INTRODUCTION TO MATHEMATIC AL ECONOMICS

ECONOMICS 607 FALL 1983

Chapter 1: Introduction

Chapter 2: Differentials 2.1 Difference and Differential 2.2 The Taylor Expansion with Remainder 2.3 The Taylor Expansion of Multi-variable Case 2.4 Differentials of the Composite Functions 2.5 The Elasticity of Substitution 2.6 Homogeneous Function

Prof. Frank Hsiao TTh - 11:00-12:15

Appendix to 2.3 Trigonometric Functions and Directional Cosine

Chapter 3: Static and Comparative Static Analysis 3.1 A Numerical Model of a Simple Keynesian Model 3.2 The Parametric Model 3.3 Non-Linear Model and the Implicit Function Theorem

Chapter 4: Unconstrained Optimization 4.1 Maxima and Minima of a Function of One Variable 4.2 The Necessary and the Sufficient Conditions 4.3 Maxima and Minima of Multi-variable Functions 4.4 Signs of Quadratic Forms and the Second Order Conditions 4.5 Example - Properties of the Profit Function 4.6 Examples - Least Squares Estimation and Maximum Likelihood

Estimation

Chapter 5: Constrained Optimization Problem - Necessary Conditions 5.1 The Two Variables, One Constraint 5.2 Some Remarks on the Lagrange Function and Method 5.3 The Second Order Condition II - The Bordered Hessian 5.4 Sensitivity Analysis and the Envelope Theorem 5.5 Examples - General Equilibrium Theory of Production

Chapter 6: Cost Minimization and Utiltiy Maximization 6.1 The cost Minimization Problem 6.2 Topics in Production theory and Generalization Duality 6.3 Theory of Demand 6.4 Topics in demand Theory - Duality

Chapter 7 : Input-Output Analysis and Linear Programming 7.1 The Input-Output Model 7.2 Simplex Theorem and the H-Table 7.3 Duality Theorem 7.4 Parametric Programming and Comparative Static Analysis 7.5 Economic System Theory and Economic Planning

Chapter 8 : Non-Linear Programming 8.1 Necessary Condition (the Kuhn-Tucker Conditions) 8 .2 Constraint Qualifications 8.3 Sufficient Conditions of the Maximization Problem 8.4 Saddle Value Problem and An Equivalence Theorem 8.5 Economic Applications - Automobile Industry, Portfolio

Selection

Chapter 9: Hicksian General Equilibrium Model 9.1 Pure Theory of Exchange 9.2 General Equilibrium with Production 9.3 The Walras-Cassel System of General Equilibrium

- -No Joint Product ion and Fixed Input 9.4 Linear Programming and General Equilibrium--the Fixed

Point Theo rem

Econ. 607 Fall 1983

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Mathematical Econanics- Statics References

Professor Hsiao

TEXTBOOKS: Hsiao, F.S.T. Mathematical Programming and Economic TheoryLecture Notes.

Silberberg, E. The Structure of Economics, A Mathematical Analysis, r-tGraw-Hill, 1978.

SURVEYS OF THE TOPICS:

Newman, P. ( 1968) Readings in Mathematical Economics, Johns-Hopkins Press.

Arrow, K.J. and M.D. Intriligator, ed. (1981) Handbook of Mathema.tical Economics, in 3 volumes, North-Hollans, 1981.

Hsiao, FST. "Quantitative Training in Economics-A Personal Guide," mimeographed, 1982.

Tower, E. ed. "Mathematical Economics and Mathematical Models of Economic Growth," Vol. 19 of F.conanics Reading Lists, Cburse outlines, Exams Puzzles and Problems, Eno River Press, 1981 .

MAIN REFERENCES

Arrow, K.J . and M.D. Intriligator, ed. Handbook for Mathematical Economicsin 3 volumes, North-Holland, 1981 .

Allen, R.G.D. (Allen II) Mathematical Economics, 2nd edition, St. Martin, 1959.

