Chiang_Ch1-3

# Chiang_Ch1-3 - Chapters 1-4 Part 1 Introduction(set theory...

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Chapters 1-4 Part 1 Introduction (set theory, algebra) Part 2 Static Analysis (matrix algebra) Part 3 Comparative Static Analysis (derivatives w/ matrix algebra) Part 4 Optimization Problems (derivatives w/ constraints w/ matrix algebra, 2 nd order conditions)

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Objectives for mathematical  economics  • To understand mathematical economics problems by  stating the unknown, the data and the conditions • To plan solutions to these problems by finding a  connection between the data and the unknown • To carry out your plans for solving mathematical  economics problems • To examine the solutions to mathematical economics  problems for general insights into current and future  problems (Polya, G. How to Solve It, 2 nd  ed, 1975)
Ch. 1 The Nature of Mathematical Economics 1.1 Mathematical vs. Nonmathematical Economics 1.2 Mathematical Economics vs. Econometrics

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1.1 Mathematical vs. Nonmathematical Economics Advantage of Language of math in economics Precise, concise Draws on math theorems to show the way Forces declaration of assumptions Allow treatment of the n-variable case Language as a form of logic Logic per se (deduction/induction) Math as an extension of deductive logic From reality to rigor; math is a means not and end Too much rigor and too little reality
1.2 Mathematical Economics vs. Econometrics Deduction vs. induction Deduction: from general to specific Induction: from specific to general Weakness of deduction Correctness of initial assumptions Weakness of induction Correctness of final results Hume’s paradox: neither deduction or induction leads to the Truth so use both: the one is a check on the other

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Ch. 2 Economic Models 2.1 Ingredients of a mathematical model 2.2 The real-number system 2.3 The concept of sets 2.4 Relations and functions 2.5 Types of functions 2.6 Functions of two or more ind. Vars 2.7 Levels of generality
2.1 Ingredients of a mathematical model Variables, constants, parameters Equations and identities

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2.1 Ingredients of a mathematical
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Chiang_Ch1-3 - Chapters 1-4 Part 1 Introduction(set theory...

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