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CHAPTER 10
Economic Growth and Business Cycles
TEACHING OBJECTIVES
Goals of Part 3: Macroeconomics
A. Introduce the basic ideas behind economic growth and business cycles (Chapter 10), methods
of modeling the use of money (Chapter 11), the standard workhorse macroeconomic model of
aggregate demand and aggregate supply (Chapter 12), modern macroeconomic models
(Chapter 13), and the interdependence between economies of different countries (Chapter 14).
B. Why so much macroeconomics in a textbook on money and banking? Because to understand
monetary policy, students need to understand basic macroeconomic theory.
Goals of Chapter 10
A. Analyze both long-run and short-run movements of the economy’s output.
B. Look at trend output growth, focusing on productivity and increases in capital and labor as the
variables that contribute most to the economy’s overall growth.
C. Study the business cycle to analyze how the economy is deviating from its long-run path.
D. Show how the economy’s growth rate affects a worker’s future income.
TEACHING NOTES
A. Introduction
1. We split the economy into two parts:
a) Long-run trend growth of output
b) Fluctuations of output around its long-run trend; the business cycle
2. Long-run trend output growth originates in growth of productivity, capital, and labor
3. Short-run fluctuations in output include expansions and recessions (Figure 10.1)
B. Measuring Economic Growth
1. Introduction
a) What causes economic growth?
b) The trend in output has changed over time (Figure 10.2)
c) The key variables affecting output are resources (labor and capital) and productivity
d) Poor measures of capital lead us to investigate productivity it two ways: with good data
on labor productivity and with flawed data on overall productivity
2. A View of Economic Growth Based on Labor Data
a) The growth of labor in the economy can be measured by looking at the number of
workers and the number of hours they work
b) The supply of labor
(1) Labor force = employed people + unemployed people
(2) Labor-force participation rate = labor force ÷ working-age population (Figure
10.3)
c) The demand for labor determines employment

Chapter 10: Economic Growth and Business Cycles 106
d) Population is split into working-age population and others (too young, in military, in
institutions); working-age population = labor force + not in labor force; labor force =
employed + unemployed (Figure 10.4); unemployment rate = unemployed ÷ labor
force (Figure 10.5)
e) Labor productivity = output ÷ number of hours worked (Figures 10.6 and 10.7)
f) Output growth = labor productivity growth + growth in hours worked
g) Economic Liftoff is the period from 1950 to 1970; Reorganization is the period from
1971 to 1982; Long Boom is the period from 1983 to 2007 (Table 10.1; Figure 10.8);
what will be the effect of the financial crisis of 2008? Use Data Bank: Why Is the
Economy More Stable in the Long Boom?
3. A View of Economic Growth Using Data on Both Labor and Capital
a) Economy’s production function: production mainly depends on capital and labor:
Y =F(K,L) (3)
b) A specific production function fits the data well:
Y =A × Ka
× L1−a
(4)
(1) The term A is a measure of the economy’s total factor productivity, TFP
(2) The growth-rate form of equation (4) shows how TFP growth contributes to
output growth:
%ΔY = %ΔA + (a × %ΔK) + [(1 − a) × %ΔL]
Output growth = TFP growth + [a × growth rate of capital] (5)
+ [(1 – a) × growth rate of labor]
(3) TFP growth is calculated using equation (5):
%ΔA = %ΔY − [a × %ΔK] − [(1 – a) × %ΔL] (6)
(3) It is vital to remember that the data on capital are questionable, so calculations of
TFP may be far from accurate
c) Table 10.2 shows the breakdown of growth in the three periods (Economic Liftoff,
Reorganization, and Long Boom); TFP growth changes over those periods in a similar
way to growth in labor productivity
C. Data Bank: Why Is the Economy More Stable in the Long Boom?
1. Research by Stock and Watson suggests that the economy became more stable at the start
of the Long Boom (Figure 10.A)
2. Better monetary policy is responsible for just a fraction of the increased stability; the rest
may be just good luck
D. Business Cycles
1. What Is a Business Cycle?
a) A business cycle is the short-term movement of output and other key economic
variables (such as income and employment) around their long-term trends; use Figure
10.9 to illustrate a hypothetical business cycle
b) Define economic expansion and peak, recession and depression, and trough
c) The NBER’s business cycle dating committee determines when recessions and
expansions begin and end (Figure 10.9 and Table 10.3)
d) A business cycle has two main characteristics (Figure 10.10):

