Calculus

696 Pages·2010·11.71 MB·English

ABOUT THE COVER

Peter Blair Henry received his first lesson in international economics at the age of 8, when his
family moved from the Caribbean island of Jamaica to affluent Wilmette, Illinois. Upon arrival in
the United States, he wondered why people in his new home seemed to have so much more than
people in Jamaica. The elusive answer to the question of why the average standard of living can
be so different from one country to another still drives him today as an Associate Professor of
Economics in the Graduate School of Business at Stanford University.
Henry began his academic career on the campus of the University of North Carolina at Chapel
Hill, where he was a wide receiver on the varsity football team and a Phi Beta Kappa graduate in
economics. With an intrinsic love of learning and a desire to make the world a better place, he
knew that he wanted a career as an economist. He also knew that a firm foundation in mathe-
matics would help him to answer the real-life questions that fueled his passion for economics—
a passion that earned him a Rhodes Scholarship to Oxford University, where he received a B.A.
in mathematics.
PETER BLAIR HENRY
International Economist
This foundation in mathematics prepared Henry for graduate study at the Massachusetts Institute
of Technology (MIT), where he received his Ph.D. in economics. While in graduate school, he served
as a consultant to the Governors of the Bank of Jamaica and the Eastern Caribbean Central Bank (ECCB). His research at the ECCB
helped provide the intellectual foundation for establishing the first stock market in the Eastern Caribbean Currency Area. His current
research and teaching at Stanford are funded by the National Science Foundation’s Early CAREER Development Program, which recog-
nizes and supports the early career-development activities of those teacher-scholars who are most likely to become the academic
leaders of the 21st century. Henry is also a member of the National Bureau of Economic Research (NBER), a nonpartisan economics
think tank based in Cambridge, Massachusetts.
Peter Blair Henry’s love of learning and his questioning nature have led him to his desired career as an international economist
whose research positively impacts and addresses the tough decisions that face the world’s economies. It is his foundation in mathe-
matics that enables him to grapple objectively with complex and emotionally charged issues of international economic policy
reform, such as debt relief for developing countries and its effect on international stock markets. The equation on this cover comes
from a paper that investigates the economic impact of a country’s decision to open its stock market to foreign investors. The paper
uses data on investment and stock prices in an attempt to answer vital questions at the frontier of current research on an important
issue for developing countries.*
Look for other featured applied researchers in forthcoming titles in the Tan applied mathematics series:
CHRIS SHANNON MARKVANDERLAAN JONATHAND.FARLEY NAVINKHANEJA
Economics and Finance Biostatistician Applied Mathematician Applied Scientist
University of California, University of California, Massachusetts Institute of Harvard University
Berkeley Berkeley Technology
*The reference for the paper is Chari, Anusha and Peter Blair Henry “Is the Invisible Hand Discerning or Indiscriminate? Investment and
Stock Prices in the Aftermath of Capital Account Liberalizations,” NBER Working Paper, Number 10318.
LIST OF APPLICATIONS

BUSINESS AND ECONOMICS Cost of producing PDAs, 75 Financing a college education, 359, 475
401(K) investors, 315 Cost of producing solar cell panels, 414 Financing a home, 239, 241
Accumulated value of an income stream, 498 Cost of producing surfboards, 150 Forecasting commodity prices, 239
