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## BCom 1st Year Elasticity of Demand Notes Study Material

### Meaning of Elasticity of Demand

We have seen that a number of variables determine the quantity of a particular good or service that consumers are willing to buy. A “measure of the degree to which the quantity purchased will respond to a change in any single variable is called its elasticity with respect to that variable.” And the measure of responsiveness of the quantity demanded of a good relative to a change in its price is called the price elasticity of demand for the good.

In other words, the price elasticity of demand is a measure of the responsiveness of demand to price changes; it measures the curvature of the demand curve. In other words, it quantifies how consumption responds to changes in price, i.e., by how much consumption will change as a result of change in price.

Since demand changes due to changes in income as well, response of demand to price changes is called the price elasticity of demand and response of demand to income changes as income elasticity of demand. However, the expression elasticity of demand is always understood to refer to the price elasticity of demand and it can be defined as:

“The proportional change in the quantity purchased divided by the proportional change in price.” –Hirshleifer and Glazer

“The percentage change in the quantity demanded divided by percentage change in price that brought it about.” —Lipsey and Chrystal

“The price elasticity of demand (sometimes simply called ‘price elasticity) measures how much the quantity demanded of a good changes when its price changes. The precise definition of the price elasticity is the percentage change in quantity demanded divided by the percentage change in price.” –Samuelson and Nordhaus

“The elasticity (or, responsiveness) of demand in a market is great or small according as the amount demanded increases much or little for a given fall in price, and diminishes much or little for a given rise in price.” —Alfred Marshall

“The price elasticity of demand is the ratio of the percentage change in the quantity demanded of a good or service to the percentage change in its price, all other things remaining the same.” –Truett and Truett

### Measurement of Price Elasticity of Demand

There are different ways of measuring price elasticity of demand (often referred to merely as elasticity of demand or sometimes just elasticity). Following methods may be noted:

#### (1) Percentage Method

The Greek letter eta (ƞ) is usually used to denote price elasticity of demand. It is measured as a ratio thus:

ƞ = Percentage change in quantity demanded /Percentage change in price

Now,     Percentage change in quantity demanded = Change in quantity demanded (∆Q)/Initial quantity (Q)

And,     Percentage change in price = Change in price (∆P)/Initial price (P)

Symbolically,    ƞ=∆Q/Q/∆P/P = ∆Q/Q x P/∆P =P∆Q/Q∆P

The value of ƞ is negative since an increase in price is accompanied by a decrease in the quantity demanded, while a decrease in price is accompanied by an increase in the quantity demanded. It means that the price and the quantity will always change in the opposite directions. One change will be positive and the other negative. This makes the measure of elasticity of demand negative. In elementary treatment of the subject, the negative sign is usually dropped. We follow this practice here too.

The numerical value of elasticity can vary from zero to infinity. The following five types of elasticity are important:

(i) ƞ is zero if there is no change in quantity demanded when price changes. Here the quantity demanded does not respond to a price change.

(ii) The numerical value of elasticity exceeds zero when the response of the quantity demanded to a change in price is positive. Larger the response the greater is the elasticity. Suppose the elasticity of demand is greater than zero but less than one. Here the demand is said to be inelastic.

(iii) Suppose that the numerical value of elasticity is one (ƞ = 1). It is the case of unit elasticity or elasticity is said to be unity. Unit elasticity means that the percentage change in quantity is equal to percentage change in price.

(iv) Let us take the case of the numerical value of elasticity greater than one (ƞ>1). Such a demand is said to be an elastic demand. An elastic demand curve is a flatter curve. In this case the percentage change in quantity demanded is greater than the percentage change in price.

(v) When the demand is infinitely elastic, there exists some small price reduction that will raise demand from a zero to infinity. Above this critical price, & nothing is purchased. At this critical price, consumers purchase all that they can get.

