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Chapter 2: Economic Theories, Data, and Graphs

This chapter provides an introduction to the methods economists use in their research. We integrate
a detailed discussion of graphing into our discussion of how economists present economic data and
how they test economic theories.

In our experience, students typically do not learn enough about the connection between
theory and evidence, and how both are central to understanding economic phenomena. We therefore
recommend that considerable emphasis be placed on Figure 2-1, illustrating the process of going
from model building to generating hypotheses to confronting data and testing hypotheses, and then
returning to model building (or rebuilding). There is no real beginning or end to this process, so it
is difficult to call economics an entirely “theory driven” or “data driven” discipline. Without the
theory and models, we don’t know what to look for in the data; but without experiencing the world
around us, we can’t build sensible models of human behaviour and interaction through markets.
The scientific approach in economics, as in the “hard” sciences, involves a close relationship
between theory and evidence.

***

The chapter is divided into four major sections. In the first section, we make the important
distinction between positive and normative statements and advice. Students must understand this
distinction, and that the progress of any scientific discipline relies on researchers’ ability to separate
what evidence suggests is true from what they would like to be true. We conclude this section by
explaining why economists are often seen to disagree even though there is a great deal of agreement
among them on many specific issues. This leads to a box on where economists typically get jobs
and the kind of work they often do.

The second section explains the elements of economic theories and how they are tested.
We emphasise how a theory’s or model’s definitions and assumptions lead, through a process of
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logical deduction, to a set of conditional predictions. We then examine the testing of theories. It
is here that we focus on the interaction of theory and empirical observation (Figure 2-1). We

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Instructor’s Manual for Ragan, Economics, Fifteenth Canadian Edition

emphasize the importance of the distinction between correlation and causation, with a simple
example.

The chapter’s third section deals with economic data. We begin by explaining the
construction of index numbers, and we use them to compare the volatility of two sample time
series. Index numbers are so pervasive in discussions of economic magnitudes that students must
know what these are and how they are constructed. We then make the distinction between cross-
sectional and time-series data, and at this point students are introduced to two types of graph.

This brings us to the chapter’s final section, on graphing. We show how a relation can be
expressed in words, in a table, in an equation, or on a graph. We then go into considerable detail
on linear functions, slope, non-linear functions, and functions with minima and maxima. In this
discussion, the student is introduced to the concept of the margin, described as the change in Y in
response to a one-unit change in X. In all cases, the graphs apply to real-world situations rather
than abstract variables. Pollution abatement, hockey-stick production, firm profits, and fuel
consumption are our main examples.

Answers to Study Exercises

Question 1

a) normative (“The government should impose…” is inherently a value judgement.)

b) positive (In principle, we could determined the impact that foreign aid actually has.)

c) positive (In principle, we could determine the extent to which fee increases affect access.)

d) normative (What is or is not unfair is clearly based on a value judgement.)

e) normative (Use of the expression “too much” is a value judgement.)

Question 2

a) In the Canadian wheat sector, the amount of rainfall on the Canadian prairies is an exogenous
variable; the amount of wheat produced is an endogenous variable.
b) To the Canadian market for coffee, the world price of coffee is exogenous; the price of a cup
of coffee at Tim Horton’s is endogenous.
c) To any individual student, the widespread unavailability of student loans is exogenous; their
own attendance at university or college is endogenous.

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 Chapter 2: Economic Theories, Data, and Graphs

d) To any individual driver, the tax on gasoline is exogenous; his or her own decision regarding
which vehicle to purchase is endogenous.

Question 3

a) models (or theories)

b) endogenous; exogenous

c) (conditional) prediction; empirical

d) (positively) correlated; causal

e) self-interest; utility; profits

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Instructor’s Manual for Ragan, Economics, Fifteenth Canadian Edition

Question 4

The observed correlation cannot lead to a certain inference about causality. It is consistent with
the theory that the increase in demand for homes leads to an increase in the price of lumber
(which is generally a pretty sensible theory!), but it is also consistent with a different theory –
one in which some unobserved factor leads to both the increase in demand for homes and
separately to the increase in the price of lumber. Correlation does not imply causality!

Question 5

a) These data are best illustrated with a time-series graph, with the month shown on the
horizontal axis and the exchange rate shown on the vertical axis.

b) These cross-sectional data are best illustrated with a bar chart.

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 Chapter 2: Economic Theories, Data, and Graphs

c) These cross-sectional data are best illustrated in a scatter diagram; the “line of best fit” is clearly
upward sloping, indicating a positive relationship between average investment rates and average
growth rates.

