deficit depend
on the level of income, allowing the possibility of “automatic stabilization.” The chapter ends by
separating net exports into an autonomous component, NXa (determined by exogenous factors), and
an induced component, nxY, which is inversely related to income because increases in income
cause imports to rise. This again shrinks the multiplier by increasing the marginal rate of leakages
from income. The final equation for equilibrium income expresses the model in its complete
algebraic form.

Changes in the Twelfth Edition
Chapter 3 has also undergone significant changes from the previous edition. Gordon has changed
the titles of some subsections, updated data and figures, added more explanations about several
concepts, rewritten one section, deleted several things (such as case studies, box on international
perspectives, box on shifts in consumer confidence and household wealth as a source of demand
shocks), revised a few equations in several cases, deleted numerical examples completely, and
added several new boxes (Global Economic Crisis Focus and Understanding the Global economic
Crisis). However, the basic ideas and explanations in this chapter remain quite the same as in the
11th edition.
In Section 3-1, he has changed the title of the subsection from “The Reduced Volatility of Business
Cycles: The Great Moderation” to “The Volatile Business Cycles: The Global Economic Crisis
Follows the Great Moderation.” He has replaced the discussion about this topic completely in the
light of current economic experiences and added a box Global Economic Crisis Focus: What Were
the Shocks That Made the 2008-09 Economic Crisis So Severe? He has updated the data in the
Figure 3-1 to the year 2010.
Discussion in Section 3-2 has been changed slightly with a more emphasis on unemployment rate.
Section 3-3 remains more or less the same as in the 11th edition, although he has changed one
subtitle from “Autonomous Consumption, the Interest Rate, and the Stock market” to
“Autonomous Consumption, the Interest Rate the Asset Values, and Financial Markets.” He also
eliminated the numerical examples completely. He has deleted the case study in Section 3-4 and
Figure 3-3, but added a box Global Economic Crisis Focus: Financial Market Instability as the
Main Cause of the Global Economic Crisis.
©2012 Pearson Education, Inc. Publishing as Addison Wesley
Answers to Questions in Textbook
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In Section 3-4, he explains the concept of equilibrium with the help of a diagram. He has changed
the axes of the Figures 3-3 and 3-4 by eliminating the reference to numbers to represent real income
and expenditures. He has made a minor change in Table 3-1
In Section 3-5, entitled “The Multiplier Effect,” all reference to numerical examples has been
eliminated.
In Section 3-6, numerical examples have been replaced. The first paragraph after the subtitle
“Government Spending and Taxation” has been deleted and the self-test in this section has been
changed. The paragraph after the subtitle “Fiscal Expansion” has been rewritten, and the
International Perspective box has been deleted.
Section 3-7 has remained more or less unchanged. However, Section 3-8 has gone through
substantial changes. The subsection “Example of an Airlines Investment Decision” and the Box on
“Shifts in Consumer Confidence and Household Wealth as Sources of Demand Shocks” have been
deleted. A new topic box “Understanding the Global Economic Crisis: A Central Explanation of
Business Cycles Is the Volatility of Investment” has been added.
Section 3-9 has gone through moderate changes as Gordon has rewritten the discussion about the
Figure 3-6, (where numbers have been eliminated from the axes). Last Section 3-10 has remained
mostly unchanged.
Summary section has also gone through moderate changes. Number 2 has been briefed whereas
numbers 3 and 10 have been rewritten completely.
Appendix has changed. Numerical examples have been eliminated and some paragraphs have been
rewritten.

Answers to Questions in Textbook
1. Movements in endogenous variables are explained by the theory; movements in exogenous variables
are not. Here and throughout the book, Gordon makes no distinction between exogenous variables and
parameters. Both are determined outside the model and fixed for each period of analysis. Both,
however, may be variables for purposes of problems and exercises. Thus, although the marginal
propensity to consume is treated as a fixed parameter throughout the chapter, the end-of-chapter
problems contain examples where MPC takes a different value.
