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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 programProvide 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
United States 272,639,608
Indonesia 216,108,345
Brazil 171,853,126
Russia 146,393,569
Pakistan 138,123,359
Bangladesh 127,117,967
Japan 126,182,077
Nigeria 113,828,587
Mexico 100,294,036
Germany 82,087,361
Philippines 79,345,812
Vietnam 77,311,210
Egypt 67,273,906
Turkey 65,599,206
Iran 65,179,752
Thailand 60,609,046
Ethiopia 59,680,383
United Kingdom 59,113,439
France 58,978,172
Italy 56,735,130
Congo, Democratic Republic of the 50,481,305
Ukraine 49,811,174
Burma 48,081,302
Korea, South 46,884,800
South Africa 43,426,386
Colombia 39,309,422
Spain 39,167,744
Poland 38,608,929
Hong Kong 6571
Singapore 5540
Gaza Strip 3091
Bahrain 1015
Bangladesh 949
Taiwan 685
Korea, South 477
Netherlands 466
Puerto Rico 434
Lebanon 348
Belgium 337
Japan 337
India 337
Rwanda 327
West Bank 286
Israel 283
El Salvador 282
Philippines 266
Haiti 250
Jamaica 245
United Kingdom 245
Vietnam 238
Germany 235
Cyprus - Turkish Sector 225
Italy 193
Switzerland 183
Nepal 178
Korea, North 178
Pakistan 177
China 134
Poland 127
Denmark 126
Persons per square km
Tanzania 35
Cameroon 33
Eritrea 33
Estonia 33
Yemen 32
Guinea 31
Liberia 30
United States 30
Faroe Islands 29
Zimbabwe 29
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
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
0
100
200
300
400
500
600
700
2000 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100
year
population (millions)
US population
Mexican population
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
0
200
400
600
800
1000
1200
1400
200020102020203020402050206020702080209021002110212021302140
year
population (millions)
US population
Mexican population
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 LincolnState of the Union Address 1862
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