Lord Kelvin, a well known English scholar, says that: “Your knowledge is of meager and unsatisfactory kind if you cannot measure what you are speaking about.”

We must know some methods to measure elasticity of demand to reflect our sound knowledge about this concept. This credit goes to Marshall that he has introduced the concept of “unity” which serves as benchmark to measure elasticity of demand. Generally we observe the following three possibilities of degrees of elasticity of demand:

- Ed = 1
- Ed > 1
- Ed < 1

Let’s dive into the concepts of elasticity of demand measurement.

## Total Expenditure / Total Outlay Method

### Ep = 1

If there is no change in total expenditures due to a change in price, it indicates that there is an equal proportional change in price and quantity demanded which reflects that price elasticity of demand is equal to unity. Symbolically,

Both the table and diagram confirm that Ep = 1.

Moreover, we derive a normal demand curve which also indicates that Ep = 1.

### Ep > 1

If there is a negative relationship between change in price and total expenditures, it indicates that proportional change in quantity demanded is greater than proportional change in price which reflects that price elasticity of demand is greater than unity. Symbolically,

*See the table and diagram*

Both the table and diagram confirm the situation and as a result, we get flatter demand curve which is the indication that Ep > 1.

**Ep < 1**

If there is a positive relationship between change in price and total expenditures, it indicates that proportional change in quantity demanded is less than proportional change in price which reflects that price elasticity of demand is less than unity. Symbolically,

The given data confirm the situation and as a result we get a steeper demand curve which shows that Ep<1

## Percentage Method / Flux Method:

In this method, we find price elasticity of demand with the help of following formula.

Prof. Flux introduced this method

**EP = Percentage change is Quantity Demanded / Percentage change in Price**

Now we discuss different possibilities of degrees of price elasticity of demand under this method:

### Ep = 1

If there are equal percentage changes in quantity demanded and price, it indicates that Ep = 1. For example, if 10% change in price leads to 10% change in Qd, it means that Ep=1. According to the formula, we have:

**EP = 10% / 10% = 1**

### Ep > 1

If percentage change in Qd is greater than a percentage change in price, it indicates that Ep > 1. For instance, if 10% change in price leads to 20% change in Qd, it reveals that :

**EP = 20% / 10% = 2 > 1**

### Ep < 1

If the percentage change in Qd is less than a percentage change in price, it means that Ep<1. For example, if 10% change in price leads to 5% change in Qd, it reflects that:

## Arithmetic Method:

We can measure point and arc elasticity of demand with the help of the arithmetic method.

### Point Elasticity of Demand

The elasticity of demand at a particular point of the demand curve is known as point elasticity. This situation appears when there are so minor changes in price and Qd that two points on the demand curve apparently look like one point. In such a case, we measure price elasticity of demand by the following formula

Prof. Marshall introduced the concept of point elasticity.

A negative sign represents the negative relationship between price and quantity demanded and it is ignored when we decide the degree of elasticity of demand. In the present problem, we have **EP = 1 / 2 < 1**

### Arc Elasticity of Demand:

By arc elasticity, we mean an average elasticity of demand at two distinctive points lying on a demand curve:

In the words of Boumal,

“Arc elasticity is a measure of the average responsiveness to price changes exhibited by a demand curve over some finite stretch of the curve.”

The concept of arc elasticity appears when there are remarkable changes in price and quantity demanded and as a result, we get distinctive points on an arc demand curve. We can measure arc elasticity of demand by the following formula

The concept of arc elasticity was introduced by Dalton and then it was further developed by Lerner

## Geometric Method

Geometrically, point elasticity and arc elasticity of demand can be measured under two cases:

- Straight demand curve
- Arc demand curve

## MEASUREMENT OF POINT ELASTICITY

Case – i

### Straight Demand Curve

The demand curve is extended to quantity – axis and price- axis. Now we can measure price elasticity at a particular point with the help of following formula:

Case – ii,

### Arc Demand Curve

We draw a tangent line at the given point and extend it to quantity-axis and price – axis. The previous procedure is repeated to measure price elasticity of demand. See the figure:

If we are interested to measure Ep at point “A”, we draw a tangent line which serves as demand curve. We extend this curve up to quantity-axis and price – axis and find Ep as under:

Since numerator is greater them denominator, hence Ep > 1

To sum up, we conclude that point elasticity is:

- Equal to unity at mid-point of the demand curve.
- Less than unity at the point lying right to the mid-point of the demand curve
- Greater than unity at the point lying to the left of the mid-point of the demand curve
- Equal to zero at the point lying on the extreme right to the mid-point of the demand curve
- Equal to infinity at the point lying on the extreme left to the mid-point of the demand curve

### MEASUREMENT OF ARC ELASTICITY

Case – i,

#### Straight Demand Curve

If we are interested to measure arc elasticity (i.e. average straight elasticity) at two distinctive points on a straight demand curve, we take mid-point of the two distinctive points of the demand curve. The point elasticity at the mid-point represents arc elasticity of the two points. It is explained in the following figure.

In the given figure, mid-point i.e. “B” represents arc elasticity of the two distinctive points “A” and ‘C” It is worth mentioning here that mid-point formula is associated with R.G.D. Allen.

Case – ii

### Arc Demand Curve

We connect the two distinctive points by drawing a chord. The elasticity at the mid-point of the chord represents arc elasticity of demand between two points on a curved demand curve. But how to find an elasticity of demand at mid-point of the chord?

In this connection, we draw a parallel line which becomes tangent to the curved demand curve.

Now we find demand elasticity at tangent point by extending the tangent line up to Q-axis and P-axis (as discussed above) and find an elasticity of demand at the given point. The tangent point elasticity represents elasticity of mid-point of the chord which in turn represents arc elasticity of demand between two points on a curved demand curve.

In the given figure, we are interested to measure arc elasticity of demand between two points “A” and “B”.For this purpose, we draw a chord by connecting these two points. We take mid-point “C” The elasticity at this point represents average or arc elasticity. The elasticity at mid-point is indicated by the elasticity at tangent point, “T”.

We find elasticity at point “T” by following the procedure adopted under the measurement of point elasticity. In the given diagram, elasticity at point “T” on the tangent line is equal to unity. Hence at “C” on chord is also equal to unity.

Subsequently, arc elasticity between two distinctive points “A” and “B” is equal to unity. At the same pattern, we can find different degrees of arc elasticity by following this procedure

## DEGREES OF PRICE ELASTICITY OF DEMAND

Degrees of price elasticity of demand can be discussed under five cases:

If there is no change in price but Qd changes infinitely, it shows perfectly elastic demand/ elastic demand/ infinite elasticity of demand. Symbolically,

It is also termed as classification of degrees of responsiveness of Qd due to changes in own price i.e. the price of good itself.

If infinite change in price leads to no change in quantity demanded, it is known as perfectly inelastic demand or zero elasticity of demand. Symbolically,

Note: Above-mentioned both cases are considered extreme cases of price elasticity of demand.

If proportional change in quantity demanded is equal to proportional change in price, it is called unitary elastic demand. Symbolically,

If proportional change in quantity demanded is greater than proportional change in price, it is called more elastic demand or simply elastic demand. Symbolically,

If a proportional change in quantity demanded is less than proportional change in price, it is known as less elastic demand or simply inelastic demand. Symbolically

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