Question 6

a) Using 2000 as the base year means that we choose $85 as the base price. We thus divide the
actual prices in all years by $85 and then multiply by 100. In this way, we will determine, in
percentage terms, how prices in other years differ from prices in 2000. The index values are as
follows:

Year Price ($) Physics textbook price index

2000 85 (85/85)  100 = 100
2001 87 (87/85)  100 = 102.4
2002 94 (94/85)  100 = 110.6
2003 104 (104/85)  100 = 122.4
2004 110 (110/85)  100 = 129.4
2005 112 (112/85)  100 = 131.8
2006 120 (120/85)  100 = 141.2
2007 125 (125/85)  100 = 147.1
2008 127 (127/85)  100 = 149.4
2009 127 (127/85)  100 = 149.4
2010 130 (130/85) × 100 = 152.9

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Instructor’s Manual for Ragan, Economics, Fifteenth Canadian Edition

b) The price index in 2005 is 131.8, meaning that the price of the physics textbook is 31.8
percent higher in 2005 than in the base year, 2000.

c) From 2007 to 2010, the price index increases from 147.1 to 152.9but this is not an increase of
5.8 percent. The percentage increase in the price index from 2007 to 2010 is equal to [(152.9-
147.1)/147.1]×100 = 3.94 percent.

d) These are time-series data because the data are for the same product at the same place but at
different points in time.

Question 7

a) Using Calgary as the “base university” means that we choose $6.25 as the base price. Thus we
divide all actual prices by $6.25 and then multiply by 100. In this way, we will determine, in
percentage terms, how prices at other universities differ from Calgary prices. The index values
are as follows:

University Price per Index of pizza prices

pizza
Dalhousie $6.50 (6.50/6.25)100 = 104
Laval 5.95 (5.95/6.25)100 = 95.2
McGill 6.00 (6.00/6.25)100 = 96
Queen’s 8.00 (8.00/6.25)100 = 128
Waterloo 7.50 (7.50/6.25)100 = 120
Manitoba 5.50 (5.50/6.25)100 = 88
Saskatchewan 5.75 (5.75/6.25)100 = 92
Calgary 6.25 (6.25/6.25)100 = 100
UBC 7.25 (7.25/6.25)100 = 116
Victoria 7.00 (7.00/6.25)100 = 112

b) The university with the most expensive pizza is Queen’s, at $8.00 per pizza. The index value
for Queen’s is 128, indicating that pizza there is 28 percent more expensive than at Calgary.

c) The university with the least expensive pizza is Manitoba, at $5.50 per pizza. The index value
for Manitoba is 88, indicating that the price of pizza there is only 88 percent of the price at Calgary.
It is therefore 12 percent cheaper than at Calgary.

d) These are cross-sectional data. The variable is the price of pizza, collected at different places
at a given point in time (March 1, 2016). If the data had been the prices of pizza at a single
university at various points in time, they would be time-series data.

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 Chapter 2: Economic Theories, Data, and Graphs

Question 8

Year Exports Export Index Imports Import Index

2005 8662 (8662/8662)(100) = 100 3139 (3139/3139)(100) = 100
2006 8899 (8899/8662)(100) = 102.7 2977 (2977/3139)(100) = 94.8
2007 9331 (9331/8662)(100) = 107.7 3124 (3124/3139)(100) = 99.5
2008 9302 (9302/8662)(100) = 107.4 3010 (3010/3139)(100) = 95.9
2009 7902 (7902/8662)(100) = 91.2 2945 (2945/3139)(100) = 93.8

a) Using 2005 as the base year for an index number requires that we divide the value of exports
(and imports) in each year by the value in 2005, and then multiply the result by 100. This is done
in the table above.

b) It appears that exports were more volatile over this period than imports. Exports increased
over four years by over 7 percent and then fell suddenly by approximately 20 percent. Imports
trended downwards by about 6 percent over the five years with some smaller fluctuations.

c) From 2007 to 2009, the export index falls from 107.7 to 91.2. The percentage change is equal
to (91.2 - 107.7)/107.7 which is -15.3 percent. For imports the percentage change is (93.8 -
99.5)/99.5 which is -5.7 percent.

d) The global financial crisis began in the fall of 2008 and a large recession followed. Most
international trade fell sharply from 2007 to 2009, including Canadian exports. This is likely the
best explanation of the observed decline in Canada’s energy exports.

Question 9

a) Along Line A, Y falls as X rises; thus the slope of Line A is negative. For Line B, the value of
Y rises as X rises; thus the slope of Line B is positive.

b) Along Line A, the change in Y is –4 when the change in X is 6. Thus the slope of Line A is
ΔY/ΔX = -4/6 = -2/3. The equation for Line A is:

Y = 4 – (2/3)X

c) Along Line B, the change in Y is 7 when the change in X is 6. Thus the slope of Line B is
ΔY/ΔX = 7/6. The equation for Line B is:

Y = 0 + (7/6)X

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Instructor’s Manual for Ragan, Economics, Fifteenth Canadian Edition

