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Objectives of Learning:


Economic theories are formulated to explain different phenomenon. They try to explain the relationship between two or more variables. While formulating theories a number of tools are used by experts in this field. The tools of economic analysis are found in the realm of Mathematics. Mathematics is being profusely used in modern economic analysis. Mathematics is regarded as the second language for the students of economics. Geometry is being increasingly resorted to in order to provide pictorial presentation of economic behavior. Diagrams and Graphs provide visual impact and help to grasp and learn economics with interest and ease. A Chinese proverb says “A picture is worth a thousand words”.

Modern economists have turned to Calculus, Matrix, Algebra and Derivatives to use them as fundamental tools to express complicated aspects of economic theories and models more precisely and accurately. All these applications of mathematics are significant as a tools and techniques to impart conciseness, precision and rigour to economic analysis.

In brief, get acquainted with the terms such as Variables, Ceteris Paribus, Functions, Equations Identities, Graphs and Diagrams, Lines and curves, Slopes, Limits and Derivatives, Time Series and so on. These are the basic tools of economic analysis.


Variables play an important role in economies theories and models. A variable is a magnitude of interest can be defined and measured. In other words a variable is something whose magnitude can change. It assumes different values at different times or places. Variables frequently used in economics are income, expenditure, saving, interest, profit, investment, consumption, imports, exports, cost and so on. It is represented by a symbol instead of a specific number.

Variables can be endogenous and exogenous. An endogenous variable is a variable that is explained within a theory. An exogenous variable influences endogenous variables, but the exogenous variable is itself is determined by factors outside the theory.


All things remaining the same this assumption eliminates the influence of other factors which may negative the efforts to establish a scientific statement regarding the behavior of economic variables. For instance, if we try to establish the relationship between demand and price, there may be other variables which may also influence demand besides price. The influence of other factors may invalidate the hypothesis that quantity demanded of a commodity is inversely related to its price. If rise in price takes place along with an increasing in income or a change technology, then the effect of price change may not be the same. However, we try to eliminate the interrupting influences of other variables by assuming them to remain unchanged.

Ceteris paribus is a Latin phrase meanings, “all other things remaining the same” or all relevant factors being equal. In Economics the term “Ceteris Paribus” is used quite often to assume all other factors to remain the same, while analyzing the relationship between any two variables.

Ceteris Paribus is an assumption which we are compelled to make due to complexities in the reality. It is necessary for the sake of convenience. The limitations of human intelligence and capacity compel us to make this assumption. Besides, without the assumption we cannot reach on economic relations, sequences and conclusions. In fact, there are large number of variables interacting simultaneously at a given time. If our analysis has to be accurate we may have to examine two variables at a time which makes it inevitable to assume other variables to remain unchanged.


Function explains the relationship between two or more economic variables. A simple technical term is used to analyze and symbolizes a relationship between variables. It is called a function. It indicates how the value of dependent variable depends on the value of independent or other variables. It also explains how the value of one variable can be found by specifying the value of other variable.

For instance, economist generally links demand for good depends upon its price. It is expressed as D = f (P). Where D = demand, P = price and f = functional relationship.

Functions are classifieds into two type namely explicit function and implicit function. Explicit function is one in which the value of one variable depends on the other in a definite form. For instance, the relationships between demand and price Implicit function is one in which the variables are interdependent.


Economic theory is a verbal expression of the functional relationships between economic variables. When the verbal expressions are transformed into algebraic form we get Equations. The term equation is a statement of equality of two expressions or variables. The two expressions of an equation are called the sides of the equation. Equations are used to calculate the value of an unknown variable. The most simple equation; C = f (Y) states that C is related to Y. It says nothing about the form that this relation takes.

An equation specifies the relationship between the dependent and independent variables. Each equation is a concise statement of a particular relation. For example, the functional relationship between consumption and income can take different forms.

Here, C = f (Y) can be expressed in a simple equation as

C = a Y

Where ‘a’ is constant and it has a value greater than zero but less than one. Thus the equation shows that C is a constant proportion of income. For instance, if ‘a’ is 1/2then the consumer would always consume Rs. 0.50 out of any extra income of Rs. 1. The equation shows that if income is zero, consumption will also be zero.


An identity explains an equilibrium condition or a definitional condition. A definitional identity explains that two alternative expressions have exactly the same meaning. For example, total profit is defined as the excess of total revenue over total cost, and we can denote as:


Where π is total profit, TR is total revenue and TC is total cost.

As an another expression, Saving is defined as the difference between income and Consumption expenditure and we can say;


You are required to note that the identities are denoted by three- bar sign.

