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Transcript of BACHELOR OF ARTS IN ECONOMICS Econ 114 – MATHEMATICAL ECONOMICS Pangasinan State University Social...
BACHELOR OF ARTS IN ECONOMICS Econ 114 – MATHEMATICAL ECONOMICS
Pangasinan State UniversitySocial Science Department
CHAPTER 1INTRODUCTION TO MATHEMATICAL ECONOMICS2nd Semester, S.Y 2013 – 2014
BACHELOR OF ARTS IN ECONOMICS Econ 114 – MATHEMATICAL ECONOMICS
Pangasinan State UniversitySocial Science Department
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
Mathematics and Economics
BACHELOR OF ARTS IN ECONOMICS Econ 114 – MATHEMATICAL ECONOMICS
Pangasinan State UniversitySocial Science Department
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.
BACHELOR OF ARTS IN ECONOMICS Econ 114 – MATHEMATICAL ECONOMICS
Pangasinan State UniversitySocial Science Department
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
BACHELOR OF ARTS IN ECONOMICS Econ 114 – MATHEMATICAL ECONOMICS
Pangasinan State UniversitySocial Science Department
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.
BACHELOR OF ARTS IN ECONOMICS Econ 114 – MATHEMATICAL ECONOMICS
Pangasinan State UniversitySocial Science Department
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
BACHELOR OF ARTS IN ECONOMICS Econ 114 – MATHEMATICAL ECONOMICS
Pangasinan State UniversitySocial Science Department
Types of Economic Model
Descriptive– Like the Circular Flow
Analytical– Assumptions – Mathematical model ( functions and
equations)– Graphical analysis
BACHELOR OF ARTS IN ECONOMICS Econ 114 – MATHEMATICAL ECONOMICS
Pangasinan State UniversitySocial Science Department
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 functionQd = 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
BACHELOR OF ARTS IN ECONOMICS Econ 114 – MATHEMATICAL ECONOMICS
Pangasinan State UniversitySocial Science Department
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)
BACHELOR OF ARTS IN ECONOMICS Econ 114 – MATHEMATICAL ECONOMICS
Pangasinan State UniversitySocial Science Department
Dependent and Independent Variables
A Function is 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
BACHELOR OF ARTS IN ECONOMICS Econ 114 – MATHEMATICAL ECONOMICS
Pangasinan State UniversitySocial Science Department
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.
BACHELOR OF ARTS IN ECONOMICS Econ 114 – MATHEMATICAL ECONOMICS
Pangasinan State UniversitySocial Science Department
Inverse Function
If the original function is
then
and so the inverse function is
BACHELOR OF ARTS IN ECONOMICS Econ 114 – MATHEMATICAL ECONOMICS
Pangasinan State UniversitySocial Science Department
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
Direct vs. Inverse Relationship
BACHELOR OF ARTS IN ECONOMICS Econ 114 – MATHEMATICAL ECONOMICS
Pangasinan State UniversitySocial Science Department
Inverse and Direct Relationship
Inverse Relationship Direct Relationship
BACHELOR OF ARTS IN ECONOMICS Econ 114 – MATHEMATICAL ECONOMICS
Pangasinan State UniversitySocial Science Department
Negative Linear Relationship
X
Y
BACHELOR OF ARTS IN ECONOMICS Econ 114 – MATHEMATICAL ECONOMICS
Pangasinan State UniversitySocial Science Department
Positive Linear Relationship
Y
X