Question 10

Given the tax-revenue function T = 10 + .25Y, the plotted curve will have a vertical intercept of
10 and a slope of 0.25. The interpretation is that when Y is zero, tax revenue will be $10 billion.
And for every increase in Y of $100 billion, tax revenue will rise by $25 billion. The diagram is
as shown below:

Question 11

a) For each relation, plot the values of Y for each value of X. Construct the following table:

(i) Y = 50 + 2X (ii) Y = 50 + 2X + .05X2 (iii) Y = 50 + 2X - .05X2

X Y X Y X Y
0 50 0 50 0 50
10 70 10 75 10 65
20 90 20 110 20 70
30 110 30 155 30 65
40 130 40 210 40 50
50 150 50 275 50 25

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 Chapter 2: Economic Theories, Data, and Graphs

Now plot these values on scale diagrams, as shown below. Notice the different vertical scale on
the three different diagrams.

b) For part (i), the slope is positive and constant and equal to 2. For each 10-unit increase in X,
there is an increase in Y of 20 units. For part (ii), the slope is always positive since an increase in
X always leads to an increase in Y. But the slope is not constant. As the value of X increases, the
slope of the line also increases. For part (iii), the slope is positive at low levels of X. But the function
reaches a maximum at X=20, after which the slope becomes negative. Furthermore, when X is
greater than 20, the slope of the line becomes more negative (steeper) as the value of X increases.

c) For part (i), the marginal response of Y to a change in X is constant and equal to 2. This is the
slope of the line. In part (ii), the marginal response of Y to a change in X is always positive, but the
marginal response increases as the value of X increases. This is why the line gets steeper as X
increases. For part (iii), the marginal response of Y to a change in X is positive at low levels of X.
But after X=20, the marginal response becomes negative. Hence the slope of the line switches from
positive to negative. Note that for values of X further away from X=20, the marginal response of Y
to a change in X is larger in absolute value. That is, the curve flattens out as we approach X=20 and
becomes steeper as we move away (in either direction) from X=20.

Question 12

The four scale diagrams are shown on the next page, each with different vertical scales. In each
case, the slope of the line is equal to Y/X, which is often referred to as “the rise over the run” –
the amount by which Y changes when X increases by one unit. (For those students who know
calculus, the slope of each curve is also equal to the derivative of Y with respect to X, which for
these curves is given by the coefficient on X in each equation.)

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Instructor’s Manual for Ragan, Economics, Fifteenth Canadian Edition

Question 13

This is a good question to make sure students understand the importance of using weighted
averages rather than simple averages in some situations.

a) The simple average of the three regional unemployment rates is equal to (5.5 + 7.2 + 12.5)/3 =
8.4. Is 8.4% the “right” unemployment rate for the country as a whole? The answer is no because
this simple, unweighted (or, more correctly, equally weighted) average does not account for the
fact that the Centre is much larger in terms of the labour force than either the West or East, and
thus should be given more weight than the other two regions.

b) To solve this problem, we construct a weighted average unemployment rate. We do so by

constructing a weight for each region equal to that region’s share in the total labour force. From
the data provided, the country’s total labour force is 17.2 million. The three weights are
therefore:

West: weight = 5.3/17.2 = 0.308

Centre:weight = 8.4/17.2 = 0.488

East: weight = 3.5/17.2 = 0.203

These weights should sum exactly to 1.0, but due to rounding they do not quite do so. Using
these weights, we now construct the average unemployment rate as the weighted sum of the three
regional unemployment rates.

Canadian weighted unemployment rate = (.308  5.5) + (.488  7.2) + (.203  12.5) = 7.75

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 Chapter 2: Economic Theories, Data, and Graphs

This is a better measure of the Canadian unemployment rate because it correctly weights each
region’s influence in the national total. Keep in mind, however, that for many situations the relevant
unemployment rate for an individual or a firm may be the more local one rather than the national
average.

Question 14

The six required diagrams are shown below. Note that we have not provided specific units on the
axes. For the first three figures, the tax system provides good examples. In each case, think of
earned income as being shown along the horizontal axis and taxes paid shown along the vertical
axis. The first diagram might show a progressive income-tax system where the marginal tax rate
rises as income rises. The second diagram shows a proportional system with a constant marginal
tax rate. The third diagram shows marginal tax rates falling as income rises, even though total tax
paid still rises as income rises.

For the second set of three diagrams, imagine the relationship between the number of
rounds of golf played (along the horizontal axis) and the golf score one achieves (along the vertical
axis). In all three diagrams the golf score falls (improves) as one golfs more times. In the first
diagram, the more one golfs the more one improves on each successive round played. In the second
diagram, the rate of improvement is constant. In the third diagram, the rate of improvement
diminishes as the number of rounds played increases. The actual relationship probably has bits
of all three parts—presumably there is a lower limit to one’s score so eventually the curve
must flatten out.

