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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
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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):
Chapter 10: Economic Growth and Business Cycles 107
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(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)
Chapter 10: Economic Growth and Business Cycles 108
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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%
Chapter 10: Economic Growth and Business Cycles 109
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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%
Chapter 10: Economic Growth and Business Cycles 110
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= 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
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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.
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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
Chapter 10: Economic Growth and Business Cycles 113
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[( 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
Chapter 10: Economic Growth and Business Cycles 114
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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.
Chapter 10: Economic Growth and Business Cycles 115
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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-
Chapter 10: Economic Growth and Business Cycles 116
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a license distributed with a certain product or service or otherwise on a password-protected website for classroom use
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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closed his lips and made no response.
But a little later, while John Hubbard was at luncheon and he was
left alone in the office, he proceeded to examine some of these
criticized accounts, and was almost paralyzed upon discovering how
his books appeared to compromise him.
There were evidences that some one had been critically examining
them, for there were frequent marginal notes, while the balance
seemed to show that he had been cleverly and systematically
robbing his employer for a long time.
With a very white face and sternly compressed lips, Gerald took a
powerful magnifying-glass and brought it to bear along the various
columns of figures.
“I thought so!” he hoarsely muttered, at last, “they have been
tampered with! Some of my threes and sixes have been changed to
eights; my ones, in numberless instances, have been made into
twos, fours, and sevens, but so skilfully that no one would believe
me if I should assert it—I could never prove that he did it. Great
Heaven! and it has been going on for many months. This was what
he had in mind when he crushed my rose and warned me to beware
of a similar fate.”
Gerald was sick at heart as he realized that he was standing upon
the brink of a fearful precipice and was powerless to help himself—
how he had become entangled in a skilfully contrived net from which
there seemed to be no possible way of escape.
If Mr. Brewster had been well he would have appealed at once to
him, stated his suspicions, and tried to point out the changes he had
discovered in the figures, but in the man’s present precarious
condition he dared not trouble him with the matter, even if he were
allowed an interview with him.
A week passed, and then, to his great joy, he received a note from
Mr. Brewster asking him to call upon him at a certain hour the
following Saturday, as he had a special commission for him.
He presented himself at the Brewster mansion promptly at the hour
mentioned in the note, and was at once conducted to his employer’s
presence.
He was greatly shocked at the change in the man—not having seen
him since his attack—for he had grown very thin, and seemed to
have aged many years. Mr. Brewster greeted him very kindly, and
seemed heartily glad to see him, but almost immediately broached
the business concerning which he had desired to see him.
“Gerald, I have a secret commission with which I wish to entrust
you,” he began, a grave look settling over his face. “I know that I
can trust you absolutely, and that is why I have chosen you in
preference to any one else.”
“Thank you, sir,” Gerald replied, with a glowing face, his sorely
wounded heart greatly comforted by this assurance.
“You have been inside the bank vault?”
“Yes, sir, often; you have frequently sent me to the drawer which
contains your private documents.”
“Yes—yes, I know, and —— But before I go on I want you to give
me your word of honor that no one shall ever learn from you the
secret I am about to commit to you,” said the banker.
“Certainly, sir, I will promise that I will never betray any confidence
that you repose in me,” Gerald responded.
“That is enough,” he said. “Now, behind that drawer, which contains
those private papers, there is a small, secret vault, which I had built
there to store certain valuables during my absence from town. No
one save the man who made it, and I, know that it is there; no one
would suspect it, for, on removing the drawer, there seems to be
nothing but the brick wall behind it. On the contrary, there is an iron
plate, or panel, painted to resemble bricks. At the bottom of this
panel there is a small slot. You will insert in this a tiny key which I
shall give you; turn it half-around, and the panel will spring outward.
You can then swing it upward, when you will discover behind it two
boxes, take them out, being careful to relock the panel, and bring
them to me.”
“Yes, sir; I shall be very glad to do as you wish,” Gerald remarked.
“But how will I be able to get into the vault and remove the boxes
without the knowledge of others?”
“I have keys that will admit you to it, and you must go to the bank
when no one else is there,” said the banker, with a slight frown, as if
he did not exactly relish this part of the commission. “To-morrow will
be Sunday, and you had best go as soon after you have had your
breakfast as you can; then come directly to me. Be careful not to
excite the suspicion of any one whom you may meet, for one of the
boxes contains valuable jewels that belonged to Mrs. Brewster. I
want them for Allison; the other holds nothing of special value to
any one except myself.”
Mr. Brewster had become very white during this last statement, and
Gerald feared he was talking too much for his strength.
“Here are my keys,” he continued, after a moment, and, taking a
bunch from a drawer in the table beside him, “this one unlocks the
outer door, this the inner; the brass one opens the gate of the iron
fence; the heavy one will admit you to the vault; this unlocks my
private drawer, and the little, flat one the panel that conceals the
secret vault. Quite a lesson to learn, isn’t it?” he added, with a slight
smile; “but I think you will have no difficulty in remembering how to
use them.”
“No, sir; four of them I know already, so that leaves only those
belonging to your drawer and the secret vault to be distinguished,
and that is easily done,” Gerald replied, as he examined each key
attentively.
“Very well, then, I shall look for you here again some time to-
morrow forenoon. I want to get those boxes into my possession as
soon as possible,” Mr. Brewster observed, with a faint but impatient
sigh.
“I will try to be here some time between ten and eleven o’clock,”
Gerald returned, then added, losing some of his color: “And now, Mr.
Brewster, if you are not too tired, I have something to tell you about
my work.”
“I am not too tired, go ahead,” said the man; whereupon Gerald
gave him a brief account of the conversation that had recently
passed between himself and John Hubbard, and what he had
discovered afterward in connection with his work.
Mr. Brewster listened to him with growing astonishment, never once
removing his eyes from the young man’s face during his recital.
“These are very strange statements, Gerald—very grave statements,”
he remarked, with some sternness, as he concluded.
“They are, indeed, sir, and they involve my honor, my reputation,
and, unless my past dealings with you and my assurance are
sufficient guarantee to you of my integrity, the evidence is there to
prove that I have been doing very crooked business in your office.
The balances are all right, apparently, but the entries, if examined,
would seem to be conclusive testimony that I have been
systematically robbing you. Mr. Brewster, I firmly believe that those
figures have been skilfully changed for the sole purpose of ruining
me.”
“By whom?”
“That, of course, I cannot say positively, but I have long known that
Mr. Hubbard dislikes me,” was the somewhat reluctant reply.
“Do you mean to imply that John Hubbard would doctor the
accounts to injure you?” exclaimed Mr. Brewster, with a start.
“I have no right to assert that he would, for I cannot prove it; but
some one has done it, and he is the only one who, to my
knowledge, has had access to the books. I can only say I know he
hates me, and—I also say, Mr. Brewster”—and the honest fellow
here straightened himself with conscious integrity, and lifted an
unfaltering look to his employer—“that I have never made a false
entry upon one of your books.”
Neither was conscious of the presence of a third person in the room
as the banker heartily responded:
“I am sure you have not, Gerald; I would stake my fortune upon
your integrity and upon your unswerving faithfulness to my interests.
I will look into this matter just as soon as I am able. Ah! Allison, I
did not hear you come in. What is it, dear?” he concluded, turning,
as he caught the sound of her step behind him.
She came forward, blushing and smiling a welcome to Gerald.
“It is time for your beef broth, papa,” she said, as she placed a small
salver containing a cup before him.
Then she turned to our hero with outstretched hand.
“What an age it is since I saw you last, Gerald,” she remarked, and
then flushed again as she recalled her last interview with him.
He returned her greeting with what warmth he dared in Mr.
Brewster’s presence, but with a hand-clasp that spoke volumes.
CHAPTER V.
THE BANK ON SUNDAY MORNING.
Allison had come into the room where Gerald and her father were
conversing so earnestly just in season to catch the words of
commendation uttered by the latter.
