FUNCTIONAL RELATIONS AND TOOLS FOR ECONOMIC ANALYSIS

Economic analyses are based on looking for relevant cause-effect relations between different variables and then taking decisions on the basis of the analyses. Some of the important concepts and tools of economic analysis are discussed here.

### 1. VARIABLES TOOLS FOR ECONOMIC ANALYSIS

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** **Economic theories and models are constructed to explain economic activities. An economic model is a simplified representation of real world phenomena. For example, the Law of Demand is used to understand the relationship between price and quantity demanded.

Since the real world is extremely complex and ever changing, it is necessary to build a model with some restrictions or assumptions, to understand the relationships between different variables that matter. A variable is a magnitude of interest that can be defined and measured. In other words a variable is something whose magnitude can change or can take on different Variables.

frequently used in business economics are price, profit, revenue, cost, investment. Since each variable can have different values, it Is represented by a symbol. For instance price may be represented by P, cost by C, and so on.

Variables can be endogenous and exogenous. An endogenous variable may be a variable that's explained inside a theory. An exogenous variable influences endogenous variables however the exogenous variable is itself is set by factors outside the idea. For example, the theory of value helps to determine the equilibrium price with the help of demand and supply curves, In this model, price and quantity demanded and supplied are endogenous variables as they are within the model or they are controllable variables in the model. When price changes, the respective quantities also change in response. But there are other factors that determine demand and supply. Some of these are consumer preferences, prices of related commodities, input costs, advertisement, government policies and so on. These are exogenous variables as they are outside the model but they also have an influence on price, demand and supply.

### 2.FUNCTIONS TOOLS FOR ECONOMIC ANALYSIS

FUNCTIONS TOOL A operate shows the link between 2 or additional variables. It indicates how the value of one variable (i.e. dependent variable) depends on the value of one or more other (i.e. independent) variables. It also shows how the value of one variable can be found by specifying the value of other variable.
For instance, economists generally link the volume of consumption by the households to the receipts of disposable income (income left after deduction of taxes and addition of transfer incomes like pension, subsidies). Such behaviour is specified by saying that consumption is a function of disposable income. This functional relationship between consumption and disposable income can be expressed as

C=(f)Y

where C is aggregate consumption, Y is disposable income and f stands for the functional relation. This functional expression means that aggregate consumption depends upon the disposable income. Similarly, in business economics, functional relations between the price of a commodity (P) and quantity demanded (Q) can be expressed as Q= f (P).

### 3. EQUATIONS TOOLS FOR ECONOMIC ANALYSIS

The expression Q=f(P) states that Q is related to P. It says nothing concerning the shape that this relation takes,

An equation specifies the relationship between the dependent and price and quantity demanded can take different forms. The specific independent variables. For instance, the functional relationship between relationship between two or more variables is specified in the form of an equation

For instance the function Q= f (P) can be expressed in a simple equation as

d9- =0 …...(1)

Where, b is a constant and it has a value greater than zero but less than one. Thus the equation (1) shows that Q is a constant proportion of price. For example, if b is 0.5 then the quantity demanded would fall by 0.5 for y unit rise in price. The negative sign indicates the inverse relationship every between price and quantity demanded. The equation (1) also shows that if price is zero, quantity demanded will also be zero.

The function Q = f (P) can also be expressed in the form of an alternative equation as

Q = a - bP ...(2).

where a and b are parameters and have values greater than zero. The equation (2) also shows that quantity demanded is an inverse linear function of price. The coefficient a denotes quantity demanded at zero price. The parameter a has a positive value and is independent of price. When price 1S zero, bP will be zero, but quantity demanded will not be zero but will be equal to a. In the above equation, b measures the slope of the demand curve. It is measured as ∆Q/∆P. The demand curve has a negative slope, hence the negative sign.

Therefore, equations specify the functional relationship between dependent and independent variables. Each equation could be a brief statement of a specific relation.

### 4. ECONOMIC DATA AND TOOLS TOOLS FOR ECONOMIC ANALYSIS

Economists make use of evidence to test the relevance of a specific prediction of theories and models. They also try to explain, analyse and predict observed real world economic behaviour of people. To analyse economic issues and the relationship between variables economists use data relevant, quantifiable it absolutely essential for making business decisions.

Tools for Economic Analysis

The relationship between variables can be expressed either in words, in numerical schedules or tables, in mathematical equations, or in graphs. For example, the relationship between the quantity supplied of a commodity and its price can be expressed in the following ways:

(i)A sentence explaining the direct relationship

(ii) A supply equation Qex = -c + dPx %3D

(iii) A table giving different levels of supply at different prices

(Iv) An Upward rising curve with price on the Y-axis and supply on the X- axis.

### 5. GRAPHS TOOLS FOR ECONOMIC ANALYSIS

Graphs are geometrical tools used to express the relationship between variables. Graphs are essential in economics because they allow us to analyse economic concepts and examine historical data. Business economics makes extensive use of graphs to analyse economic relations.

A graph is a diagram showing how two or more sets of data or variables are related to one another.

The details to grasp a couple of graph square measure :

(i) The horizontal line on a graph is referred to as the horizontal axis, or sometimes the x axis. The vertical line is known as vertical axis or y axis.

(ii) The lower left hand corner where the two axes meet is called the origin. It signifies 0.

(iii) The variables are represented on the two axes.

