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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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INTRODUCTION TO MATHEMATICAL ECONOMICS
2nd Semester, S.Y 2013 – 2014
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
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.
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 functionFunction
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
R = 10x (Revenue function)
TC = a + bX (Cost)
C = a + bY (Consumption)
Qd = a – bY (Quantity Demanded)Variable and Constant
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 variableDependent and Independent Variables
then in the inverse function x will be a function of y, i.e.Inverse Function