“I am sure you have not, Gerald,” he had said; “I would stake my
fortune upon your integrity and upon your unswerving faithfulness to
my interests.”
She had noted, with the keen perception of a loving heart, the
troubled look in Gerald’s eyes, the anxious expression upon his brow,
and she instantly knew that something had gone amiss with him, in
spite of the fact that he seemed in perfect health, and was
handsomer and more manly than ever.
But in the excitement of greeting him—when she saw his face light
up with joy in her presence, when she felt the warm, lingering clasp
of his hand, and detected the old-time thrill in his voice—she forgot
all about it, for the time, and thought only of the pleasures of this
unexpected meeting.
When Gerald finally left the house it was with a very much lighter
heart than when he entered. His employer’s hearty and unqualified
assurance of confidence was like balm to his wounded spirit; while
his little interview with Allison had set all his pulses vibrating afresh
with his deep and abiding love for her.
He had not seen her for many months, and she seemed to have
grown a hundredfold more lovely than when he had bidden her
adieu on that bright Sunday morning so long ago.
He wondered if she had forgotten the evening previous—their
interview upon the veranda, where, with the moonlight streaming
upon them in its soft effulgence, they had been conscious only of
each other’s presence and the happiness that had thrilled every fiber
of their being. Did she remember their parting when the clock struck
ten? That blissful moment when their lips met in that involuntary
caress? That look into each other’s eyes, that low-breathed “Allison!”
“Gerald!” which had expressed so much?
She seemed a trifle more mature; she had acquired a little air of
dignity which, on the whole, he decided only added to her charms,
although at first it had chilled him slightly—at least, until he found
himself looking down into the expressive eyes.
He hoped he should see her again on the morrow, when he returned
with the boxes which Mr. Brewster had commissioned him to get
from the secret vault.
He smiled and uttered a sigh of content, as he passed his hand over
the pocket which held the keys the banker had given to him, and
realized that he never would have been entrusted with them if he
had not possessed the entire confidence of the man.
He hurried back to his lodging, where, in this happy frame of mind,
he settled down to the preparation of some lessons which were to
be recited that evening to a certain professor with whom he had
been studying for three years.
As we know, Gerald, at the time of his aunt’s death, had been in the
second year of the high school, but for a time after that his studies
were interrupted, as he found that his daily duties taxed his strength
to the utmost.
But as he became accustomed to his work, he began to get hungry
for his books again, and for a while attended evening school,
although his progress was thus necessarily slow.
Then he made the acquaintance of a professor by the name of
Emerson, who, becoming interested in the bright, ambitious lad,
offered to help him perfect his education and arranged for Gerald to
recite three times a week to him.
He was now in his twenty-first year, and expected by the coming
June to complete the studies of the second year of a regular college
course.
After partaking of a light supper, he repaired to the house of his
friend, Professor Emerson, where he acquitted himself most
creditably in his recitations.
The gentleman had become quite fond of his enterprising pupil, and
it was a great delight to him to teach one who was so eager for
knowledge and so quick to comprehend.
“By the way, Gerald, what do you intend to make of yourself when
you get through with your course?” he inquired to-night, as he
closed his book after the last recitation, and bent an inquiring look
on the handsome face before him.
“I think—since I am so well started in the banking business, I shall
stick to it, learn it thoroughly, and, if fortune favors me, perhaps
become a banker myself, by and by,” he replied, but with a smile at
his egotism in aspiring to a position such as Adam Brewster
occupied.
Professor Emerson eyed him curiously for a moment, then remarked:
“You’ll achieve it, if you undertake it, and, rightly conducted, banking
is a good business; still, I wish you might go a little higher,
intellectually—you would make a fine lawyer, your mental grasp is so
keen and accurate.”
“Thank you,” said Gerald, flushing at the compliment, “but it would
take me several years to prepare for the bar, after completing my
college course, and, since I have my own canoe to paddle, I think I
will adhere to what I have begun. I wish, though,” he added gravely,
as his mind suddenly reverted to John Hubbard, “I have time to
become thoroughly posted in law, and could combine the two, for
then I should always be sure of the faithfulness of my legal adviser.”
“Why, Winchester! I did not suppose you possessed so suspicious a
nature!” said his friend, smiling, but with a note of surprise in his
tones. “If every one was governed by such distrust I fear the
lawyers would fare hard.”
“I am not naturally suspicious,” replied Gerald, reddening, “and my
remark must seem narrow and intolerant to you; it was prompted by
the fact that one lawyer whom I know is anything but an honest and
conscientious man.”
“But, ‘one swallow does not make a summer,’ my boy,” retorted his
friend, laughing.
“I know it, sir, and I have no business to be suspicious of all men
because of one man’s failings. I will try to be more charitable toward
lawyers in the future,” said the young man, as he rose to leave.
He felt half-ashamed of having allowed himself to be so swayed by
his antipathy against John Hubbard, but all the way back to his
lodgings he was haunted by the face of the man and the malignant
scowl which had distorted it when he accused him of unfaithfulness
and dishonesty in his work.
Even in his sleep during the night he could not divest himself of the
consciousness of his vicious individuality—he seemed to be
continually pursuing and persecuting him until his visions became so
real that they finally drove him from his bed long before his usual
hour for rising on Sunday morning.
It was not yet dawn when he arose on Sunday morning, and, upon
looking from his window, Gerald saw that it was snowing.
He dressed himself with unusual care, for he hoped to see Allison
again, and, loverlike, desired to make as good an appearance in her
sight as possible. Then he hurried out for his morning meal, after
which he wended his way to the bank, where he arrived about half-
past eight.
The steps leading up to the door were covered with snow, and,
strangely enough, as he mounted them, leaving a footprint upon
every one, an uncomfortable sensation which was akin to guilt,
began to creep over him, causing his errand to become suddenly
repulsive to him, and making him long to go back to his room and
remain there.
But, throwing back his head with an air of conscious rectitude—for
was he not there at his employer’s command?—he quickly let himself
into the building, removing the key and relocking the door on the
inside to make sure that no one would follow him.
Passing through the inner door, he carefully wiped his feet upon the
mat, and removed his overshoes lest they should leave tracks upon
the floor—that same uncanny feeling which he had experienced
outside still pursuing him.
The bank was so still every footfall echoed noisily through it, and
sent a nervous shiver creeping down his spine.
“Good gracious!” he exclaimed, with an impatient shrug of his
shoulders, “I am no thief stealing in here to rob the place! Why on
earth should I feel like one? It is positively absurd!”
Proceeding directly to the vault, he drew the heavy bolts, unlocked
and swung open the massive iron-plated door. The place was cold
and gloomy, and again Gerald shivered with a nervous chill as he
stepped within those solid walls which so securely guarded their
hoarded treasure.
Proceeding directly to Mr. Brewster’s private drawer, the number of
which he had long known, he unlocked and drew it out, setting it
upon the floor.
It contained several packages of papers. But these held no interest
for him; he merely gave them a passing glance, then began to look
for the slot in the iron panel at the back of the aperture.
It required close searching to find it, but his efforts were finally
rewarded, whereupon he inserted the last of his keys, turned it half-
around, when the panel sprang outward, as Mr. Brewster had
described.
It appeared to be swung upon hinges, and, lifting it up, Gerald could
distinguish within the little vault thus disclosed a box of some
description.
He drew it from its place of concealment.
It proved to be a beautiful Japanese affair, inlaid with gold and
mother-of-pearl in an intricate pattern. There was a tiny key in its
lock, and for fear that it might drop out and be lost, Gerald removed
it and transferred it to a pocket in his vest, without once thinking
that he had it in his power to inspect the contents of the casket, if
he chose to do so.
Putting it carefully down upon the floor, he looked for the other. He
found it shoved away back in the secret vault. It was much larger
than the other—a common, though strong, wooden receptacle—and
it was also locked, while there was no key with it.
