math-2011-note1 - Mathematics for Economists 1 Introduction...

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Unformatted text preview: Mathematics for Economists 1 Introduction 1.1 Motivation • Why do we need to know mathematics in order to learn economics? • What is economics? • In economics we learn how the economy works in various situations. • An economy consists of various people (consumers and producers) and resources. • In order to learn how the economy works, we need to know – how people behave in a given situation, and – what are the consequences of their behavior. • A situation that people face is represented by – the resources and technologies available to them, – their preference, etc. • Their behavior is driven by their goals. • We assume that people want to optimize, that is, to obtain the best outcome given the various constraints like resources and technologies. • Optimization problem can be solved using mathematical tools. • We also need to know how people’s behavior affect each other. • The relationship among variables can be represented by functions. • An economy can be represented by a set of functional relationships, which is called an economic model, a simplified version of a real economy. • One can use the economic model to predict what will happen after the govern- ment do something. • All this requires various techniques to handle variables and functions, which is the subject of mathematics. 1 Figure 1: What is economics? 1.2 Examples of Economic Questions • A monopolist has inverse demand function p ( x ) = 50- 2 x . The total cost func- tion is c ( x ) = 20 + 2 x + . 5 x 2 . What are the profit maximizing price and output?...
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math-2011-note1 - Mathematics for Economists 1 Introduction...

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