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Microeconomics for business/Price Elasticity of Demand/Solution to Mathematical Problems


Elasticity of Demand 

The concept of elasticity of demand was introduced by economists like Cournot, J.S. Mill, etc. However, the application of it in economics was popularized by Alfred Marshall. The law of demand is only able to show the direction of change of demand and its determinants, whereas elasticity of demand can explain both direction and magnitude of change in demand and its determinants.

In economics, the demand elasticity (elasticity of demand) refers to how sensitive the demand for a good is to changes in determinants of demand, such as prices, consumer income, prices of related goods, advertisement, and so on. Demand elasticity is calculated as the percent change in the quantity demanded divided by a percent change in another economic variable (determinants of demand).  Higher demand elasticity for an economic variable means that consumers are more responsive to changes in this variable.

There are as many types of elasticity of demand as there are types of economic variables determining the demand. However, there are four main types of elasticity of demand namely; Price elasticity of demand, Income elasticity of demand, Cross elasticity of demand, and advertisement elasticity of demand.

Price Elasticity of Demand

Among these types, the price elasticity of demand is the most important one. Price elasticity of demand is the degree of how much the quantity demanded of a commodity varies when its price changes, other things remaining the same.

Precisely saying, the price elasticity of demand measures the ratio of the percentage change in the quantity demanded of a commodity to a percentage change in the price of that commodity.

Mathematical Calculation of Price Elasticity of Demand, BBS

As we know that the theory of demand specifies only a route of alteration in quantity needed in response to a change in price. This does not tell us by how much or to what level the quantity demanded will be affected or changed with the change in its price. 

This information as to how much or to what extent the quantity demanded of a commodity will change as a result of the change in price is provided by the concept of price elasticity of demand. So, this concept has a significant role in economic literature and in business decision making. 

Only the nature and direction of a relationship between various economic variables can not establish and provide  guidance for the application of the law of demand and supply for making pricing decisions by the business firms and for the government to formulate its pricing and taxation policies in the areas like; price determination of public utilities, fixing prices of essential goods, food grains and medicines, determination of the rate of commodity taxes, and determination of export and import duties.

Thus, price elasticity of demand is the responsiveness of demand for a commodity divided by the percentage change in the price. that is,
Microeconomics for business/Price Elasticity of Demand/Solution to Mathematical Problems
The formula of Price Elasticity of Demand

Here, the elasticity of demand is denoted by Ep. The arithmetic value of Eis known as the coefficient of price the elasticity of demand. The general formula for measuring the price elasticity of demand is derived as;
price elasticity of demand, BBS first year note
Here, Qis initial demand, Qis demand after the price change, Pis the original price, and P2 is the changed price. Q2- Q1 denotes the change in quantity demanded and noted by DQ and P2- P1 denotes the change in the price of the commodity and noted by DP Replacing the notation in the above expression we get,
Microeconomics note BBS first year, Price elasticity of demandSolution to mathematical problems of elasticity of demand, BBS first year

Uses of Price Elasticity of Demand 

The concept of price elasticity is of great practical importance in the formulation and understanding of economic policies and problems. In business decision making, price elasticity is applicable directly and indirectly. 

The businessman must know the effect of the price change on quantity demanded of the product and factors in the market and such can be gained from the concept of price elasticity. Thus, from consumers to the government the concept of price elasticity is useful in different stages. The application of the concept of price elasticity of demand in commercial decision making can be pointed as below:

Determination of price policy

While fixing the price of any product, a businessman has to consider the elasticity of demand for the product. He should consider whether a lowering of the price will stimulate demand for his product, and if so to what extent and whether his profits will also increase a result thereof. If the demand for the product is elastic, business may earn more revenue by setting the lower price and if the elasticity is less, one can set the higher price of the product.

Price discrimination

Price discrimination refers to the act of selling the technically same products at different prices to different sections of consumers or in different sub-markets. In the market with elastic demand for the product, the discriminating monopolist fixes low price and in the market with less elastic demand, he charges a high price.

Pricing of public utilities

The concept of price elasticity of demand further helps in fixing the prices for the services rendered by public utilities. If the demand is inelastic, a high price can be charged and in case of elastic demand, a lower price should be charged.  

Pricing of joint product

For the pricing of joints products like wool and mutton, paddy and straw, chicken, and eggs, the concept of price elasticity of demand is needed. In the case of joint product, the measurement of separate cost of the production of each commodity sometimes may not be possible and in such case, the pricing of these products could be fixed by the elasticity of demand.

Demand forecasting

Given the elasticity of demand and the state of an independent variable, it is always possible to forecast the demand for a particular good.

Importance in International trade

The concept of price elasticity of demand is very useful in order to fix the term and conditions of multinational trade and commerce. The countries can get benefit from international trade with the help of the concept of price elasticity of demand. 

When the nation exports those goods whose elasticity of demand in the foreign market is high then the price must be competitive and low and if the product of internal the market has inelastic demand in the foreign market then price should be higher and thereby countries can get benefits from their foreign trade.  

Helps in taxation policy formulation

Government can impose higher rate of taxes on those goods which have inelastic demand in the market and lower taxes on goods having higher elasticity in the consumer market. The demand of those products having inelastic demand will not be affected more by imposing high taxes by the authority and this will ensure more tax revenue to the government. 

On another side, the lower tax rate should be charged in those products which have elastic demand in the market to generate more revenue from taxes.

Mathematical Calculation of Price Elasticity of Demand/Solution to Mathematical Problems of Price Elasticity of Demand


In the market, different products show different types of responses to the price. It means goods are available in greater variation in terms of elasticity of demand. Some goods are of those types whose demand is not highly affected by changes in prices like salt, medicine, wheat, rice, and so on. 

But we have also different products whose demand is highly fluctuated with the change in their prices. For example, the demand for products like laptops, computers, television, is highly affected when there is a change in their price. so the goods whose demand is highly affected are called elastic one and non-affecting are called inelastic products. 

Price could be high in case of less elastic or inelastic goods but the price should be less in case of elastic goods. So, to know the nature of goods and their capability to satisfy human wants, the measurement of price elasticity demand is essential.  It has occupied a significant role in the study of microeconomic theories and behaviors in theory as well as practice.  

Here you can find the solution to mathematical problems on the price elasticity of demand. It is very useful for your academic courses as well as for competitive exams inside the country as well as outside the country. You can find a comprehensive solution to all the possible problems from the topic price elasticity of demand. To download the PDF file of the solution to mathematical problems of price elasticity of demand. Click below









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