Accumulation years of baby boomers, 197 Cost of removing toxic waste, 181, 296 Forecasting profits, 239, 281
Advertising, 86, 150, 239, 278, 329, 543, 575 Cost of wireless phone calls, 245 Forecasting sales, 158, 416
Ailing financial institutions, 129, 147 Creation of new jobs, 195 Franchises, 475, 498
Aircraft structural integrity, 259 Credit card debt, 88, 407 Frequency of road repairs, 531
Air travel, 390 Crop yield, 148, 371 Fuel consumption of domestic cars, 510
Alternative energy sources, 461 Cruise ship bookings, 195 Fuel economy of cars, 172, 248
Alternative minimum tax, 281, 337 Demand for agricultural commodities, 239 Gasoline prices, 291
Amusement park attendance, 196, 497 Demand for butter, 531 Gasoline self-service sales, 57
Annual retail sales, 95, 154 Demand for computer software, 535 Gas station sales, 531
Annuities, 359, 391, 475 Demand for DVDs, 576 Gender gap, 60
Assembly time of workers, 278, 383, 434 Demand for digital camcorder tapes, 481 Google’s revenue, 282
Authentication technology, 580 Demand for electricity, 582 Gross domestic product, 150, 166, 217, 239, 276, 311
Auto financing, 445 Demand for perfume, 367 Growth of bank deposits, 56
Auto replacement parts market, 89 Demand for personal computers, 195, 387 Growth of HMOs, 173, 490
Average age of cars in U.S., 300 Demand for RNs, 279 Growth of managed services, 261
Banking, 56, 147, 405 Demand for videocassettes, 83 Growth of service industries, 512
Black Monday, 285 Demand for wine, 368 Growth of Web sites, 336
Blackberry subscribers, 87 Demand for wristwatches, 181, 195 Health-care costs, 170, 407
Book design, 91, 323 Depletion of Social Security funds, 315 Health club membership, 158, 189
Box office receipts, 114, 181, 296 Depreciation, 88, 365, 448 Home mortgages, 545, 546
Broadband Internet households, 61 Designing a cruise ship pool, 589 Home sales, 173
Budget deficit and surplus, 68, 252 Determining the optimal site, 570 Home-shopping industry, 135
Business spending on technology, 281 Digital camera sales, 168 Hotel occupancy rate, 75, 89, 194
Cable ad revenue, 96 Digital TV sales, 280 Households with microwaves, 389
Cable TV subscription, 244, 407, 418, 448 Digital TV services, 44 Housing prices, 358, 447
Capital value, 521 Digital TV shipments, 95 Housing starts, 76, 195, 225
Cargo volume, 266 Digital vs film cameras, 88 Illegal ivory trade, 88
Cash reserves at Blue Cross and Blue Shield, 282 Disability benefits, 217 Income distribution of a country, 481
CDs, 351, 489 Disposable annual incomes, 86 Income streams, 468, 519
Cellular phone subscription, 262 Document management, 87 Incomes of American families, 370
Charter-flight revenue, 84, 92 Driving costs, 81, 114, 154 Indian gaming industry, 94
Chip sales, 87 Driving range of an automobile, 10 Inflation, 215
City planning, 118, 182 Drug spending, 281 Information security software sales, 578
Coal production, 447, 489 DVD sales, 176, 407 Installment contract sales, 481
Cobb-Douglas production function, 556, 557, 590, Effect of advertising on bank deposits, 278 Inventory control and planning, 129, 321, 322, 325,
593, 610 Effect of advertising on hotel revenue, 281 329, 330
COLAs, 61 Effect of advertising on profit, 150, 239 Investment analysis, 359, 469, 475
Commissions, 130 Effect of advertising on sales, 86, 169, 235, 273, 387, Investment options, 358
Commodity prices, 130, 158, 368, 489 461 Investment returns, 240, 358, 394
Common stock transactions, 4, 358 Effect of housing starts on jobs, 195 IRAs, 470
Commuter airlines, 488 Effect of inflation on salaries, 359 Keogh accounts, 240, 481
Compact disc sales, 489 Effect of luxury tax on consumption, 194 Land prices, 557, 570, 606
Comparison of bank rates, 359 Effect of mortgage rates on housing starts, 75, 239 Life span of color television tubes, 531
Complementary commodities, 553, 558 Effect of price increase on quantity demanded, 239, Life span of light bulbs, 525, 528
