UNIT 3 ANALYSIS OF MARKET DEMAND AND DEMAND ELASTICITIES …application.dbuglobal.com/assets/Pu18ME1002/CPu18M… · · 2011-08-12NOTES Self-Instructional Material 65 Analysis of

UNIT 3 ANALYSIS OF MARKET DEMAND AND

DEMAND ELASTICITIES

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Self-Instructional Material 63

Analysis of Market Demand andDemand ElasticitiesUNIT 3 ANALYSIS OF MARKET

DEMAND AND DEMANDELASTICITIES

Structure

3.0 Introduction3.1 Unit Objectives3.2 Analysis of Market Demand

3.2.1 Meaning of Market Demand; 3.2.2 Types of Demand;3.2.3 Determinants of Market Demand

3.3 Demand Function3.3.1 Linear Demand Function; 3.3.2 Non-linear Demand Function;3.3.3 Multi-variate or Dynamic Demand Function

3.4 Elasticities of Demand3.4.1 Importance of the Elasticity Concept; 3.4.2 Price Elasticity of Demand;3.4.3 Measuring Price Elasticity from a Demand Function; 3.4.4 Price Elasticity and TotalRevenue; 3.4.5 Price Elasticity and Marginal Revenue; 3.4.6 Determinants of PriceElasticity of Demand; 3.4.7 Cross-Elasticity of Demand; 3.4.8 Income-Elasticity ofDemand; 3.4.9 Advertisement or Promotional Elasticity of Sales; 3.4.10 Elasticity ofPrice Expectations; 3.4.11 Some Estimates of Demand Elasticities

3.5 Summary3.6 Answers to ‘Check Your Progress’3.7 Exercises and Questions3.8 Further Reading

3.0 INTRODUCTION

From the analysis of individual demand, we move on in this Unit to analyse the marketdemand for a product. The analysis of total demand for a firm’s product plays a crucialrole in business decision-making. For its successful operation the firm has to plan forfuture production, the inventories of raw materials and advertisement, and setting upsales outlets. Therefore, the information regarding the magnitude of the current andfuture demand for the product is indispensable. Theory of demand provides an insightinto these problems. From the analysis of market demand, business executives can know

(i) the factors which determine the size of demand,(ii) elasticities of demand, i.e., how responsive or sensitive is the demand to the

changes in its determinants,(iii) possibility of sales promotion through manipulation of prices,(iv) responsiveness of demand to advertisement expenditure, and(v) optimum levels of sales, inventories and advertisement cost, etc.

In this Unit, we have discussed the meaning of market demand, types of demandand their distinctive features, determinants of demand for a product, elasticities ofdemand and their measurement, i.e., measurement of degree of sensitiveness or respon-siveness of demand to the changes in its determinants.

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64 Self-Instructional Material

Analysis of Market Demand andDemand Elasticities 3.1 UNIT OBJECTIVES

To analyse market demand, its types and its determinantsTo introduce demand function and its applicationTo explain the concept measurement of different kinds of demand elasticitiesTo show the relationship between price elasticity of demand and average andmarginal revenuesTo show the application of demand elasticities in business decisions

3.2 ANALYSIS OF MARKET DEMAND

3.2.1 Meaning of Market DemandThe market demand is the sum of individual demands for a product at a price per unitof time. We may recall that the quantity demanded of a commodity by an individual perunit of time, at a given price, is known as ‘individual demand’ for that commodity. Theaggregate of individual demands for a product is called market demand for the product.In other words, the total quantity that all the consumers/users of a commodity arewilling to buy per unit of time at a given price, all other things remaining the same, iscalled ‘market demand’ for the that product.Horizontal summation of individual demand schedule produces the market demandschedule. For example, suppose there are three consumers A, B and C of a commodityX and that their individual demands are given as in Table 3.1. The last column presentsthe market demand schedule, i.e., the aggregate of individual demands by the threeconsumers at different prices. The market demand curve can be obtained by plotting themarket demand schedule, i.e., the quantity demanded (last column) at different prices(in the first column).

Table 3.1: Price and Quantity Demanded

Price of X Quantity of X demanded by MarketA B C demand

10 5 1 0 68 7 2 0 96 10 4 1 154 14 6 2 222 20 10 4 340 27 15 8 50

Fig. 3.1: Derivation of Market Demand Curve

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Analysis of Market Demand andDemand Elasticities

The demand schedules of A, B and C are plotted as Da, Db and Dc in Fig. 3.1. Horizontalsummation of these individual demand curves gives the market demandcurve as shown by Dm. The market demand curve can also be obtained by plottingthe total demand given in the last column against the corresponding price in the firstcolumn.Graphically, market demand curve is horizontal summation of individual demand curves.The graphical derivation of the market demand curve through the horizontal summationof the individual demand curves is illustrated in Fig. 3.1.

3.2.2 Types of DemandThe demand for various goods is generally classified on the basis of the the consumersof a product, suppliers of the product, nature of goods, duration of consumption of acommodity, interdependence of demand, period of demand and nature of use of thegoods (intermediate or final). We have have discussed here the major types of demandthat figure in business decisions.Individual and Market Demand. As mentioned earlier, the quantity of a commoditywhich an individual is willing to buy at a particular price during a specific time period,given his money income, his taste and prices of other commodities (particularlysubstitutes and complements), is called ‘individual’s demands for a commodity’.As explained, above, the total quantity which all the consumers of a commodity arewilling to buy at a given price per time unit, given their money income, taste and pricesof other commodities (mainly substitutes) is known as ‘market demand for thecommodity’. In other words, the market demand for a commodity is the sum ofindividual demands by all the consumers (or buyers) of the commodity, over a timeperiod and at a given price, other factors remaining the same. (See also the previoussection).Demand for Firm’s Product and Industry’s Products. The quantity of a firm’sproduct that can be disposed of at a given price over a time period connotes the demandfor the firm’s product. The aggregate of demand for the product of all the firms of anindustry is known as the market demand or demand for industry’s product. Thisdistinction between the two demand is not of much use in a highly competitivemarket—since it merely signifies the distinction between a sum and its parts.However, where market structure is oligopolistic, a distinction between the demand fora firm’s product and for the industry’s product is useful from the managerial point ofview. For, in such markets, products of each firm are so differentiated from theproducts of the rival firms that consumers treat each product as different from the other.This gives firms an opportunity to manoeuver the price, capture a larger market sharethrough advertisement and, thereby, to enhance their own profit. For instance, marketsfor motor cars, radios, TV sets, refrigerators, scooters, toilet soaps, toothpastes etc.belong to this category of markets.In the case of monopoly and perfect competition, the distinction between demand for afirm’s product and that of the industry is not of much use from managerial point of view.In case of monopoly, the industry is a one-firm industry and the demand for the firm’sproduct is the same as that of the industry. In case of perfect competition, products ofall firms of the industry are homogeneous; consumers do not distinguish betweenproducts of different firms; and price for each firm is determined by the market forces(i.e., demand and supply for the industry as whole). Firms have only little opportunityto manoeuvre the prices permissible under local conditions and advertisement by a firmbecomes effective for the whole industry. Therefore, conceptual distinction betweendemand for a firm’s product and for that of the industry is not of much use in businessdecisions-making.

