## Student Solutions Manual for Mathematics for Economics

by Hoy, Livernois, McKenna, Rees, Stengos

### Instructor Requests

Solutions to odd-numbered exercises in the fourth edition of Mathematics for Economics.

This student solutions manual contains solutions to odd-numbered exercises in the fourth edition of Mathematics for Economics.

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Contents (pg. v)
Introduction (pg. vii)
Chapter 1: Algebra and Arithmetic Reviews and Self-Tests (pg. 1)
1.1 Review of Basic Arithmetic (pg. 1)
1.2 Review of Basic Algebra (pg. 9)
Chapter 2: Review of Fundamentals (pg. 27)
Section 2.1 (page 29) (pg. 27)
Section 2.2 (page 38) (pg. 27)
Section 2.3 (page 51) (pg. 28)
Section 2.4 (page 69) (pg. 29)
Review Exercises (page 72) (pg. 31)
Chapter 3: Sequences, Series, and Limits (pg. 33)
Section 3.1 (page 77) (pg. 33)
Section 3.2 (page 82) (pg. 33)
Section 3.3 (page 95) (pg. 34)
Section 3.4 (page 100) (pg. 35)
Section 3.5 (page 111) (pg. 35)
Review Exercises (page 113) (pg. 36)
Chapter 4: Continuity of Functions (pg. 40)
Section 4.1 (page 126) (pg. 40)
Section 4.2 (page 138) (pg. 42)
Review Exercises (page 141) (pg. 45)
Chapter 5: The Derivative and Differential for Functions of One Variable (pg. 48)
Section 5.1 (page 151) (pg. 48)
Section 5.2 (page 159) (pg. 48)
Section 5.3 (page 165) (pg. 49)
Section 5.4 (page 192) (pg. 50)
Section 5.5 (page 206) (pg. 52)
Section 5.6 (page 219) (pg. 53)
Review Exercises (page 221) (pg. 53)
Chapter 6: Optimization of Functions of One Variable (pg. 58)
Section 6.1 (page 239) (pg. 58)
Section 6.2 (page 259) (pg. 59)
Section 6.3 (page 279) (pg. 60)
Review Exercises (page 280) (pg. 61)
Chapter 7: Linear Equations and Vector Spaces (pg. 66)
Section 7.1 (page 293) (pg. 66)
Section 7.2 (page 303) (pg. 66)
Section 7.3 (page 326) (pg. 67)
Review Exercises (page 329) (pg. 68)
Chapter 8: Matrices (pg. 70)
Section 8.1 (page 338) (pg. 70)
Section 8.2 (page 351) (pg. 70)
Section 8.3 (page 355) (pg. 70)
Section 8.4 (page 361) (pg. 71)
Review Exercises (page 362) (pg. 71)
Chapter 9: Determinants and the Inverse Matrix (pg. 73)
Section 9.1 (page 378) (pg. 73)
Section 9.2 (page 383) (pg. 73)
Section 9.3 (page 389) (pg. 74)
Section 9.4 (page 400) (pg. 75)
Section 9.5 (page 403) (pg. 76)
Review Exercises (page 404) (pg. 76)
Chapter 10: Further Topics in Linear Algebra (pg. 78)
Section 10.1 (page 421) (pg. 78)
Section 10.2 (page 429) (pg. 78)
Review Exercises (page 439) (pg. 79)
Chapter 11: Calculus for Functions of n Variables (pg. 81)
Section 11.1 (page 454) (pg. 81)
Section 11.2 (page 461) (pg. 82)
Section 11.4 (page 481) (pg. 82)
Section 11.5 (page 496) (pg. 83)
Section 11.6 (page 500) (pg. 83)
Section 11.7 (page 509) (pg. 85)
Section 11.8 (page 514) (pg. 85)
Review Exercises (page 516) (pg. 85)
Chapter 12: Optimization of Functions of n Variables (pg. 89)
Section 12.1 (page 529) (pg. 89)
Section 12.2 (page 541) (pg. 90)
Section 12.3 (page 546) (pg. 92)
Review Exercises (page 548) (pg. 94)