(v) The kind of relationship between the variables on the axis is depicted in the curve or curves shown in the graph. For example, if the relationship between the variables is inverse, then the curve will be downward sloping or will have a negative slope.

### 6.CURVES TOOLS FOR ECONOMIC ANALYSIS

The functional relationship between the variables specified in the form of equations can be shown by drawing lines in the graph. The line depicts the relationship between the variables. For instance, the relationship between consumption and income shown in equation (2) is expressed by drawing å line as in Fig. 1.1.

The line CC, is a straight line and has a positive slope. It shows that aggregate consumption is positively related to aggregate disposable income. It shows that an increase in disposable income will lead to an increase in consumption. In this case the relationship between the variables is direct. Direct relationships occur once variables move within the same direction, that is, they increase or decrease along. On the other hand, inverse relationships occur when the variables move in the opposite direction.

### 7.SLOPES TOOLS FOR ECONOMIC ANALYSIS

One important way to describe the relationship between two variables is Slope of a line Slopes show us how fast or, at what rate, the dependant variable is changing in response to a change in the dependent variable. By looking at the slope of the line we can quantify the average relation between the variables. The slope is defined as the amount of change in the dependent variable measured (usually on the vertical or Y-axis) per unit change in the independent variable measured)

( Usually horizontal or X-axis). Therefore, the slope is equal to ∆Y/ ∆X, where

Y is the dependent variable; X is the independent variable and delta (∆) stands for a change.

Inother words, the slope is an exact numerical measure of the relationship between the change in Y and the change in X. For instance the slope of a demand curve is measured as

∆Q/∆P. (Though In most cases, the dependent variable is represented on the vertical axis and the independent variable is represented on the horizontal axis, the notable exceptions to this convention are the demand and supply curves, in whose case it is the reverse)

(a) Slope of a Straight Line : The measurement of slope of the straight| (Linear) line is shown in Figs. 1.2 (a) and 1.2 (b).

The movement of A to B on the lines DD1

and SS1 in Fig. 1.2 (a) and 1.2 (b) may occur in two stages. First there is a horizontal movement from A to C, indicating one unit increase in X. Second, there is a corresponding vertical movement up or down from C to B. The length of CB indicates the change in Y per unit change in X. Thus, the slope measures the change in Y per unit change in X. Since in Fig. 1.2 (a) and 1.2 (b) BC corresponds to change in Y (∆Y) and ∆C corresponds to change in X (∆X) the slope of the line ∆B is ∆Y/∆X.

In Fig. 1.2 (a) the two variables change in opposite directions, that is, when one variable increases the other decreases. So the two ∆s will always be of opposite sign. Therefore, their ratio, which is the slope of the line DD1 is always negative.

In Fig. 1.2 (b) the two variables change in the same direction. So both changes will always be either positive or negative. Therefore, their ratio, which is the slope of this line SS1 is always positive.

If the road is straight its slope is constant all over.

The slope of the line indicates whether the relationship between the two variables is direct or inverse. The relationship is direct when the variables in the same direction, that is, they increase or decrease together. Thus a positive slope indicates a direct relationship as in Fig. 1.2 (b). On the other hand, the relationship is inverse when the variables move in opposite directions, that is, one increases as the other decreases. A negative slope indicates the inverse relationship as in Fig. 1.2 (a).

(b) Slope of a Curved Line : A curved or a non-linear line has different measurements of slope at different point:

Measurement of slope of a curved line is shown by drawing a dome shape curve as in Fig. 1.3.

The curve ABCDE in Fig. 1.3 increases initially, reaches a maximum point at Cand then declines. The slope of the curved line at a point is given by the slope of the straight line, that is, tangent drawn to the curve at the given point. For instance, if we want to find out the slope or the curve at point B we have to draw a straight line t1 t1 as a tangent to the curve at point B. By calculating the slope of the straight line t, t, we can find out the slope of the curved line at point B. We can see from

Fig. 1.3 that it has a positive slope. Similarly, we can find out the slopes at different points by drawing tangents to respective points.

For instance, we can find out the slopes at the C and D by drawing Bents t3t4 and t5 t6 respectively, It can be seen from the Fig. I. hat the slope of the curve is positive in the rising region from A to C and negative in the falling region C to E. At the maximum point of the curve, that is, at point C, the slope is zero. A zero slope indicates that a small change in the variable X around the maximum point of the curve has no effect on the value of the variable Y.

Similarly, A We can also find out the slopes of a"U" shaped It's slopes curve"U" fashioned I curve initial falls, reaches a minimum purpose thus rises. can be found out by the same technique as shown in Fig.

1.3, that is, by the slopes of the tangents drawn to the curve. In the falling region the slope of the curve is negative and in the rising region the slope is positive. At the minimum point of the “U" shaped curve the slope is zero.

(C) Intercepts : The intercept is the point at which the line or the curve crosses the vertical axis. In other words it is the height of the graph where the line crosses the vertical axis. In Fig. 1.1 at point C the line CC, crosses the vertical axis. In other words OC is the height of the vertical axis where the line CC, crossed the vertical axis. Therefore, OC is the intercept. It shows the value of consumption when income is zero.

In the equation, C = a1 + a1Y

a1 is the intercept i.e. the value of C when Y is zero. There can be vertical and horizontal intercepts. The vertical intercepts shows the value of Y variable when X variables is zero. On the other hand, the horizontal intercept shows the value of X variable when Y variable is zero

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