Computer game sales, 535 242 Linear depreciation, 61, 88
Computer resale value, 480 Effect of speed on operating cost of a truck, 235 Loan amortization, 370, 545, 546
Construction jobs, 76, 103, 184 Effect of TV advertising on car sales, 461 Loan consolidation, 358
Consumer decisions, 30 Efficiency studies, 169, 280, 438 Loans at Japanese banks, 367
Consumer demand, 168, 181, 245, 394 Elasticity of demand, 205, 208, 210, 211, 230 Locating a TV relay station, 568
Consumer price index, 169, 273, 394 E-mail usage, 87 Lorentz curves, 472, 475, 498
Consumers’ surplus, 467, 473, 474, 476, 477, 481, Energy conservation, 452, 460 Magazine circulation, 403
497, 502, 511 Energy consumption and productivity, 130, 358 Management decisions, 281, 469
Consumption function, 61 Energy efficiency of appliances, 367 Manufacturing capacity, 67, 173, 266, 284
Consumption of electricity, 435 Establishing a trust fund, 521 Manufacturing capacity operating rate, 307
Consumption of petroleum, 509 Expected demand, 394 Manufacturing costs, 74
Cost of laying cable, 26, 30 Expressway tollbooths, 532 Marginal average cost function, 200, 201, 209, 210
Cost of producing calculators, 329 Federal budget deficit, 68, 252 Marginal cost function, 198, 199, 209, 210, 437, 480
Cost of producing guitars, 406 Federal debt, 96, 314 Marginal productivity of labor and capital, 552
Cost of producing loudspeakers, 303 Female self-employed workforce, 309 Marginal productivity of money, 591
(continued)
List of Applications (continued)
Marginal profit, 203, 209, 210 Product reliability, 531 Venture-capital investment, 311

Marginal propensity to consume, 210 Production costs, 208, 209, 433 Wages, 145
Marginal propensity to save, 210 Production of steam coal, 489 Web hosting, 262
Marginal revenue, 203, 209, 210, 311, 367, 480 Productivity of a country, 557 Wilson lot size formula, 546
Market equilibrium, 83, 91, 95, 157, 158, 466 Productivity fueled by oil, 368 Worker efficiency, 62, 86, 169, 280, 329
Market for cholesterol-reducing drugs, 78 Profit of a vineyard, 92, 325 World production of coal, 447, 481
Market for drugs, 579, 583 Projected Provident funds, 262 Worldwide production of vehicles, 197
Market share, 148, 404 Projection TV sales, 480 Yahoo! in Europe, 377
Markup on a car, 10 Purchasing power, 358 Yield of an apple orchard, 91
Mass transit subsidies, 578 Quality control, 10, 406
Maximizing crop yield, 323 Racetrack design, 325 SOCIAL SCIENCES
Maximizing oil production, 368 Rate of bank failures, 220, 266, 314 Age of drivers in crash fatalities, 263
Maximizing production, 593 Rate of change of DVD sales, 176 Aging drivers, 86
Maximizing profit, 303, 309, 310, 328, 329, 567, 569, Rate of change of housing starts, 225 Aging population, 193, 218, 617
576, 588, 591, 592 Rate of return on investment, 358, 490 Air pollution, 194, 262, 263, 267, 282, 408, 511
Maximizing revenue, 310, 324, 367 Real estate, 355, 359, 428, 447, 510 Air purification, 217
Maximizing sales, 593 Reliability of computer chips, 387 Alcohol-related traffic accidents, 489
Meeting profit goals, 10 Reliability of microprocessors, 532 Annual college costs, 583
Meeting sales targets, 10 Reliability of robots, 531 Arson for profit, 545
Metal fabrication, 322 Resale value, 387 Bursts of knowledge, 124
Minimizing construction costs, 322, 329, 592, 593 Retirement planning, 358, 359, 481 Continuing education enrollment, 194
Minimizing container costs, 319, 323, 329, 593 Revenue growth of a home theater business, 358 Closing the gender gap in education, 61
Minimizing costs of laying cable, 324 Revenue of a charter yacht, 324 College admissions, 43, 578
Minimizing heating and cooling costs, 571 Reverse annuity mortgage, 475 Commuter trends, 480
Minimizing packaging costs, 323, 329 Sales forecasts, 51 Continuing education enrollment, 194
Minimizing production costs, 310 Sales growth and decay, 44 Cost of removing toxic waste, 114, 178, 181, 296
