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Methods of Measuring Price Elasticity of Demand: Percentage and Geometric Method

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  • Last Updated : 22 Aug, 2022
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The quantity of a good or service that a consumer is willing and able to purchase at different price levels available during a given time period is known as Demand. Generally, demand is interchangeably used with want and desire; however, in economics these terms are different. Desire is just a wish of a consumer to purchase a commodity even though he is unable to buy it. However, demand is a consumer’s desire to purchase a commodity, provided he is willing to spend and has sufficient purchasing power. 

Elasticity of Demand

The demand for a commodity is affected by different factors such as the consumer’s income, price of the commodity, price of related goods, etc. The percentage change in the demand for a commodity because of the percentage change in any of the factors affecting demand for that commodity is known as Elasticity of Demand. It can be calculated as:

Elasticity~of~Demand=\frac{Percentage~Change~in~Demand~for~X}{Percentage~Change~in~a~factor~affecting~the~Demand~of~X}

The three quantifiable determinants of demand for which its elasticity is measured are the price of the commodity, the price of related goods, and the income of the consumer. Therefore the three types of Elasticity of Demand are Price Elasticity of Demand, Cross Elasticity of Demand, and Income Elasticity of Demand. 

Price Elasticity of Demand

The percentage change in the demand for a commodity because of the percentage change in its price is known as the Price Elasticity of Demand. In other words, Price Elasticity of Demand is the degree of responsiveness of demand for a commodity with reference to changes in the price of such commodity. For example, +1.5 price elasticity of demand means that if there is a one percent rise in the price of a commodity, it will lead to a 1.5 percent fall in its demand, or a one percent fall in the price will lead to 1.5 percent rise in the demand. Price is the most important determinant of demand; therefore, price elasticity of demand is also known as Elasticity of Demand, Demand Elasticity, or Elasticity. 

An important fact about Price Elasticity of Demand is that, while keeping other factors constant, it establishes a quantitative relationship between the price of a commodity and its quantity demanded. Also, if the value of price elasticity of demand is high, it means that the change in the price of the commodity will have a larger impact on the quantity demanded. 

A change in the price can result in a small change in demand for some goods and a greater change in demand for other goods. For example, if there is a 20% fall in the price of two commodities X and Y, and 5% and 15% rise in their demand respectively, it would mean that Good Y is more elastic as compared to Good X, as there is a high rise in the demand for Y as compared to X. 

Price Elasticity of Demand is determined by two methods: Percentage Method and Geometric Method. 

Percentage Method of Determining Price Elasticity of Demand

The most common method of measuring Price Elasticity of Demand (Ed) is the Percentage Method, which was introduced by Prof. Marshall. According to the Percentage Method, also known as Flex Method, Proportionate Method, or Mathematical Method, the elasticity of a commodity is measured by dividing the percentage change in its quantity demanded by the percentage change in the price. Therefore, the formula for calculating price elasticity of demand by Percentage Method is:

Elasticity~of~Demand(E_d)=\frac{Percentage~change~in~Quantity~demanded}{Percentage~change~in~Price}

Where,

Percentage~change~in~Quantity~demanded=\frac{Change~in~Quantity~(\Delta{Q})}{Initial~Quantity~(Q)}\times{100}

Change~in~Quantity~(\Delta{Q})=Q_1-Q

Percentage~change~in~Price=\frac{Change~in~Price~(\Delta{P})}{Original~Price~(P)}\times{100}

Change~in~Price~(\Delta{P})=P_1-P

Proportionate Method 

The percentage method of measuring elasticity of demand can be converted into the proportionate method by taking the absolute changes in the price and quantity demanded of the commodity, and the formula for the same is,

E_d=\frac{\frac{\Delta{Q}}{Q}\times{100}}{\frac{\Delta{P}}{P}\times{100}}=\frac{\frac{\Delta{Q}}{Q}}{\frac{\Delta{P}}{P}}

E_d=\frac{\Delta{Q}}{\Delta{P}}\times{\frac{P}{Q}}

Where,

Q=Initial~Quantity~demanded

\Delta{Q}=Change~in~the~Quantity~demanded

P_1=New~Price

Q_1=New~Quantity~demanded

P=Initial~Price

\Delta{P}=Change~in~Price

For example:

Calculate the Price Elasticity of Demand if the demand for Good X increases from 5 units to 7 units due to fall in price from Rs. 10 to Rs. 6.

Solution:

Elasticity~of~Demand(E_d)=\frac{Percentage~change~in~Quantity~demanded}{Percentage~change~in~Price}

Percentage~change~in~Quantity~demanded=\frac{Change~in~Quantity~(\Delta{Q})}{Initial~Quantity~(Q)}\times{100}

=\frac{7-5}{5}\times{100}

= 40%

Percentage~change~in~Price=\frac{Change~in~Price~(\Delta{P})}{Original~Price~(P)}\times{100}

=\frac{6-10}{10}\times{100}

= -40%

=\frac{-40\%}{40\%}

= -1 or 1

Important facts about Percentage Method:

1. Negative Sign is ignored

While determining the value of price elasticity of demand of a commodity, the negative sign is ignored. The negative sign of the price elasticity of demand is due to the inverse relationship between the price and demand of a commodity; therefore, only the absolute value is considered. For example, if the price elasticity of demand for a commodity is -1.5, then only 1.5, i.e., absolute value will be considered.

2. Elasticity of a commodity is affected by the percentage change

Price elasticity of demand for a commodity is not affected by the absolute change in its price or demand, instead, it is affected by the percentage change in price and demand of the commodity. For example, there is a fall in the quantity demanded of Good X from 6 units to 4 units due to a rise in price from Rs 5 to Rs 8, and there is a rise in quantity demanded of Good Y from 4 units to 6 units due to a fall in price from Rs 8 to Rs 5. The Price Elasticity of Demand for Good X and Y are -0.5 and 1.3, respectively. Now, it can be seen that the absolute change in the quantity demanded (2 units) and price of the commodity (Rs 3) for both Goods X and Y are the same, still, the price elasticity of demand for both commodities is different. It is because the percentage change in price and demand for Good X is 60% and 33.3%. However, the percentage change in price and demand for Good Y is 37.5% and 50%, respectively. 

3. Elasticity is a Unit Free Measure

It means that the coefficient of price elasticity of demand is a pure number and is interdependent on quantity units and price. In simple terms, there is no effect on the price elasticity of demand of a commodity whether its quantity demanded is measured in tonnes, kilograms, or grams and whether its price is calculated in Rupees or Yen. It is because the price elasticity of demand for a commodity is affected by the percentage change in quantity demanded and the price of a commodity. Therefore, with the help of price elasticity of demand, it is easy to compare expensive and inexpensive goods. 

Geometric Method of Determining Price Elasticity of Demand

This method was also suggested by Prof. Marshall. According to the Geometric Method, also known as the Graphic Method, Point Method, or Arc Method, the elasticity of demand for a commodity is measured at a point on the demand curve. The Geometric Method of determining the Price Elasticity of Demand is used when there an infinitely small changes in the demand and price of a commodity. It means that the Elasticity of Demand for such commodities is different at different points on the same straight line demand curve. The formula to measure Ed of a commodity under the Geometric Method is:

Elasticity~of~Demand=\frac{Lower~Segment~of~Demand~Curve}{Upper~Segment~of~Demand~Curve}

 


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