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Autonomous and Derived Demand. An Autonomous demand or direct demand for acommodity is one that arises on its own out of a natural desire to consume or possessesa commodity. An autonomous demand is independent of the demand for any othercommodity. For example, consider the demand for commodities which arise directly fromthe biological or physical needs of human beings, e.g., demand for food, clothes, shelteretc. Demand for the these goods and the like is autonomous demand. Autonomous demandmay also arise as a result of ‘demonstration effect’ of a rise in income, increase inpopulation and advertisement of new products.On the other hand, the demand for a commodity that arises because of the demand forsome other commodity, called ‘parent product’, is called derived demand. For instance,demand for land, fertilizers and agricultural tools and implements is a derived demandbecause these goods are demanded because food is demanded. Similarly, demand forsteel, bricks, cement etc. is a derived demand—derived from the demand for house andother buildings. In general, the demand for producer goods or industrial inputs is aderived one. Also the demand for complementary goods (which complement the use ofother goods) or for supplementary goods (which supplement or provide additional utilityfrom the use of other goods) is a derived demand. For instance, petrol is acomplementary good for automobiles and a chair is a complement to a table.Consider some examples of supplementary goods. Butter is a supplement to bread;mattress is a supplement to cot; and sugar is a supplement to tea-for some, it is acomplement. Therefore, demand for petrol, chair and sugar would be considered asderived demand.The conceptual distinction between autonomous deamand (i.e., demand for a ‘parentproduct’) and derived demand would be useful from a businessmen’s point of view tothe extent that the former can serve as an indicator of the latter.Demand for Durable and Non-durable Goods. Demand is also often classified underdemand for durable and non-durable goods. Durable goods are those whose total utilityor usefulness is not exhausted in a single or short-run use. Such goods can be usedrepeatedly or continuously over a period of time. Durable goods may be consumer goodsas well as producer goods. Durable consumer goods include clothes, shoes, houses,furniture, utensils, refrigerator scooters, cars, etc. The durable producer goods includemainly the items under ‘fixed assets’, such as building, plant, machinery, office furnitureand fixtures etc. The durable goods, both consumer and producers goods, may be furtherclassified as ‘semi-durables’ (e.g., clothes and furniture) and ‘durables’ (e.g., residentialand factory building cars etc.).Non-durable goods on the other hand are those which can be used or consumed onlyonce (e.g., food items) and their total utility is exhausted in a single use. This categoryof goods too may be grouped under non-durable consumer goods and nondurableproducer goods. All food items, drinks, soaps, cooking fuel, (gas, kerosene, coal etc.),lighting, cosmetics etc., fall in the former category. In the latter, fall goods such as rawmaterials, fuel and power, finishing materials and packing items etc.The demand for non-durable goods depends largely on their current prices, consumers’income and fashion and is subject to frequent change whereas the demand for thedurable good is also influenced by their expected price, income and change intechnology. The demand for durable goods changes over a relatively longer period.There is another point of distinction between the demand for durable and non-durablegoods. Durable goods create replacement demand whereas nondurable goods do not.Also, the demand for nondurable goods increases (or decreases) lineally whereas thedemand for durable goods increases (or decreases) exponentially due to an increase instock of durable goods and hence accelerated depreciation.

Check Your Progress1. How is market demand

defined?2. Distinguish between autono-

mous and derived demand.3. What is the difference between

consumer durables andnon-durables?

4. Distinguish between short-term and long-term demand fora product.

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Short-term and Long-term Demand

Short-term demand refers to the demand for goods that are demanded over a shortperiod. In this category are found mostly the fashion consumer goods, goods ofseasonal use, inferior substitutes during the scarcity period of superior goods, etc. Forinstance, the demand for fashion wear is short-term demand though the demand forgeneric goods (trousers, shoes, ties, etc.) continues to remain a long-term demand.Similarly demand for umbrella, raincoats, gum-boots, cold-drinks, ice-creams etc., is ofseasonal nature. The demand for such goods lasts till the season lasts. Some goods ofthis category are demanded for a very short period (1–2 weeks), e.g., New Year Greetingcards, candles and crackers on the occasion of Diwali.Although some goods are used only seasonally they are of durable nature, e.g., electricfans, woollen garments, etc. The demand for such goods is of a durable nature but itis subject to seasonal fluctuation. Sometimes, demand for certain goods suddenlyincreases because of scarcity of their superior substitutes. For example, when supplyof cooking gas suddenly decreases, demand for kerosene, cooking coal and charcoalincreases. In such cases, additional temporal demand is of a short-term nature.The long-term demand, on the hand, refers to the demand which exists over a longperiod. The change in long-term demand is perceptible only after a long period. Mostgeneric goods have long-term demand. For example, demand for consumer andproducer goods, durable and nondurable goods is long-term demand, though theirdifferent varieties or brands may only have a short-term demand.Short-term demand depends, by and large, on the price of commodities, price of theirsubstitutes, current disposable income of the consumer, their ability to adjust theirconsumption pattern and their susceptibility to advertisement of a new product. Thelong-term demand depends on the long-term income trends, availability of bettersubstitutes, sales promotion, consumer credit facility, etc.The short-term and long-term concepts of demand are useful in designing new productsfor established producers and choice of products for the new entrepreneurs, in pricingpolicy, and in determining and phasing the advertisement expenditure.