#### (2) Total Outlay Method

Total outlay method is also called the total revenue method. Here we look at the reaction of consumer’s total expenditure when the price of the product changes. The change in total expenditure of the consumer brought about by a change in price has a relation with the elasticity of demand. This relationship can be put in the following ways:

(i) Elastic Demand: A fall in price increases total expenditure of the consumer on the good and a rise in price reduces it. Total expenditure is price multiplied by the quantity demanded. Each type of elasticity is explained with the help of a table and a diagram. In Table, elastic demand is shown and it is graphically presented in Fig. From Table, we get that as the price falls from Rs. 10 to Rs. 9, quantity demanded increases from 100 units to 125 units. Consequently, total expenditure of the consumer goes up from Rs. 1,000 to Rs. 1,125. Fig. shows that at price P1, the quantity demanded is Q1 and the total expenditure of the consumer is the rectangle P1Q1. At the lower price of P2, quantity demanded is Q2 and total expenditure is the rectangle P2Q2. Since the area of the rectangle P2Q2 is bigger than the rectangle P1Q1, total expenditure has increase when price falls. So the demand is elastic

(ii) Inelastic Demand: The case inelastic demand is shown in Table and fig, where a fall in price reduces total expenditure and a rise in price increases it. In Table, we see that at the price of Rs. 10, quantity demanded is 100 units and total expenditure is Rs. 1,000. When price falls to Rs. 9, quantity demanded increases to 110, but total expenditure declines to Rs.990. It is a case of inelastic demand. In Fig, as a result of the price fall, total expenditure as shown by the rectangle P2Q2 is smaller in area than the rectangle P1Q1. So demand is inelastic.

(iii) Unit Elasticity: In this case a rise or a fall in price leaves total expenditure on the good unaffected. Table and Fig. depict this situation. It can be seen in Table that when price falls, the quantity demanded so changes that total expenditure remains the same, i.e., it does not change. As shown in Fig, the demand curve in the case of unit elasticity is a rectangular hyperbola. Consequently, the two rectangles P1Q1 and P2Q2 are equal in area, i.e., total expenditure remains unaffected due to a rise or fall in price of the good.

### Points of Caution

While using the above methods of measuring elasticity of demand, there is need for some caution. The following points need to considered:

First, to portray elastic demand as a relatively flat curve and inelastic demand as a relatively steep curve is a convention which might work in some cases, but not in others. It is for the reason that the slope of demand curve is

∆P/∆Q but elasticity is P∆Q/Q∆P.

Second point relates to scale on the axis of a diagram. For an elastic demand to be represented by a flat curve, the scale must be appropriate.

Suppose the price axis has the scale 10, 9, 8, 7, etc., while the quantity axis has the scale 1, 2, 3, 4, etc. The demand curve in this case would be flat. The demand will also be elastic. Now let us assume that the price axis remains the same but quantity axis has the scale of 101, 102, 103, etc. In this case demand is inelastic but the demand curve should still be relatively flat. Third, interpretation of changes in prices is also important. As shown in Fig, price rises from P1 to P2. From this information alone no definite conclusion about elasticity can be drawn. It is so because the price increase may be due to an increase in demand as shown by the upward shift in demand curve from D1 to D2. Both of these demand curves are relatively elastic.

On the other hand, the rise in price could take place along the unchanged and inelastic demand curve, D3. Information about price increase alone is not enough to know whether the demand remains unchanged or has increased. For this additional information on buyer’s incomes and tastes and on movements of prices of substitutes is necessary.

The fourth factor to note is about another kind of misinterpretation. It relates to drawing wrong conclusions from reflection on personal experience. Let us take an example. Suppose the bus fare goes up by 10 paise. In spite of this increase, you keep on riding the bus just as often as before. Will it be correct from this to jump to the conclusion that the demand for the bus service is highly or completely inelastic? It will not be correct to do so because the demand for bus service comes from thousands of people in the city.