Endogenous
Exogenous
Consumption
Net exports
GDP
Tax revenue
Disposable income
Saving
Foreign trade surplus (deficit)
Government budget surplus (deficit)
Autonomous taxes
Marginal propensity to consume
Exports
Price level
Interest rate
Investment
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Chapter 3
Income and Interest Rates: The Keynesian Cross Model and the IS Curve
2. We distinguish between the two types of consumption for two reasons. First, each type of spending is
determined by a different cause: induced consumption is determined by the level of disposable income
and the marginal propensity to consume, while autonomous consumption is determined by factors
other than income. Second, changes in autonomous consumption cause a multiplier effect in the
economy, but changes in induced consumption do not.
3. The Understanding the Global Economic Crisis box on pages 62–63 shows how the booms in housing
prices from 2000 through April 2006 and stock prices from 2003 through 2007 resulted in increases in
total assets, net worth, and the household net worth relative to personal disposable income up to 2007.
Those increases in wealth caused consumption expenditures to rise relative to personal disposable
income as indicated by the decline in the personal saving rate over those same years.
The drop in housing prices after April 2006 and declining stock prices in 2008 caused falls in real
wealth and consumption expenditures, as shown by a sharp rebound in the personal saving rate after
2006.
4. Businesses reduce production during a recession primarily because of falling demand for their goods
and services. One of the first indications businesses get that demand has fallen is that they have more
unsold goods in inventories than they would like. That is, businesses see an unintended rise in
inventories, which causes them to reduce output. On the other hand, once businesses become confident
that the economy is on the rebound, then they will start to build up inventories in anticipation of higher
sales.
5. Positive unintended inventory investment results if income is greater than planned expenditure and
businesses’ inventories build up. To avoid the costs of financing and storing unwanted inventories,
businesses cut production, which causes income to fall. Negative unintended inventory investment
occurs if income is less than planned expenditure and businesses’ inventories shrink. To meet current
sales and replenish inventories, businesses raise production, causing income to rise.
6. The impact of a change in investment will be greater the larger the marginal propensity to consume.
Although the initial impact of the change in autonomous investment is the same in any case, the larger
the MPC, the greater will be the secondary effects on consumer spending.
7. Expansionary fiscal policy would include increasing government spending or decreasing taxes. In each
case, the size of the deficit would increase. If the budget were initially in surplus, however, the same
policy choice would decrease the surplus.
8. The IS curve is downward sloping because a fall in the interest rate results in a rise in consumption and
planned investment, the two interest rate sensitive components of autonomous planned spending. That
increase in planned spending results in a rise in income as businesses increase output in response to the
greater demand for goods and services. Income continues to rise until the commodity market is once
again in equilibrium. Note that the higher level of income takes place at a lower interest rate, which is
shown graphically as a movement down the IS curve. A shift of the IS curve takes place when
autonomous planned spending changes due to something other than a change in the interest rate. For
example, suppose that there is a change in fiscal policy which reduces autonomous planned spending.
That decrease causes a fall in income as business firms cut output in response to the lower demand for
goods and services. Income continues to fall until the commodity market is once again in equilibrium.
Note that the lower level of income takes place at the same interest rate, which is shown graphically as
a shift left of the IS curve.
9. The rise in the investment–GDP ratio in the four quarters leading up to the recession of 1981–82
would be reflected in a rise in autonomous planned spending which would shift the IS curve to the
right. However, starting in mid-1981, the IS curve shifts left as the investment–GDP ratio decrease
would be reflected in a fall in autonomous planned spending. Note that the investment–GDP ratio
©2012 Pearson Education, Inc. Publishing as Addison Wesley
Answers to Problems in Textbook
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starts to decline even before the onset of the 2007–09 recession due to a collapse in housing
construction following the bursting of the house price bubble. Furthermore, the larger and longer
decline in the investment–GDP ratio in the 2007–09 recession when compared to the 1981–82
recession means that the IS curve shifts left more and for a longer period of time during the 2007–09
recession when compared to the earlier downturn. Finally, the investment–GDP ratio returns to its prerecession level within 10 quarters of the onset of the 1981–82 recession, something that does happen in
the same period following the end of the recent recession. This means there is less of a shift right of
the IS curve in 2010 in comparison to the shift right of the IS curve in 1983–84.
