Microeconomics Essay

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Lecture Notes 1 Microeconomic Theory Guoqiang TIAN Department of Economics Texas A&M University College Station, Texas 77843 (gtian@tamu.edu) August, 2002/Revised: December 2011 1 This lecture notes are only for the purpose of my teaching and convenience of my students in class, but not for any other purpose. It is greatly acknowledged that some materials are drawn from the references in the end of each charter. Contents 1 Preliminaries on Modern Economics 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 Used 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 Conversion between Economic and Mathematical Languages . . . . 11 Distinguish between Necessary and Sufficient 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 Convex Functions . . . . . . . . . . . . . . . . . . . . 14 Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 The Envelope Theorem . . . . . . . . . . . . . . . . . . . . . . . . . 19 Point-to-Set Mappings . . . . . . . . . . . . . . . . . . . . . . . . . 21 Continuity of a Maximum . . . . . . . . . . . . . . . . . . . . . . . 25

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