Gerald felt quite sure that the Japanese casket must contain the
jewels of which Mr. Brewster had spoken, and which were to be
given to Allison. Doubtless they were very valuable, and would be
doubly precious to her because they had once belonged to and been
worn by her mother.
He would probably see them upon her person some day; but,
strange to say, he did not feel half so curious about them as he did
regarding the contents of the larger box, for he had been impressed
by Mr. Brewster’s manner and expression when he had said that it
contained “nothing of special value to any one—except myself.”
However, he felt that it was no business of his what either held; his
duty lay simply in conveying them safely to his employer.
Putting the drawer back in its place, he relocked it, when, gathering
the boxes from the floor, he turned to leave the vault. At that instant
a shadow obscured the light admitted by the open door.
Gerald started forward with a sudden and terrible heart-throb. His
face flushed hotly, then paled to the hue of marble as he was
confronted by John Hubbard, who was standing upon the threshold,
a sardonic grin distorting his sinister countenance.
“Aha! my young burglar,” the man exclaimed, in a tone of fiendish
triumph, “is this the way you are in the habit of spending your
Sundays?”
The sound of the expert’s voice at once restored Gerald’s
composure, although every nerve in his body was tingling with anger
at his manner of addressing him.
“I am no burglar, Mr. Hubbard, and you know it,” he coldly returned.
“I am not in the habit of coming here—I have never been in the
bank on Sunday before this; but——”
“What have you there?” sternly interposed his companion, and
indicating by a gesture the boxes in Gerald’s hands.
“Some things belonging to Mr. Brewster.”
“So I judged. How came you here?”
“By his orders,” the young man briefly replied, and then wondered at
the almost satanic leer which swept over the features of the man
before him.
“Indeed! but how did you pass all these barriers?” with a nod
backward over his shoulder.
“Why, by means of these keys, which Mr. Brewster himself gave to
me, when he asked me to perform this errand for him,” the young
man responded, as he held up the bunch by the ring, and which Mr.
Hubbard instantly recognized as belonging to the banker.
“When did you see Mr. Brewster?” he questioned, a look of
perplexity flashing over his face.
“Yesterday afternoon—he sent for me to go to him,” Gerald
explained.
“H’m!” ejaculated the expert, with a frown. Then, after a moment of
thought, he added: “What is in those boxes?”
Again Gerald flushed. Then he threw back his handsome head
haughtily.
“Excuse me,” he said freezingly, “but that is a question which Mr.
Brewster alone is qualified to answer.”
“Ha! ha!” laughed his companion, but with so weird a note in the
sound, which echoed and re-echoed mockingly through the vault,
that Gerald’s blood almost seemed to congeal in his veins. “You are
very non-committal, my fine fellow,” he continued, with a snarl, “but
do you dare to tell me that you don’t know what either of those
boxes contains?”
“I must decline to discuss the matter with you, Mr. Hubbard,” was
the terse reply.
“Indeed!” sneered his companion. Then he observed, served,
authoritatively, as he went a step nearer Gerald. “Very well, we
won’t discuss it; but since I am Mr. Brewster’s attorney, I will relieve
you of all further care of them. Give them to me.”
“No, sir!” said Gerald resolutely, and retreating from him.
“Give them to me, I tell you!” commanded the man angrily.
“I cannot do that, Mr. Hubbard,” Gerald calmly returned. “Mr.
Brewster requested me to come here for them, and then bring them
directly to him. I shall deliver them to no other hands.”
Once more that strange laugh echoed through the dismal vault.
“You will have to go a long journey to do that, young man,” said
John Hubbard, showing his white teeth in a horrible grin.
“How so?” queried Gerald, in surprise, but with a strange numbness
stealing over him, “I—I do not understand you.”
“Adam Brewster is dead!” said John Hubbard.
CHAPTER VI.
GERALD SUFFERS AN INDIGNITY.
There was a dead silence in that gloomy place for the space of a full
minute after John Hubbard’s terrible announcement.
“It cannot be possible!” Gerald finally gasped, as he staggered back
against the side of the vault, almost paralyzed from horror. As he did
so, the topmost box in his hands slipped from his grasp, and fell with
a crash to the floor.
The lock was either broken or forced from its socket by the
concussion, and the lid flew back, thus disclosing to the curious eyes
of John Hubbard various articles of valuable jewelry.
“Aha! diamonds! pearls! rubies and emeralds!” he exclaimed, as he
stooped to examine them more closely. “Truly, young man, you were
taking time by the forelock to feather your nest before an inventory
could be taken of your employer’s effects.”
“What do you mean, sir?” he exclaimed, starting forward, a
dangerous gleam in his eyes. “Do you dare assert that I knew that
Mr. Brewster was not living, and stole here to rob him?”
“I am forced to admit that it looks very much like it,” was the
deliberate and cruel response.
A terrible shock went quivering through Gerald at these words, for
he realized but too well that the man would do his utmost to injure
him by putting the worst possible construction upon the situation.
“You know better!” he cried, hot indignation and resentment flaming
up within him; “you know I would not touch a penny that did not
belong to me.”
“Ahem! that all sounds very well, my would-be paragon of honor,”
sneered the expert, “but you will have to prove it, you know.”
“Prove it! Why, of course, I can prove it,” replied Gerald, a little smile
of scorn for his recent fear curling his lips, and a consciousness of
rectitude and security supplanting it, “I have Mr. Brewster’s note of
yesterday, asking me to come to him, as he had a special
commission for me, and then the very fact of my having his keys
proves that I am here under orders,” and again he held them up to
his companion’s view.
“H’m! so he wrote you to come to him, did he?” queried John
Hubbard thoughtfully. “Where is the note? I should like to see it.”
Gerald put his hand into his coat-pocket; then suddenly remembered
that he had put on his best suit that morning.
“Ah!” he said, “it is in the pocket of my other coat.”
John Hubbard’s eyes gleamed with a cunning light at this
information.
“Well, you will doubtless need all the proof you can bring to get you
out of this scrape,” he gruffly observed. “Maybe you can produce
such a note, but I doubt it. Did any one see Mr. Brewster give you
those keys?”
Gerald’s heart sank at the question, as he remembered that he and
his employer had been utterly alone throughout their interview,
except for the few minutes that Allison was in the room, and he was
sure she had heard nothing that would prove the truth of what he
had asserted. At least he knew she was not there when the keys
were given to him.
“You have no right to question me like this, or to doubt my word,
and I will have no further conversation with you about the matter,”
he responded, after a moment of thought.
But he was deathly pale as he stooped to recover the box that had
fallen. He found that it was not broken; the lock had only been
forced by the fall. He carefully arranged the jewels which had been
somewhat displaced, although, fortunately, none had been spilled;
then, shutting the box, he relocked it with the key which he took
from his vest-pocket.
John Hubbard watched him warily while he was thus engaged. “I will
take charge of those things,” he sternly observed, as Gerald was
about to replace the key in his pocket.
“Excuse me; but I do not think you will,” the young man coldly
returned.
“I am Mr. Brewster’s attorney, and it will be my duty to settle his
estate; consequently all his property will pass through my hands.
Give me those boxes!” the man concluded authoritatively.
“No, sir. Mr. Brewster authorized me to take them to his house; I
shall do as he ordered, and since you say he is no longer living, give
them to Miss Brewster; he stated that he wanted the jewels for her.”
And he started to leave the vault as he concluded.
“You will do no such thing, you young upstart!” snarled John
Hubbard, at the same time making an agile spring backward out of
the vault, when he swung to the ponderous door almost before
Gerald comprehended his intention.
“Now, you beggarly upstart, I have you just where I want you,” he
cried, in a cruel, exultant tone, and putting his lips to the keyhole, “I
once gave you an object-lesson regarding your fate if you continued
to stand in my way.”
Gerald did not deign to reply to these taunts and presently he knew,
by the closing of the outer door of the bank, that he was alone.
