Immigration in America:
Understanding the Numbers
This presentation is available at
http://www.macalester.edu/~bressoud/talks
June 21–25, 2004
David Bressoud, Mathematics, Macalester College
Kathy Fennelly, Immigration & Public Policy, Humphrey
Institute of Public Affairs, U MN
Steve Holland, Economics & Political Science, Macalester
College
lit·er·ate adj.
1. Able to read and write
2. Educated, knowledgeable
lit·er·ate adj.
1. Able to read and write
2. Educated, knowledgeable
nu·mer·ate adj.
1. Able to do arithmetic and simple geometry
2. Educated, knowledgeable
Quantitatively literate citizenship:
•Understand comparative magnitudes of risk and significance
of very small numbers (10 ppm)
•Understand that unusual events can easily occur by chance (eg.
Cancer clusters)
•Analyze economic and demographic data to support or oppose
policy proposals
•Understand difference between rates of change and changes in
rates, between average and marginal rates, and between linear
and exponential rates of growth
•Appreciate common sources of bias in surveys
"Numeracy is not the same as mathematics, nor is it an alternative to
mathematics. Rather, it is an equal and supporting partner in helping students
learn to cope with the quantitative demands of modern society. Whereas
mathematics is a well-established discipline, numeracy is necessarily
interdisciplinary. Like writing, numeracy must permeate the curriculum. When
it does, also like writing, it will enhance students' understanding of all subjects
and their capacity to lead informed lives."
Lynn Arthur Steen, Mathematics and Democracy: The Case for Quantitative
Literacy, NCED, 2001.
"Numeracy is not the same as mathematics, nor is it an alternative to
mathematics. Rather, it is an equal and supporting partner in helping students
learn to cope with the quantitative demands of modern society. Whereas
mathematics is a well-established discipline, numeracy is necessarily
interdisciplinary. Like writing, numeracy must permeate the curriculum. When
it does, also like writing, it will enhance students' understanding of all subjects
and their capacity to lead informed lives."
Lynn Arthur Steen, Mathematics and Democracy: The Case for Quantitative
Literacy, NCED, 2001.
"Numeracy is not the same as mathematics, nor is it an alternative to
mathematics. Rather, it is an equal and supporting partner in helping students
learn to cope with the quantitative demands of modern society. Whereas
mathematics is a well-established discipline, numeracy is necessarily
interdisciplinary. Like writing, numeracy must permeate the curriculum. When
it does, also like writing, it will enhance students' understanding of all subjects
and their capacity to lead informed lives."
Lynn Arthur Steen, Mathematics and Democracy: The Case for Quantitative
Literacy, NCED, 2001.
Quantitative Methods for
Public Policy
• Goals of the program
Provide a useful, quantitative education to students
throughout the College, including those who are utterly
uninterested in mathematics.
Bring together faculty from varied disciplines,
including those disciplines that avoid quantitative work,
to send a clear message to students about the advantages
of examining issues from a quantitative perspective
Assist faculty from all disciplines to understand the
relevance of quantitative methods to their own
scholarship, and enable them to make connections to
quantitative methods in their classes.
Is a big population good or bad?
• Increased drain on fixed natural resources
• Crowding, congestion, traffic
• Lower wages (supply exceeds demand)
BUT
• Larger economy => economies of scale
– E.g., public transportation requires high density
– Larger markets for movies, books, newspapers =>
diversity
• Greater specialization of workers
– Benefits of open markets/free trade
Is population increase good or bad?
• Depends on whether we are above or below the ideal target
population.
• Too fast an increase stresses infrastructure.
• Demographic issues: age structure of population, wage
structure for workers.
• Cultural issues: assimilation and tolerance
• Can we benefit from “draining the brains” and capital of
other countries?
• Growth as a component of planning [adding without
cutting]
Population
• One way to estimate what our ideal
population should be is to look at countries
that we admire, and copy them.
