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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]
College of Education
School of Continuing and Distance Education
2014/2015 – 2016/2017
Session Overview
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”, McGraw 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
• A variable is something whose magnitude can change
ie. Something that can take on different values.
• Examples of variables frequently used in economics
include price, revenue, cost, national income,
consumption, investment, imports, exports etc.
• Since each variable can assume various values, it must
be represented by a symbol instead of a specific
number.
• For example: we may represent price by P, profit by
𝜋, revenue by R, cost by C and national income by Y..
• When we write P=3 or C= 8, we are ‘freezing’ these
variables at specific values.
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 9P or 0.2Y.
• 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 aP instead of 7P 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
• Due to its special feature, it is given a distinctive name parametric
constant or simply a parameter.
• It must be emphasized that even though parameters can take on
different values in a model, they are treated as datum in the model . In
this regard, parameters resemble exogenous variables since they are
both treated as givens in the model.
• As a matter of convention, parametric constants are normally
represented by symbols such as a, b, c or their counterpart Greek
alphabets: 𝛼, 𝛽 𝑎𝑛𝑑 𝛾
Slide 18
Equations and Identities
• In economic applications, we may distinguish between three types of
equations namely:
• Definitional equations
• Behavioural equations
• Equilibrium equations
• A definitional equation sets up an identity between two alternate
expressions that have exactly the same meaning. For such an equation ,
the identical –equality sign ≡ (read : identical to) is often employed in
place of the = although this is also acceptable.
• Example: Total Profit is defined as the excess of total revenue (R) over
total cost ( C). We can therefore express total profit as : 𝜋 ≡ 𝑅 − 𝐶
Slide 19
Equations and Identities
• A behavioural equation specifies the manner in which a variable
behaves in response to changes in other variables.
• This may involve human behaviour ( eg. Aggregate consumption and
how it relates to national income) or non human behaviour ( eg. How
total cost changes with changes in output levels)
• Equilibrium equations/ conditions are only relevant if the model
involves the notion of equilibrium. If it does, then the equilibrium
condition is an equation that describes the pre-requisite for at
attainment of equilibrium.
• Ex: quantity demanded = quantity supplied : 𝑄𝑑 =𝑄𝑠
• Intended Saving = Intended Investment : S= I
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