The distinction between identities and equation is very subtle and important. An identity is a relation that is true for all values of the variables; no values can be found that will contradict it. For instance, (x +y) = x2 + 2xy +2y is an expression which is true for any numerical value of x and y. Identities are statements that are compatible with any state of the universe. In case of National Income accounting we have an important identity between National Income≡ National Output ≡National Expenditur

Hence; Y ≡ O ≡ C

Equations are relations that are true only for some values of the variables but can be contradicted by other values. Moreover, identities are mere “truisms” they cannot form the basis of any theory.


A graph is a diagram which presents the relationship between two or more sets of data or variables are related to one another. Graph is most commonly used tool in modern economics. Graph depicts the functional relationship between two or more economic variables. The use of graph provides a better understanding of the economic generalizations. Graph presents a visual picture of an abstract idea. Also it is useful for accuracy and precision.

Graph can be drawn only two dimensional figures on a plain paper. It represents the values of only two variables at a time. The common method of constructing a diagram is described as below-A graph has a horizontal line termed as horizontal axis and a vertical line termed as Y axis. The point of intersection between X an Y axis is termed as Origin point.

The surface is divided into four parts, each part called Quadrants. The four quadrants are numbered anticlockwise direction as depicts in following diagram.

The first quadrant depicts the positive values of both X and Y. It is called positive quadrant. Generally, economic theories are deals with the positive quadrants.

At times the terms “Graph” and “Diagram” are used interchangeably. Diagrams, like graphs, are pictorial presentations. Diagrams may be in the form of figures such as explaining the circular flow of national income. Graphs are quite meticulous whereas diagrams can be based on abstraction. For instance, Pie diagram is a best example of a diagram that indicates through slicing the percentage- wise composition of a phenomenon, such as how much percentage of national income is generated from which sector of the economy.


The functional relationship between the variables may be Linear or non-linear. A Line or a Curve is nothing but the locus of various points. The line depicts the relationship between the variables. For example, the relationship between consumption and income

The line CC1 is a straight line and has a positive slope. It depicts that aggregate consumption is positively related to aggregate disposable income. It explains that, an increase in disposable income will promote to an increase in consumption.

Many economists try to set up the relationship between economic variables in different ways. One of the most popular and easy method is through curves. A non linear function of graph is depicted in terms of curve. Let us consider the following curves.

In the following diagram ‘A’shown a smooth downward sloping non linear demand curve. DD1 curve explained the relationship between quantity demanded of x at various prices of x. Moreover, S-S1 upward sloping supply curve also has a non-linear flavor.


Slope is an important term in modern economic analysis. Slope is defined as the amount of change in the variable measured on the vertical or Y axis per unit change in the variable measured on the horizontal or X axis. In other words, ∆Y/∆X, where delta (∆) stands for a change in the variable The slope of a curve is an exact numerical measure of the relationship between the change in the variable Y to change the variable X.

Slope is also popularly termed as ‘the rise over the run’. Here rise is the vertical distance while run is the horizontal distance. The measurement of slope can be shown as follows:

In both the cases slope = vertical distance / horizontal distance. i. e. CD / BC. However, in the above (A) diagram, slope is negative as the relationship between X and Y is inverse. In Diagram (B) the curve is slopping upwards indicating the positive relationship between X and Y. If the curve is non-linear, then a tangent is drawn at the given point and then slope is measured as the vertical distance.

The main properties of slope are: i) It can be numerically measured. ii) In a straight line, the slope is constant one. iii) The nature of the relationship between two variables can be indicated with the help of slope. If the slope is negative then it indicates inverse relationship between the two variables and if the slope is positive, it indicates direct relationship. Slope is not the same as steepness. The scale of the graph determines steepness, while the slope indicates the change in one variable due to a change in other variable.

A curve or anon –linear line is whose slope changes. Sometimes it is necessary to indicate the slope of a line at a given point. The slope of a curved line at a point is given by the slope of the straight line which is tangent to the curve at the given point.

In the above diagram, the slope of the tangent at point B can be measured by, first drawing the line FBJ tangent to the curve at point B. Then the slope of the line which is tangent is measured as NJ / MN. Similarly, the tangent line GDH gives us the slope of the line at point D of AE curve.


The concept of Production Possibility Curve (PPC) is developed by the famous economist Prof. Samuelson. It deals with the basic tool and core subject matter of modern economics particularly scarcity, choice and efficiency of resources.