His heart was very heavy, for he began to realize that his case was
desperate. Fate and his evil-minded foe had conspired to so involve
him in a network of compromising circumstances, it seemed likely
that he was destined to be proved a graceless scamp and a daring
robber.
His employer, the only one who had it in his power to exonerate him
from blame and prove his innocence, was dead.
He felt almost sure that John Hubbard intended to bring an officer
there to arrest him, with the evidences of his guilt around him.
With this thought there came the temptation to restore those boxes
to the secret vault from which he had taken them.
Mr. Brewster had said that no one, save himself and the man who
constructed it, knew of its existence. If he should conceal those
jewels and the other box, there would be no evidence, beyond John
Hubbard’s word, to prove that he had attempted to take them from
the bank. His word would be just as good as that of his enemy, upon
whom the burden of proving his own accusations would have to rest.
“But I should have to deny all knowledge of them. I should be
obliged to lie, and that I will not do, even to save my—myself from
prison,” he said to himself, with an air of proud resolution. “No, I will
tell the truth and take my chance; I have Mr. Brewster’s note telling
me to come to him; I have also his keys, and the two taken together
ought to be strong points in my defense.”
Nevertheless, these arguments were small consolation in view of his
unfortunate situation.
Then his thoughts reverted to Mr. Brewster, and hot tears rushed
into his eyes as he realized that the man was lying still in death, and
they would never meet in this life again. He was still weak from the
shock he had experienced upon learning the fact so suddenly, and
he wondered what could have caused the unlooked-for attack.
He had appeared to be very comfortable, and hopeful of soon
getting out again, when he had seen him the previous day, and it
seemed awful to him that he should have been so ruthlessly cut
down, just in the prime of life, and in the height of prosperity.
He was wild with impatience to learn the particulars, and chafed
restively against his confinement in that tomb-like place.
“Poor Allison! It will be a terrible blow to her,” he mused; “she will be
all alone in the world now; but she is fortunate to be left an heiress,
and thus shielded from the hardships of life.”
Alas! he little thought that the fortune which would fall to the girl
was destined to bring upon her dangers and trials from which he
would have shrunk appalled could he have foreseen them.
He sprang to his feet and began to pace the vault restlessly, for a
feeling of faintness and sickness came over him; he also experienced
a difficulty in breathing, as the air in the place began to be vitiated.
Suppose John Hubbard should not return in season to release him
before suffocation overtook him, he thought, a nervous chill creeping
over him; but he discarded it with a bitter smile.
He well knew that the man would not dare to let him die there—that
he was planning for him a worse fate than death, out of a cruel spirit
of revenge, because he had dared to love the girl whom he, for
some strange reason, coveted. He believed that he meant to so
crush and humiliate him that he would never want to seek Allison
Brewster again, or meet the gaze of her pure, clear eyes.
“He shall not do it! by Heaven! he shall not succeed in his atrocious
designs!” he cried out, in a sudden anguish, as those torturing
thoughts flitted through his brain. “I am an honest man, and I swear
I will yet prove it to the world, in spite of the worst that he can do.”
A little later he heard the outer door of the bank open and close
again, then the sound of steps and voices drawing near him, until
presently, the bolt which fastened the door of the vault was shot
back, and the next moment John Hubbard, accompanied by a
policeman, stood in his presence.
“Here, Mr. Officer, is your prisoner, and that,” pointing to the two
boxes upon the floor, “is the booty with which he was about to make
off when I caught him,” the man explained, as he shot a look of
malignant triumph at his victim.
“Humph!” ejaculated the officer, as he darted a comprehensive
glance around the place, and at the same time taking the measure
of Gerald.
“It is very fortunate that I happen here just as I did,” Mr. Hubbard
went on. “I seldom come to the bank on Sunday, but there were
some papers here which I was obliged to have to-day, and thus I
came upon him in the midst of his depredations.”
“H’m! you look rather young and green to be a bank-robber,” the
policeman remarked, not unkindly, as he searched the pale,
handsome face of his prisoner; “you don’t seem like the sort, either,
that would be up to such business.”
“I am no bank-robber,” said Gerald, with quiet dignity, and meeting
the man’s searching look unflinchingly, “I am here under orders.”
“Whose orders?”
“My employer’s, Mr. Brewster’s,” and Gerald proceeded to give him a
brief account of the facts of the case, though he said nothing about
the secret vault.
“That sounds all straight and right,” said the policeman, as he
gravely turned to Mr. Hubbard.
“Yes; he tells a very plausible story,” was the sneering response, “but
it is perfectly absurd, when you come to think of it, that Mr. Brewster
should intrust such a commission to a mere boy, when I have been
his attorney, and have conducted his affairs for years; and on
Sunday, with so much secrecy, too! That was not Adam Brewster’s
way of doing business; it is far more likely that he would have sent
for what he wanted, openly and aboveboard, and on some day
during regular banking hours. No, sir; he can’t pull the wool over my
eyes; and as I feel bound to protect the interests of my late client, I
shall expect you to do your duty, and take the fellow in charge,” he
concluded authoritatively.
“Well, I suppose I must,” the man responded, with evident
reluctance, adding, as he drew from a capacious pocket a pair of
steel bracelets, “hold out your hands, my young man.”
Gerald shrank back a step.
“Oh! not that!” he said, with pale lips; “I beg you will not handcuff
me. I will go with you peaceably.”
“Well, maybe you would. I’m inclined to believe you; but it’s my rule
to make sure of my birds, and I don’t make any exceptions,” said the
man, as he dexterously slipped the shackles upon the wrists of his
prisoner; but with an air that betrayed he did not very much relish
the business in hand.
“The keys, Mr. Officer; I must have the keys,” John Hubbard
interposed, as they were about to leave the vault.
“Where are they, youngster?” demanded the man. “Hand them over.”
“They are in the left pocket of my coat,” said Gerald, with difficulty
repressing a groan over his ignominious and utter failure to execute
his employer’s commission.
He was impressed that the larger box contained some secret which
Mr. Brewster would not, on any account, have made known to the
world, and he could not bear the thought that John Hubbard would
now learn it, and perhaps put it to an ignoble use.
The expert plunged his hand into the pocket designated, and drew
forth the keys, after which he stooped to secure the boxes, and left
the vault, followed by the officer and his prisoner.
“Now you may go and cage your bird,” he remarked to the former. “I
will let you out of the bank, but I have some business here, and
shall remain a while longer.”
He unlocked the outer door, and the two men passed out into the
storm. John Hubbard stood looking after them for a few moments, a
fiendish expression on his thin face.
“Gad! what luck!” he muttered. “If ever I made a shrewd move, it
was in coming here this morning to get those papers.”
He returned to the vault, which he securely locked, also the gate to
the iron inclosure.
Then, taking the two boxes, he went inside the banker’s private
office, and deposited them upon the table there.
“Humph!” he observed, as he fastened a keen, curious glance upon
the larger, “there is no key to that, but I’m going to know what it
contains, all the same.”
Whereupon he sat down, drew it to him, and deliberately began to
pick the lock.
CHAPTER VII.
MR. BREWSTER’S WILL.
After Gerald left Mr. Brewster, on Saturday afternoon, the banker—
Allison also having retired—sat for a long time in deep thought, an
anxious look on his thin face, a stern expression in his shrewd, gray
eyes.
“It certainly looks bad,” he muttered; “somebody has evidently been
meddling with my private accounts; but Gerald is not the rogue—he
is true to the core. I never knew any one possessing a finer sense of
honor. If I thought that Hubbard was up to any rascality—and I am
sometimes inclined to think he is too sharp—I’d cut him loose
without ceremony; and yet”—with a scowl of annoyance—“that
might not be so easily done, for some of our transactions have
become strangely mixed. Somehow, I have never had quite so much
confidence in him since that day when he proposed for Allison. I—I
really would like to break away from him before she gets through
school next summer, for, of course, she will never want to marry
him, and I am very sure I do not want him for a son-in-law.”