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Instructor’s Manual for Ragan, Economics, Fifteenth Canadian Edition

Question 15

a) The slope of the straight line connecting two points is equal to the change in Y between the
points divided by the change in X between the points. In this case, the change in Y from the first
point to the second is 3; the change in X is 9. Thus the slope of the straight line is 3/9 = 1/3.

b) From point A to point B, the change in Y is 20 and the change in X is -10. Thus the slope of
the straight line is -20/10 = -2.

c) The slope of the function is the change in Y brought about by a one-unit change in X, which is
given by the coefficient on X, -0.5.

d) The slope of the function is the change in Y brought about by a one-unit change in X, which is
given by the coefficient on X, 6.5.

e) The slope of the function is the change in Y brought about by a one-unit change in X, which is
given by the coefficient on X, 3.2.

f) The Y intercept of a function is the value of Y when X equals 0. In this case the Y intercept is
1000.

g) The Y intercept of a function is the value of Y when X equals 0. In this case the Y intercept is
- 100.

h) The X intercept of a function (if it exists) is the value of X when Y equals 0. In this case,
when Y equals 0 we have the equation 0 = 10 – 0.1X which yields -10 = -0.1X which gives us X
= 100.

i) The equation for advertising (A) as a function of revenues (R) is A = 100,000 + (0.15)R.

Question 16

a) The slope of any curve at any point is equal to the slope of a tangent line to that curve at that
point. At point A on the curve shown in the question, the slope of the tangent line is ½ = 0.5, and
hence this is the slope of the curve at point A. For point B, the slope of the tangent line is 1 and
so this is the slope of the curve at point B. For point C, the slope of the tangent line is 2/.5 = 4
and so this is the slope of the curve at point C.

b) The marginal cost of producing good X is shown by the slope of the curve (the change in total
cost as output increases by one unit). The slope is clearly rising as the monthly level of
production rises, showing that marginal cost increases as output increases.

c) The slope of the function is positive and increasing (getting steeper) as the level of monthly
production increases.
*****

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 CHART V.

Death rates from all causes by weeks in

certain large cities of the United States
during the winter of 1918–19. (Pearl.)
 CHART VI.

Death rates from all causes by weeks in

certain large cities of the United States
during the winter of 1918–19. (Pearl.)
 CHART VII.

Death rates from all causes by weeks in

certain large cities of the United States
during the winter of 1918–19. (Pearl.)