Minimizing shipping costs, 29 Sales of digital signal processors, 95, 169 Crime, 217, 239, 257, 311
Morning traffic rush, 267 Sales of digital TVs, 86 Cube rule, 62
Mortgage rates, 496 Sales of drugs, 582 Curbing population growth, 170
Multimedia sales, 220, 285 Sales of DVD players vs VCRs, 89 Decline of union membership, 67
Navigation systems, 44, 48 Sales of functional food products, 262 Demographics, 388
Net investment flow, 448 Sales of GPS equipment, 579 Dependency ratio, 282
Net sales, 578 Sales of mobile processors, 281 Disability benefits, 217
New construction jobs, 184 Sales of pocket computers, 438 Disability rates, 336
Newsmagazine shows, 418 Sales of prerecorded music, 60 Dissemination of information, 388
Nielsen television polls, 134, 147 Sales of a sporting good store, 38 Distribution of incomes, 10, 360, 473, 475
Office rents, 311 Sales of video games, 535 Educational level of senior citizens, 40, 577
Oil production, 448, 460, 481, 487 Sales promotions, 367 Effect of budget cuts on crime rate, 280
Oil spills, 230, 506, 535 Sales tax, 61 Effect of smoking bans, 280
Online ad sales, 407 Satellite radio subscriptions, 406 Elderly workforce, 262
Online banking, 366, 390 Selling price of DVD recorders, 87, 193 Endowments, 519, 521
Online buyers, 168, 377 Shopping habits, 531 Energy conservation, 456
Online hotel reservations, 328 Sickouts, 314 Energy needs, 435
Online retail sales, 358 Sinking funds, 471 Family vs annual income, 360
Online sales of used autos, 579 Social Security beneficiaries, 136 Female life expectancy, 192, 418, 610
Online shopping, 96 Social Security contributions, 43 Food stamp recipients, 315
Online spending, 96, 579 Social Security wage base, 579 Foreign-born residents, 311
Operating costs of a truck, 235 Solvency of the Social Security system, 299, 315 Gender gap, 60
Operating rates of factories, mines, and utilities, 307 Spending on Medicare, 169 Global epidemic, 440
Optimal charter flight fare, 324 Starbucks’ annual sales, 582 Global supply of plutonium, 75
Optimal market price, 364 Starbucks’ store count, 578 Growth of HMOs, 173, 284
Optimal selling price, 368 Stock purchase, 4 Health-care spending, 73, 170
Optimal speed of a truck, 325 Substitute commodities, 553, 558, 610 HMOs, 79
Optimal subway fare, 318 Supply and demand, 83, 90, 168, 226, 230, 418 Immigration, 89, 386
Outpatient service companies, 408 Tax planning, 358 Income distributions, 473
Outsourcing of jobs, 87, 193, 281 Testing new products, 217 Increase in juvenile offenders, 371
Ownership of portable phones, 168 Time on the market, 285, 314 Index of environmental quality, 329
Packaging, 52, 91, 317, 319, 329, 570, 571 Tread-lives of tires, 512 Intervals between phone calls, 532
PC shipments, 281 Truck leasing, 61 Lay teachers at Roman Catholic schools, 385, 391
Pensions, 358, 359 Trust funds, 525 Learning curves, 124, 129, 181, 239, 387, 418
Perpetual net income stream, 521 TV-viewing patterns, 134, 193 Logistic curves, 385
Perpetuities, 535 VCR ownership, 497 Male life expectancy, 245, 580
Personal consumption expenditure, 210 Use of diesel engines, 314 Marijuana arrests, 96, 440
Portable phone services, 168, 580 Value of an art object, 39 Married households, 336
Present value of a franchise, 490 Value of an investment, 74 Married households with children, 168
Present value of an income stream, 475 U.S. daily oil consumption, 511 Mass transit, 318, 578
Prime interest rate, 130 U.S. drug sales, 579 Medical school applicants, 262
Producers’ surplus, 467, 473, 474, 476, 481, 497, 511, U.S. nutritional supplements market, 88 Membership in credit unions, 448
535 U.S. online banking households, 579 Narrowing gender gap, 44
Product design, 323 U.S. strategic petroleum reserves, 511 Nuclear plant utilization, 43
(continuedon back endpaper)
B R D
ASIC ULES OF IFFERENTIATION

d
1. (cid:2)(cid:2)(c)(cid:3)0, ca constant