Again he dropped into profound thought, which was finally
interrupted by the entrance of his attendant, with the light repast
which constituted his supper.
A little later, Allison came again, to read the evening paper to him,
after which they chatted socially for a while, when the banker said
he felt weary, and would retire.
His attendant was assisting him to prepare for bed when he
suddenly put his hand to his head and made an exclamation as if he
were in pain.
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  • 5. © 2015 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use 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
  • 6. Chapter 10: Economic Growth and Business Cycles 106 © 2015 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use 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):
  • 7. Chapter 10: Economic Growth and Business Cycles 107 © 2015 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use (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)
  • 8. Chapter 10: Economic Growth and Business Cycles 108 © 2015 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use 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%
  • 9. Chapter 10: Economic Growth and Business Cycles 109 © 2015 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use 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%
  • 10. Chapter 10: Economic Growth and Business Cycles 110 © 2015 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use = 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
  • 11. Chapter 10: Economic Growth and Business Cycles 111 © 2015 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use 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.
  • 12. Chapter 10: Economic Growth and Business Cycles 112 © 2015 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use 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
  • 13. Chapter 10: Economic Growth and Business Cycles 113 © 2015 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use [( 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
  • 14. Chapter 10: Economic Growth and Business Cycles 114 © 2015 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use 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.
  • 15. Chapter 10: Economic Growth and Business Cycles 115 © 2015 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use 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-
  • 16. Chapter 10: Economic Growth and Business Cycles 116 © 2015 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use 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.
  • 17. Discovering Diverse Content Through Random Scribd Documents
  • 18. closed his lips and made no response. But a little later, while John Hubbard was at luncheon and he was left alone in the office, he proceeded to examine some of these criticized accounts, and was almost paralyzed upon discovering how his books appeared to compromise him. There were evidences that some one had been critically examining them, for there were frequent marginal notes, while the balance seemed to show that he had been cleverly and systematically robbing his employer for a long time. With a very white face and sternly compressed lips, Gerald took a powerful magnifying-glass and brought it to bear along the various columns of figures. “I thought so!” he hoarsely muttered, at last, “they have been tampered with! Some of my threes and sixes have been changed to eights; my ones, in numberless instances, have been made into twos, fours, and sevens, but so skilfully that no one would believe me if I should assert it—I could never prove that he did it. Great Heaven! and it has been going on for many months. This was what he had in mind when he crushed my rose and warned me to beware of a similar fate.” Gerald was sick at heart as he realized that he was standing upon the brink of a fearful precipice and was powerless to help himself— how he had become entangled in a skilfully contrived net from which there seemed to be no possible way of escape. If Mr. Brewster had been well he would have appealed at once to him, stated his suspicions, and tried to point out the changes he had discovered in the figures, but in the man’s present precarious condition he dared not trouble him with the matter, even if he were allowed an interview with him. A week passed, and then, to his great joy, he received a note from Mr. Brewster asking him to call upon him at a certain hour the following Saturday, as he had a special commission for him.
  • 19. He presented himself at the Brewster mansion promptly at the hour mentioned in the note, and was at once conducted to his employer’s presence. He was greatly shocked at the change in the man—not having seen him since his attack—for he had grown very thin, and seemed to have aged many years. Mr. Brewster greeted him very kindly, and seemed heartily glad to see him, but almost immediately broached the business concerning which he had desired to see him. “Gerald, I have a secret commission with which I wish to entrust you,” he began, a grave look settling over his face. “I know that I can trust you absolutely, and that is why I have chosen you in preference to any one else.” “Thank you, sir,” Gerald replied, with a glowing face, his sorely wounded heart greatly comforted by this assurance. “You have been inside the bank vault?” “Yes, sir, often; you have frequently sent me to the drawer which contains your private documents.” “Yes—yes, I know, and —— But before I go on I want you to give me your word of honor that no one shall ever learn from you the secret I am about to commit to you,” said the banker. “Certainly, sir, I will promise that I will never betray any confidence that you repose in me,” Gerald responded. “That is enough,” he said. “Now, behind that drawer, which contains those private papers, there is a small, secret vault, which I had built there to store certain valuables during my absence from town. No one save the man who made it, and I, know that it is there; no one would suspect it, for, on removing the drawer, there seems to be nothing but the brick wall behind it. On the contrary, there is an iron plate, or panel, painted to resemble bricks. At the bottom of this panel there is a small slot. You will insert in this a tiny key which I shall give you; turn it half-around, and the panel will spring outward. You can then swing it upward, when you will discover behind it two
  • 20. boxes, take them out, being careful to relock the panel, and bring them to me.” “Yes, sir; I shall be very glad to do as you wish,” Gerald remarked. “But how will I be able to get into the vault and remove the boxes without the knowledge of others?” “I have keys that will admit you to it, and you must go to the bank when no one else is there,” said the banker, with a slight frown, as if he did not exactly relish this part of the commission. “To-morrow will be Sunday, and you had best go as soon after you have had your breakfast as you can; then come directly to me. Be careful not to excite the suspicion of any one whom you may meet, for one of the boxes contains valuable jewels that belonged to Mrs. Brewster. I want them for Allison; the other holds nothing of special value to any one except myself.” Mr. Brewster had become very white during this last statement, and Gerald feared he was talking too much for his strength. “Here are my keys,” he continued, after a moment, and, taking a bunch from a drawer in the table beside him, “this one unlocks the outer door, this the inner; the brass one opens the gate of the iron fence; the heavy one will admit you to the vault; this unlocks my private drawer, and the little, flat one the panel that conceals the secret vault. Quite a lesson to learn, isn’t it?” he added, with a slight smile; “but I think you will have no difficulty in remembering how to use them.” “No, sir; four of them I know already, so that leaves only those belonging to your drawer and the secret vault to be distinguished, and that is easily done,” Gerald replied, as he examined each key attentively. “Very well, then, I shall look for you here again some time to- morrow forenoon. I want to get those boxes into my possession as soon as possible,” Mr. Brewster observed, with a faint but impatient sigh.
  • 21. “I will try to be here some time between ten and eleven o’clock,” Gerald returned, then added, losing some of his color: “And now, Mr. Brewster, if you are not too tired, I have something to tell you about my work.” “I am not too tired, go ahead,” said the man; whereupon Gerald gave him a brief account of the conversation that had recently passed between himself and John Hubbard, and what he had discovered afterward in connection with his work. Mr. Brewster listened to him with growing astonishment, never once removing his eyes from the young man’s face during his recital. “These are very strange statements, Gerald—very grave statements,” he remarked, with some sternness, as he concluded. “They are, indeed, sir, and they involve my honor, my reputation, and, unless my past dealings with you and my assurance are sufficient guarantee to you of my integrity, the evidence is there to prove that I have been doing very crooked business in your office. The balances are all right, apparently, but the entries, if examined, would seem to be conclusive testimony that I have been systematically robbing you. Mr. Brewster, I firmly believe that those figures have been skilfully changed for the sole purpose of ruining me.” “By whom?” “That, of course, I cannot say positively, but I have long known that Mr. Hubbard dislikes me,” was the somewhat reluctant reply. “Do you mean to imply that John Hubbard would doctor the accounts to injure you?” exclaimed Mr. Brewster, with a start. “I have no right to assert that he would, for I cannot prove it; but some one has done it, and he is the only one who, to my knowledge, has had access to the books. I can only say I know he hates me, and—I also say, Mr. Brewster”—and the honest fellow here straightened himself with conscious integrity, and lifted an
  • 22. unfaltering look to his employer—“that I have never made a false entry upon one of your books.” Neither was conscious of the presence of a third person in the room as the banker heartily responded: “I am sure you have not, Gerald; I would stake my fortune upon your integrity and upon your unswerving faithfulness to my interests. I will look into this matter just as soon as I am able. Ah! Allison, I did not hear you come in. What is it, dear?” he concluded, turning, as he caught the sound of her step behind him. She came forward, blushing and smiling a welcome to Gerald. “It is time for your beef broth, papa,” she said, as she placed a small salver containing a cup before him. Then she turned to our hero with outstretched hand. “What an age it is since I saw you last, Gerald,” she remarked, and then flushed again as she recalled her last interview with him. He returned her greeting with what warmth he dared in Mr. Brewster’s presence, but with a hand-clasp that spoke volumes.