10. a. The decline in sales of American agricultural exports reduces net exports. Therefore, autonomous
planned spending decreases at a given interest rate. The reduction results in a fall in equilibrium
income at a given interest rate, which is shown graphically as a shift left of the IS curve.
b. The collapse in consumer confidence reduces consumption. Therefore, autonomous planned
spending decreases at a given interest rate. The reduction results in a fall in equilibrium income at a
given interest rate, which is shown graphically as a shift left of the IS curve.
c. The collapse in business confidence reduces planned investment. Therefore, autonomous planned
spending decreases at a given interest rate. The reduction results in a fall in equilibrium income at a
given interest rate, which is shown graphically as a shift left of the IS curve.
d. The reluctance of some banks to make car and housing loans following the financial crisis of
2007–08 reduces the amount of consumption and planned investment expenditures at each interest
rate. Therefore, autonomous planned spending decreases at a given interest rate. The reduction
results in a fall in equilibrium income at a given interest rate, which is shown graphically as a shift
left of the IS curve.
11. Since a demand shock is a significant change in desired spending by consumers, business firms, the
government, or foreigners, a demand shock causes a change in autonomous planned spending at a
given interest rate. That change in autonomous planned spending results in a change in equilibrium
income, given the interest rate, and is shown graphically as a shift in the IS curve. Thus the hypothesis
that the increased stability of the U.S. economy since 1985 is due to smaller and less important
demand shocks can be interpreted to mean that shifts of the IS curve have become smaller.
12. C = a + c(Y – T) = a + cY – c(Ta + tY) = a – cTa + c(1 – t)Y.
S = –a + s(Y – T) = –a + sY – s(Ta + tY) = –a – sTa + s(1 – t)Y.
13. The greater the MPC, the smaller is the marginal leakage rate. Therefore, the impact of a change in
investment will be greater the smaller the marginal leakage rate. It will take more rounds of spending
and saving to generate the necessary increase in leakages to match the initial change in autonomous
spending.
14. The marginal leakage rate in this case is s + nx, so the balanced budget multiplier is s/(s + nx), which is
less than one.

Answers to Problems in Textbook
1. a. Consumption equals 1,400 + 0.6(10,000 – 1,750) = 1,400 + 4,950 = 6,350.
b. Saving equals disposable income minus consumption, which equals 8,250 – 6,350 = 1,900.
c. The level of planned investment equals 1,800. To compute the level of actual investment, I,
remember that income and expenditures (E) are always equal, and since net exports equal zero in
this problem, E = C + I + G, so that I = Y – C – G or I = 10,000 – 6,350 – 1950 = 1,700. Since
unintended inventory investment, Iu = I – IP, Iu = 1,700 – 1,800 = –100.
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Chapter 3
Income and Interest Rates: The Keynesian Cross Model and the IS Curve
d. Leakages equal saving plus taxes = 1,900 + 1,750 = 3,650. Injections equal investment plus
government = 1,700 + 1,950 = 3,650. So both leakages and injections equal 3,650.
e. Since planned expenditure exceeds income, the economy is not in equilibrium. In this economy, the
equilibrium level of income equals Ap/s, where s is the marginal propensity to save. Autonomous
planned spending, Ap, equals Ca – cT + Ip + G = 1,400 – 0.6(1,750) + 1,800 + 1,950 = 4,050. The
marginal propensity to save equals 1 – c = 1 – 0.6 = 0.4. Therefore, the equilibrium level of income
equals 4,100/0.4 = 10,250.
f. At the equilibrium level of income, there is a government deficit of 200 billion since taxes equal
1,750 and government spending on goods and services equals 1,950.
2. a. The marginal propensity to save, s, equals 1 – c = 1 – .6 = .4.
b. Autonomous planned spending, Ap, equals Ca – cTa + Ip + G + NX = 1,500 – 10r –.6(1,800) + 2,400
– 50r + 2,000 – 200 = 4,620 – 60r. Therefore, at an interest rate equal to 3, autonomous planned
spending equals 4,620 – 60(3) = 4,440.
c. Since the marginal propensity to save equals .4 and the equilibrium level of income equals Ap/s, the
equilibrium level of income equals 4,440/.4 = 11,100, given the interest rate equals 5.
d. Since autonomous consumption changes by four percent of any change in household wealth and the
decline in the housing market from 2006–09 and drop in the stock market from 2007–09 reduces
household wealth by $3 trillion, the decrease in autonomous consumption that results from the
decline in household wealth equals .04(3000) = 120 billion.
