Elasticity of Demand

Introduction:-

In general, “Elasticity of Demand refers to the degree of responsiveness of quantity demanded of a commodity to a change in any of its determinants”, i.e., price of the commodity, price of the other commodities and the income of the consumers. It measures of how sensitive the quantity demanded of a commodity is to change in any of the factors influencing demand. E*=Percentage change in the quantity demanded(Q) Percentage change in any of its determinants (P)*Where E denotes Elasticity of demand

Types of Elasticity of Demand:- There are as many types of elasticity of demand as there are types of economic variables determining demand. However, there are three main types of elasticity of demand, which are as follows-

1) Price elasticity of demand.2) Cross elasticity of demand.3) Income elasticity of demand.

1. PRICE ELASTICITY :-

Classification of price elasticity of demand:- The price elasticity of demand is a measure of how much the quantity demanded changes when the price changes.” Price elasticity of demand may be defined as the degree of responsiveness of quantity demanded of a commodity in response to change in its price “.By degree here means the rate of change .Therefore, more precisely, price elasticity of demand refers

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to the ratio of the percentage change in the quantity demanded of a commodity to a given percentage change in its price. Thus, Ep*=Percentage change in quantity demanded Percentage change in price*Where Ep denotes price elasticity of demand

Different Magnitudes Of Price Elasticity Of Demand

There are five different kind of price elasticity of demand which are as follows:-

1) Perfectly elastic demand:-When the consumers are prepared to purchase all that the can get at a particular price but nothing at all at a slightly higher price, then the price elasticity of demand for a commodity is said to be infinite. In this case a very small fall in the price causes the demand to increase to infinity. A demand curve of infinite elasticity is known perfectly or completely elastic demand curve. In this case, demand is perfectly elastic .Demand curve (D), which is parallel to X-axis, illustrates perfectly elastic demand .At price OP nothing is demanded, but at a slightly lower price OP a large amount of commodity is demanded. This is the extreme upper limit of price elasticity .Case of perfectly elastic demand (Ep=∞).

2) Perfectly inelastic demand:-When quantity

PRICE QUANTITY DEMANDED

05 0205 05


05 0510 05

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demanded of a commodity does not respond to a change in its price, then the elasticity of demand is zero. In this case quantity demanded remains same irrespective of any rise or fall in its price. A demand curve of zero elasticity is known a perfectly inelastic or completely inelastic demand curve .In this case, the demand curve, which is parallel to Y-axis, is perfectly inelastic demand curve. The amount purchased remains OQ irrespective of whether price is OP to OP1.Cases of perfectly inelastic demand are very rare even in the case of basic necessary goods like food because even demand for necessities changes because of change in price (Ep=0).

3) Unitary elastic demand:-When a given percentage change in price of a commodity causes an equivalent percentage change in the quantity demanded, then the elasticity of demand is said to be unity (or one).For example, if a fall in the price of the commodity by 10% causes an increase in the amount purchased by 10%, the elasticity of demand equal to one. Demand curve D has unitary elasticity at all the point on the curves. Such a curve is known as a rectangular hyperbola curve. A rectangular hyperbola is a curve in which the total area at different points on the curve is same. Such a curve extends towards the X-axis and the Y-axis


05 2010 10

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in a uniform way, but never touches them .Cases of unitary elastic demand are area indeed (Ep=1).

4) Relatively Elastic Demand:-When the percentage change in quantity demanded of a commodity exceeds the percentage change in its price, the elasticity of demand is greater than unity. Demand is said to be relatively elastic here. For example, if a fall in price of the commodity by 10% causes an increase in amount demanded by 15%, the demand is said to be in elastic .Demand curve D is the elastic between A and B because the percentage change in quantity demanded from OQ to OQ1 is respectively larger than the percentage change in price from OP to OP1 (Ep>1).