Intriligator, M.D. Mathematical Optimization and Economic 'lheory, Prentice Hall, 1971.

Lancaster K.

Sydsateter, K. Press 1981

Takayama A.

Mathematical Econanics, MacMillan 1968.

Topics in Mathematical Analysis for Econanists, Academic (HB 135 S88).

Mathematical Economics, The Dryden Press, 1974 .

GENERAL REFERENCES

Mathematical for Economists - Statics, Introductory to Advanced

Chiang, A. (1974) Fundamental Methods in Mathematical Economics McGrawHill, 2nd ed. (Popular elementary text)

Yamane, T. (1962) Mathematics for Economists, Prentice-Hall, (Elementary)

Allen R.G.D., ( 1938) Mathematical Analysis for Economists MacMillanclassic textbooks, many important topics)

Allen, R.G. D., (1963) Mathematical Econanics, Macmillan, 2nd ed. (Classic t ext, basic topics in two decades ago) •

Nikaido, H., (1970) Introduction to Sets and Mapping in Moden Economics,North-Holland. (Elementary introduction to abstract mathematics)

Koopmans, T.C., (1957) Three Essays on the State of Econanic Science, McGraw-Hill. (Essay one, introduction to abstract econcmics)

Benavie, A. (1972) Mathematical Techniques for Economics Analysis, Prentice-Hall. ( Statics and dynamics, with proofs of mathematical theorems)

Koo, Dl, (1977) Elements of Optimization with Applications in Economics and Business, Springer-Verlag. EMphasis on mathematical programming

Intriligator, M., (1971) Mathematical Optimization and Economic Theory, Prentice-Hall. (casual introduction to the topics)

l K., (1968) Matherratical Economics, Macmillan. (An unbalanced early treatment of the topics)

Gale, D., (1970) Linear Economic Models M:Graw-Hill. (Rigorous introduction of linear models hard notations)

Sydsaetor, K. , (1981) Topics in Matherratical Analysis for Economists , Academic Press . (Introductory to intermediate materials

Takayama A., (1974) Mathematical Econanics, Dryden. Comprehensivetreatment of the topics)

Nikaido, H., (1968) Convex Structure and Economic Theory, Academic. {Special topics in then-space)

Karlin, s . , (1959) Mathematical Methods and Theory in Games, Progranrning, and Economics, Vol. 1, Addison-Wesley. (An earlier work by aa mathematician

Klein, E. , (1979) Matherratical Methods in Theoretical Economics: 'Ibpological and Vector Space Foundations of EquilibriumAnalysis, Academic Press . (Introduction to axiomatic, topological, economic models)

Murata, Y., (1977) Mathematics for Stability and Optimization of Economic Systems Academic Press . {Rigorous treatment of special topics)

Mathematics - calculus Apostol, T.M., calculus, I, II, Braisdel, 1962, 1967 . (Introductory to

intermediate text, good examples)

Thomas, G.B . , calculus and Analytic Geometry, Addison-Wesley, 1953. {a popular introductory text)

Hardy, G.H., (1952) A Course of Pure Ma.thematics, 10th ed(A classical treatise in England)

Courant, R., (1937) Differential and Integral calculus, Vol. I and II, Interscience Publishers, 2nd ed (A classical treatise in Germany

Diendonne, J., Foundation of Modern Analysis, 1960. (A classic treatise in France, very abstract)

Apostal, T.M., methematical Analysis, A modernApproach to Advanced calculus, .Addison-Wesley, 1957 . (The theory of functions of several variables, more abstract than most

Buck, R.C., Advanced calculus, McGraw-Hill, 1956. (Many topics are specialized to 3-space)

Bc::,..ma.n, F. and F.A. Gerard, Higher calculus, cambridge University Press, 1967. intermediate to advanced treatise, good arrangement of topics for econanists), QA 303 B86) .

Franklin, P., methodsof Advanced calculus, McGraw-Hill 1944. (Treatment of special topics)