3.2.3 Determinants of Market DemandThe knowledge of the determinants of market demand for a product and the nature ofrelationship between the demand and its determinants proves very helpful in analysingand estimating demand for the product. It may be noted at the very outset that a hostof factors determine the demand for a product.In general, however, following are the factors which determine, by and large, the marketdemand for a product:

1. Price of the product, 2. Price of the related goods—substitutes, complements and supplements, 3. Level of consumer’s income, 4. Consumer’s taste and preference, 5. Advertisement of the product, 6. Consumer’s expectations about future price and supply position, 7. Demonstration effect and ‘band-wagon effect’, 8. Consumer-credit facility, 9. Population of the country (for the goods of mass consumption),10. Distribution pattern of national income, etc.

To this list, one may add such factors as off-season discounts and gifts, number of usesof a commodity, level of taxation and the general social and political environment of thecountry (especially with respect to demand for capital goods).

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All these factors are, however, not equally important. Besides, some of them are not evenquantifiable. For example, consumer’s preferences, utility, demonstration effect,expectations, etc., are difficult to measure. Nevertheless, we will discuss here bothquantifiable and nonquantifiable determinants of the demand for a product.1. Price of the ProductThe price of a product is one of the most important determinants of its demand in thelong run and the only determinant in the short run. The price of a product and itsquantity demanded are inversely related. The law of demand (discussed in the previousUnit) states that the quantity demanded of a product which its consumers/users wouldlike to buy per unit of time, increases when its price falls and decreases when its priceincreases, other factors remaining constant. The assumption ‘other factors remainingconstant’ implies that income of the consumers, prices of the substitutes andcomplementary goods, consumer’s taste and preference and number of consumers,remain unchanged. The price-demand relationship assumes a much greater significancein the oligopolistic market in which the outcome of price-war between a firm and itsrival determines the level of success of the firm. The firms have to be fully aware ofprice elasticity of demand for their own product and that of the product of the rivalfirms.2. Price of the Related GoodsThe demand for a commodity is also affected by the changes in the price of its relatedgoods. Related goods may be substitutes or complementary goods.Substitutes. Two commodities are deemed to be substitutes for one an other if changein the price of one affects the demand for the other in the same direction. For instance,commodities X and Y are considered as substitutes for one an other if a rise in the priceof X increases demand for Y and vice versa. Tea and coffee, hamburgers and hot-dog,alcohol and drugs are some examples of substitutes in the case of consumer goods.

Fig. 3.2: Demand for Substitutes and Complements

By definition, the relation between demand for a product and price of its substitute isof positive nature. Assuming goods X and Y to be substitutes for one another, thedemand function for X and Y with respect to the price of their substitutes can be writtenas follows.

Dx = f(Py), ΔDx/ΔPy > 0and Dy = f(Px), ΔDy/ ΔPx > 0

When price of a substitute good (say, coffee) of a product (tea) falls (or increase), thedemand for the product falls (or increases). The demand-price relationship of this natureis given in Fig. 3.2 (a).

Pric

e of

cof

fee

(Rs.)

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Complements. A commodity is deemed to be a complement for another when itcomplements the use of the other or when the use of the two goods goes together sothat their demand changes (increases or decreases) simultaneously. For example, petrolis a complement to cars and scooters, butter and jam to bread, milk and sugar to teaand coffee, mattress to cot, etc. In economic sense, two goods are termed ascomplementary to one another if an increase in the price of one causes a decrease indemand for the other. By definition, there is an inverse relation between the demand fora good and the price of its complement. For instance, an increase (or decrease) in theprice of petrol causes a decrease (or an increase) in the demand for car and other petro-leum vehicles, other things remaining the same. The demand function for car (Dc) inrelation to petrol price (Pp) can be written as

Dc = f(Pp), DDc /DPp < 0The relationship between the demand for a product (car) and the price of its complement(petrol) is given in Fig. 3.2 (b).3. Consumer’s IncomeIncome is the basic determinant of quantity of a product demanded since it determinesthe purchasing power of the consumer. That is why people with higher currentdisposable incomes spend a larger amount on consumer goods and services than thosewith lower income. Income-demand relationship is of a more varied nature than thatbetween demand and its other determinants. While other determinants of demand, e.g.,product’s own price and the price of its substitutes are more significant in the short-run, income as a determinant of demand is equally important in both short run and longrun.The relationship between the demand for a commodity, say X, and the household income(Y), assuming all other factors to remain constant, is expressed by a demand functionsuch as

Dx = f(Y), DDx /DY > 0Before we proceed to discuss income-demand relationships, it will be useful to note thatconsumer goods of different nature have different relationship with income of differentcategories of consumers. The managers need, therefore, to be fully aware of the goodsthey are dealing with and their relationship with the income of consumers, particularlyin regard to the assessment of both existing and prospective demand for a product.For the purpose of income-demand analysis, consumer goods and services may begrouped under four broad categories, viz. (a) essential consumer goods, (b) inferiorgoods, (c) normal goods, and (d) prestige or luxury goods. Let us now look into therelationship between income and the different goods. The relationship between incomeand the different consumer goods is presented through Engel curves.1

(a) Essential consumer goods (ECG). The goods and services in this category arecalled ‘basic needs’ and are consumed by all persons of a society, e.g., foodgrains, salt,vegetable oils, matches, cooking fuel, minimum clothing and housing. Quantitydemanded of this category of goods increases with increase in consumer’s income butonly upto a certain limit, even though the total expenditure may increase in accordancewith the quality of goods consumed, other factors remaining the same. The relationshipbetween goods of this category and consumer’s income is shown by the curve ECGin Fig. 3.3. As the curve shows, a consumer’s demand for essential goods increasesonly until his income rises to OY2. It tends to saturate beyond this level of income.(b) Inferior goods (IG). Inferior and superior goods are widely known to bothconsumers and sellers. For instance, every consumer knows that millet is inferior towheat and rice; bidi (indigenous cigarette) is inferior to cigarette, coarse textiles areinferior to refined ones, kerosene is inferior to cooking gas; travelling by bus is inferiorto travelling by taxi, so on and so forth. In an economic sense, however, a commodityis deemed to be inferior if its demand decreases with the increase in consumer’s income