  • 23. CHAPTER V. THE BANK ON SUNDAY MORNING. Allison had come into the room where Gerald and her father were conversing so earnestly just in season to catch the words of commendation uttered by the latter. “I am sure you have not, Gerald,” he had said; “I would stake my fortune upon your integrity and upon your unswerving faithfulness to my interests.” She had noted, with the keen perception of a loving heart, the troubled look in Gerald’s eyes, the anxious expression upon his brow, and she instantly knew that something had gone amiss with him, in spite of the fact that he seemed in perfect health, and was handsomer and more manly than ever. But in the excitement of greeting him—when she saw his face light up with joy in her presence, when she felt the warm, lingering clasp of his hand, and detected the old-time thrill in his voice—she forgot all about it, for the time, and thought only of the pleasures of this unexpected meeting. When Gerald finally left the house it was with a very much lighter heart than when he entered. His employer’s hearty and unqualified assurance of confidence was like balm to his wounded spirit; while his little interview with Allison had set all his pulses vibrating afresh with his deep and abiding love for her. He had not seen her for many months, and she seemed to have grown a hundredfold more lovely than when he had bidden her adieu on that bright Sunday morning so long ago.
  • 24. He wondered if she had forgotten the evening previous—their interview upon the veranda, where, with the moonlight streaming upon them in its soft effulgence, they had been conscious only of each other’s presence and the happiness that had thrilled every fiber of their being. Did she remember their parting when the clock struck ten? That blissful moment when their lips met in that involuntary caress? That look into each other’s eyes, that low-breathed “Allison!” “Gerald!” which had expressed so much? She seemed a trifle more mature; she had acquired a little air of dignity which, on the whole, he decided only added to her charms, although at first it had chilled him slightly—at least, until he found himself looking down into the expressive eyes. He hoped he should see her again on the morrow, when he returned with the boxes which Mr. Brewster had commissioned him to get from the secret vault. He smiled and uttered a sigh of content, as he passed his hand over the pocket which held the keys the banker had given to him, and realized that he never would have been entrusted with them if he had not possessed the entire confidence of the man. He hurried back to his lodging, where, in this happy frame of mind, he settled down to the preparation of some lessons which were to be recited that evening to a certain professor with whom he had been studying for three years. As we know, Gerald, at the time of his aunt’s death, had been in the second year of the high school, but for a time after that his studies were interrupted, as he found that his daily duties taxed his strength to the utmost. But as he became accustomed to his work, he began to get hungry for his books again, and for a while attended evening school, although his progress was thus necessarily slow. Then he made the acquaintance of a professor by the name of Emerson, who, becoming interested in the bright, ambitious lad,
  • 25. offered to help him perfect his education and arranged for Gerald to recite three times a week to him. He was now in his twenty-first year, and expected by the coming June to complete the studies of the second year of a regular college course. After partaking of a light supper, he repaired to the house of his friend, Professor Emerson, where he acquitted himself most creditably in his recitations. The gentleman had become quite fond of his enterprising pupil, and it was a great delight to him to teach one who was so eager for knowledge and so quick to comprehend. “By the way, Gerald, what do you intend to make of yourself when you get through with your course?” he inquired to-night, as he closed his book after the last recitation, and bent an inquiring look on the handsome face before him. “I think—since I am so well started in the banking business, I shall stick to it, learn it thoroughly, and, if fortune favors me, perhaps become a banker myself, by and by,” he replied, but with a smile at his egotism in aspiring to a position such as Adam Brewster occupied. Professor Emerson eyed him curiously for a moment, then remarked: “You’ll achieve it, if you undertake it, and, rightly conducted, banking is a good business; still, I wish you might go a little higher, intellectually—you would make a fine lawyer, your mental grasp is so keen and accurate.” “Thank you,” said Gerald, flushing at the compliment, “but it would take me several years to prepare for the bar, after completing my college course, and, since I have my own canoe to paddle, I think I will adhere to what I have begun. I wish, though,” he added gravely, as his mind suddenly reverted to John Hubbard, “I have time to become thoroughly posted in law, and could combine the two, for then I should always be sure of the faithfulness of my legal adviser.”
  • 26. “Why, Winchester! I did not suppose you possessed so suspicious a nature!” said his friend, smiling, but with a note of surprise in his tones. “If every one was governed by such distrust I fear the lawyers would fare hard.” “I am not naturally suspicious,” replied Gerald, reddening, “and my remark must seem narrow and intolerant to you; it was prompted by the fact that one lawyer whom I know is anything but an honest and conscientious man.” “But, ‘one swallow does not make a summer,’ my boy,” retorted his friend, laughing. “I know it, sir, and I have no business to be suspicious of all men because of one man’s failings. I will try to be more charitable toward lawyers in the future,” said the young man, as he rose to leave. He felt half-ashamed of having allowed himself to be so swayed by his antipathy against John Hubbard, but all the way back to his lodgings he was haunted by the face of the man and the malignant scowl which had distorted it when he accused him of unfaithfulness and dishonesty in his work. Even in his sleep during the night he could not divest himself of the consciousness of his vicious individuality—he seemed to be continually pursuing and persecuting him until his visions became so real that they finally drove him from his bed long before his usual hour for rising on Sunday morning. It was not yet dawn when he arose on Sunday morning, and, upon looking from his window, Gerald saw that it was snowing. He dressed himself with unusual care, for he hoped to see Allison again, and, loverlike, desired to make as good an appearance in her sight as possible. Then he hurried out for his morning meal, after which he wended his way to the bank, where he arrived about half- past eight. The steps leading up to the door were covered with snow, and, strangely enough, as he mounted them, leaving a footprint upon
  • 27. every one, an uncomfortable sensation which was akin to guilt, began to creep over him, causing his errand to become suddenly repulsive to him, and making him long to go back to his room and remain there. But, throwing back his head with an air of conscious rectitude—for was he not there at his employer’s command?—he quickly let himself into the building, removing the key and relocking the door on the inside to make sure that no one would follow him. Passing through the inner door, he carefully wiped his feet upon the mat, and removed his overshoes lest they should leave tracks upon the floor—that same uncanny feeling which he had experienced outside still pursuing him. The bank was so still every footfall echoed noisily through it, and sent a nervous shiver creeping down his spine. “Good gracious!” he exclaimed, with an impatient shrug of his shoulders, “I am no thief stealing in here to rob the place! Why on earth should I feel like one? It is positively absurd!” Proceeding directly to the vault, he drew the heavy bolts, unlocked and swung open the massive iron-plated door. The place was cold and gloomy, and again Gerald shivered with a nervous chill as he stepped within those solid walls which so securely guarded their hoarded treasure. Proceeding directly to Mr. Brewster’s private drawer, the number of which he had long known, he unlocked and drew it out, setting it upon the floor. It contained several packages of papers. But these held no interest for him; he merely gave them a passing glance, then began to look for the slot in the iron panel at the back of the aperture. It required close searching to find it, but his efforts were finally rewarded, whereupon he inserted the last of his keys, turned it half- around, when the panel sprang outward, as Mr. Brewster had described.