(1) Many economic variables move together
(2) Many economic variables deviate from their long-term growth trends for
substantial periods
2. The Causes of Business Cycles
a) Erratic growth of the money supply
(1) Monetarists make this argument
(2) In support of their argument: large declines in the money supply in the Great
Depression
(3) Other researchers disagree: money should affect prices and inflation more than real
variables, and statistical models do not confirm money’s role
b) Swings of optimism and pessimism that cause business investment in capital goods to
fluctuate
(1) Some Keynesian economists support this view as the main cause of business cycles
(2) But explaining the optimism or pessimism is difficult
(3) Keynesians argue that shifts in aggregate demand occur, causing the economy to
deviate from equilibrium, thanks to sticky wages and prices that do not restore
equilibrium immediately
(4) Skeptics argue that wage and price stickiness seem unlikely to be the main source of
recessions
c) Sudden changes in productivity growth
(1) TFP fluctuations lead to output fluctuations, according the real business cycle
(RBC) theory
(2) Skeptics argue that RBC theory does not account for the intensity with which firms
use their workers, so the RBC researchers measure TFP fluctuations badly
(3) Adherents of monetarism and RBC theories are called classical economists
d) Changes in the prices of key factors of production, such as oil
(1) Hamilton argues that nearly every recession was preceded by a significant rise in oil
prices
(2) But oil is not significant enough in the economy to cause such a dramatic effect
e) If none of these theories are completely valid, what causes business cycles?
(1) Perhaps all the theories together have some validity
(2) It may take several of the factors together to cause a recession
(3) Refer to Data Bank: The Anxious Index
E. Application to Everyday Life: How Does Economic Growth Affect Your Future Income?
1. A comparison of labor productivity and workers’ compensation shows a close
relationship in the Economic Liftoff period, but little relationship in the Long Boom; see
Table 10.4
2. However, the level of compensation per hour of work was much higher in the long boom
period, thanks to earlier growth
F. Data Bank: The Anxious Index
1. The anxious index is the probability of a decline in real GDP in the next quarter, as
measured by the Survey of Professional Forecasters.
2. The index tends to rise just before recessions begin, especially when the index exceeds 20
percent (Figure 10.B)

ADDITIONAL ISSUES FOR CLASSROOM DISCUSSION
1. Take a poll of your students’ expectations for major macroeconomic variables and the
probability of a decline in real GDP for the next quarter. Compare their results to the Survey of
Professional Forecasters (on the Internet at: http://www.phil.frb.org/econ/spf/index.html).
2. Over the last 10 years, the labor force participation rate has trended down significantly, as
Figure 10.3 shows. Discuss the difficulty of determining trends at the end of a sample of data,
when no one knows what will happen to the variable next. For example, note the slight
downward trend in the early 1960s, which was only temporary.
3. Discuss why we need a committee to determine when business cycles begin and end. Even
looking at just the data in this chapter, not all variables change direction at the official peaks
and troughs of the cycle. You can look at the NBER’s web site (www.nber.org) to see some of
the current discussion about the state of the business cycle by the business cycle dating
committee.
ANSWERS TO TEXTBOOK NUMERICAL
EXERCISES AND ANALYTICAL PROBLEMS
Numerical Exercises
11. a. Working-age population ÷ population = 83/127 = 0.654 = 65.4 percent
b. Labor force = working-age population − number of people not in labor force = 83 − 25 =
58
Labor-force participation rate = labor force ÷ working-age population = 58/83 = 0.699 =
69.9 percent
c. Number of unemployed = labor force − employed = 58 − 52 = 6
Unemployment rate = number unemployed/labor force = 6/58 = 0.103 = 10.3 percent
12. a. Growth of output between;
1959 and 1969 =
2900 1864
1864
−
= 0.556 = 55.6%
1969 and 1979 =
4173 2900
2900
−
= 0.439 = 43.9%
1979 and 1989 =
5710 4173
4173
−
= 0.368 = 36.8%
1989 and 1999 =
8251 5710
5710
−
= 0.445 = 44.5%
1999 and 2009 =
9563 8251
8251
−
= 0.159 = 15.9%