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beyond a certain level of income. The relation between income and demand for aninferior good is shown by the curve IG in Fig. 3.3 under the assumption that otherdeterminants of demand remain the same. Demand for such goods rises only upto acertain level of income (say, OY1) and declines as income increases beyond this level.(c) Normal goods. Technically, normal goods are those which are demanded inincreasing quantities as consumers’ income rises. Clothing, household furniture andautomobiles are some of the important examples of this category of goods. The natureof relation between income and demand for the goods of this category is shown by thecurve NG in Fig. 3.3. As the curve shows, demand for such goods increases with theincrease in income of the consumer, but at different rates at different levels of income.Demand for normal goods increases rapidly with the increase in the consumer’s incomebut slows down with further increases in income.

Fig. 3.3: Income Demand Curves

It may be noted from Fig. 3.3, that upto a certain level of income (Y1) the relationbetween income and demand for all types of goods is similar. The difference is only ofdegree. The relation becomes distinctly different beyond the Y1 level of income. Froma managerial point of view, therefore, it is important to view the income-demandrelations in the light of the nature of product and the level of consumer’s income.(d) Luxury and Prestige goods. What is and what is not a luxury good is a matter ofconsumer’s perception of the need for a commodity. Conceptually, however, all suchgoods that add to the pleasure and prestige of the consumer without enhancing hisearning fall in the category of luxury goods. For example, stone-studded jewellery, costlybrands of cosmetics, luxury cars, accommodation in 5-star hotels, travel by first-classreailway AC cars, upper class air travel, etc. can be treated as luxury goods. A specialcategory of luxury goods is that of prestige goods, e.g., precious stones, ostentatiousdecration of buildings rare paintings and antiques, diamond-studded jewellery andwatches, prestigious schools, etc. Demand for such goods arises beyond a certain levelof consumer’s income, i.e., consumption enters the area of luxury goods. Producers ofsuch items, while assessing the demand for their product, should consider the incomechanges in the richer section of the society, not only the per capita income (see curve,LG in Fig. 3.3).4. Consumer’s Taste and PreferenceConsumer’s taste and preference play an important role in determining the demand fora product. Taste and preference generally depend, on life-style, social customs, religiousvalues attached to a commodity, habit of the people, the general levels of living of thesociety and age and sex of the consumers. Change in these factors changes consumers’

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taste and preferences. As a result, consumers reduce or give up the consumption ofsome goods and add new ones to their consumption pattern. For example, following thechange in fashion, people switch their consumption pattern from cheaper, old-fashionedgoods over to costlier ‘mod’ goods, so long as price differentials are commensurate withtheir preferences. Consumers are prepared to pay higher prices for ‘mod goods’ evenif their virtual utility is virtually the same as that of old-fashioned goods. This piece ofinformation is useful for the manufacturers of goods and services subject to frequentchanges in fashion and style, at least in two ways: (i) they can make quick profits bydesigning new models of their product and popularising them through advertisement, and(ii) they can plan production better and can even avoid over-production if they keep aneye on the changing fashions.5. Advertisement ExpenditureAdvertisement costs are incurred with the objective of promoting sale of the product.Advertisement helps in increasing demand for the product in at least four ways:(a) by informing the potential consumers about the availability of the product; (b) byshowing its superiority over the rival product; (c) by influencing consumer’s choiceagainst the rival products; and (d) by setting new fashions and changing tastes. Theimpact of such effects shifts the demand upward to the right. In other words, otherfactors remaining the same, as expenditure on advertisement increases, volume of salesincreases to an extent. The relationship between sales (S), and advertisement outlays(AD) is expressed by the function S = f(AD). The relation between advertisement outlayand sales is shown in Fig. 3.4.

Fig. 3.4: Advertisement and Sale

AssumptionsThe relationship between demand and advertisement cost shown in Fig. 3.4 is based onthe following assumptions:

(a) Consumers are fairly sensitive and responsive to various modes of advertise-ment,

(b) The rival firms do not react to the advertisements made by a firm,(c) The level of demand has not already reached the saturation point. Once demand

reaches the saturation point, advertisement makes only marginal impact ondemand,

(d) Advertisement cost added to the price does not make the price prohibitive forconsumers, compared to the price of substitutes,

(e) Other determinants of demand, e.g., income and tastes, etc. are not operatingin the reverse direction.

In the absence of these conditions, the effect of advertisement on sales may beunpredictable.6. Consumer’s ExpectationsConsumer’s expectations regarding the future prices, income, and supply position ofgoods, etc. play an important role in determining the demand for goods and services in

Check Your Progress5. What are determinants of mar-

ket demand for a product?6. How does change in price of

substitute goods affect thedemand for a product?

