SCHAUMS
                                                 OUTLINE OF
                         Theory and Problems of
                                          INTRODUCTION TO
         MATHEMATICAL
                             ECONOMICS
                                                       Third Edition
                        EDWARDT.DOWLING,Ph.D.
                                               Professor and Former Chairman
                                                      Department of Economics
                                                            Fordham University
                                           Schaums Outline Series
                                                                 McGRAW-HILL
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                           To the memory of my parents,
                       Edward T. Dowling, M.D. and Mary H. Dowling
     EDWARD T. DOWLING is professor of Economics at Fordham University. He was Dean of Fordham College from 1982 to 1986 and 
     Chairman of the Economics Department from 1979 to 1982 and again from 1988 to 1994. His Ph.D. is from Cornell University and his 
     main areas of professional interest are mathematical economics and economic development. In addition to journal articles, he is the author 
     of Schaum’s Outline of Calculus for Business, Economics, and the Social Sciences, and Schaum’s Outline of Mathematical Methods for 
     Business and Economics. A Jesuit priest, he is a member of the Jesuit Community at Fordham.
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                                PREFACE
     Themathematics needed for the study of economics and business continues to grow with each passing
     year, placing ever more demands on students and faculty alike. Introduction to Mathematical
     Economics, third edition, introduces three new chapters, one on comparative statics and concave
     programming, one on simultaneous differential and difference equations, and one on optimal control
     theory. To keep the book manageable in size, some chapters and sections of the second edition had to
     beexcised. These include three chapters on linear programming and a number of sections dealing with
     basic elements such as factoring and completing the square. The deleted topics were chosen in part
     because they can now be found in one of my more recent Schaum books designed as an easier, more
     detailed introduction to the mathematics needed for economics and business, namely, Mathematical
     Methods for Business and Economics.
      The objectives of the book have not changed over the 20 years since the introduction of the first
     edition, originally called Mathematics for Economists. Introduction to Mathematical Economics,third
     edition, is designed to present a thorough, easily understood introduction to the wide array of
     mathematical topics economists, social scientists, and business majors need to know today, such as
     linear algebra, differential and integral calculus, nonlinear programming, differential and difference
     equations, the calculus of variations, and optimal control theory. The book also offers a brief review
     of basic algebra for those who are rusty and provides direct, frequent, and practical applications to
     everyday economic problems and business situations.
      The theory-and-solved-problem format of each chapter provides concise explanations illustrated
     by examples, plus numerous problems with fully worked-out solutions. The topics and related
     problems range in difficulty from simpler mathematical operations to sophisticated applications. No
     mathematical proficiency beyond the high school level is assumed at the start. The learning-by-doing
     pedagogy will enable students to progress at their own rates and adapt the book to their own
     needs.
      Those in need of more time and help in getting started with some of the elementary topics may
     feel more comfortable beginning with or working in conjunction with my Schaums Outline of
     Mathematical Methods for Business and Economics, which offers a kinder, gentler approach to the
     discipline. Those who prefer more rigor and theory, on the other hand, might find it enriching to work
     along with my Schaums Outline of Calculus for Business, Economics, and the Social Sciences,which
     devotes more time to the theoretical and structural underpinnings.
      Introduction to Mathematical Economics, third edition, can be used by itself or as a supplement
     to other texts for undergraduate and graduate students in economics, business, and the social sciences.
     It is largely self-contained. Starting with a basic review of high school algebra in Chapter 1, the book
     consistently explains all the concepts and techniques needed for the material in subsequent
     chapters.
      Since there is no universal agreement on the order in which differential calculus and linear algebra
     should be presented, the book is designed so that Chapters 10 and 11 on linear algebra can be covered
     immediately after Chapter 2, if so desired, without loss of continuity.
      This book contains over 1600 problems, all solved in considerable detail. To get the most from the
     book, students should strive as soon as possible to work independently of the solutions. This can be
     done by solving problems on individual sheets of paper with the book closed. If difficulties arise, the
     solution can then be checked in the book.
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