Production Possibility Curve is a graphic presentation of alternative production possibilities facing an economy. As the total productive resources of the economy are limited, the economy has to choose between different goods. The productive resources can be employed for the production of various alternative goods. It has to be decided which goods are to be produced more and which one less. In deciding what amount of different goods are to be produced, the society would in fact be deciding about the allocation of resources among different possible goods. How much labour should go into raising wheat on the farms and how much should be employed in the manufacturing cloth. How many factories would produce armaments for the army and how many should produce consumer goods for civilians. We assume fixed resources, full employment, complete technical efficiency and a given technology.

Production Possibility Curve can be illustrated by an example. Let us suppose an economy has certain amount of resources which can be used for producing two goods namely mo Technological progress by improving bils and clothes. If all the resources used for producing mobiles then production of clothes is impossible and vice versa. The economy is supposed to produce a combination of both the goods. The various production possibilities of both the goods can be depicted through a table and a diagram.

Possibilities Clothes (Thousands Meters.) Mobiles
A O 20
B 1 19
C 2 17
D 3 14
E 4 10
F 5 00

With the above possibilities, if all resources are used for the production of Mobiles, then production of clothes will be zero. On the other hand if the resources are entirely used for production of clothes then production of mobiles will be zero. In between these two extremes, there are a number of other possibilities. When the production of clothes is increased the production of mobiles will come down and vice versa. The production possibilities can be shows with the help of below diagram.

In the above diagram, PP1 is the production possibility curve. It explains the schedule along with the two goods can be substituted for each other. If all the resources are used for the production of clothes, production of mobiles will be zero and vice versa. Points B,C, D and E represents the combinations of both the goods. If combination B is selected more of mobiles and less of clothes will be produced. On the other hand, combination of E signifies production of more clothes and less of mobiles. PPC shows the maximum amount of the two goods that can be produced given the inputs and technology.

The PPC has two properties: (a) PPC slopes downwards from left to right and (b) It is concave to the Origin point.PPC helps to find out solutions for basic problems such as- what to produce, how to produce, whom to distribute, how to achieve optimum utilization of resources, etc..

The problem of scarcity and concept of Opportunity cost are well brought out by production curve. PPF also indicates the level of efficiency attained by an economy in resource utilization. Moreover, the stage of development of the economy is also indicated by PPC.

Economic Growth and Shift in the Production Possibility Curve:

It is important to understand, if the productive resources expand or increase the PPC will shift outward and to the right showing that more of both goods can be produced than before. Further, when the economy makes progress in technology, that is, when the scientists discover new and innovative ways of doing things, the PPC will shift to the right and will indicate the possibility of producing more of both the goods such as from P-P1 to P2- P3 in the below diagram. The following diagram depicts the shift in the process of development.

Technological progress by improving productive efficiency allows the society to produce more of both the goods with the given and fixed amount of resources. This will mean full utilization of available labour and capital resources, the level of national income, output and employment will rise and the existing unemployment and under utilization of productive capacity will be removed. These measures aimed at generating economic growth will involve stepping up of the rate of capital accumulation and making progress in technology.


It is in the form of a chart indicating the relationship between two variables. One variable is represented on the X axis and the other on the Y axis. One dot on the graph will represent the value of both the variables. The relation between the two variables is indicated by the way the dots lies in the scatter diagram. Correlation between the two variables is indicated by either an upward or downward movement. If it is not possible to trace any trend in the diagram, then the variable do not have any correlation chart. Scatter diagrams can shows in the following different shapes:


The term derivative can be understood by looking into the function Y = f(x). In this case the value of ‘y’ also depends on the changes in the value of x. In such a case we can find the rate of change in y in response to change in x.

The derivative explains the rate of change in y when ∆x is very small. If units in which x and y , are given or known, the derivative can be expressed as so many units of y per units of x. The derivatives is itself is a function of x. In other words, for ach value of x, there is unique corresponding value for the derivatives function. The derivative of a function gives rate of change of f (x) at x. If it is positive the function is increasing at x and if it is negative, the function is decreasing at x.

One of the major problems calculus deals with is ‘to find the slope of the tangent line at a point on a curve’.

Given a simple function consider, a fn f(x) and any two points P (x1y1) and Q (x2 y2) on it.

The slope of the chord PQ is obtained by ΔyΔx. As q move closer and closer to point P, the curve reduces itself to a straight line which just touches f (x) only at a point and passes off. This is the geometrical tangent to f(x) at P, and the slope of this tangent is called the derivative. However, derivative is the slope of the tangent at a point on the curve. Therefore we have to take


If the limit of the incremental ratio at x, given by:

limh→0f(x=h-(x)exists, it is called the derivatives of f(x) at x.





  1. Lipsey and Steiner: Economics,
  2. Lipsey: An Introduction to Positive Economics,
  3. Samuelson Paul: Economics,