7. What is the effect of increasein income on the demand foran inferior good?

8. What is demonstration effect?How does it influence thedemand for a product?

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the-short run. If consumers expect a high rise in the price of a storable commodity, theywould buy more of it at its high current price with a view to avoiding the pinch of ahigh price rise in future. On the contrary, if consumers expect a fall in the price ofcertain goods, they postpone their purchase of such goods with a view to takingadvantage of lower prices in future, mainly in the case of non-essential goods. Thisbehaviour of consumers reduces the current demand for goods whose prices areexpected to decrease in the future.Similarly, an expected increase in income increases demand. For example, announcementof ‘dearness allowance’, bonus, revision of pay-scale, etc., induces increase in currentpurchases. Besides, if scarcity of certain goods is expected by the consumers/users onaccount of a reported fall in future production, strikes on a large scale, diversion of civilsupplies towards military use etc., the current demand for such goods tends to increase,more so if their prices show an upward trend. Consumers demand more for futureconsumption and profiters demand more to make money out of an expected scarcity.7. Demonstration EffectWhen new commodities or new models of existing ones appear in the market, richpeople buy them first. For instance, when a new model of a car appears in the market,rich people would mostly be the first buyers. Colour TV sets and VCRs were first seenin affluent households. Some people buy goods or new models of goods because theyhave a genuine need for them or have excess purchasing power. Some others do sobecause they want to exhibit their affluence. But once new commodities are in vogue,many households buy them not because they have a genuine need for them but becausetheir neighbours have bought these goods. The purchases made by the latter categoryof the buyers arise out of such feelings as jealousy, competition and equality in the peergroup, social inferiority and the desire to raise their social status. Purchases made onaccount of these factors are the result of what economists call ‘demonstration effect’or the ‘.’ These effects have a positive effect on demand. On the contrary, when acommodity becomes the thing of common use, some people, mostly rich, decrease orgive up the consumption of such goods. This is known as the ‘Snob Effect’. It has anegative effect on the demand for the related goods2.8. Consumer-Credit FacilityAvailability of credit to the consumers from the sellers3, banks, relations and friends, orfrom other source encourages the consumers to buy more than what they would buy inthe absence of credit availability. That is why consumers who can borrow more canconsume more than those who cannot borrow. Credit facility mostly affects the demandfor durable goods, particularly those which require bulk payment at the time of purchase.The car-loan facility may be one reason why Delhi has more cars than Calcutta, Chennaiand Mumbai all put together. The managers who are assessing the prospective demand fortheir products should, therefore, take into account the availability of credit to theconsumers.9. Population of the CountryThe total domestic demand for a product of mass consumption depends also on the sizeof the population. Given the price, per capita income, taste and preference etc., the largerthe population, the larger the demand for a product. With an increase (or decrease) inthe size of population and with the employment percentage remaining the same, demandfor the product tends to increase (or decrease). The global perception that India offersthe most vast market in the world is based on the fact that she has the second largestpopulation albeit with a low purchasing power.10. Distribution of National IncomeThe level of national income is the basic determinant of the market demand for aproduct—the higher the national income, the higher the demand for all normal goods and

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services. Apart from its level, the distribution pattern of national income is also animportant determinant of a product. If national income is unevenly distributed, i.e., if amajority of the population belongs to the lower income groups, market demand foressential goods including inferior ones, will be the largest whereas the demand for othergoods will be relatively lower.

3.3 DEMAND FUNCTION

In mathematical language, a function is a symbolic statement of relationship between thedependent and the independent variables. Demand function states the relationshipbetween the demand for a product (the dependent variable) and its determinants (theindependent variables). Let us consider a very simple case of demand function. Supposeall the determinants of demand for commodity X, other than its price, remain constant.This is a case of a short-run demand function. In the case of a short-run demand function,quantity demanded of X, (Dx) depends on its price (Px). The demand function can thenbe stated as ‘demand for commodity X, (Dx) depends on its price (Px)’. The samestatement may be symbolically written as

Dx = f (Px) ...(3.1)In this function, Dx is a dependent and Px is an independent variable. The function (3.1)reads ‘demand for commodity X (i.e., Dx) is the function of its price (Px). It impliesthat a change in Px (the independent variable) causes a change in Dx (the dependentvariable). The function (3.1) however does not reveal the change in Dx for a givenpercentage change in Px, i.e., it does not give the quantitative relationship between Dxand Px . When the quantitative relationship between Dx and Px is known, the demandfunction may be expressed in the form of an equation. The general form of a lineardemand function is written as

Dx = a – bPx ...(3.2)where ‘a’ is a constant, denoting total demand at zero price and b = ΔD/ΔP4, is alsoa constant—it specifies the change in Dx in response to a change in Px.The form of a demand function depends on the nature of demand-price relationship. Thetwo most common forms of demand-price relationship are linear and non-linear.Accordingly, the demand function may assume a linear5 or a non-linear form.

3.3.1 Linear Demand FunctionA demand function is said to be linear when it results in a linear demand curve. Eq. (3.2)represents a linear form of the demand function. Assuming that in an estimated demandfunction a = 100 and b = 5, function (3.2) can be written as

Dx = 100 – 5Px ...(3.3)By substituting numerical values for Px, a demand schedule may be prepared as givenin Table 3.2.

Table 3.2: Demand Schedule

Px Dx = 100 – 5 Px Dx

0 Dx = 100 – 5 × 0 1005 Dx = 100 – 5 × 5 75

10 Dx = 100 – 5 × 10 5015 Dx = 100 – 5 × 15 2520 Dx = 100 – 5 × 20 0

This demand schedule when plotted gives a linear demand curve as shown in Fig. 3.5.Note that the linear demand curve has a constant slope (DPx/DDx).

NOTES



Fig. 3.5: Linear Demand Function Fig. 3.6: Non-Linear Demand Function

From the demand function, one can easily obtain the price function. For example, giventhe demand function (3.2), the price function may be written as follows.

Px = a Db

x−

Px = ab b−

1 Dx

Assuming a/b = a1 and 1/b = b1, the price function may be written asPx = a1 – b1 Dx ...(3.4)

3.3.2 Non-linear Demand FunctionA demand function is said to be non-linear or curvilinear when the slope of the demandcurve, (ΔP/ΔD) changes all along the curve. A non-linear demand function yields ademand curve instead of a demand line, as shown in Fig. 3.6. A non-linear demandfunction takes the form of a power function of the form given below.

Dx = aPx–b …(3.5)

and Dx = aP c

bx +

− …(3.6)

where a > 0, b > 0 and c > 0.It should be noted that the exponent of the price variable in a non-linear demand function(3.5) is the coefficient of price elasticity of demand.