5) Relatively Inelastic Demand:-Demand is inelastic when the percentage change in the quantity demanded of a


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15 0420 02

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commodity is less than the percentage change in its price. The elasticity of demand here is less than unity. for example ,if a fall in price of a commodity by 10% leads to an increase in quantity demanded by 8%,the demand is inelastic .Demand curve D is in elastic between C and D because the percentage change in quantity demanded from OQ1 to OQ2 is smaller than the percentage change in price from OP1 to OP2 (Ep<1).

Measurement of Price elasticity of demand:-

Elasticity of demand for different goods is different. It is important to measure elasticity of demand in order to compare elasticity of demand for different goods. The measurement of elasticity of demand can be looked at from two views points:(i) Point elasticity (ii) Arc elasticity.

(i)Point elasticity:-When price elasticity of demand is measured at a point on a demand curve, it is called point elasticity. If we want to know the elasticity of demand at point R on the demand curve, we call it point elasticity. The method used for measuring point elasticity is called Point method.

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(ii)Arc elasticity:-When elasticity of demand is measured over a finite range or ‘arc’ of a demand curve, it is called arc elasticity of demand. For example, the measure of elasticity between point R and R1 on the demand curve is the measure of arc elasticity. The arc elasticity of demand can be measured by Percentage Method and Total Expenditure Method.Thus, there are three methods of measurement of price elasticity of demand. There are:

1) Percentage or proportionate method. 2) Total expenditure method.3) Point method or geometric method.

1). Percentage or Proportionate Method:- In this method, Price elasticity of demand is measured by the ratio of percentage change in quantity demanded to percentage change in price of the commodity. Thus:

Ep=Percentage change in quantity demanded Percentage change in price =Change in quantity demanded Initial Quantity × 100 Change in price Initial Price × 100 = ∆Q × 100 Q = ∆Q ÷ ∆P ∆P × 100 Q P

=∆Q ×P = ∆Q × P Q ∆P ∆P Q

Thus: Ep*=∆Q ×P

∆P Q

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*Where Ep stands for price elasticity of demand.Q stands for quantity (initial).P stands for price (initial)∆P stands for change in price∆Q stands for change in quantity. While using this formula for calculating price elasticity of demand, we must keep one thing in mind that is mathematically speaking, price elasticity of demand is a negative number because of negative slope of the demand curve. In view of the negative slope of the demand curve, the price and quantity change in opposite directions from each other. One change will be positive and other negative. Thus, while calculating price elasticity of demand by percentage method, common practice is to ignore the negative signs that is we should take only the obsolete values and not their signs. The convention among economists is simply refer to the elasticity as a number prefer to put a negative signs in front of the formula, that is, Ep= − ∆Q ×P , in view of negative slope ∆P Q of demand curve. Another important feature of the price elasticity of demand is that it does not depend on the unit’s o0f measurement of quantity of demand .It is unit free measure because it uses percentage changes in price and quantity demanded. There fore, we can compare the price sensitivity of demand for different goods regardless of the units for measuring either price or quantity. This indeed is a major advantage. The advantage of percentage method of measuring price elasticity is that it gives a precise and exact measure of elasticity. Larger values for price elasticity of demand indicate that demand is more sensitive to changes in price; smaller values indicate that demand is less sensitive to price changes. However, one of the problems of using percentage method is that the percentage change depends on the base or the starting point. Should we take the initial quantity/price or the new quantity/price as the starting point? In case of small change, it does not matter whether we take the initial price quantity/price or new quantity/price .But if two points on the demand curve are quite apart from each other that is , when changes in quantity and price are large, then the value of elasticity will differ significantly

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depending upon whether we take the initial values or new values. That is why percentage formula of calculating elasticity has been modified to take care of this problem. However, this modified formula is beyond your level

2). Total expenditure method:-

One of the methods of measuring the price elasticity of demand suggested by Marshall is the “Total expenditure method”. Total expenditure or total outlay is the expenditure incurred by households on the purchase of a commodity. It is the product of a price of a commodity and the quantity demanded at that price, that is, TE=P×Q, where TE stands for total expenditure, P and Q stands for price and quantity respectively.