Concerning geographical position, he did find some slight

relationship with linear distance from the city of Boston, where the
epidemic was supposed first to have begun in this country:
“This result means that the greater the linear distance of a city
from Boston the less explosive did the outbreak of epidemic
mortality in that city tend to be. This is in accord with the general
epidemiological rule that the force of an epidemic tends to diminish
as it spreads from its primary or initial focus. It must be noted,
however, that the correlation coefficient in this case is not large. It is
barely past the value where it may safely be regarded as statistically
significant. This fact may probably be taken to mean that influenza
does not follow the epidemiological law referred to with anything like
such precision as do some other epidemic diseases, notably
poliomyelitis.”
These factors having been found to be of little value in his attempt
to explain the varying curves in the 39 different cities, Pearl next
correlated the explosiveness of the epidemic mortality with deaths
from all causes, deaths from pulmonary tuberculosis, from organic
heart disease, from acute nephritis and Bright’s disease, from
influenza, from pneumonia (all forms), from typhoid fever, from
cancer and from measles, in the various cities.
“The outstanding fact which strikes one at once from this table is
the high order of the correlation which exists between the
explosiveness of the outbreak of epidemic mortality in these
communities and the normal death rate from certain causes of death
in the same communities. In the first four lines of the table the
correlation coefficients range from about 6 to more than 10 times the
probable errors. There can be no question as to the statistical
significance of coefficients of such magnitude.
“The highest correlation coefficient of all is that on the first line of
the table, for the correlation of epidemicity index with death rate
from all causes. The existence of this high correlation at once
indicates that an essential factor in determining the degree of
explosiveness of the outbreak of epidemic influenza in a particular
city was the normal mortality conditions prevailing in that city. In
the group of communities here dealt with, those cities which had a
relatively high normal death rate had also a relatively severe and
explosive mortality from the influenza epidemic. Similarly, cities
which normally have a low death rate had a relatively low, and not
sharply explosive, increase in mortality during the epidemic.
“It will also be noted that the correlation in the next three lines of
the table, namely those of pulmonary tuberculosis, so-called, organic
diseases of the heart, and chronic nephritis and Bright’s disease, are
of the same order of magnitude as that between the death rate from
all causes and the explosiveness of the epidemic outbreak of
influenza.”
 Pearl suggests that this correlation might arise because of
differences in the constitution of populations in the different cities,
or, that it was a factor of geographical position, such as the distance
from the Atlantic seaboard; but that even after correction of the
results for age distribution and geographical position, the net
correlations were actually higher than were the gross uncorrected
correlations.
“We may conclude that the most significant factor yet discovered
in causing the observed wide variation amongst these 39 American
cities in respect of the explosiveness of the outbreak of epidemic
influenza mortality in the autumn of 1918 was the relative normal
liability of the inhabitants of the several cities to die of one or
another of the three great causes of death which primarily result
from a functional breakdown of one of the three fundamental organ
systems of the animal body, the lungs, the heart and the kidneys.”
Winslow and Rogers studied the relation of the pneumonia death
rate from 1901 to 1916 to the influenza death rate of 1918 in 40 large
cities of the United States and found a distinct correlation. The cities
which have been characterized by a high pneumonia rate in the past
are precisely the cities which suffered most severally in the 1918
outbreak. This is not due especially to virulent types of pneumonia
organisms in certain sections of the country because they found this
same high correlation between total death rates and influenza death
rates, in the same cities.
They believe that these high correlations may be the result of
weaknesses in the population due to high incidences of organic
diseases and tuberculosis in earlier years, or more probably that the
correlation is an indirect one, due to the relation between each of the
factors studied and one or more underlying conditions affecting
both, such as age distribution of the population, race distribution, or
social and economic conditions in the various cities studied. Or,
finally, it may be that the high rate from tuberculosis and organic
disease in 1916 was due to these latter factors, while the high
incidence of influenza was due chiefly to proximity to the original
focus of infection. None of these explanations are considered entirely
satisfactory.
It is important to call attention to the fact that the American
observers quoted have been studying the death rate from influenza
as it is revealed in the increase of death rate from all causes, whereas
Leichtenstern and Wutzdorff, and Greenwood, in his studies in the
Royal Air Force have concerned themselves with morbidity. The
comparison of morbidity and mortality cannot be easily made as we
will show when discussing these two subjects, so we cannot conclude
that the work of Pearl and of Winslow and Rogers is at variance with
the other work quoted. The mortality curves form another
characteristic of the local spread of influenza in a community.
It is characteristic of influenza that the curve of deaths does not
fall as rapidly as does the curve for influenza cases. Thus in
morbidity curves we may expect to find a symmetrical curve for a
primary epidemic, but the mortality is rarely if ever symmetrical, the
curve rising rapidly and falling very much more slowly.
Morbidity curves in 1920 recurrences.—The curves of influenza
incidence in the recurrence of 1920 have varied in different localities,
but in certain communities where the record has been carefully
reported the epidemic appears to be characterized by a symmetrical
evolution and usually a lower death rate as compared with 1918. The
curve of incidence in the State of Massachusetts in January,
February and March, 1920, is symmetrical, if anything falling away
more rapidly than it ascends, and the duration is at least ten weeks.
The crest of the influenza wave in Massachusetts was reached on