3.3.3 Multi-variate or Dynamic Demand FunctionWe have discussed above a single variable demand function, i.e., one with price as a singleindependent variable. This may be termed as a short-term demand function. In the longrun, however, neither the individual nor the market demand for a product is determinedby any one of its determinants because other determinants do not remain constant. Thelong-run demand for a product depends on the composite impact of all its determinantsoperating simultaneously. Therefore, for the purpose of estimating long-term demand fora product, all its relevant determinants are taken into account. They are then expressedin a functional form. The function describes the relationship between the demand(a dependent variable) and its determinants (the independent variables). A demand functionof this kind is called a multi-variate or dynamic demand function. For instance, considerthis statement: the demand (Dx) for a commodity X, depends on its price (Px), consumer’sincome M, price of its substitute Y, (Py), price of complementary goods (Pc) and

Check Your Progress9. What is meant by demand

function? What is a short-rundemand function?

10. What is the difference betweena linear and non-linear demandfunction?

11. Suppose a demand function isgiven as D = 50 – 2P. Finddemand at P =10.

12. What is a multi-variate demandfunction? What is its signifi-cance in business decision-making?

NOTES



consumer’s taste (T) and advertisement expenditure (A). This statement can be expressedin a functional form as,

Dx = f (Px, M, Py, Pc, T, A) ...(3.7)The function (3.7) describes the demand for commodity X which depends on suchdeterminants as Px, M, Py, Pc, T and A. If the relationship between Dx, and thequantifiable independent variables, Px, M, Py, Pc and A is of linear form, the estimableform of the demand function is expressed as

Dx = a + bPx + cM + dPy + gPc + jA ...(3.8)where ‘a’ is a constant term and constants b, c, d, e, g and j are the coefficients ofrelation between Dx and the respective independent variable.In a market demand function for a product, other independent variables, viz., size ofpopulation (N) and a measure of income distribution, i.e., Gini-coefficient, (G) may alsobe included.

3.4 ELASTICITIES OF DEMAND

3.4.1 Importance of the Elasticity ConceptWe have earlier discussed the nature of relationship between demand and itsdeterminants. From managerial point of view, however, the knowledge of nature ofrelationship alone is not sufficient. What is more important is the extent of relationshipor the degree of responsiveness of demand to the changes in its determinants. Thedegree of responsiveness of demand to the change in its determinants is called elasticityof demand.The concept of elasticity of demand plays a crucial role in business-decisions regardingmanoeuvering of prices with a view to making larger profits. For instance, when costof production is increasing, the firm would want to pass the rising cost on to theconsumer by raising the price. Firms may decide to change the price even without anychange in the cost of production. But whether raising price following the rise in costor otherwise proves beneficial depends on:

(a) the price-elasticity of demand for the product, i.e., how high or low is theproportionate change in its demand in response to a certain percentage changein its price; and

(b) price-elasticity of demand for its substitute, because when the price of aproduct increases the demand for its substitutes increases automatically even iftheir prices remain unchanged.

Raising the price will be beneficial only if (i) demand for a product is less elastic; and(ii) demand for its substitute is much less elastic. Although most businessmen areintuitively aware of the elasticity of demand of the goods they make,6 the use of preciseestimates of elasticity of demand will add precision to their business decisions.In this section, we will discuss various methods of measuring elasticities of demand.The concepts of demand elasticities used in business decisions are: (i) Price elasticity,(ii) Cross-elasticity; (iii) Income elasticity; and (iv) Advertisement elasticity, and(v) Elasticity of price expectation.

3.4.2 Price Elasticity of DemandPrice elasticity of demand is generally defined as the responsiveness or sensitiveness ofdemand for a commodity to the changes in its price. More precisely, elasticity of demandis the percentage change in demand as a result of one per cent change in the price ofthe commodity. A formal definition of price elasticity of demand (ep) is given as

NOTES


Analysis of Market Demand andDemand Elasticities ep = Percentage change in quantity demanded

Percentage change in price

A general formula7 for calculating coefficient of price elasticity, derived from thisdefinition of elasticity, is given as follows:

ep = Q P Q PQ P Q PΔ Δ Δ

÷ = ×Δ

= Q PP Q

Δ×

Δ…(3.9)

where Q = original quantity demanded, P = original price, ΔQ = change in quantitydemanded and ΔP = change in price.It is important to note here that a minus sign (–) is generally inserted in the formulabefore the fraction with view to making the elasticity coefficient a non-negative value.8

The elasticity can be measured between two points on a demand curve (called arcelasticity) or on a point (called point elasticity).Arc Elasticity. The measure of elasticity of demand between any two finite points ona demand curve is known as arc elasticity. For example, measure of elasticity betweenpoints j and k (Fig. 3.7) is the measure of arc elasticity. The movement from point jto k on the demand curve (Dx) shows a fall in the price from Rs. 20 to Rs. 10 so thatΔP = 20 – 10 = 10. The fall in price causes an increase demand from 43 units to 75units so that ΔQ = 43 – 75 = – 32. The elasticity between points j and k (moving fromj to k) can be calculated by substituting these values into the elasticity formula asfollows:

ep = – Q PP Q

Δ⋅

Δ (with minus sign)

= 32 20 1.49

10 43−

− ⋅ = ...(3.10)

This means that a one percent decrease in price of commodity X results in a 1.49 percent increase in demand for it.

Fig. 3.7: Linear Demand Curve

Problem in using arc elasticity. The arc elasticity should be measured, interpreted andused carefully, otherwise it may lead to wrong decisions. Arc elasticity coefficients differbetween the same two finite points on a demand curve if direction of change in price

NOTES



is revsersed. For instance, as estimated in Eq. (3.10), the elasticity between points J andK — moving from J to K equals 1.49. It may be wrongly interpreted that the elasticityof demand for commodity X between points J and K equals 1.49 irrespective of directionof price change. But it is not true. A reverse movement in the price, i.e., the movementfrom point K to J implies a different elasticity co-efficient (0.43). Movement from pointK to J gives P = 10, ΔP = 10 – 20 = –10, Q = 75 andΔQ = 75 – 43 = 32. By substituting these values into the elasticity formula, we get

ep = – 32 10.10 75−

= 0.43 ...(3.11)