Accordingly to expenditure method, elasticity of demand can be measured by considering the change in total expenditure as a result of change in the price of the commodity. We compare the total expenditure before and after the price change and thereby we can know about the price elasticity of demand for good. By using this method, we can categories three types of elasticities:

a) Elastic demand: - When a fall in price of the commodity results in an increase in total expenditure, a rise in the price leads to decrease in total expenditure, elasticity of demand will be greater than one. In this case, change in quantity demanded more than offsets the change in price. This is shown in the table.

Demand schedule shows that when the price falls from Rs 6 to Rs 5, total expenditure rises from 60 to 65. This information is plotted on the demand curve to give demand curve D1D1. Total expenditure corresponding to Rs 6 is represented by rectangle QA and total expenditure corresponding to Rs 5 is represented by rectangle OB. As price falls, total expenditure increases from Rs 60 to Rs 65.Thus, demand curve D1D1 is elasticity between A and B.

Price Quantity Total expenditure 6 5

10 13

EP>1 60 65

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b)Inelastic demand:-When a fall in price of a commodity reduces total expenditure and a rise in price increases it, price elasticity of demand will be less than one. In this case, change in price more than offsets the change in quantity. This type of demand elasticity is illustrated by the demand schedule and graphically.

In Table demand is inelastic because with a fall in price from Rs 6 to Rs 5, total expenditure falls from Rs 60 to Rs 55. The same information is illustrated graphically, where demand curve D2D2 is inelastic between point A and B as the area of rectangle OB is smaller than the area of rectangle OA.

c) Unitary elastic:-When total expenditure does not change with the change in price of the commodity, the elasticity of demand is equal to unity. In this case, change in quantity demanded just offsets the change in

Price Quantity Total expenditure

6 5

10 11

EP<1 60 55

Price Quantity Total expenditure 6 5

10 12

EP=1 60 60

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price. This type of elasticity is illustrated by the demand scheduled in the table.

In table demand is unitary elastic as with fall in price from Rs 6 to Rs 5, total expenditure remains unchanged at Rs 60. The same information is conveyed graphically, where the demand curve D3is a rectangle hyperbola with rectangles OA and OB being equal in areas showing that a change in price of commodity does not bring about a change in total expenditure.

We can summaries these results explained above in the following Table. We can show the relationship between the elasticity of and total expenditure. Here, instead of drawing an ordinary demand curve, we have plotted total expenditure on X axis and price on the Y-axis.

Types of price elasticity of demandUnitary elastic Ep=1

Inelastic Ep<1

Elastic Ep>1

Te remains Constant

Te remains constant

Te falls

Te rise

Te rise

Te falls

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TT1 curve represented total expenditure. When price of the commodity falls from OP to OP1, total expenditure increases from OM to OM1. Thus elasticity of demand here is more than unity. As the price falls from OP1 to OP2, total expenditure remains unchanged at level of OM1. Therefore, elasticity here is equal to unity. Finally, when the price falls from OP2 to OP3, the total expenditure falls from OM1 to OM. The elasticity of demand is less than unity in this case. Thus, we can generalize that between T and B price elasticity of demand is greater than unity; between B and C elasticity is less than unity. It should be noted that in total expenditure method enables us to know only whether price elasticity of demand is equal to one, greater than one, or less than one. But we cannot get the exact measure of the price elasticity. Thus, total expenditure method gives only a general measure of price elasticity of demand.

3). Point method (Geometric method):- Geometrically, price elasticity of demand can be measure with the help of what is known as Point method. According to this method, price elasticity of demand at any point on the demand curve can be measured by:

Ep=Line segment below the point on the demand curve Line segment above the point on the demand curve

a) On a straight line demand curve:-Suppose we want to measure price elasticity of demand at point R on a linear or a straight line demand curve AB, which is intercepted by both the axes. It is obvious from the figure that the lower line segment is RB and the upper line segment is RA.