Populations of Largest Countries
China
1,246,871,951
India
1,000,848,550
Turkey
65,599,206
Iran
65,179,752
Thailand
60,609,046
Ethiopia
59,680,383
United States
272,639,608
Indonesia
216,108,345
Brazil
171,853,126
United Kingdom
59,113,439
Russia
146,393,569
France
58,978,172
Pakistan
138,123,359
Italy
56,735,130
Bangladesh
127,117,967
Japan
126,182,077
Congo, Democratic
Republic of the
50,481,305
Nigeria
113,828,587
Ukraine
49,811,174
Mexico
100,294,036
Burma
48,081,302
Korea, South
46,884,800
South Africa
43,426,386
Germany
82,087,361
Philippines
79,345,812
Colombia
39,309,422
Vietnam
77,311,210
Spain
39,167,744
Egypt
67,273,906
Poland
38,608,929
Persons per square km
El Salvador
282
Philippines
266
Hong Kong
6571
Haiti
250
Singapore
5540
Jamaica
245
Gaza Strip
3091
Bahrain
1015
United Kingdom
245
Vietnam
238
Germany
235
Cyprus - Turkish Sector
225
Italy
193
Bangladesh
949
Taiwan
685
Korea, South
477
Netherlands
466
Puerto Rico
434
Switzerland
183
Lebanon
348
Nepal
178
Belgium
337
Korea, North
178
Japan
337
Pakistan
177
India
337
China
134
Rwanda
327
Poland
127
West Bank
286
Denmark
126
Israel
283
Indonesia
118
Uganda
114
Guatemala
114
Kuwait
112
Slovakia
111
Hungary
110
France
108
Portugal
108
Malawi
106
Serbia
103
Egypt
68
Ethiopia
53
Mexico
52
Iraq
52
Jordan
51
Somalia
11
Congo, Republic of the
8
Canada
3
Australia
2
Tanzania
Cameroon
Eritrea
35
33
33
Estonia
Yemen
Guinea
33
32
31
Liberia
United States
Faroe Islands
30
30
29
Zimbabwe
29
Population Density is Uneven
A Population Question
The population of the US is approximately 300M.
The population of Mexico is approx. 100M.
The US added about 30M in population over the last
decade and Mexico added about 20M.
QUESTION: If this sort of growth continues in both
countries, will the population of Mexico ever
exceed that of the US?
Arithmetic Growth Model
• Add a constant amount each time period.
• Rate is described in terms of a number per
time period: e.g., 30M per decade
• This is an intuitive form of growth: water
into a bathtub, distance travelled at a
constant velocity, age of a child.
Arithmetic Growth Model
700
population (millions)
600
500
US population
Mexic an population
400
300
200
100
0
2000 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100
year
Geometric Growth Model
• Growth is proportional to size.
• Growth rate is described as a proportion or
percentage per time period.
• Examples:
– Population
– Bank interest
– Inflation
• For geometric growth, the quantity doubles in a
fixed period of time, the “doubling time.”
• More modern term, “Exponential growth.”
Doubling Time and the US
Population
US Census data
Doubling time: 25 years
(today, the doubling time
of the US population
is about 70 years)
year
Population
1790
3,929,827
1800
5,305,925
1810
7,239,814
1820
9,638,151
1830
12,866,020
1840
17,062,566
Geometric Growth Model
1400
1000
800
600
400
US population
Mexic an population
200
year
40
21
20
30
21
21
00
10
21
21
80
90
20
20
60
70
20
20
40
50
20
20
20
30
20
20
20
00
10
0
20
population (millions)
1200
Doubling Time: Rule of 72
• To approximate the doubling time corresponding to small
growth rates, divide 72 by the rate in percent.
• US: approximately 1% per year, corresponds to a doubling
time of 72 years.
• Mexico: approximately 1.8% per year; doubling time of 40
years.
• In 140 years, US would double twice, Mexico about 3 and
a half times: 2*2*2*√2 ≈ 12 times the original population!
Thus time alone relieves a debtor nation, so long as its
population increases faster than unpaid interest
accumulates on its debt.
This fact would be no excuse for delaying payment of
what is justly due [compensation for owners(!) of
slaves to be emancipated in the year 1900], but it
shows the great importance of time in this connection –
the great advantage of a policy by which we shall not
have to pay until we number 100,000,000 what by a
different policy we would have to pay now, when we
number but 31,000,000.
-Abraham Lincoln
State of the Union Address 1862