February 4th, 5th and 6th. The peak is recorded as being in the week
of February 7th.
During the 1920 epidemic the author made a house-to-house
canvass in six representative districts in the city of Boston covering a
population of 10,000 individuals. The curve of incidence of influenza
corresponds closely with the curves for the city and the state as a
whole. The peak was reached in the same week, the week ending
February 7th, the curve was symmetrical, and the duration of the
entire epidemic was about the same. The morbidity rate for 1920,
according to our influenza census, was but half of that for 1918 for
the same population. The recurrent epidemic as we will show later
was decidedly milder (see Chart XVIII).
In Detroit the 1920 epidemic reached its peak for morbidity on the
9th day, and that for mortality on the 16th. In 1918 the morbidity
peak was not attained until the 15th day and the death peak on the
22d. The recurrent outbreak had nearly run its course within three
weeks. The following comparison between the influenza incidence in
1918 and 1920 in Detroit is taken from a report by H. F. Vaughan,
Commissioner of Health for that city. In it is shown a comparison of
the total figures on the twenty-seventh day of each of the two
epidemics:
A Comparison of the 1918 and 1920 Epidemics of Influenza in Detroit.
Statistics Made to Include Through the Twenty-seventh Day of Each
Epidemic.
Excess
Normal
Deaths influenza
influenza
from and
Influenza and
influenza pneumonia
cases pneumonia
and deaths
deaths for
pneumonia above
this season
normal
1920 (Jan.–Feb.) 11,202 1,642 197 1,445
1918 (Oct.–Nov.) 16,423 1,286 124 1,162
There had been fewer cases reported on the twenty-seventh day of
the 1920 epidemic, but these had resulted in a greater number of
deaths. On this day the recurrent epidemic had run its course, while
the 1918 one was still in full swing. On the twenty-seventh day of
1918 there were 137 influenza cases reported and 49 deaths. On this
day in 1920 there were but 24 cases and 34 deaths. Thus the second
outbreak was of shorter duration, but was more deadly while it
lasted.
Seven weeks of the 1920 epidemic in Detroit killed 0.20 per cent.
of the population, two out of every one thousand people. A similar
period at the beginning of the epidemic of 1918 witnessed the death
of 0.17 per cent. of the population. This was a smaller number, but
the epidemic at this time had not completed its course, and
continued to be more or less prevalent for twenty-one weeks,
resulting finally in the death of 0.28 per cent. of the population. The
recurrent epidemic was more highly fatal, but, being of shorter
duration, Detroit actually suffered less from it.
 Spread in Countries and Continents.
The spread of influenza is usually not limited to a single
community. Almost invariably it will travel on to another locality,
carried thither by human intercourse, and will there build again a
local epidemiologic picture more or less modified by changes in the
environment and changes in the virulence of the virus itself.
Spread, in primary waves.—Reference to the table of epidemics in
history will show that in many of the epidemics and in most of the
widespread epidemics and pandemics there appears to have been a
definite, clearcut, direction of spread from one locality to others. In
the recent literature there has appeared considerable discussion
concerning the site of origin, the endemic focus of pandemic
influenza. Briefly the question raised is as to whether there are single
or multiple foci. We will for the time ignore this perplexing question.
In either case, after the influenza virus has once attained such
communicability as to produce a pandemic it does follow a direct
course over countries and continents. This may be followed in
resumé in our table.
The disease does not at any time spread more rapidly than the
available speed of human communication between the areas affected.
If influenza does appear simultaneously in two widely separated
communities without having been brought there from a common
source it must be that it arose spontaneously from simultaneous
increase in virulence of the virus in those localities.
Influenza was prevalent in Turkestan, Western Asia, in May of
1889. It spread first to Tomsk in Siberia and did not appear in
Petrograd until the end of October. By the middle of November it had
reached Berlin and Paris, and one month later it was epidemic in
New York and Boston. Four months had been required for the
disease to reach Petrograd from Bokhara in Turkestan, while within
two months thereafter it had traveled from Russia to the United
States. In both cases the rapidity of spread corresponded to the
rapidity of the means of communication of the locality; the caravan
in Turkestan and the transatlantic liner to America. North America
was widely infected in January of 1890. So, also, Honolulu, Mexico,
Hong Kong, Japan. Ceylon first experienced the epidemic early in
February, India at the end of the month, Borneo and Australia on the
first of March, Mandalay towards the first of May, China and Iceland
in July, Central Africa in August and Abyssinia in November of 1890.
It should be noted that influenza was reported to have been
prevalent in Greenland at about the same time that it was in
Bokhara. There appears to have been no relationship between these
two outbreaks.
The spread of the pandemic may be followed also by recording the
period of greatest mortality in the various cities. This period at
Stockholm followed that at Petrograd by three weeks, and that of
Berlin by another week. The period for Paris was a week later than
for Berlin, that for London another week later, and that for Dublin
three weeks later than that for London. The week of highest
mortality in Dublin was later than that for New York or Boston.
The earlier epidemics progressed more slowly. That of 1762
prevailed in Germany in February, in London in April, in France in
July, and in America in October. In 1782 it attacked London in May,
Exeter two weeks later and Edinburgh early in June. In 1830–1832
the spread from Moscow and Petrograd through Germany required
no less than eight months to cover the latter country.
In 1872 the time required for spread from Leipzig to Amsterdam
was eighteen days, the same time that was required for a merchant in
the latter town to reach Leipzig.
There are many instances on record in which influenza has passed
by small towns in its onward course to attack a larger city and only at
some later date has the small town, not on the main line of
communication, been affected. Not only is the speed of
transportation between two communities of importance, but also the