e. Since the decrease in autonomous consumption that results from the decline in household wealth
equals 120 billion, autonomous planned spending decreases by that amount as well. Therefore, the
new amount of autonomous planned spending equals 4,440 – 120 = 4,320. Therefore, the new
equilibrium level of income equals 4,320/.4 = 10,800, given the interest rate equals 3.
f. The multiplier, k, equals Y/Ap = (10,800 – 11,100)/(4,320 – 4,440) = (–300)/(–120) = 2.5.
g. Since the multiplier equals 2.5 and income must increase by 300 billion to restore income to its
initial equilibrium level of 11,100, fiscal or monetary policymakers must take actions that increase
autonomous planned spending by 120 billion in order to restore equilibrium income to 11,100.
i. If fiscal policymakers increase government spending, G, and there are no changes in either
taxes or the interest rate, then Ap = 120 = G. Therefore, fiscal policymakers must increase
government spending by 120 billion to restore equilibrium income to 11,100, given no changes
in taxes or the interest rate.
ii. If fiscal policymakers decrease taxes, Ta, and there are no changes in either government
spending or the interest rate, then Ap = 120 = –cTa = –.6Ta. Therefore, 120/(–.6) = –200 =
Ta. Therefore, fiscal policymakers must cut taxes by 200 billion to restore equilibrium
income to 11,100, given no changes in government spending or the interest rate.
iii. If fiscal policymakers increase government spending and taxes, then given no change in the
interest rate, Ap = G – .6Ta = 120. Furthermore, since fiscal policymakers at the same time
don’t change the government budget balance, then G = Ta, so that Ap = G – .6G = 120
or .4G = 120 or G = 300. Therefore, fiscal policymakers increase both government
spending and taxes by 300 billion to restore equilibrium income to 11,100, given no changes in
the government budget balance or the interest rate.
iv. The parameter on the interest rate in the equation for autonomous planned spending indicates
that autonomous planned spending increases by 60 billion for every one percentage point drop
in the interest rate. Therefore, since autonomous planned spending must increase by 120
billion to restore equilibrium income to 11,100, monetary policymakers must reduce the
©2012 Pearson Education, Inc. Publishing as Addison Wesley
Answers to Problems in Textbook
29
interest rate by two percentage points to restore equilibrium income to 11,100, given no
changes in government spending or taxes.
3. a. The marginal propensity to save equals 1 – c = 1 – .6 = .4.
b. The equation for autonomous planned spending, Ap, equals 1,500 – 20r – .6(1,750) + 2,450 – 60r +
1,980 – 200 = 4,680 – 80r. When the interest rate equals 0, autonomous planned spending equals
4,680. When the interest rate equals 2, autonomous planned spending equals 4,680 – 80(2) = 4,520.
When the interest rate equals 4, autonomous planned spending equals 4,680 – 80(4) = 4,360, and
when it equals 6, autonomous planned spending equals 4,680 – 80(6) = 4,200.
c. The equilibrium level of income equals Ap/s. At an interest rate of 0, the equilibrium level of
income equals 4,680/.4 = 11,700. At an interest rate of 2, the equilibrium level of income equals
4,520/.4 = 11,300. At an interest rate of 4, the equilibrium level of income equals 4,360/.4 =
10,900, and at an interest rate of 6, it equals 4,200/.4 = 10,500. 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
four points on your IS curve are: (11,700, 0); (11,300, 2); (10,900, 4); and (10,500, 6).
d. The decrease in government spending of 80 billion decreases autonomous planned spending by the
same amount at each interest rate. Therefore, when the interest rate equals 0, autonomous planned
spending equals 4,680 – 80 = 4,600. When the interest rate equals 2, autonomous planned spending
equals 4,520 – 80 = 4,440. When the interest rate equals 4, autonomous planned spending equals
4,360 – 80 = 4,280, and when it equals 6, autonomous planned spending equals 4,200 – 80 = 4,120.