Chapter 13: Constrained Optimization (pg. 98)
Section 13.1 (page 571) (pg. 98)
Section 13.2 (page 577) (pg. 100)
Section 13.3 (page 586) (pg. 100)
Review Exercises (page 594) (pg. 101)
Chapter 14: Comparative Statics (pg. 104)
Section 14.1 (page 601) (pg. 104)
Section 14.2 (page 621) (pg. 105)
Section 14.3 (page 630) (pg. 107)
Review Exercises (page 632) (pg. 109)
Chapter 15: Nonlinear Programming and the Kuhn-Tucker Conditions (pg. 113)
Section 15.1 (page 654) (pg. 113)
Section 15.2 (page 671) (pg. 115)
Review Exercises (page 673) (pg. 117)
Chapter 16: Integration (pg. 122)
Section 16.1 (page 687) (pg. 122)
Section 16.2 (page 700) (pg. 122)
Section 16.3 (page 709) (pg. 125)
Section 16.4 (page 719) (pg. 126)
Section 16.5 (page 725) (pg. 127)
Review Exercises (page 727) (pg. 128)
Chapter 18: Linear, First-Order Difference Equations (pg. 130)
Section 18.1 (page 755) (pg. 130)
Section 18.2 (page 761) (pg. 130)
Review Exercises (page 762) (pg. 130)
Chapter 19: Nonlinear, First-Order Difference Equations (pg. 132)
Section 19.1 (page 774) (pg. 132)
Section 19.2 (page 779) (pg. 132)
Review Exercises (page 781) (pg. 133)
Chapter 20: Linear, Second-Order Difference Equations (pg. 135)
Section 20.1 (page 808) (pg. 135)
Section 20.2 (page 813) (pg. 135)
Review Exercises (page 814) (pg. 136)
Chapter 21: Linear, First-Order Differential Equations (pg. 137)
Section 21.1 (page 832) (pg. 137)
Section 21.2 (page 838) (pg. 137)
Review Exercises (page 840) (pg. 137)
Chapter 22: Nonlinear, First-Order Differential Equations (pg. 139)
Section 22.1 (page 851) (pg. 139)
Section 22.2 (page 854) (pg. 140)
Review Exercises (page 855) (pg. 140)
Chapter 23: Linear, Second-Order Differential Equations (pg. 141)
Section 23.1 (page 875) (pg. 141)
Section 23.2 (page 881) (pg. 141)
Review Exercises (page 882) (pg. 141)
Chapter 24: Simultaneous Systems of Differential and Difference Equations (pg. 143)
Section 24.1 (page 907) (pg. 143)
Section 24.2 (page 929) (pg. 145)
Section 24.3 (page 943) (pg. 145)
Review Exercises (page 945) (pg. 146)
Chapter 25: Optimal Control Theory (pg. 149)
Section 25.1 (page 962) (pg. 149)
Section 25.2 (page 974) (pg. 150)
Section 25.3 (page 988) (pg. 151)
Section 25.4 (page 1002) (pg. 152)
Section 25.5 (page 1012) (pg. 153)
Section 25.6 (page 1019) (pg. 154)
Review Exercises (page 1021) (pg. 155)

#### Michael Hoy

Michael Hoy is Professor in the Department of Economics and Finance at the University of Guelph.

#### John Livernois

John Livernois is Professor in the Department of Economics at the University of Guelph

#### Chris McKenna

Chris McKenna is formerly a Professor in the Department of Economics and Finance at the University of Guelph.

#### Ray Rees

.Ray Rees is Professor of Economics Emeritus at the Center for Economic Studies (CES) at the University of Munich.

#### Thanasis Stengos

Thanasis Stengos is Professor in the Department of Economics and Finance at the University of Guelph.

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