Growth of hours worked between;
1959 and 1969 =
58.88 49.15
49.15
−
= 0.198 = 19.8%
1969 and 1979 =
70.16 58.88
58.88
−
= 0.192 = 19.2%
1979 and 1989 =
83.14 70.16
70.16
−
= 0.185 = 18.5%
1989 and 1999 =
97.63 83.14
83.14
−
= 0.174 = 17.4%
1999 and 2009 =
88.36 97.63
97.63
−
= ˗0.095 = ˗ 9.5%
b. %∆ output = %∆ labor productivity + %∆ hours worked
Therefore, %∆ labor productivity = %∆ output %∆ hours worked
Therefore, 1959 to 1969 = 55.6% ˗ 19.8% = 35.8%
1969 to 1979 = 43.9% ˗ 19.2% = 24.7%
1979 to 1989 = 36.8% ˗ 18.5% = 18.3%
1989 to 1999 = 44.5% ˗ 17.4% = 27.1%
1999 to 2009 = 15.9% ˗ (˗ 9.5%) = 25.4%
c. Fastest growth in output is recorded in the 1960s, and the slowest growth in output is
recorded in the 2000s. The growth in output per hour worked is fastest in the 1960s and
slowest in the 1980s. The slow growth in output in the 2000s can be attributed to the
financial crisis of 2008 and the Great Recession. The fastest growth in output, recorded in
the 1960s, can be attributed to the Economic Liftoff.
13. From equation (4): Y = A × Ka
× L1−a
, so A = Y/( K 0.2
× L0.8
)
For 2013: A = Y/(K0.2
× L0.8
) = 10,000/(4500.2
× 5,0000.8
) = 3.2373
For 2014: A = Y/(K0.2
× L0.8
) = 10,300/(4800.2
× 5,0500.8
) = 3.2655
%ΔA = (3.2655 – 3.2373)/3.2373 = 0.87%.
14. We use the equation %ΔA = %ΔY − (a × %ΔK) − [(1 − a) × %ΔL].
In Bigcap, a = 0.3, %ΔK = 10%, %ΔL = 1%, %ΔY = 5%, so
%ΔA = %ΔY − (a × %ΔK) − [(1 − a) × %ΔL]
= 5% − (0.3 × 10%) − [(1 − 0.3) × 1%]
= 5% − 3% − 0.7%

= 1.3%.
TFP is growing fast because of much capital growth.
In Smallcap, a = 0.1, %ΔK = 3%, %ΔL = 2%, %ΔY = 4%, so
%ΔA = %ΔY − (a × %ΔK) − [(1 − a) × %ΔL]
= 4% − (0.1 × 3%) − [(1 − 0.1) × 2%]
= 4% − 0.3% − 1.8%
= 1.9%.
This economy is growing slower than Bigcap’s because capital and labor are growing more
slowly, but fast TFP growth helps economic growth.
15. If you retire at age seventy, you will have worked for forty-nine years. If your salary increases 5
percent per year, you will earn $30,000 × 1.0549
= $327,640. If your salary increases 3 percent
per year, you will earn $30,000 × 1.0349
= $127,687. This is a huge difference, which shows that
growth rates matter!
Analytical Problems
16. Per-capita growth (growth rate of output per person) matters for well-being; per-capita growth
rate = output growth rate − growth rate of population.
Country A: per-capita growth rate = 6% − 4% = 2%
Country B: per-capita growth rate = 4% − 1% = 3%
Thus, people in country B are better off because their output per person is rising faster.
17. In economic expansions:
a. Output per hour rises because labor productivity rises.
b. Hours worked per worker rises because overtime work increases.
c. Employment as a fraction of the labor force increases because more people are employed.
d. The labor force as a fraction of the population increases because people re-enter the labor
force when wages increase and jobs are plentiful.
All four of these factors cause output to grow more rapidly in expansions.
ADDITIONAL TEACHING NOTES
What Causes Productivity to Change?
Changes in productivity growth cause changes in trend output growth, so investigating the forces
driving productivity growth will help us understand the sources of output growth. In the case of