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Ep at point R=Lower line segment Upper line segment = RB RA

Here Ep>1 because RB> RA. Similarly, if we want to measure elasticity at any other point on the demand curve, say at K,

Ep at K= KB

KA Here Ep<1 since KB<KA.

Price elasticity of demand at different points on a straight line demand curve:-We can use the above the method of point elasticity in measuring elasticity at different points on a straight line demand curve starting from Y-axis and terminating at X-axis. We can easily explain that the price elasticity of demand at different points of demand curve is different. From figure we can see that AB is a straight line demand curve, with A as its Y intercept, B as X intercept and D as its mid-point. The point method of measuring the elasticity as the ratio of line segment below the point and line segment above the points on the linear demand curve.

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(1) At point A (where the demand curve touches the vertical axis).

Ep=Line segment below A Line segment above A

=AB = infinity (∞) 0

(2) At any point above the mid-point but below A, say at E

Ep at E=BE > 1 because the lower segment is greater EA than the upper segment

(3) At the mid-point D

Ep at D= BD = 1 because the lower segment equals DA the upper segment

(4) At any point below the mid-point but above B, say at C.

Ep at C= BC < 1 because the lower segment is smaller CA than the upper segment

(5) At point B( where the demand curve touches the horizontal axis)

Ep at B= O = 0 AB

Thus, as we travel downwards from left to right on a straight line demand curve, price elasticity of demand steadily varies from

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infinity at Y- intercept to zero at X-intercept; being greater than unity(elastic demand) at any point above the mid point, equals to unity at the mid point . From this, we can generalise that a straight line demand curve is more elastic towards its left-hand end and less elastic towards the right-hand end.

b) On the non-linear demand curve:-We can measure the price

elasticity of demand on a demand curve which is not a straight line by using the point method. In order to calculate price elasticity of demand at any point on a curved demand curve, we have to draw a tangent to the demand curve through the chosen point and measure the elasticity of the tangent at this point as the ratio of the lower line segment to upper line segment. This gives the price elasticity of demand curve at that particular point on the demand curve. Suppose we want to measure the elasticity at point R on the demand curve DD. We draw a line AB tangent to the demand curve D at point R. Since the slope of the demand curve at R equals the slope of the tangent at that point, the price elasticity of the demand curve at R will be equal to the elasticity of the tangent AB at point R.

2. CROSS ELASTICITY :-

Classification of Cross elasticity of demand:- Cross elasticity of demand is used to express such a situation. The degree of responsiveness of quantity demanded of one commodity to change in the price of another commodity is called cross elasticity of demand. More precisely, cross elasticity of demand is defined as the percentage change in quantity demanded

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of a commodity with respect to the change in the price of its related commodity. Cross elasticity of demand can be measured help of the following formula: Exy=Percentage change in the quantity demanded of commodity X Percentage change in the price of commodity Y

*Where Exy denotes the cross elasticity demand.

Different Magnitudes Of Cross Elasticity Of Demand

The cross elasticity of demand is of three types as below:

1) Positive cross elasticity of demand:-Cross elasticity of demand is said to be positive, when increase in the price of one commodity (Y) leads to an increase in the demand for the other commodity (X). When two goods are substitutes for each other, cross elasticity will be positive because increase in price of one increases the demand for the other .For example, tea and coffee. A fall in the price of coffee (Y) increases the quantity of coffee demanded, but reduces the quantity of tea (X) demanded. Changes in price of coffee and in the quantity of tea demanded will, therefore, have the same sign, that is, cross elasticity is positive.

2) Negative cross elasticity of demand:-Cross elasticity of demand is said to be negative when increase in the price of Y leads to a fall in the demanded for (X). Complementary goods have negative cross elasticities. For example, bread and butter are complementary goods. A fall in price of butter causes an increase in the quantity purchased of not only butter, but also bread. Thus, a change in the price of butter and in the quantity of bread demanded will have opposite sign, that is cross elasticity is negative.

