 # Some Mathematical Tools Used in Economics

## IntroductionVarious concepts of economics and statistics are expressed in terms of numbers like, demand, supply, price, national income, etc. These economic variables are often related to each other. One way to express the relationship is functions. A function is a relationship amongst two or more variables. In a functional relationship one variable is related to another variable in such a way that, to every value of the one variable (say, X), there is one and only one possible value of the other variable (say, Y). Functional forms refer to the nature of the relationship between variables in the function. There are two types of relation    Positive relation: When two variables move in the same direction, they are said to be positively related. For e.g., income of a consumer and its consumption.    Negative relation: When two variables move in the opposite direction, they are said to be negatively related. For e.g., price and quantity demanded.The slope of a straight line is the magnitude of a change in variable measured on the Y- axis divided by per unit change in the variable measured on the X – axis. An upward sloping line has a positive slope while a downward sloping line has a negative slope.

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• Q1

Distinguish between dependent variable and independent variable?

Marks:2

Mathematical Formula for any relationship can be written as:

Y=f(X)

 Independent variable Dependent variable It can take any value. It’s value is determined by the value of independent variable. In the equation, X is the independent variable. In the equation, Y is the dependent variable. It is written on the left hand side of equation. It is written on the right hand side of the equation.

• Q2

What is a function?

Marks:2

It is a relationship amongst two or more than two variables. In a functional relationship one variable is related to another variable in such a way that, to every value of the one variable (say, X), there is one and only one possible value of the other variable (say, Y).

• Q3

What is the value of the slope if Y=6+2x

Marks:1

On comparing it with general form of equation i.e. Y=a+bX we get slope equals to 2.

• Q4

What does b indicates in the given equation Y = a + b X.

Marks:1

The parameter ‘b’ in the equation indicates the value of slope.