labor productivity, we are interested in the amount of output produced by an hour of work. Thus,
anything that allows workers to produce more per hour, increases labor productivity. An increase
in capital is one reason workers could be more productive; if workers have more or better tools to
use they can produce more output per hour of work. Keep in mind that tools need not be physical.
Education and knowledge contribute to output as well. Smarter, better-trained, and more
experienced workers typically produce much more output in a given amount of time than novices
can. That is why, after all, people in a given job are usually paid more if they have more education
and experience. Economists call a person’s knowledge and experience human capital.
Finally, it is not just physical capital and human capital that increase labor productivity, but also
how work is organized. Producers, who can improve production methods, as Henry Ford did
when he manufactured cars using the assembly line, increase the productivity of their workers.
When other firms copy these techniques, the productivity of the entire economy increases.
In the mid-1990s, it appeared that productivity growth increased substantially in the U.S. economy.
Was there some revolutionary new invention, an increase in education, or an increase in capital that
caused this change? The answer is that all three were responsible for the observed productivity
growth, at least according to some economists who have studied the question. These economists
attribute the increase in productivity that began in the mid-1990s to the improved quality of capital
in the form of computers and software, combined with a more efficient means of employing
computers and software, along with training and experience of the workforce in using these new
tools.
We can conclude that changes in productivity drive changes in economic growth. The growth of
productivity has changed over the last fifty years, with more rapid growth in the economic liftoff
and the long boom than in the reorganization. But, is there any way to determine why productivity
growth changes over time? What economic forces lead to such changes? To answer those
questions, we need a model of economic growth, which we introduce next.
A Simple Model of Economic Growth
Economists have studied economic growth and its causes for many years. In 1958, Nobel laureate
Robert Solow proposed a simple way to identify some of the factors that cause the economy to
grow. His model has been modified and updated over the past forty-five years, but the basic idea of
the model remains clear and convincing. Output depends on the amount of capital and labor, and
businesses can only buy new capital if they can borrow from people who save.
Output in the Solow model is produced with capital and labor according to the production
function that we used earlier in equation
Yt = F(Kt, Lt), (7)
where we have added the subscripts t to indicate that the equation shows the relationship between
capital, labor, and output at a date t . The model is one that accounts for the movements of output,
capital, and labor over time, so the subscript is needed to keep track of the values of the variables
at different dates.