volume of the transportation undoubtedly plays a part in the rapidity
of development in a second locality. When the disease is carried by a
vessel the first places to be attacked are the seaports and the coast
towns, be the land a continent or an island. From there it spreads
inland either rapidly or slowly according to the transportation
facilities. Formerly the question was raised whether influenza spread
in continuous lines or radiated in circles. Naturally it follows the
direct lines of communication, most of which are radially distributed
around large centers.
Leichtenstern calls attention to the fact that in the 1898 epidemic,
as in the previous one, the general direction of spread was from East
to West across Europe. This was also true of the epidemics of 1729,
1732, 1742, 1781, 1788, 1799, 1833, and 1889.
There have been in Europe two general routes followed by
pandemics, a Northern one through Russia and following the lines of
travel into Germany and through the countries of Europe; and a
Southern path coming from Asia, through Constantinople, and
entering Europe from the South, particularly Italy. With the latter,
after reaching Europe, the spread is northerly; with the former it is
southerly, and usually Spain was the country last infected.
In the United States as well, pandemic influenza usually has
spread from East to West, entering the country at or near New York
or Boston, and spreading West and South. This was true in the
autumn epidemic of 1918.
Spread in recurrences.—As a rule the manner of spread of a
secondary epidemic following the primary pandemic wave is quite
different. At a longer or shorter interval following the first spread the
disease breaks out anew in one locality or another, sometimes
simultaneously in widely separated districts. Sometimes we can
distinguish a direction of spread in the relatively small community
affected, it frequently being observed that the disease will start up in
a large city which has experienced the illness during the first
pandemic, and from there will spread to small nearby localities
which may have remained free until that time. Again, any clearcut
direction of spread may be entirely lacking. It is rare indeed that an
epidemic following another by a short interval will follow a definite
line over an entire country or continent. Such an example is,
however, to be found in the epidemic of 1833, which traveled over
Europe from Russia, spreading to the west and the south and
following practically the identical path that it had taken in 1830.
Even so it was not as widespread, for while the epidemic of 1830 had
covered the entire earth, America appears to have escaped the
second epidemic.
These disseminated and independent outbreaks are believed to
arise from endemic foci in which the virus has been deposited during
the progress of its first spread and in which the germ has survived
until it has acquired once again exalted virulence.
Usually these endemic outbreaks show in their local configuration,
a secondary type of wave. That this is not always the case we have
already indicated. The epidemic of 1732–1733 was a recurrence of
that of 1729–1730. The epidemic of 1782 had as its source the
epidemic of the years 1780–1781. The epidemic of 1788 recurred
until 1800, and was quite possibly associated with those of 1802,
1803 and 1805–1806. That of 1830 recurred in 1831–1832. Next we
have in 1833 the true pandemic originating in Russia. Recurrences of
the epidemic of 1836–1837 were found in 1838 and in 1841. Those
spreads which occurred in 1847 and 1848 found successors in the
year 1851. In 1890 the influenza outbreaks were as a rule single or
isolated and occurred in only a few places of Europe, particularly in
Lisbon, Nürnberg, Paris, Copenhagen, Edinburgh, Riga, London, etc.
It is reported that there was an unusually severe local outbreak in
Japan in August, 1890. In 1891 no general direction of spread was
manifested, yet in heavily populated areas, or states rich in lines of
communication, especially those of Europe and North America, one
could frequently trace some definite direction followed by the disease
within these relatively small territories.
A. Netter made the following observation at that time: “La Grippe
a fait des explosions simultanées ou successives, et on n’a pu en
aucune façon subordonner ces différents foyers comme cela avait été
possible en 1889–90. Il parait y avoir eu des reveils de l’épidémie sur
divers points.”
Leichtenstern describes the subsequent spread of the disease: “The
transfer of the disease by ships which played such an important role
in the first epidemic appeared to be insignificant in 1891, in spite of
the fact that influenza was present in many of the English colonies.
The third real epidemic spread of influenza was a true pandemic
which began in the autumn (October) of 1891 and lasted through the
whole winter until the spring of 1892. It involved all of Europe and
North America and spread to all other lands, but here again the
geographic distribution followed no rule. There was no spread of
influenza from a central point, no continuous spread following lines
of communication, and there was no longer an early predominance
in the cities lying on the lines of communication or in the larger cities
and commercial centers, as had been the case in the first epidemic.
In England in 1891 the first outbreaks occurred frequently in country
districts. The epidemic raged nearly four months in the northern part
before it finally reached London in May. The same was true of
Australia.
“One peculiarity of the recurrent epidemic lay in the much more
contagious character of the disease and the remarkably greater
mortality. In Sheffield the mortality in the recurrent epidemic was
greater than in the pandemic, even though the epidemic picture was
that of a primary wave.”
By way of summary of our knowledge of the primary and
secondary spread in general up to the epidemic of 1918, we may
enumerate the more important characteristics:
1. Occurrence of true pandemics at wide intervals, primarily
intervals of several decades.
2. Indefinite knowledge and conflicting evidence regarding site
and manner of origin.
3. Apparent transmission chiefly or entirely through human
intercourse.
4. Rapid spread over all countries, the rapidity roughly paralleling
the speed of human travel.
5. Rapid evolution of the disease in the communities where
outbreaks occur, with nearly equally rapid subsidence after several
weeks’ duration.
6. Apparent lack of dependance on differences of wind or weather,
seasons or climate.
7. Generally low mortality in contrast to enormous morbidity.
Variation in the incidence of disastrous secondary infections.
8. Tendency to successive recurrences at short intervals.
