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CHAPTER 1 INTRODUCTION TO MATHEMATICAL ECONOMICS 2 nd Semester, S.Y 2013 – 2014

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CHAPTER 1 INTRODUCTION TO MATHEMATICAL ECONOMICS 2 nd Semester, S.Y 2013 – 2014. Mathematics and Economics. Mathematics is a very precise language that is useful to express the relationships between related variables .

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CHAPTER 1

INTRODUCTION TO MATHEMATICAL ECONOMICS

2nd Semester, S.Y 2013 – 2014

mathematics and economics
Mathematics and Economics
  • Mathematics is a very precise language that is useful to express the relationships between related variables.
  • Economics is the study of the relationships between resources and the alternative outputs.
  • Therefore, math is a useful tool to express economic relationships
what is mathematical economics
What is Mathematical Economics?
  • A approach to economic analysis in which the economists make use of the mathematical symbols in the statement of the problem and also draw upon known mathematical theorems to aid in reasoning
  • Refers to economic principles and analyses formulated and developed through mathematical symbols and methods.
  • It is concerned with the empirical determination of laws of economics, using the theory and technique of mathematics and statistics.
mathematical versus non mathematical economics
Mathematical versus Non-mathematical Economics

Since mathematical economics is merely an approach to economic analysis, it should not differ from the nonmathematical approach to economic analysis in any fundamental way. The difference between these two approaches is that in the former, the assumptions and conclusions are stated in mathematical symbols rather than words and in equations rather than in sentences

economic model

Economic Model

This is a simple analytic frame which shows the relationship between the main factors, and explains the behavior of an economic theory or phenomenon

Economists use models to simplify reality in order to improve our understanding of the world

When we use it as a mathematical equation it is called a mathematical and economic model.

what makes a good model
What makes a good model?
  • Clearly and simply explains a principle without extraneous detail
  • In economics we generally use math (graphs)
  • Equations linking complex factors to study the effects of change
types of economic model
Types of Economic Model
  • Descriptive
    • Like the Circular Flow
  • Analytical
    • Assumptions
    • Mathematical model ( functions and equations)
    • Graphical analysis
function
A relationship between the values of two or more variables can be defined as a function when a unique value of one of the variables is determined by the value of the other variable or variables.

Examples of Function

R = f(X) – revenue function

Qd = f(P) – demand function

Qd = f (Price, Income, Tastes, Population, POR, ect.)

Qs = f (P, Cost of Production, Technology, etc)

Q = f (K,L) – production function)

C = f(Y) – consumption function

Function
variable and constant
Variable – A quantity that assumes different values in a particular problem. It is a value that may change within the scope of a given problem or set of operations.

Constant – a quantity whose value remains unchanged throughout a particular problem.

Numerical Constant – has the same value in all problems

Parametric Constant (Parameter) – has the same value throughout the problem but may assume different values in different problems

Ex.

R = 10x (Revenue function)

TC = a + bX (Cost)

C = a + bY (Consumption)

Qd = a – bY (Quantity Demanded)

Variable and Constant
dependent and independent variables
A Functionis a relationship between two or more variables such that a unique value of one variable is determined by the values taken by the other variables in the function. These variables can be:

Independent Variable – the variable representing the value being manipulated or changed.

Dependent Variable – observed result of the independent variable being manipulated

If every value of x is associated with exactly one value of y, then y is said to be a function of x

y = f (x). Where y is the dependent variable and x is the independent variable

Dependent and Independent Variables
inverse function
An inverse function reverses the relationship in a function. If we confine the analysis to functions with only one independent variable, x, this means that if y is a function of x, i.e.

then in the inverse function x will be a function of y, i.e.

Inverse Function
inverse function1
If the original function is

then

and so the inverse function is

Inverse Function
direct vs inverse relationship
Direct vs. Inverse Relationship

Direct Relationship

  • a positive relationship between two variables in which change in one variable is associated with a change in the other variable in the same direction.
  • In a direct relationship, as one variable, say x, increases, the other variable, say y, also increases, and if one variable decreases, the other variable decreases

Inverse Relationship

  • a negative relationship between two variables in which change in one variable is associated with a change in the other variable in the opposite direction
  • In a direct relationship, as one variable, say x, increases, the other variable, say y, decreases, and if one variable decreases, the other variable increases. For example, there is an inverse relationship between education and unemployment — that is, as education increases, the rate of unemployment decreases
inverse and direct relationship
Inverse and Direct Relationship

Inverse Relationship

Direct Relationship