3) Zero cross elasticity of demand:-Cross elasticity of demand is said to be zero when a change in the price of one commodity (Y) does not affect the demand fore another commodity (X). If the

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two goods are not related to each other, say tea and T.V. set, cross elasticity of demand will be zero .A change in price of tea is not likely to influence the demand for T.V.

3. INCOME ELASTICITY :- Classification of Income elasticity of demand:-

Income elasticity of demand measures the degree of responsiveness of quantity demanded of a commodity to changes in income of the consumers. More precisely, income elasticity of demand may be defined as the ratio of the proportionate change in quantity demanded of a commodity to the proportionate change in income of the consumers. Income elasticity of demand can be measured with the help of following formula: Ey*=Percentage change in quantity demanded Percentage change in income *Where Ey is the income elasticity of demand

Different Magnitudes Of Income Elasticity Of Demand

Income elasticity of demand is of three types as below:

1) Positive income elastic:-Income elasticity of demand is said to be positive when with increase in income of the consumers, the amount purchased of a commodity increases and vice-versa. For most of the commodities income elasticity of demand is positive because an increase in income leads to an increase in quantity demanded. Goods with positive income elasticity are called normal goods. For normal commodities, we can classify income elasticity into three categories.

a) Income elastic:-If the percentage change in quantity demanded of a commodity is greater than the percentage in income will exceed by unity. The demand for the commodity is said to be income elastic in this case (Ey>1).

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b) Income inelastic:-If the percentage change in quantity demanded is smaller than the percentage change in income will be less than unity. The demand for the commodity is said to be income inelastic.

c) Unit income elasticity:-If the percentage change in quantity demanded is equal to percentage change in income, will be equal to unity. The commodity has a unit income elasticity in this case .Income elasticity of unity represents a dividing line between income elastic and income inelastic demand.

2) Negative income elastic: - Income elasticity of demand is said to be negative when increase in income of the consumers leads to a fall in the amount purchased of a commodity and vice-versa. In case of inferior commodities, an increase in income leads to fall in the quantity demanded that is less is demanded at higher income and more is brought at lower incomes. Income elasticity of demand in such cases is negative .For example, income elasticity of inferior food grains like maize and bajra is negative. When income increases consumers will switch over from inferior food grain like rice and wheat.

3) Zero income elasticity of demand:-Income elasticity of demand may be zero in some exceptional cases. Zero income elasticity of demand for a good implies that a rise in income leaves quantity demanded unchanged. For instance, income elasticity of demand for salt may be zero because an increase in income beyond a certain level may not bring about change in demand for salt. Thus, except in case of inferior goods and inexpensive goods, income elasticity of demand for most of the commodities is positive.

Importance Of Income Elasticity The concept of income elasticity of demand is very important in economic analysis. National income of a country increases in course of economic development. Hence, the income of the individual citizen of the country also increases over time. It is important to know how the demand for different commodities will change in response to this increase in income. (Because it will

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be necessary to adjust the production plans accordingly.) It has been seen that food and other necessary articles of consumption have low income elasticities of demand, i.e., the demand for these goods do not rise very fast when income increases. Demands for such luxury items such as cars or washing machines have high income elasticities. In the developed countries, the demands for various services show high income elasticities.

Importance of the concept of the Elasticity of Demand

1) Price Setting:-Producers often base their price setting policies on the elasticity of demand for the commodity produced. If the elasticity is low they set the price at a high level because a low elasticity means that the consumer will not be able to reduce demands even when the price rises. (e.g., the demand for railway services is relatively inelastic because of the non-existence of close substitutes. Hence, the government can easily raise the railway fares to increase its revenue).

2) Wage Bargaining:-The same argument applies to the price of labour, i.e., the wage rates. Trade unions demand high wage rates if the elasticity of demand for labour is low.

3) International Prices:-When two countries engage in trade, the terms of trade are determined by the reciprocal elasticities of demand of the two countries for each other’s goods.