The measure of elasticity coefficient in Eq. (3.11) for the reverse movement in price isobviously different from one given by Eq. (3.10). It means that the elasticity dependsalso on the direction of change in price. Therefore, while measuring price elasticity, thedirection of price change should be carefully noted.Some Modifications. Some modifications have been suggested in economic literature toresolve the problems associated with arc elasticity.First, the problem arising due to the change in the direction of price change may beavoided by using the lower values of P and Q in the elasticity formula, so that

ep = – . l

l

PQP Q

ΔΔ

where Pl = 10 (the lower of the two prices) and Ql = 43 (the lower of the twoquantities). Thus,

ep = – 32 10.10 43 = 0.74 ...(3.12)

This method is however devoid of the logic of calculating percentage change becausethe choice of lower values of P and Q is arbitrary—it is not, in accordance with therule of calculating percentage change.Second, another method suggested to resolve this problem is to use the average of upperand lower values of P and Q in fraction P/Q. In that case the formula is

ep = – 1 2

1 2

( ) / 2( ) / 2

P PQP Q Q

+Δ⋅

Δ +

or ep = – 1 2 1 2

1 2 1 2

( ) 2.( ) 2

Q Q P PP P Q Q− +− +

…(3.13)

where subscripts 1 and 2 denote lower and upper values of prices and quantities.Substituting the values from our example, we get,

ep = – 43 75 (20 10) 2.20 10 (43 75) 2

− +− +

= 0.81.This method has its own drawbacks as the elasticity coefficient calculated through thisformula, refers to the elasticity mid-way between P1 P2 and Q1 Q2. The elasticity co-efficient (0.81) is not applicable for the whole range of price-quantity combinations atdifferent points between J and K on the demand curve (Fig. 3.7)—it only gives a meanof the elasticities between the two points.

Point Elasticity

Point elasticity on a linear demand curve. Point elasticity is also a way to resolve theproblem in measuring the elasticity. The concept of point elasticity is used for measuringprice elasticity where change in price is infinitesimally small.

NOTES



Fig. 3.8: Point Elasticity

Point elasticity is the elasticity of demand at a finite point on a demand curve, e.g., atpoint P or B on the linear demand curve MN (Fig. 3.8). This is in contrast to the arcelasticity between points P and B. A movement form point B towards P implies changein price (DP) becoming smaller and smaller, such that point P is almost reached. Herethe change in price is infinitesimally small. Measuring elasticity for an infinitesimallysmall change in price is the same as measuring elasticity at a point. The formula formeasuring point elasticity is given below.

Point elasticity (ep) =P QQ P

∂⋅∂ ...(3.14)

Note that QP

∂∂

has been substituted for QP

ΔΔ

in the formula for arc elasticity. The

derivative QP

∂∂ is reciprocal of the slope of the demand curve MN. Point elasticity is

thus the product of price-quantity ratio at a particular point on the demand curve andthe reciprocal of the slope of the demand line. The reciprocal of the slope of the straight

line MN at point P is geometrically given by QNPQ

. Therefore,

QP

∂∂

= QNPQ

Note that at point P, price P = PQ and Q = OQ. By substituting these values in Eq.(3.14), we get

ep = PQ QN QNOQ PQ OQ

⋅ =

Given the numerical values for QN and OQ, elasticity at point P can be easily obtained.We may compare here the arc elasticity between points J and K and point elasticity atpoint J in Fig. 3.3. At point J,

ep = QNOQ =

108 4343−

= 1.51

Note that ep = 1.51 is different from various measures of arc elasticities (i.e., 1.49, 0.43,0.7, 0.81).As we will see below, geometrically, QN/OQ = PN/PM. Therefore, elasticity of demandat point P (Fig. 3.8) may be expressed as

ep = PNPM

NOTES



Proof. The fact that ep = PN/PM can be proved as follows. Note that in Fig. 3.8, thereare three triangles—DMON, DMRP and DPQN—and –MON, –MRP and –PQN areright angles. Therefore, the other corresponding angles of the three triangles will alwaysbe equal and hence, DMON, DMRP and DPQN are similar.According to geometrical properties of similar triangles, the ratio of any two sides ofa triangles arc always equal to the ratio of the corresponding sides of the other triangles.By this rule, between DPQN and DMRP,

QNPN =

RPPM

Since RP = OQ, by substituting OQ for RP in the above equation, we getQNPN =

OQPM

It follows thatQNOQ =

PNPM

It may thus be concluded that price elasticity of demand at point P (Fig. 3.8) is givenby

ep = PNPM

It may thus be concluded that the price elasticity of demand at any point on a lineardemand curve is equal to the ratio of lower segment to the upper segments of the line,i.e.,

ep = Lower segmentUpper segment

Point elasticity on a non-linear demand curve. The ratio DD /DP in respect of a non-linear demand curve is different at each point. Therefore, the method used to measurepoint elasticity on a linear demand curve cannot be applied straightaway. A simplemodification in technique is required. In order to measure point elasticity on a non-lineardemand curve, the chosen point is first brought on a linear demand curve. This is doneby drawing a tangent through the chosen point. For example, suppose we want to

Fig. 3.9: Price and Demand

measure elasticity on a non-linear demand curve, DD (Fig. 3.9) at point P. For thispurpose, a tangent MN is drawn through point P. Since demand curve DD and the line

NOTES



MN pass through the same point (P), the slope of the demand curve and that of the lineat this point is the same. Therefore, the elasticity of demand curve at point P willbe equal to that of the line at this point. Elasticity of the line at point P can bemeasured as

ep = P PQ P

∂⋅∂

= PQ QN QNOQ PQ OQ

⋅ =

As proved above, geometrically, QNOQ =

PNPM .

Fig. 3.10: Point Elasticities of Demand

To conclude, at midpoint of a linear demand curve, ep = 1, as shown at point P in Fig.3.10. It follows that at any point above the point P, ep > 1, and at any point below thepoint P, ep < 1. According to this formula, at the extreme point N, ep = 0, and at extremepoint M, ep is undefined because division by zero is undefined. It must be noted herethat these results are relevant between points M and N and that the elasticities at theextreme points M and N are, in effect, undefined.