dx

d du
2. (cid:2)(cid:2)(un)(cid:3)nun(cid:4)1(cid:2)(cid:2)
dx dx
d du d√
3. (cid:2)(cid:2)(u(cid:5)√)(cid:3)(cid:2)(cid:2)(cid:5)(cid:2)(cid:2)
dx dx dx
d du
4. (cid:2)(cid:2)(cu)(cid:3)c(cid:2)(cid:2), ca constant
dx dx
d d√ du
5. (cid:2)(cid:2)(u√)(cid:3)u(cid:2)(cid:2)(cid:6)√ (cid:2)(cid:2)
dx dx dx
du d√
√ (cid:2)(cid:2)(cid:4)u(cid:2)(cid:2)
6. (cid:2)d(cid:2)!(cid:2)u(cid:2)@(cid:3) (cid:2)dx (cid:2)dx
dx √ √2
d du
7. (cid:2)(cid:2)(eu)(cid:3)eu(cid:2)(cid:2)
dx dx
8. (cid:2)d(cid:2)(lnu)(cid:3)(cid:2)1(cid:2)(cid:7)(cid:2)d(cid:2)u
dx u dx
B R I
ASIC ULES OF NTEGRATION
1. (cid:181) du(cid:3)u(cid:6)C
2. (cid:181) kf(u)du(cid:3)k(cid:181)f(u)du, ka constant
3. (cid:181)[f(u)(cid:5)g(u)]du(cid:3)(cid:181)f(u)du(cid:5)(cid:181)g(u)du
un(cid:6)1
4. (cid:181)undu(cid:3)(cid:2)(cid:2)(cid:6)C, n(cid:8)(cid:4)1
n(cid:6)1
5. (cid:181)eudu(cid:3)eu(cid:6)C
du
6. (cid:181)(cid:2)(cid:2)(cid:3)ln(cid:2)u(cid:2)(cid:6)C
u
Calculus
for the Managerial, Life,
and Social Sciences
Seventh Edition
This page intentionally left blank
Calculus
for the Managerial, Life,
and Social Sciences
Seventh Edition
S. T. TAN
STONEHILL COLLEGE
Australia • Canada • Mexico • Singapore • Spain
United Kingdom • United States
Executive Publisher:Curt Hinrichs Permissions Editor:Sarah Harkrader

Development Editor: Danielle Derbenti Production:Cecile Joyner, The Cooper Company
Senior Assistant Editor:Ann Day Text Designer:Diane Beasley
Editorial Assistant: Fiona Chong Photo Researcher:Stephen Forsling
Technology Project Manager:Earl Perry Copy Editor:Betty Duncan
Marketing Manager: Tom Ziolkowski Illustrator:Better Graphics, Inc.; Accurate Art
Marketing Assistant: Jessica Bothwell Cover Designer:Irene Morris
Advertising Project Manager: Nathaniel Bergson-Michelson Cover Image:Portrait of Peter Blair Henry by Peter Kiar
Project Manager, Editorial Production: Sandra Craig Cover Printer:Phoenix Color Corp
Art Director:Lee Friedman Compositor:Better Graphics, Inc.
Print/Media Buyer: Doreen Suruki Printer:R. R. Donnelley/Willard
©2006 Thomson Brooks/Cole, a part of The Thomson Corporation. Thomson Higher Education
Thomson, the Star logo, and Brooks/Cole are trademarks used herein 10 Davis Drive
under license. Belmont, CA 94002-3098
USA
ALL RIGHTS RESERVED. No part of this work covered by the copy-
right hereon may be reproduced or used in any form or by any means— Asia (including India)
graphic, electronic, or mechanical, including photocopying, recording, Thomson Learning
taping, Web distribution, information storage and retrieval systems, or in 5 Shenton Way
any other manner—without the written permission of the publisher. #01-01 UIC Building
Singapore 068808
Printed in the United States of America
1 2 3 4 5 6 7 09 08 07 06 05 Australia/New Zealand
Thomson Learning Australia
102 Dodds Street
For more information about our products, contact us at: Southbank, Victoria 3006
Thomson Learning Academic Resource Center Australia
1-800-423-0563
Canada
For permission to use material from this text or product, Thomson Nelson
submit a request online at http://www.thomsonrights.com. 1120 Birchmount Road
Any additional questions about permissions Toronto, Ontario M1K 5G4
can be submitted by email to Canada
[email protected].
UK/Europe/Middle East/Africa
Thomson Learning
High Holborn House
©2006 Thomson Learning, Inc. All Rights Reserved. Thomson Learning
50/51 Bedford Row
WebTutorTMis a trademark of Thomson Learning, Inc.
London WC1R 4LR
United Kingdom
Library of Congress Control Number: 2004114814
Latin America
Student Edition: ISBN 0-534-41986-0
Thomson Learning
Seneca, 53
Instructor’s Edition: ISBN 0-534-42000-1
Colonia Polanco
11560 Mexico
International Student Edition: ISBN: 0-495-01533-4
D.F. Mexico
(Not for sale in the United States)
Spain (including Portugal)
Thomson Paraninfo
Calle Magallanes, 25
28015 Madrid, Spain
TO PAT, BILL, AND MICHAEL