4) Indirect Taxation:-The concept of elasticity is also important for the government, when it tries to fix the rate of indirect taxes (for example, sales tax), because these taxes affect the prices of the commodities. Suppose that the rate of sale tax on a commodity has to be decided. Whenever the tax is imposed, the price of the commodity will go up. If the elasticity of demand is high, this rise in price will result in a sharp fall in the quantity purchased. The revenue of the Government will be small. For this reason, if

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obtaining high tax revenue is the objective, the Government puts sales taxes on commodities with low elasticities of demand.

5) Devaluation Policy:-Sometimes, when a country suffers from an adverse balance of payments, (i.e., the value of import exceeds the value of exports), the Government devalues the currency, i.e., reduces the price of the domestic currency in terms of foreign currency. This helps in solving the balance of payments problem by increasing the prices of imported goods in the domestic market and hence, reducing the demand for imports. For instance, suppose that the exchange rate between the Indian rupee and the U.S. dollars is 1 dollar = 40 rupees. Suppose that the rupee is devaluated and the exchange rate becomes 1 dollar = 45 rupees. An American good priced at 1 dollar would sell at 40 rupees before the devaluation and at 45 rupees after it. Hence, the Indian consumers demand for this American good will fall. India’s import will fall. This will solve the balance of payments problem.

Determinants of Elasticity

The Elasticity of Demand depends on a number of factors:1) Nature of a Commodity:-An important determinant of elasticity

of demand for a good is the nature of the good itself. If the good is a necessity of life, its demand will not change much when its price changes. The elasticity of the demand will be low.

2) Existence of Substitutes:-The Elasticity of demand for a commodity also depends on the existence of substitutes commodities. If substitute exist this will be used in place of the commodity in question when its price increases. The demand for that commodity will fall sharply.

3) Variety of Uses:-The demand for a commodity which can be put to a variety of uses will be relatively elastic. For instance, electricity can cut down on some of the uses of electricity, instead of more urgent uses. The demand for electricity therefore will be elastic.

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4) Income of the Purchaser:-If the purchaser is rich, he will not be bothered for small change in price. Such changes will leave is demand unaffected. His demand therefore will be inelastic. A poor consumer on the other hand will attach importance even to small change in price. His demand therefore will be elastic.

5) Role of Habits:-Habits also plays a role in the determination of elasticities. For instance, a person has developed a habit of smoking. He will be not be able to reduce his consumption of cigarette even the prices goes up. His demand for cigarette will be inelastic.

6) Durability of the Goods:-In case of durable good (for instance, a piece of furniture) a change in price would not affect demand very much, because most of the consumers will not buy a new piece of furniture until the old one is totally worn out. For this reason, durable goods usually have low elasticities of demand.

7) Importance of the Good in the Consumer’s Budget:-If the expenditure on a good is only a very small percentage of total spending, the consumer will not be bothered by small price changes. Such goods therefore have low elasticities of demand. Pins, matches, etc., are example of these types of goods.

8) Possibility of Postponing Consumption:-If the good is such that it is possible to postpone its consumption, it will obviously have a high elasticity of demand. When the price of cement rises, people can postpone their plans for house building. For this reason the demand for cement is elastic.

9) The Price Level:-Finally, we must remember that the elasticity of demand is different at different price levels. Thus, the price level itself is an important determinant of elasticity. Usually, at a high price, the demand for the commodity is low. Hence, even a small rise in demand will result in a large percentage change. For example, if demand rises from 1 unit to 2 units, it is a

2-1 ×100=100 per cent rise in demand. But when the price is 1 very low and, therefore, demand is already high, a further rise in

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demand will imply a small percentage change. For instance, if demand rises from 100 units to 101 units, it is only a

101-100 ×100=1 percent rise in demand. Thus, the general rule is 100 that the higher the price level, the higher is the elasticity of demand for the commodity.

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Elasticity of Demand