SECTION II.
 Influenza Epidemics Since 1893.
In this section of our report we will describe with as great accuracy
as our sources of information will permit, and in as great detail as
space will allow the events which have led up to the epidemics of
1918–20 and the various phases of the epidemics themselves. Points
of similarity with previous epidemics will be made obvious; the
differences, when of significance, will be described and studied in
detail.
 Occurrence Since 1893.
Attempts even today to determine when and where influenza has
prevailed in the world since the great pandemic of the last century
are met with great difficulties. There are several reasons for this,
chief among which is the absence of definite characteristics by which
the disease may be recognized. The isolated solitary case baffles
positive diagnosis. Nearly every year there are reports in the
literature of small outbreaks in institutions or communities in which
the clinical picture is that of epidemic influenza. As a rule the
conclusion has been in these cases that because the bacteriologic
findings did not show a predominance of Pfeiffer’s bacillus the
epidemic was not true influenza. This is particularly true in the
outbreaks in which the streptococcus predominated. Today our views
concerning the bacteriology have changed distinctly, and I believe it
is safe to say that the predominance of a streptococcus in a local
epidemic in no way rules out influenza, and that the only criteria by
which we may judge are the clinical picture and the evidence of high
infectivity, together with the epidemiologic characteristics of the
local outbreak.
Period 1893–1918.—A review of the medical literature between
1889 and 1918 gives one a certain impression which may be
summarized as follows: Between 1890 and 1900 the disease was in
general more highly prevalent in most localities than at any time
during the preceding thirty years. At no time during this decade did
the annual death rate from influenza in England and Wales fall to
anywhere near the figures that had prevailed consistently between
1860 and 1889. Between 1900 and 1915 there was a gradual
diminution, but still not to the extent that had prevailed previous to
1889. Since 1915 there appears to have been a gradual increase.
During the entire period there has been difficulty in distinguishing
between the disease in question and other respiratory tract
infections, particularly coryza, sore throat, tonsillitis, and bronchitis.
Many of the local epidemics which appear probably to have been true
influenza have had associated with them a high incidence of sore
throats. We describe this as sore throat, rather than tonsillitis,
because the clinician remarks that although the throat is sore there is
little if any demonstrable inflammation of the tonsils.
Chart VIII published by Sir Arthur Newsholme, showing the death
rate per million of population from influenza in England and Wales
gives some idea of the prevalence of the disease in the first part of the
interpandemic period in those countries. It should be remarked that
the record is for deaths from influenza only.
For records in this country it is convenient to refer to the death
rate in the State of Massachusetts; first, because the records in that
State have been carefully kept for a long period; and second, because
influenza has been carefully studied in this State during both
epidemics by two most competent epidemiologists. For the period
preceding 1889 we quote herewith from Abbott:
“For the past 45 years or more, or during the period of registration
which began with the year 1842, no epidemic of influenza has
prevailed within the State to such an extent as to have manifested
itself in any serious manner in the annual lists of deaths. An
examination of the registration reports for each year since 1842
shows that in no year were recorded more than 100 deaths from this
cause; the highest number from influenza in a single year (92)
occurred in 1857, and the least number (8) in 1884. The average
annual number of deaths from this cause reported in the State for the
period 1842 to 1888 was 38. The average number during the first
half of this period was greater than that of the last half, especially
when considered with reference to the increase of population. From
these statistics of nonepidemic influenza between the years 1842 and
1888 it appears that its greatest prevalence, or rather the years in
which the mortality from this cause was greatest, were also years of
unusual mortality from pneumonia, and in some instances from
bronchitis.”
Frost has charted the death rate per 100,000 from influenza and
from all forms of pneumonia in Massachusetts by month, from 1887
to 1916. From it he concludes that the epidemic of 1889–1892
developed in three distinct phases, the first culminating in January,
1890, the second in April and May, 1891, and the third in January,
1892. The mortality was higher in 1891 than in 1890, and still higher
in 1892, while in 1893, although there was no distinct epidemic, the
pneumonia mortality for the year was even higher than that of 1892.
Frost remarks that this corresponds to the experience in England,
and that it apparently represents the general experience in other
countries (see charts IX and X).
 CHART VIII.

Death rates per million from influenza in England and Wales from
1845 to 1917. (Newsholme.)
 CHART IX.

Monthly death rates per 100,000 from

influenza and from pneumonia in
Massachusetts from 1887 to 1916.
(Frost.)
 CHART X.

Monthly death rates per 100,000 from

influenza and pneumonia in three cities
of the United States from 1910 to 1918,
inclusive. (Frost.)

In the absence of comparable statistics for Massachusetts in 1917

and 1918, Frost has studied for those years certain other localities,
particularly Cleveland, San Francisco and New York City. The
mortality in all of these places, as well as in Massachusetts, was fairly
regular from 1910 to 1915, but in December of the latter year and
January of 1916 there occurred in New York and Cleveland a sudden
sharp rise in mortality. This was not shown distinctly in the San
Francisco curve, but it was a rise which was almost universal and
synchronous over the entire registration area. It is of interest as
indicating the operation of some definite and widespread factor, and
suggesting in this group of diseases an epidemic tendency which is
perhaps, as Frost remarks, not sufficiently appreciated. In January of
1916 he found that influenza was reported to be epidemic in twenty-
two states, including all sections of the country. The epidemic was
very mild. In the early spring of 1918 there was another sharp rise,
which we shall discuss in greater detail later.