e. Again, the equilibrium level of income equals Ap/s. At an interest rate of 0, the new equilibrium
level of income equals 4,600/.4 = 11,500. At an interest rate of 2, the new equilibrium level of
income equals 4,440/.4 = 11,100. At an interest rate of 4, the new equilibrium level of income
equals 4,280/.4 = 10,700, and at an interest rate of 6, it now equals 4,120/.4 = 10,300. The four
points on your new IS curve are: (11,500, 0); (11,100, 2); (10,700, 4); and (10,300, 6). Note that the
decrease in autonomous planned spending that results from the decline in government spending
shifts the IS curve left.
f. The increase in government spending of 160 billion increases autonomous planned spending by the
same amount at each interest rate. Therefore, when the interest rate equals 0, autonomous planned
spending equals 4,680 + 160 = 4,840. When the interest rate equals 2, autonomous planned
spending equals 4,520 + 160 = 4,680. When the interest rate equals 4, autonomous planned
spending equals 4,360 + 160 = 4,520, and when it equals 6, autonomous planned spending equals
4,200 + 160 = 4,360.
g. Again, the equilibrium level of income equals Ap/sw. At an interest rate of 0, the new equilibrium
level of income equals 4,840/.4 = 12,100. At an interest rate of 2, the new equilibrium level of
income equals 4,680/.4 = 11,700. At an interest rate of 4, the new equilibrium level of income
equals 4,520/.4 = 11,300, and at an interest rate of 6, it now equals 4,360/.4 = 10,900. The four
points on your new IS curve are: (12,100, 0); (11,700, 2); (11,300, 4); and (10,900, 6). Note that the
increase in autonomous planned spending that results from the rise in government spending shifts
the IS curve right.
h. Your graph of the IS curve from Part e shows that monetary policymakers will decrease the interest
rate to 3 if they wish to maintain equilibrium level at 10,900, the natural level of real GDP, given
the decline in government spending. Your answer to Part g shows that monetary policymakers will
increase the interest rate to 6 if they wish to maintain equilibrium level at 10,900, the natural level
of real GDP, given the rise in government spending.
4. a. Ap = 660 – 0.8(200) + 500 + 500 + 300 = 1,800.
b. Multiplier = 1.0/(0.2(1 – 0.2) + 0.2 + 0.04) = 2.5.
©2012 Pearson Education, Inc. Publishing as Addison Wesley
30
Chapter 3
Income and Interest Rates: The Keynesian Cross Model and the IS Curve
c. Y = 1800  2.5 = 4,500.
d. C = 660 + .8(4,500 – 200 - .2(4,500)) = 660 + .8(3,400) = 660 + 2,720 = 3,380
e. Leakages = S + T = 20 + 1100 = 1120. Injections = I + G + NX = 500 + 500 + 120 = 1,120.
f. Since the multiplier is 2.5, the decline in Ap of 150 means a decline in Ep. Y now exceeds Ep and
there is unintended inventory accumulation. Firms lay off workers and Y declines. Ep declines as
well but at a slower rate. Eventually, equilibrium is re-attained at a lower Y.
g. Equilibrium income decreases by 375 from 4,500 to 4,125.
5. a. The marginal propensity to save equals 1 – c = 1 – 0.5 = 0.5. The multiplier, k, equals the inverse of
the marginal propensity to save = 1/0.5 = 2.
b. The equation for autonomous planned spending, Ap, equals Ca – cT + Ip + G + NX = 1,400 –
15r – 0.5(1,600) + 2,350 – 35r + 1,940 – 200 = 4,690 – 50r.
c. The equation for the IS curve equals Y = 2(4,690 – 50r) = 9,380 – 100r.
d. At an interest rate of 0, the equilibrium level of income equals 9,380. At an interest rate of 3, the
equilibrium level of income equals 9,380 – 100(3) = 9,080. At an interest rate of 6, the equilibrium
level of income equals 9,380 – 100(6) = 8,780.
e. The slope of the IS curve, r/Y, equals (2 – 0)/(9,180 – 9,380) = (4 – 2)/(9,180 – 8,980) =
2/(–200) = –0.01.
f. A rise in consumer confidence causes a rise in consumption expenditures. The new equation for
autonomous planned spending equals 1,440 – 15r – 0.5(1,600) + 2,350 – 35r + 1,940 – 200
= 4,730 – 50r. The new equation for the IS curve equals 2(4,730 – 60r) = 9,460 – 100r.