The mass response to the change in bus fare is the demand behaviour that we are examining here. Mass behaviour may not be reflected in the behaviour of a particular individual. The mass or market demand for a commodity can be elastic, even though the demand of many of the buyers is inelastic. This is particularly true in the case of “petty goods”. These commodities are so cheap that all consumers may not try to economize in buying them. Demand for such consumers is highly inelastic. Since people differ in temperament, income and social patterns of behaviour, what is a petty good to one may not be so for the other.

### Point Elasticity of Demand

Marshall has provided a formula to know the elasticity of demand at & point on the demand curve. If the diesel price problem has to do with the range from 100 to 102 paise per litre, why not between 100 and 101 paise or between 100 and 100.5 paise or between 100 and 100.1 paise. Price ranges can be narrowed. Logically it can be made so small that it becomes a point on a demand curve. When elasticity is measured at a point on a demand curve, it is called point elasticity of demand. Marshall’s method of measuring it is shown in fig. In this diagram, DD is a demand curve and P a point on it. Let a straight line touching the curve at point P meet OX at A and OY at B. The measure of elasticity at point P is the ratio of PA to PB (PA/PB). If PA > PB, then demand is elastic. If PA <PB, then demand is inelastic. When PA= PB, demand is unity.

Marshall’s formula can be utilised to know elasticity of a linear demand curve. Linear curve is a straight line. Elasticity of linear demand is tricky as it is different at every point. It has been shown in Fig. As shown in Fig, elasticity at any one point is the ratio of the lower part of the straight line to the upper part. At the mid-point A of the demand curve, elasticity is CA/BA = 1, since CA = BA. As we move down along the demand curve, the numerical value of elasticity declines and is less than one. So between A and C, demand is inelastic.

At point C, elasticity is zero. As we move above point A along the demand curve, elasticity rises above one. So demand is elastic. At point B, elasticity is infinity.

### Arc Elasticity of Demand

In all the above measures of elasticity, the terms elastic and inelastic have been applied to the whole demand for a commodity. But a demand curve may not have the same elasticity over every part of the curve. It can be elastic in one price range and inelastic in another, as shown in Fig. In Fig. (A), demand is elastic at high prices and inelastic at low prices. In Fig. (B), demand is inelastic at high prices and elastic at low prices. Both kinds of demand curves are possible. Here measurement of elasticity presents difficulty. Fig. presents this difficulty. Arc elasticity is the elasticity at the mid-point of an arc of a demand curve.

Arc Elasticity = Change in Quantity/Sum of Quantities/2 + Change in Price/Sum of Prices/2

Thus, elasticity is unity. If percentage method is used to measure elasticity, demand will turn out to be elastic.

### Income Elasticity of Demand

The relation between changes in income and changes in consumption good can be expressed through the concept of income elasticity of demand.

the ratio of the percentage change in the quantity demanded to the percentage change in income. Thus

ƞY = ∆Q/Q/∆Y/Y

where,

ƞY = income elasticity of demand

Q = quantity demanded

Y= income of the consumer

“Income elasticity of demand is the proportional change in the quantity purchased divided by the proportional change in income.” -Hirshleifer and Glazer

Important values of the income elasticity are shown in Fig. For most goods, increases in income lead to increases in quantity demanded and so income elasticity is positive. For such goods, income elasticity is subdivided in the same way as price elasticity. All such sub-divisions of income elasticity are shown in the diagram by the demand curves D2, D3, D4 and D5. They show the following:

(i) Income changes causing no change in the quantity demanded result in zero elasticity (ƞY = 0) as shown by demand curve D2 drawn at a right angle on X-axis.

(ii) Equal percentage change in income and quantity demanded results in the income elasticity of 1 (ƞY = 1). It is shown by the demand curve D4 drawn at an angle of 45°. Income elasticity of 1, i.e., unity is again as important here as in the case of price elasticity of demand. It is the dividing line between elastic and inelastic demand.

(iii) When one percentage increase in income leads to less than one percentage increase in the quantity demanded, income elasticity is less than one as shown by demand curve D3. Numerical value of income elasticity between 0 and 1 stands for inelastic demand.

