# Measuring Price Elasticity of Demand: Percentage, Total Outlay, Point and Arc Methods

## What is price elasticity of demand?

Price elasticity of demand is a measure of the degree of change in demand of a commodity to the change in price of that commodity.

In other words, price elasticity of demand is the rate of change in quantity demanded in response to the change in the price. It is often referred to as ‘price elasticity’ and is denoted by Ep or PED.

### Methods of Measuring Price Elasticity of Demand

There are basically four ways by which we can measure price elasticity of demand. These methods are

i.Percentage method

ii.Total outlay method

iii.Point method

iv.Arc method

## Percentage Method

Percentage method is one of the commonly used approaches of measuring price elasticity of demand under which price elasticity is measured in terms of rate of percentage change in quantity demanded to percentage change in price.

According to this method, price elasticity of demand can be mathematically expressed as

For an example: When the price of a commodity was Rs 10 per unit, its demand in the market was 50 units per day. When the price of the commodity fell to Rs 8, the demand rose to 60 units. Here, price elasticity of demand can be calculated as

Unlike price elasticity of supply, price elasticity of demand is always a negative number because quantity demanded and price of the commodity share inverse relationship. This means, higher the price, lower will be the demand, and lower the price, higher be the demand of the commodity.

## Total Outlay Method

Total outlay method, also known as total expenditure method of measuring price elasticity of demand was developed by Professor Alfred Marshall. According to this method, price elasticity of demand can be measured by comparing total expenditure on a commodity before and after the price change.

While comparing the expenditure, we may get one of three outcomes. They are

### Elasticity of demand will be greater than unity (Ep > 1)

When total expenditure increases with fall in price and decreases with rise in price, the value of PED will be greater than 1. Here, rise in price and total outlay or expenditure move in opposite direction.

### Elasticity of demand will be equal to unity (Ep = 1)

When total expenditure on commodity remains unchanged in response to change in price of the commodity, the value of PED will be equal to 1.

### Elasticity of demand will be less than unity (Ep < 1)

When total expenditure decreases with fall in price and increases with rise in price, the value of PED will be less than 1. Here, price of commodity and total outlay move in same direction.

Cases |
Price (P) |
Quantity demanded (Q) |
Total outlay or expenditure (E = PXQ) |
Price elasticity of demand (PED) |

I |
6 |
1 |
6 |
PED = 10/6, > 1 |

5 |
2 |
10 |
||

II |
4 |
3 |
12 |
PED = 12/12, = 1 |

3 |
4 |
12 |
||

III |
2 |
5 |
10 |
PED = 6/10, < 1 |

1 |
6 |
6 |

When the information from the above table is plotted in the graph, we get graph like the one shown below.

In the graph, total outlay or expenditure is measured on the X-axis while price is measured on the Y-axis. In the figure, the movement from point A to point B shows elastic demand as we can see that total expenditure has increased with fall in price. The movement from point B to point C shows unitary elastic demand as total expenditure has remained unchanged with the change in price. Similarly, the movement from point C to point D shows inelastic demand as total expenditure as well as price has decreased.

Total outlay method of measuring price elasticity of demand does not provide us exact numerical measurement of elasticity of demand but only indicates if the demand is elastic, inelastic or unitary in nature. Therefore, this method has limited scope.

## Point Method

The point method of measuring price elasticity of demand was also devised by prof. Alfred Marshall. This method is used to measure the price elasticity of demand at any given point in the curve.

According to this method, elasticity of demand will be different on each point of a demand curve. Thus, this method is applied when there is small change in price and quantity demanded of the commodity.

According to this method, price elasticity of demand (PED) is mathematically expressed as

However, the method of calculating PED depends upon the nature of the demand curve. These methods are explained below.

### Price elasticity on a linear demand curve

If the demand curve is of linear nature, PED is simply calculated by applying the expression given above, i.e.

**IMAGE HERE: Price elasticity of a linear demand curve**

In the figure, MN is a linear demand curve and P is the mid-point of the curve.

Therefore, at point P,

In the same way,

### Price elasticity on a non-linear demand curve

If the demand curve is of non-linear or convex nature, then a tangent line is drawn at the point of which the PED is to be measured. Then PED is once again calculated as

**IMAGE HERE: price elasticity of a non-linear demand curve**

In the given figure, DD is a non-linear demand curve. If P is the point where we want to measure price elasticity, then we have to first draw a tangent through that point. Thus, tangent MN has been drawn through point P. Now, PED can be measured as

## Arc Method

Any two points on a demand curve make an arc, and the coefficient of price elasticity of demand of an arc is known as arc elasticity of demand. This method is used to find out price elasticity of demand over a certain range of price and quantity. Thus, this method is applied while calculating PED when price or quantity demanded of the commodity is highly changed.

**IMAGE HERE: arc elasticity of demand**

In the figure, we can see that AB is an arc on the demand curve DD, and point C is the mid-point on AB. If we followed point method to measure PED at points A and B in the curve DD, we get different coefficients as a result of using different bases. To avoid this discrepancy, elasticity is measured by taking mean values of price and quantity demanded in arc method.

The average of price and quantity demanded is calculated as

Once the average value of price and quantity demanded are determined, PED at point C can be calculated by applying following formula

Where,

ΔQ = change in quantity demanded = Q2 – Q1

Q1 = initial quantity demanded

Q2 = new quantity demanded

ΔP = change in price = P2 - P1

P1 = new price

P2 = initial price