We make some assumptions that make the model easy to understand. We assume that the
production function is one for which an increase in both capital and labor in equal proportions
causes output to increase in the same proportion. This assumption allows us to simplify the model
by writing output and capital in terms of amounts per person. We can then rewrite the production
function as
yt = f(kt), (8)
and where f is the production function relating capital per person to output per person. We assume
that this production function has some standard properties, namely that as the ratio of capital to
labor (k) increases, the ratio of output to labor (y) also increases, but by decreasing amounts.
Our next task is to figure out what determines the amount of capital per person. To do this, we use
the assumption that businesses can only buy new capital if someone saves. For example, a small
business firm’s owners might save and buy new capital, a corporation could retain some of its
earnings, or a firm could borrow funds from a bank, which is transferring those funds from a
number of individual savers who have deposited their savings in the bank. So, if we make some
assumptions about the amount of savings in the economy, we can learn how much new capital
firms will purchase, which is investment. The amount of capital in the economy is its capital stock. The
capital stock changes over time for two reasons: firms invest and existing capital depreciates. We
assume that a certain percentage of the existing capital stock depreciates every period, an amount
equal to d × Kt ; for example, if capital depreciates 15 percent every year, then d = 0.15. We thus
represent the change of the capital stock over time with the equation
K t +1 = Kt − (d × K t ) + I t , (9)
where I represents investment.
If the amount of labor is growing at the rate g; that is, L t +1 = (1+ g)L t , then, in the steady state,
capital must grow at the same rate, so Kt +1 = (1+ g)Kt . Using this in equation (9), we can
perform some algebraic manipulations to find a relationship between investment per worker and
capital per worker in the steady state. Begin with equation (9):
K t +1 = Kt − (d × Kt ) + It .
Now substitute for K t +1 using the equation K t +1 = (1+ g)K t , and collect terms in K t :
K t +1 = K t − (d × Kt ) + I t
(1+ g)K t = K t − (d × K t ) + I t
(1 + g) K t = ( 1 − d ) K t + I t

[( 1 + g ) − ( 1 − d )] K t = I t
( g + d ) K t = I t .
Now, if we switch around the two sides of the equation, then divide both sides by L t , and use the
definitions that y = Y/L and i = I/L, then we have
(10)
We make one more assumption, which is that in the long run the economy will reach a steady state,
a situation where capital, labor, and output are growing at the same rate. This means that many of
the variables that we have defined, namely those in lowercase letters that represent output per
worker, capital per worker, and investment per worker, will not change over time, so we can drop
the time subscripts in equations (8) and (10). The main equations of the model are now
y = f(k) (11)
and
i = (g + d )k . (12)
The last equation means that to keep the capital stock growing at the rate that would maintain a
constant ratio of capital to labor, investment per worker (i) must equal the growth rate of the
population plus the depreciation rate on capital times the amount of capital per worker. The first
amount (the population growth rate) reflects the investment needed to make the capital stock
increase at the same rate as population growth. The second amount (the depreciation rate)
represents the amount of investment needed to replace machinery and equipment that has worn
out.
For investment to occur, however, people must save. We will make the same assumption that
Solow did, namely, that savings per person (s) is a constant fraction (v) of output per person. That
is,
s = v × y. (13)
In this equation, v is the fraction of income that people save, and we assume it is constant over
time.
Now, if we set savings per person equal to investment per person, so s = i using equations (11) and
(12), we get

s = i
v × y = ( g + d )k .
Dividing through both sides of this equation by v gives
(14)
So, for savings to equal investment, output per person must equal a constant times the
amount of capital per person. Equations (11) and (14) now give us two equations relating y and k,
which we can use to solve for their values.
In this model, the equilibrium values of y and k depend on the growth rate of labor ( g ), the
depreciation rate ( d ), and the savings rate ( v ). A higher value of g or d, or a lower value of v ,
would mean that the right-hand side of equation (14) would be higher for any given value of k .
There is some good intuition for these results. Consider two economies that are identical in every
way, except that one has greater population growth than the other. With greater population
growth, it takes more savings to maintain a given ratio of capital to labor. Because savings is a fixed
proportion of output, an economy with greater population growth would have a lower ratio of
capital to labor, and hence a lower ratio of output to labor. Similarly, an economy in which capital
depreciates faster will also have lower k and y in equilibrium.
On the other hand, an economy that has a higher savings rate out of income will invest more, and
in equilibrium will have a higher ratio of capital to labor and output to labor.
Overall, then, the Solow model tells us how the economy responds to changes in the long run to
the savings rate, the depreciation rate, and the population growth rate. Thus, the model has
identified some of the important factors that affect growth and zeroes in on certain variables (such
as the savings rate and the depreciation rate) that might not have been obvious otherwise. But, the
Solow model is not very good at explaining the growth of total factor productivity—in fact, it
assumes there is no such growth. The model only explains the growth in labor productivity that
arises because of additional capital relative to labor.
Models with Total Factor Productivity Growth
A major shortcoming of the Solow model is that although the economy grows, it does so (in the
long run) at the rate of population growth, because in the steady state the ratio of output to labor is
constant. Are economies doomed to grow no faster or slower than their populations grow?
The answer is no, because of the possibility of total factor productivity growth. Remember that the
Solow model began with equation (7), Y = F(K, L) , where the production function ( F ) remained
the same over time. But technological progress suggests that we should model the production
function as changing over time, so that more output can be produced with the same inputs.