g. At an interest rate of 0, the equilibrium level of income equals 9,460. At an interest rate of 3, the
equilibrium level of income equals 9,460 – 100(3) = 9,160. At an interest rate of 6, the equilibrium
level of income equals 9,460 – 100(6) = 8,860.
h. Since equilibrium income increases at each of the three interest rates, the IS curve shifted to the
right when autonomous consumption rises. The horizontal shift of the IS curve equals the change in
equilibrium income at a given interest rate (80), and since the change in equilibrium income equals
the multiplier times the change in autonomous planned spending, the horizontal shift of the IS
curve equals the multiplier times the change in autonomous planned spending (2 times 40).
6. a. The new value of marginal propensity to save equals 1 – 0.6 = 0.4. The new multiplier, k, equals the
inverse of the new marginal propensity to save = 1/0.4 = 2.5.
b. The equation for the new autonomous planned spending equals 1,400 – 15r – 0.6(1,600) +
2,350 – 35r + 1,940 – 200 = 4,530 – 50r.
c. The equation for the new IS curve equals Y = 2.5(4,530 – 50r) = 11,325 – 125r.
d. At an interest rate of 0, the equilibrium level of income equals 11,325. At an interest rate of 3 the
equilibrium level of income equals 11,325 – 125(3) = 10,950. At an interest rate of 6, the
equilibrium level of income equals 11,325 – 125(4) = 10,575.
e. The slope of the new IS curve equals r/Y = (2 – 0)/(11,075 – 11.325) = (4 – 2)/
(10,825 – 11,075) = 2/(–250) = –0.008.
f. The equation for the new autonomous planned spending equals, 1,400 – 15r – 0.6(1,600) +
2,350 – 45r + 1,940 – 200 = 4,530 – 60r.
g. The equation for the new IS curve equals Y = 2.5(4,530 – 60r) = 11,325 – 150r.
©2012 Pearson Education, Inc. Publishing as Addison Wesley
Answers to Problems in Textbook
31
h. At an interest rate of 0, the equilibrium level of income equals 11,325. At an interest rate of 3, the
equilibrium level of income equals 11,325 – 150(3) = 10,875. At an interest rate of 6, the
equilibrium level of income equals 11,325 – 150(6) = 10,425.
i. The slope of the new IS curve equals r/Y = (2 – 0)/(11,025 – 11,325) = (4 – 2)/
(10,725 – 11,025) = 2/(–300) = –0.0067.
j. As the multiplier increases from 2 to 2.5, the IS curve becomes flatter as the slope decreases from –
0.01 to –0.008 and the decrease in income for a two percentage point rise in the interest rate
increases from 200 billion to 250 billion. Similarly, the IS curve becomes flatter as the
responsiveness of planned spending to the interest rate increases from a 50 billion to a 60 billion
dollar decrease in autonomous planned spending for every one percentage point rise in the interest
rate.
7. a. The marginal propensity to save equals 1 – 0.85 = 0.15. The marginal leakage rate equals
0.15(1 – 0.2) + 0.2 + 0.08 = 0.4. The multiplier, k, equals the inverse of the marginal leakage
rate = 1/0.4 = 2.5.
b. The equation for autonomous planned spending, Ap, equals Ca – cTa + Ip + G + NXa = 225 –
10r – 0.85(100) + 1,610 – 30r + 1,650 + 700 = 4,100 – 40r.
c. The equation for the IS curve equals Y = 2.5(4,100 – 40r) = 10,250 – 100r.
d. At an interest rate of 3, the equilibrium level of income equals 9,950.
e. Taxes at the equilibrium level of income equal 100 + 0.2(9,950) = 2,090.
Consumption at the equilibrium level of income, given r = 3, equals 225 – 10(3) + 0.85(9,950 –
2,090) = 6,876. So saving equals 9,950 – 2,090 – 6,876 = 984. So leakages equal 984 + 2,090 =
3,074. Injections equal investment plus government plus net exports = 1,610 – 30(3) + 1,650 + 700
– 0.08(9,950) = 3,074. So both leakages and injections equal 3,074.
©2012 Pearson Education, Inc. Publishing as Addison Wesley