(iv) If one percent increase in the income of the consumer causes more than one percent increase in the quantity demanded, elasticity is said to be higher than one (ƞY > 1) as shown by demand curve D5. Demand in this case is elastic.

(v) Finally, there is the demand curve D1 standing for negative elasticity (ƞY < 0, i.e. negative).

Changes in income shift the demand curve for a good. In the case of all mal goods, rise in income causes more of the commodity to be bought, other ings remaining the same. It means a rightward shift in the good’s demand urve. However if the product is an inferior good, rise in income results less of thecommodity to be bought. In graphical terms, it means a leftwards shift in the demand curve of the product. Thus normal goods have positive income asticity, while inferior goods have negative income elasticity.

Zero income elasticity is the boundary line between inferior and normal goods as also between negative and positive income elasticity. Unitary income elasticity is also a boundary line but between elastic and inelastic income elasticity and between necessary and luxury goods. Furs, jewellery, automobiles,

VCRs, VCDs, etc. are examples of commodities with high income elasticities. These are luxuries. “Indeed the simplest and best way to define luxuries is to say that they are commodities with high income elasticities of demand. Similarly, necessities can be defined as commodities with low income elasticities, cigarettes, for example.” Stonier and Hague, however, are a little sceptic about defining necessities and luxuries in terms of income elasticities alone, though concede that it is a useful definition.

### Cross-elasticity of Demand

The concept of cross-elasticity of demand is useful in handling inter commodity relations. It measures the responsiveness of quantity demanded of one product (say, X) to changes in the price of the other product (say, Y). This measure is expressed as

ƞXY = Percentage change in the quantity demanded of one good (X)/Percentage change in price of another good (PY)

= ∆QX/QX/∆PY/PY

Cross-elasticity (ƞXY) can vary from minus infinity to plus infinity. It is positive in the case of substitute goods because the quantity change and the price change are in the same direction. But for complementary goods cross-elasticity is negative because changes in the price of one good cause changes in the quantity demanded of another good in the opposite direction.

Bread and butter, for example, are complementary goods. So a fall in the price of butter causes an increase in the consumption of both commodities. It means that changes in the price of butter and in the quantity of bread demanded have opposite signs. Cross-elasticity is negative.

In contrast, tea and coffee are substitutes. A fall in the price of tea increases the consumption of tea (quantity of tea demanded increases) but reduces the quantity of coffee demanded. Thus changes in the price of tea and the quantity of coffee demanded have the same sign. Cross-elasticity is positive.

### Elasticity of Price Expectations

In our discussion of price elasticity of demand the price expectations of the c consumers were not taken into consideration. It was assumed that consumers faced given prices of the commodity in question and of its substitutes and complements. Let us assume now that consumers make definite plans for their purchases of commodities in successive periods of time stretching into the future. Looking ahead into the future they make plans on how much of each commodity to buy in each period. Their plans for future purchases depend on their estimates of the prices they expect to prevail in future periods.

Just how much demand is affected by price expectations depends substantially upon the elasticity of price expectations. It is another elasticity concept devised by the English economist, J. R. Hicks, in 1939.

Hick’s says that price expectations are subject to three types of influences. They are:

(i) Entirely non-economic influences like the weather, the political news, people’s state of health, their psychology, etc.

(ii) Economic influences but not closely connected with actual price movements; they include mere market superstition, at one extreme, and crop reports, etc., on the other, which have a future hearing on demand and supply; and

(iii) Actual experience of prices, experience in the past and experience in the present.

Changes in price-expectations resulting from the first two types of influences are treated by Hicks as autonomous changes. So we are left with the influence of present prices and the influence of past prices. Since past prices are past, they are simply data with respect to the current situations. Current prices have some influence on price expectations. But this influence may have various degrees of intensity and work in various different ways. The degrees of intensity of influence of current prices on future prices is the measure of elasticity of expectations. Hicks defines this elasticity as

“I define the elasticity of a particular person’s expectations of the price of commodity X as the ratio of the proportional rise in expected future prices of X to the proportional rise in its current price.”