Economists have modeled total factor productivity growth in a variety of ways. One method, the
most popular, is to assume that total factor productivity growth occurs over time because of
improved technology. The ratios of capital to labor and output to labor would rise over time, so
total productivity rises over time. In this model, however, the rise in TFP is not explained within
the model. When a variable in a model is not explained within the model, that variable is exogenous,
so in this model, TFP is exogenous.
A variable that is determined within a model is endogenous. An alternative model, called an endogenous-
growth model, seeks to explain how total factor productivity grows, rather than simply assuming that
it does so exogenously. Productivity does not just materialize from nothing, but results from
investments that people and companies make in new technology, through research and
development. It results from knowledge and creative endeavors. It comes about because people,
firms, and governments spend resources exploring the unknown. Endogenous-growth models try
to explain some of the possible avenues through which productivity growth occurs. They also
examine the consequences for such growth on the economy.
One prediction of endogenous-growth models is that the world’s leader in technology may grow
faster than other countries. Economists have struggled to explain why countries with similar
characteristics (growth rate of labor, depreciation rate, and savings rate) grow at different rates. For
that reason, economists sometimes model how technology is adopted in different countries.
Countries that are better able to develop new technologies get an initial burst in their growth, while
those that follow are slower to grow. These models also explain why some countries continue to
grow faster than others do; whereas the Solow model suggests that countries with low incomes will
grow faster than countries with high incomes so that incomes in all countries will converge.
Because technological knowledge spreads across countries, many of the models that economists
have recently developed to study growth incorporate trade across countries. These models have
developed some interesting insights in terms of the tradeoff between different factors of
production. For example, rapid growth in Asian countries such as Singapore and Indonesia
occurred in the 1980s and 1990s in large part because they were better able to harness new
technologies and develop them for use in consumer and business products. In addition, they
invested a huge amount in physical capital. The result was economic growth that far exceeded the
growth rates of the major industrialized countries, enabling the Asian countries to catch up
substantially in terms of income.
The financial system plays a key role in aiding economic growth. As the Solow model assumed,
firms cannot invest (buy new capital) unless people save. The more efficient the financial system is,
the more funds will be available for investment, and the faster the economy will grow. So, not only
must a society save, but it must also have an efficient means of transferring those savings to
business firms so that they can purchase new capital. A society that does so will grow and prosper.
ADDITIONAL QUESTIONS
1. Suppose the labor force is growing at a rate of 2 percent (so λ = 0.02), capital depreciates at a
rate of 13 percent per year (δ = 0.13), and the savings rate is 10 percent (σ = 0.10). The
production function in terms of output per worker is y = 7.5 k − 0.5 k2
. Calculate the steady-

state values of capital per worker and output per worker. If the savings rate were only 5
percent, what would be the steady-state values of capital and output per worker?
2. According to the Solow model, which economy will grow faster in steady state, one with a high
savings rate or one with a low savings rate? Which economy will have a higher output per
worker in the steady state? Assume both economies have the same population growth rate of
workers and the same depreciation rate. Explain your answer using a diagram.
REFERENCES
Solow, Robert. “A Contribution to the Theory of Economic Growth,” Quarterly Journal of Economics,
February 1956, pp. 65-94.
Symposium on New Growth Theory, Journal of Economic Perspectives 8, (Winter 1994),
pp. 3-72.

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