  • 28. It appeared to be swung upon hinges, and, lifting it up, Gerald could distinguish within the little vault thus disclosed a box of some description. He drew it from its place of concealment. It proved to be a beautiful Japanese affair, inlaid with gold and mother-of-pearl in an intricate pattern. There was a tiny key in its lock, and for fear that it might drop out and be lost, Gerald removed it and transferred it to a pocket in his vest, without once thinking that he had it in his power to inspect the contents of the casket, if he chose to do so. Putting it carefully down upon the floor, he looked for the other. He found it shoved away back in the secret vault. It was much larger than the other—a common, though strong, wooden receptacle—and it was also locked, while there was no key with it. Gerald felt quite sure that the Japanese casket must contain the jewels of which Mr. Brewster had spoken, and which were to be given to Allison. Doubtless they were very valuable, and would be doubly precious to her because they had once belonged to and been worn by her mother. He would probably see them upon her person some day; but, strange to say, he did not feel half so curious about them as he did regarding the contents of the larger box, for he had been impressed by Mr. Brewster’s manner and expression when he had said that it contained “nothing of special value to any one—except myself.” However, he felt that it was no business of his what either held; his duty lay simply in conveying them safely to his employer. Putting the drawer back in its place, he relocked it, when, gathering the boxes from the floor, he turned to leave the vault. At that instant a shadow obscured the light admitted by the open door. Gerald started forward with a sudden and terrible heart-throb. His face flushed hotly, then paled to the hue of marble as he was
  • 29. confronted by John Hubbard, who was standing upon the threshold, a sardonic grin distorting his sinister countenance. “Aha! my young burglar,” the man exclaimed, in a tone of fiendish triumph, “is this the way you are in the habit of spending your Sundays?” The sound of the expert’s voice at once restored Gerald’s composure, although every nerve in his body was tingling with anger at his manner of addressing him. “I am no burglar, Mr. Hubbard, and you know it,” he coldly returned. “I am not in the habit of coming here—I have never been in the bank on Sunday before this; but——” “What have you there?” sternly interposed his companion, and indicating by a gesture the boxes in Gerald’s hands. “Some things belonging to Mr. Brewster.” “So I judged. How came you here?” “By his orders,” the young man briefly replied, and then wondered at the almost satanic leer which swept over the features of the man before him. “Indeed! but how did you pass all these barriers?” with a nod backward over his shoulder. “Why, by means of these keys, which Mr. Brewster himself gave to me, when he asked me to perform this errand for him,” the young man responded, as he held up the bunch by the ring, and which Mr. Hubbard instantly recognized as belonging to the banker. “When did you see Mr. Brewster?” he questioned, a look of perplexity flashing over his face. “Yesterday afternoon—he sent for me to go to him,” Gerald explained. “H’m!” ejaculated the expert, with a frown. Then, after a moment of thought, he added: “What is in those boxes?”
  • 30. Again Gerald flushed. Then he threw back his handsome head haughtily. “Excuse me,” he said freezingly, “but that is a question which Mr. Brewster alone is qualified to answer.” “Ha! ha!” laughed his companion, but with so weird a note in the sound, which echoed and re-echoed mockingly through the vault, that Gerald’s blood almost seemed to congeal in his veins. “You are very non-committal, my fine fellow,” he continued, with a snarl, “but do you dare to tell me that you don’t know what either of those boxes contains?” “I must decline to discuss the matter with you, Mr. Hubbard,” was the terse reply. “Indeed!” sneered his companion. Then he observed, served, authoritatively, as he went a step nearer Gerald. “Very well, we won’t discuss it; but since I am Mr. Brewster’s attorney, I will relieve you of all further care of them. Give them to me.” “No, sir!” said Gerald resolutely, and retreating from him. “Give them to me, I tell you!” commanded the man angrily. “I cannot do that, Mr. Hubbard,” Gerald calmly returned. “Mr. Brewster requested me to come here for them, and then bring them directly to him. I shall deliver them to no other hands.” Once more that strange laugh echoed through the dismal vault. “You will have to go a long journey to do that, young man,” said John Hubbard, showing his white teeth in a horrible grin. “How so?” queried Gerald, in surprise, but with a strange numbness stealing over him, “I—I do not understand you.” “Adam Brewster is dead!” said John Hubbard.
  • 31. CHAPTER VI. GERALD SUFFERS AN INDIGNITY. There was a dead silence in that gloomy place for the space of a full minute after John Hubbard’s terrible announcement. “It cannot be possible!” Gerald finally gasped, as he staggered back against the side of the vault, almost paralyzed from horror. As he did so, the topmost box in his hands slipped from his grasp, and fell with a crash to the floor. The lock was either broken or forced from its socket by the concussion, and the lid flew back, thus disclosing to the curious eyes of John Hubbard various articles of valuable jewelry. “Aha! diamonds! pearls! rubies and emeralds!” he exclaimed, as he stooped to examine them more closely. “Truly, young man, you were taking time by the forelock to feather your nest before an inventory could be taken of your employer’s effects.” “What do you mean, sir?” he exclaimed, starting forward, a dangerous gleam in his eyes. “Do you dare assert that I knew that Mr. Brewster was not living, and stole here to rob him?” “I am forced to admit that it looks very much like it,” was the deliberate and cruel response. A terrible shock went quivering through Gerald at these words, for he realized but too well that the man would do his utmost to injure him by putting the worst possible construction upon the situation. “You know better!” he cried, hot indignation and resentment flaming up within him; “you know I would not touch a penny that did not belong to me.”
  • 32. “Ahem! that all sounds very well, my would-be paragon of honor,” sneered the expert, “but you will have to prove it, you know.” “Prove it! Why, of course, I can prove it,” replied Gerald, a little smile of scorn for his recent fear curling his lips, and a consciousness of rectitude and security supplanting it, “I have Mr. Brewster’s note of yesterday, asking me to come to him, as he had a special commission for me, and then the very fact of my having his keys proves that I am here under orders,” and again he held them up to his companion’s view. “H’m! so he wrote you to come to him, did he?” queried John Hubbard thoughtfully. “Where is the note? I should like to see it.” Gerald put his hand into his coat-pocket; then suddenly remembered that he had put on his best suit that morning. “Ah!” he said, “it is in the pocket of my other coat.” John Hubbard’s eyes gleamed with a cunning light at this information. “Well, you will doubtless need all the proof you can bring to get you out of this scrape,” he gruffly observed. “Maybe you can produce such a note, but I doubt it. Did any one see Mr. Brewster give you those keys?” Gerald’s heart sank at the question, as he remembered that he and his employer had been utterly alone throughout their interview, except for the few minutes that Allison was in the room, and he was sure she had heard nothing that would prove the truth of what he had asserted. At least he knew she was not there when the keys were given to him. “You have no right to question me like this, or to doubt my word, and I will have no further conversation with you about the matter,” he responded, after a moment of thought. But he was deathly pale as he stooped to recover the box that had fallen. He found that it was not broken; the lock had only been forced by the fall. He carefully arranged the jewels which had been
  • 33. somewhat displaced, although, fortunately, none had been spilled; then, shutting the box, he relocked it with the key which he took from his vest-pocket. John Hubbard watched him warily while he was thus engaged. “I will take charge of those things,” he sternly observed, as Gerald was about to replace the key in his pocket. “Excuse me; but I do not think you will,” the young man coldly returned. “I am Mr. Brewster’s attorney, and it will be my duty to settle his estate; consequently all his property will pass through my hands. Give me those boxes!” the man concluded authoritatively. “No, sir. Mr. Brewster authorized me to take them to his house; I shall do as he ordered, and since you say he is no longer living, give them to Miss Brewster; he stated that he wanted the jewels for her.” And he started to leave the vault as he concluded. “You will do no such thing, you young upstart!” snarled John Hubbard, at the same time making an agile spring backward out of the vault, when he swung to the ponderous door almost before Gerald comprehended his intention. “Now, you beggarly upstart, I have you just where I want you,” he cried, in a cruel, exultant tone, and putting his lips to the keyhole, “I once gave you an object-lesson regarding your fate if you continued to stand in my way.” Gerald did not deign to reply to these taunts and presently he knew, by the closing of the outer door of the bank, that he was alone. His heart was very heavy, for he began to realize that his case was desperate. Fate and his evil-minded foe had conspired to so involve him in a network of compromising circumstances, it seemed likely that he was destined to be proved a graceless scamp and a daring robber.