Let future prices be F and current prices C. The coefficient of elasticity of price expectations, ƞpe is

ƞpe = ∆F/F x C/∆C = C∆F/F∆C

Suppose that a consumer or a businessman sees that the price of a go has just gone up by 10 per cent. If he expects that the future price of this go will go up by 20 percent, the elasticity of price expectation is then 2.

A rise in the current prices will shift the demand curve to the right if the elasticity of price expectation is greater than one. Demand increases because buyers purchase more now at the current price to avoid even higher prices expected to prevail in the future. In the case of low (less than one) or negative elasticity, a rise in current price causes demand to fall.

So the demand curva shifts to the left as buyers wait for the price to come down in future. When the elasticity of expectation is unity, a change in current price has no effect at all. on the current demand as there is no expectation of any change in this price in the future.

### Factors Influencing Price Elasticity of Demand

A number of factors influence or determine the elasticity of demand to changes in price. Important among them are:

(i) The Possibility of Substitution: The most important influence on elasticity of demand is the degree of closeness of the substitute for the good. The closer the substitute the higher the elasticity of demand. A note of caution: the substitute must be within the same price range.

(ii) The Type of Goods: Demand for necessity is inelastic; the demand for luxuries in elastic. Here too we have to note the possibility that substitution plays an important role. Demand for necessities like bread and potatoes “is inelastic because there are no close substitutes for them within the same price range and not merely because they are necessaries.” Hanson further states that “the demand for some expensive luxury goods may be very inelastic, not because they are luxuries but rather because they lack close substitutes.”

(iii) Consumers’ Income: Elasticity is closely related to person’s income. The demand of billionaire for all commodities may be quite unaffected by any changes of price. But this is not the case with the majority of the people as they have to make a choice between this or that commodity; they cannot purchase all commodities.

(iv) Redistribution of Income: A redistribution of income in favour of the poor will make the demand for some goods more inelastic (those things more particularly demanded by such people) and for other things more elastic (those things desired by people in the higher income groups).

(v) Cheap Commodities: Marshall says that “the elasticity of demand is great for high prices, and great or at least considerable for medium prices; but it declines as the price falls and gradually fades away if the fall goes so far that satiety level is reached.” Good examples of cheap commodities are matches, salt, etc.

(vi) Habit: Once certain habits of expenditure are formed, they may become sufficiently strong to offset the effect of changes in price. Tobacco is a good example. In spite of substantial increases in its price, the demand for it has remained almost unchanged.

(vii) Time: Generally speaking, demand tends to become more elastic with time. It is so because more substitutes for goods are available over longer periods of time. Another reason is that consumers have more time over longer periods to adjust their consumption patterns in response to price changes.

(viii) Proportion of Income Spent on a Good: The demand for a good is quite elastic over which consumers spend a large part of their income. It is so because even a small rise in price (say 10 per cent) is likely to reduce substantially their ability to buy this item and so result in sharp percentage declines in the quantity demanded. “In general, other things being equal, the smaller the percentage of income spent on a good, the elastic the demand unless the good is considered a dispensable luxury,” says Hyman.

### Importance of the Price Elasticity of Demand

The price elasticity of demand is useful to sellers. From the estimate of this elasticity, sellers can make predictions of changes in quantity demanded in response to price changes.

Once the sellers know this, they can decide whether to cut price or not. If they decide on cutting the price, they can also determine by how much to reduce the price.

Sellers can use the estimate of price elasticity to decide whether to place larger orders for the good to the manufacturer or to cut back on their orders and avoid lying up their funds in a large inventory of unsold stock of the good.

Producers can also use price elasticity of demand to formulate pricing strategies if they own firms that can control their prices, such as, monopoly and oligopoly firms. Let us take an example to understand the use of price elasticity of demand to formulate pricing strategies by a firm.