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Mathematics and Statistics for Economists

Gerhard Tintner · 1953

Mathematics and Statistics for Economists

70 sections
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About this work

Gerhard Tintner, Mathematics and Statistics for Economists

Gerhard Tintner’s textbook, first published in 1953 and represented here by its 1954 second printing, presents mathematical and statistical methods as tools for economic investigation. Its organizing purpose is the training of economists who can move between theoretical relationships and empirical estimation:

This book is addressed specifically to the future econometrician—a student of economics who is willing to use the tools of mathematics and statistics in his economic investigations.

The emphasis falls on methodological preparation: mathematical formulation makes economic relationships tractable, while statistics supplies procedures for estimating them and evaluating uncertain evidence. Yet tractability should not be mistaken for an exact description of economic behaviour. Tintner makes that distinction explicit in his treatment of demand:

Linear-demand functions must be considered as approximations to the true demand functions, which may be much more complicated.

Linearity thus serves as a working simplification, not a claim that economic relationships are intrinsically simple. This distinction gives the textbook’s technical instruction an important interpretive qualification: a convenient functional form must remain answerable to the phenomenon it represents.

The later sequence proceeds through sampling theory, hypothesis tests, distribution fitting, regression and correlation, and index numbers. Guidance for further study, answers to odd-numbered exercises, computational tables, and indexes support its use as a course text and working reference. Within the treatment of inference, Tintner connects a test’s formal threshold to the possibility of an erroneous decision:

The probability of the error of the first kind is given by the level of significance.

Statistical testing therefore concerns controlled uncertainty rather than the conversion of sample results into certainty. Estimation likewise requires attention to the characteristics of economic observations. Tintner motivates one technique through its suitability for such data:

One method of estimation, employing the method of least squares, is particularly appropriate with economic data, where frequently we do not have normal distributions.

The book’s central conceptual movement is from simplified economic relationships to methods for their empirical investigation, with repeated attention to the limits of what those methods establish. Its relevance lies in joining mathematical training to statistical judgment: the prospective econometrician must learn not only to calculate, but also to distinguish approximation from description and evidential support from certainty.

Sections

This work was divided into 70 sections when it entered the library's research corpus—an apparatus for search and citation, not necessarily the author's own table of contents. Each title opens its summary.

  1. 1Title Page, Publication Details, and Dedication▾
  2. 2Preface: Mathematical Preparation for Future Econometricians▾
  3. 3Bibliography of Sources for Numerical Examples▾
  4. 4Table of Contents▾
  5. 5Functions and Graphs▾
  6. 6Linear Equations and Demand▾
  7. 7Supply, Equilibrium and Taxation▾
  8. 8Systems of Linear Equations: General Equilibrium and Economic Imputation▾
  9. 9Quadratic Equations and Nonlinear Market Equilibrium▾
  10. 10Logarithms, Pareto Income Distributions, and Constant-Elasticity Demand▾
  11. 11Arithmetic and Geometric Progressions and Their Economic Applications▾
  12. 12Determinants and Solutions of Linear Systems▾
  13. 13First-Order Difference Equations: Growth, Multipliers, and Cobweb Dynamics▾
  14. 14Functions, Demand, Revenue and Cost▾
  15. 15Difference Quotients and Limits▾
  16. 16Derivatives and Marginal Economic Quantities▾
  17. 17Differentiation: Powers, Constants, Sums and Differences▾
  18. 18Differentiation: Products, Quotients and Composite Functions▾
  19. 19Natural Logarithms and Differentiation of Logarithmic and Exponential Functions▾
  20. 20Elasticity and Its Relationship to Marginal Revenue▾
  21. 21First Derivatives and Increasing or Decreasing Functions▾
  22. 22Higher Derivatives, Concavity, and Changing Marginal Costs▾
  23. 23Single-Variable Optimization, Monopoly, Average Cost, and Inflection Points▾
  24. 24Partial Derivatives, Productivity and Elasticities▾
  25. 25Differentiation of Implicit Functions▾
  26. 26Homogeneous Functions and Exercises▾
  27. 27Euler's Theorem for Homogeneous Functions▾
  28. 28Higher and Mixed Partial Derivatives▾
  29. 29Unconstrained Maxima and Minima in Several Variables▾
  30. 30Joint Production and Multiproduct Profit Maximization▾
  31. 31Constrained Extrema and Lagrange Multipliers▾
  32. 32Utility Maximization, Consumer Demand, and Indifference Curves▾
  33. 33Competitive Production and Exercises▾
  34. 34Indefinite Integrals▾
  35. 35Recovering Total and Average Costs from Marginal Cost▾
  36. 36Definite Integrals and the Fundamental Theorem of Calculus▾
  37. 37Consumers' Surplus▾
  38. 38Frequency Definition of Probability▾
  39. 39Addition and Multiplication Laws of Probability▾
  40. 40Discrete and Continuous Probability Distributions▾
  41. 41Mathematical Expectation and the Population Mean▾
  42. 42Rules for Computing Mathematical Expectations▾
  43. 43Moments about the Origin and Exercises▾
  44. 44Central Moments, Variance, Skewness, and Kurtosis▾
  45. 45Binomial and Normal Distributions▾
  46. 46Random Sampling and Properties of Estimators▾
  47. 47Frequency Distributions, Sample Statistics, and Sheppard's Correction▾
  48. 48Large-Sample Confidence Limits for Population Means▾
  49. 49Hypothesis Tests for One and Two Population Means▾
  50. 50Normal Curve Fitting, Chi-Square Goodness of Fit, and Contingency Tables▾
  51. 51Least Squares Estimation and Fitting Economic Trends▾
  52. 52Regression in Both Directions and Economic Prediction▾
  53. 53Correlation, Explained Variance, and Regression Inference▾
  54. 54Demand and Supply Identification, Cobweb Dynamics and Exercises▾
  55. 55Index Numbers and Exercises▾
  56. 56Suggestions for Further Study: Annotated Reading Guide▾
  57. 57Answer Key, Exercises 1–27: Algebra, Equations, Growth, and Difference Equations▾
  58. 58Answer Key, Exercises 28–58: Functions, Differentiation, Elasticity, and Optimization▾
  59. 59Answer Key, Exercises 59–75: Multivariable Calculus, Economic Optimization, and Integration▾
  60. 60Answer Key, Exercises 76–85: Probability Distributions, Moments, and Estimation▾
  61. 61Answer Key: Exercises86–101▾
  62. 62Table 1: Four-Place Common Logarithms▾
  63. 63Table 2: Natural Trigonometric Functions▾
  64. 64Table 3: Four-Place Natural Logarithms▾
  65. 65Table 4: Areas of the Normal Probability Curve▾
  66. 66Table 5: Student's t-Distribution▾
  67. 67Table 6: Chi-Square Probability Scale▾
  68. 68Index of Names▾
  69. 69Index of Mathematical and Statistical Terms▾
  70. 70Index of Economic Terms▾

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