  • 34. His employer, the only one who had it in his power to exonerate him from blame and prove his innocence, was dead. He felt almost sure that John Hubbard intended to bring an officer there to arrest him, with the evidences of his guilt around him. With this thought there came the temptation to restore those boxes to the secret vault from which he had taken them. Mr. Brewster had said that no one, save himself and the man who constructed it, knew of its existence. If he should conceal those jewels and the other box, there would be no evidence, beyond John Hubbard’s word, to prove that he had attempted to take them from the bank. His word would be just as good as that of his enemy, upon whom the burden of proving his own accusations would have to rest. “But I should have to deny all knowledge of them. I should be obliged to lie, and that I will not do, even to save my—myself from prison,” he said to himself, with an air of proud resolution. “No, I will tell the truth and take my chance; I have Mr. Brewster’s note telling me to come to him; I have also his keys, and the two taken together ought to be strong points in my defense.” Nevertheless, these arguments were small consolation in view of his unfortunate situation. Then his thoughts reverted to Mr. Brewster, and hot tears rushed into his eyes as he realized that the man was lying still in death, and they would never meet in this life again. He was still weak from the shock he had experienced upon learning the fact so suddenly, and he wondered what could have caused the unlooked-for attack. He had appeared to be very comfortable, and hopeful of soon getting out again, when he had seen him the previous day, and it seemed awful to him that he should have been so ruthlessly cut down, just in the prime of life, and in the height of prosperity. He was wild with impatience to learn the particulars, and chafed restively against his confinement in that tomb-like place.
  • 35. “Poor Allison! It will be a terrible blow to her,” he mused; “she will be all alone in the world now; but she is fortunate to be left an heiress, and thus shielded from the hardships of life.” Alas! he little thought that the fortune which would fall to the girl was destined to bring upon her dangers and trials from which he would have shrunk appalled could he have foreseen them. He sprang to his feet and began to pace the vault restlessly, for a feeling of faintness and sickness came over him; he also experienced a difficulty in breathing, as the air in the place began to be vitiated. Suppose John Hubbard should not return in season to release him before suffocation overtook him, he thought, a nervous chill creeping over him; but he discarded it with a bitter smile. He well knew that the man would not dare to let him die there—that he was planning for him a worse fate than death, out of a cruel spirit of revenge, because he had dared to love the girl whom he, for some strange reason, coveted. He believed that he meant to so crush and humiliate him that he would never want to seek Allison Brewster again, or meet the gaze of her pure, clear eyes. “He shall not do it! by Heaven! he shall not succeed in his atrocious designs!” he cried out, in a sudden anguish, as those torturing thoughts flitted through his brain. “I am an honest man, and I swear I will yet prove it to the world, in spite of the worst that he can do.” A little later he heard the outer door of the bank open and close again, then the sound of steps and voices drawing near him, until presently, the bolt which fastened the door of the vault was shot back, and the next moment John Hubbard, accompanied by a policeman, stood in his presence. “Here, Mr. Officer, is your prisoner, and that,” pointing to the two boxes upon the floor, “is the booty with which he was about to make off when I caught him,” the man explained, as he shot a look of malignant triumph at his victim.
  • 36. “Humph!” ejaculated the officer, as he darted a comprehensive glance around the place, and at the same time taking the measure of Gerald. “It is very fortunate that I happen here just as I did,” Mr. Hubbard went on. “I seldom come to the bank on Sunday, but there were some papers here which I was obliged to have to-day, and thus I came upon him in the midst of his depredations.” “H’m! you look rather young and green to be a bank-robber,” the policeman remarked, not unkindly, as he searched the pale, handsome face of his prisoner; “you don’t seem like the sort, either, that would be up to such business.” “I am no bank-robber,” said Gerald, with quiet dignity, and meeting the man’s searching look unflinchingly, “I am here under orders.” “Whose orders?” “My employer’s, Mr. Brewster’s,” and Gerald proceeded to give him a brief account of the facts of the case, though he said nothing about the secret vault. “That sounds all straight and right,” said the policeman, as he gravely turned to Mr. Hubbard. “Yes; he tells a very plausible story,” was the sneering response, “but it is perfectly absurd, when you come to think of it, that Mr. Brewster should intrust such a commission to a mere boy, when I have been his attorney, and have conducted his affairs for years; and on Sunday, with so much secrecy, too! That was not Adam Brewster’s way of doing business; it is far more likely that he would have sent for what he wanted, openly and aboveboard, and on some day during regular banking hours. No, sir; he can’t pull the wool over my eyes; and as I feel bound to protect the interests of my late client, I shall expect you to do your duty, and take the fellow in charge,” he concluded authoritatively. “Well, I suppose I must,” the man responded, with evident reluctance, adding, as he drew from a capacious pocket a pair of
  • 37. steel bracelets, “hold out your hands, my young man.” Gerald shrank back a step. “Oh! not that!” he said, with pale lips; “I beg you will not handcuff me. I will go with you peaceably.” “Well, maybe you would. I’m inclined to believe you; but it’s my rule to make sure of my birds, and I don’t make any exceptions,” said the man, as he dexterously slipped the shackles upon the wrists of his prisoner; but with an air that betrayed he did not very much relish the business in hand. “The keys, Mr. Officer; I must have the keys,” John Hubbard interposed, as they were about to leave the vault. “Where are they, youngster?” demanded the man. “Hand them over.” “They are in the left pocket of my coat,” said Gerald, with difficulty repressing a groan over his ignominious and utter failure to execute his employer’s commission. He was impressed that the larger box contained some secret which Mr. Brewster would not, on any account, have made known to the world, and he could not bear the thought that John Hubbard would now learn it, and perhaps put it to an ignoble use. The expert plunged his hand into the pocket designated, and drew forth the keys, after which he stooped to secure the boxes, and left the vault, followed by the officer and his prisoner. “Now you may go and cage your bird,” he remarked to the former. “I will let you out of the bank, but I have some business here, and shall remain a while longer.” He unlocked the outer door, and the two men passed out into the storm. John Hubbard stood looking after them for a few moments, a fiendish expression on his thin face. “Gad! what luck!” he muttered. “If ever I made a shrewd move, it was in coming here this morning to get those papers.”
  • 38. He returned to the vault, which he securely locked, also the gate to the iron inclosure. Then, taking the two boxes, he went inside the banker’s private office, and deposited them upon the table there. “Humph!” he observed, as he fastened a keen, curious glance upon the larger, “there is no key to that, but I’m going to know what it contains, all the same.” Whereupon he sat down, drew it to him, and deliberately began to pick the lock.
  • 39. CHAPTER VII. MR. BREWSTER’S WILL. After Gerald left Mr. Brewster, on Saturday afternoon, the banker— Allison also having retired—sat for a long time in deep thought, an anxious look on his thin face, a stern expression in his shrewd, gray eyes. “It certainly looks bad,” he muttered; “somebody has evidently been meddling with my private accounts; but Gerald is not the rogue—he is true to the core. I never knew any one possessing a finer sense of honor. If I thought that Hubbard was up to any rascality—and I am sometimes inclined to think he is too sharp—I’d cut him loose without ceremony; and yet”—with a scowl of annoyance—“that might not be so easily done, for some of our transactions have become strangely mixed. Somehow, I have never had quite so much confidence in him since that day when he proposed for Allison. I—I really would like to break away from him before she gets through school next summer, for, of course, she will never want to marry him, and I am very sure I do not want him for a son-in-law.” Again he dropped into profound thought, which was finally interrupted by the entrance of his attendant, with the light repast which constituted his supper. A little later, Allison came again, to read the evening paper to him, after which they chatted socially for a while, when the banker said he felt weary, and would retire. His attendant was assisting him to prepare for bed when he suddenly put his hand to his head and made an exclamation as if he were in pain.
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