Microeconomics

Lecture Notes

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Microeconomic hypothesis

Guoqiang TIAN Department of economics Texas A&M University College Station, Texas 77843 (gtian@tamu.edu)
August, 2002/Revised: December 2011
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This lecture notes are only for the end of my teaching and convenience of my students in class, but

not for any different purpose. It is greatly acknowledged that some materials are drawn from the references in the end of each charter.

Contents
1 Preliminaries on Modern economic science and Mathematics 1.1 Nature of Modern economics . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.1 1.1.2 1.1.3 1.1.4 1.1.5 1.1.6 1.1.7 1.1.8 Modern Economics and Economic Theory . . . . . . . . . . . . . . Key Assumptions and Desired Properties Commonly employ Economics The Basic Analytical Framework of Modern Economics . . . . . . . Methodologies for Studying Modern Economics . . . . . . . . . . . Roles, Generality, and Limitation of Economic Theory . . . . . . . 1 1 1 3 4 6 8

Roles of Mathematics in Modern Economics . . . . . . . . . . . . . 10 diversity amid Economic and Mathematical run-ins . . . . 11 Distinguish between Necessary and Su?cient Conditions as well Normative and Positive Statements . . . . . . . . . . . . . . . . . . 11

1.2 Language and Methods of Mathematics . . . . . . . . . . . . .



. . . . . . . 12 1.2.1 1.2.2 1.2.3 1.2.4 1.2.5 1.2.6 1.2.7 1.2.8 Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Separating Hyperplane Theorem . . . . . . . . . . . . . . . . . . . . 14 Concave and bulbous Functions . . . . . . . . . . . . . . . . . . . . 14 Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 The Envelope Theorem . . . . . . . . . . . . . . . . . . . . . . . . . 19 manoeuvre-to-Set Mappings . . . . . . . . . . . . . . . . . . . . . . . . . 21 Continuity of a Maximum . . . . . . . . . . . . . . . . . . . . . . . 25 Fixed Point Theorems . . . . . . . . . . . . . . . . . . . . . . . . . 26

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