# ECON 213 ELEMENTS OF MATHS FOR ECONOMISTS Session

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ECON 213 ELEMENTS OF MATHS FOR ECONOMISTS Session 0 – Nature of Mathematical Economics Lecturer: Dr. Monica Lambon-Quayefio Contact Information: [email protected]. edu. gh College of Education School of Continuing and Distance Education 2014/2015 – 2016/2017

Session Overview • This session is meant to introduce students to basic mathematical concepts and approaches in solving economic problems. Objectives • Understand the difference between mathematical and nonmathematical economics • Understand what economic models entail. Slide 2

Session Outline The key topics to be covered in the session are as follows: • Mathematical vs Nonmathematical Economics • Mathematical Economics versus Econometrics • Economic Models Slide 3

Reading List • Chiang, A. C. , “Fundamental Methods of Mathematical Economics”, Mc. Graw Hill Book Co. , New York, 1984. - • Chapter 1: Nature of Mathematical Economics • Chapter 2: Economic Models Slide 4

Topic One MATHEMATICAL VERSUS NON MATHEMATICAL ECONOMICS Slide 5

Mathematical and Nonmathematical Economics • Mathematical economics is not a distinct branch of economics as is the case of public finance, international trade etc. • It is an approach to economic analysis where economists use mathematical symbols in the statement of economic problems and use known mathematical theorems to aid in reasoning. • Mathematical economics is also described to go beyond simple geometry which presents the visual aspect of analysis. • Since mathematical economics is merely and approach, it does not differ from non mathematical approach to economics in any fundamental way. Slide 6

Mathematical and Nonmathematical Economics • The purpose of any theoretical analysis, regardless of the approach is to be able to derive a set of conclusions from a given set of assumptions. • The main difference between mathematical and non mathematical economics is that in mathematical economics, the assumptions and conclusions are formally stated in mathematical symbols and equations rather than in words and sentences as in the case of nonmathematical economics. • Inasmuch it matters little which approach is chosen, it is that perhaps beyond dispute that symbols are more convenient to use in deductive reasoning than words and sentences. • Symbols and equations are also more conducive to conciseness and preciseness of statements. • The mathematical approach also forces analysts to make their assumptions explicit at every stage of reasoning.

Mathematical and Nonmathematical Economics • In summary, the mathematical approach offers the following advantages over nonmathematical approach to analysis: • The ‘language’ ie. Symbols, equations etc. Is more concise and precise. • The approach taps into the wealth of mathematical theorems that exists for its analysis. • In forcing the analysts to clearly state all assumptions it prevents the pitfall on unintentional adoption of unwanted implicit assumptions • The approach also helps the analysts to treat the general nvariable case.

Topic Two MATHEMATICAL ECONOMICS VS ECONOMETRICS Slide 9

Mathematical Economics Versus Econometrics • Mathematical Economics is sometimes confused with another related term called Econometrics. • Econometrics is mainly concerned with the measurement of economic data while mathematical economics is mainly concerned with the application of mathematics to the purely theoretical aspects of economic analysis with little or no concern about statistical problems such as errors of measurement of the variables under study. • The course focuses more on the application of mathematics to deductive reasoning which deals primarily with theoretical rather than empirical material. • It should however be noted that theoretical and empirical analysis are often mutually reinforcing. • For example, theories can be tested against empirical data for validity before they are applied with confidence. • On the other hand, statistical work needs economic theory as a guide in order to determine the most relevant and fruitful direction of research.

Mathematical Economics Versus Econometrics: Illustration • A classic illustration of the complementary nature of theoretical and empirical studies is found in the of the aggregate consumption function. • The theoretical work of Keynes on the consumption function led to the statistical estimation of the propensity of consume. • Statistical findings from Kuznets and Goldsmith regarding the relative long-run constancy of the propensity to consume in turn stimulated the refinement of the aggregate consumption theory by Friedman and others. • In one sense, mathematical economics may be considered as the more basic of the two. • This is because, to have a meaningful statistical and econometric study, a good theoretical framework usually based on mathematical formulation is indispensable.

Topic Three ECONOMIC MODELS Slide 12

Economic Models • Like any theory, economic theory is an abstraction from the real world. • The complexity of the real economy makes is impossible to understand or study all the interrelationships at once. • The practical thing to do therefore is to pick out what appeals to our reason to be the primary factors and the relationships relevant to the problem we wish to study and focus our attention on such factors or relationships alone – this is what an economic model basically does. • An economic model is a deliberately simplified analytical framework used to enhance our understanding of the actual economy.

Ingredients of a Mathematical Model • An economic model is merely a theoretical framework. • It does not have to be mathematical as we have explained earlier. • However, if it is mathematical, it will usually consist of a set of equations designed to describe the structure of the model. • By relating a number of variables to one another in certain ways, these equations give mathematical form to the set of analytical assumptions adopted. • Relevant mathematical operations can then be applied to these equations to derive a set of conclusions which follow logically from the assumptions stated.

Variables, Constants and Parameters • Slide 15

Variables, Constants and Parameters • • When properly constructed, an economic model can be solved to give us the solution values of a certain set of variables such as the market clearing level of price or the profit maximizing output level. Such variables whose values are provided within the model are known as endogenous variables. • Sometimes, the model may also contain certain variables that are assumed to be determined by externa forces outside the model whose values are accepted as given data. These variables are called exogenous variables. • It should be noted however that, a variable which is endogenous in one economic model may be exogenous in another economic model. • For example: In an analysis of the market determination of rice price (P), the variable P is definitely endogenous. However, in the framework of a theory of consumer expenditure, P would become an exogenous variable since P is instead a datum for the individual consumer. Slide 16

Variables, Constants and Parameters • Variables usually appear in combination with fixed numbers or constants as in the expressions 9 P or 0. 2 Y. • A constant is defined as a magnitude that does not change. When a constant is joined to a variable, it is called the coefficient of that variable. • Sometimes, the coefficient may be symbolic rather than numerical. For instance the symbol a can stand for a given constant and used in the expression such as a. P instead of 7 P in a model in order to attain a higher level of generality. • The symbol a is a special case- it is supposed to represent a constant but yet it is a variable. Slide 17

Variables, Constants and Parameters • Slide 18

Equations and Identities • Slide 19

Equations and Identities • Slide 20

Session Problem Sets • What is the main difference between mathematical and nonmathematical economics? • State 4 advantages of mathematical economics over non-mathematical economics. • Differentiate between Variables, Constants and Parameters. • What are the main types of Equations? List and briefly explain. Slide 21

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