3.4.3 Measuring Price Elasticity from a Demand FunctionThe price elasticity of demand for a product can be measured directly from the demandfunction. In this section, we will describe the method of measuring price elasticity ofdemand for a product from the demand function—both linear and nonlinear. It may benoted here that if a demand function is given, arc elasticity can be measured simply byassuming two prices and working out ΔP and ΔQ. We will, therefore, confine ourselveshere to point elasticity of demand with respect to price.Price Elasticity from a Linear Demand Function. Suppose that a linear demandfunction is given as

Q = 100 – 5PGiven the demand function, point elasticity can be measured for any price. For example,suppose we want to measure elasticity at P = 10. We know that

ep = Q PP Q

δδ

⋅

The term dQ/dP in the elasticity formula is the slope of the demand curve. The slopeof the demand curve can be found by differentiating the demand function. That is,

Check Your Progress13. What is meant by elasticity of

demand?14. What is meant by price elas-

ticity of demand? How is itmeasured?

15. Suppose price elasticity co-efficient is 1.5. What does itmean?

16. Distinguish between pointelasticity and arc elasticity ofdemand.

NOTES



QP

δδ =

(100 5 ) 5PP

δδ−

= −

Having obtained the slope of the demand curve as dQ /dP = – 5, ep at P = 10 canbe calculated as follows. Since, P = 10, Q = 100 – 5(10) = 50. By substituting thesevalues into the elasticity formula, we get,

ep = (– 5) 1050 = –1

Similarly at P = 8, Q = 100 – 5(8) = 60 andep = – 5 (8/60) = – 40/60 = – 0.67

and at P = 15, Q = 100 – 5(15) = 25, andep = – 5(15/25) = – 75/25 = – 3

Price Elasticity from a Nonlinear Demand Function. Suppose a nonlinear demandfunction of multiplicative form is given as follows

Q = aP–b … (3.15)and we want to compute the price elasticity of demand. The formula for computing theprice elasticity is the same, i.e.,

ep = Q PP Q

δδ

⋅

What we need to compute the price-elasticity coefficient is to find first the value of thefirst term, dQ/dP, i.e., the slope of the demand curve. The slope can be obtained bydifferentiating the demand function, Thus,

QP

δδ = – baP–b-1 …(3.16)

By substitution, ep can be expressed as

ep = – baP–b–1PQ

= bbaP

Q

−−…(3.17)

Since Q = aP – b, by substitution, we get

ep = b

bbaPaP

−

−−

= –b … (3.18)

Equation (3.18) shows that when a demand function is of a multiplicative or powerform, price elasticity coefficient equals the power of the variable P. This means thatprice elasticity in the case of a multiplicative demand function remains constantregardless of a change in price.

3.4.4 Price Elasticity and Total RevenueA firms aiming at enhancing its total revenue would like to know whether increasing ordecreasing the price would achieve its goal. The price-elasticity coefficient of demandfor its product at different levels of its price provides the answer to this question. Thesimple answer is that if ep > 1, then decreasing the price will increase the total revenueand if eq < 1, then increasing the price will increase the total revenue. To prove thispoint, we need to know the total revenue (TR) and marginal revenue (MR) functions andmeasures of price-elasticity are required. Since TR = Q.P, we need to know P and Q.This information can be obtained through the demand function. Let us recall our demandfunction (3.2) given as

Q = 100 – 5P

NOTES



Price function (P) can be derived from the demand function asP = 20 – 0.2P …(3.19)

Given the price function, TR can be obtained asTR = P . Q = (20 – 0.2Q)Q

= 20Q – 0.2Q2

From this TR-function, the MR-function can be derived as

MR = TRQ

∂∂

= 20 – 0.4Q

The TR-function is graphed in panel (a) and the demand and MR functions are presentedin panel (b) of Fig. 3.11. As the figure shows, at point P on the demand curve, e = 1where output, Q = 50. Below point P, e < 1 and above point P, e > 1. It can be seenin panel (a) of Fig. 3.11 that TR increases so long as e > 1; TR reaches its maximumlevel where e = 1; and it decreases when e < 1.

Fig. 3.11: Price Elasticity and Total Revenue

The relationship between price-elasticity and TR is summed up in Table 3.3. As the tableshows, when demand is perfectly inelastic (i.e., ep = 0 as in the case of a vertical demandline) there is no decrease in quantity demanded when price is raised and vice versa.Therefore, a rise in price increases the total revenue and vice versa.In case of an inelastic demand (i.e., ep < 1), quantity demanded increases by less thanthe proportionate decrease in price and hence the total revenue falls when price falls. Thetotal revenue increases when price increases because quantity demanded decreases byless than the proportionate increase in price.

NOTES



If demand for a product is unit elastic (ep = 1) quantity demanded increases (ordecreases) in the proportion of decrease (or increase) in the price. Therefore, totalrevenue remains unaffected.If demand for a commodity has ep > 1, change in quantity demanded is greater than theproportionate change in price. Therefore, the total revenue increases when price falls andvice versa.The case of infinitely elastic demand represented by a horizontal straight line is rare.Such a demand line implies that a consumer has the opportunity to buy any quantity ofa commodity and the seller can sell any quantity of a commodity, at a given price. Itis the case of a commodity being bought and sold in a perfectly competitive market. Aseller, therefore, cannot charge a higher or a lower price.

Table 3.3: Elasticity, Price-change and Change in TR

Elasticity Change in Change inCo-efficient Price TR

e = 0 Increase IncreaseDecrease Decrease

e < 1 Increase IncreaseDecrease Decrease

e = 1 Increase No changeDecrease No change

e > 1 Increase DecreaseDecrease Increase

e = ∞ Increase Decrease to zeroDecrease Infinite increase*

* Subject to the size of the market.

3.4.5 Price Elasticity and Marginal RevenueThe relationship between price-elasticity and the total revenue (TR) can be known moreprecisely by finding the relationship between price-elasticity and marginal revenue (MR).MR is the first derivative of TR-function and TR = P.Q (where P = price, and Q =quantity sold). The relationship between price-elasticity, MR and TR is shown below.Since TR = P.Q,

MR = ( )P Q PP Q

Q Q∂ ⋅ ∂

= +∂ ∂

= 1 Q PPP Q

⎛ ⎞∂+ ⋅⎜ ⎟⎝ ∂ ⎠

…(3.20)

Note that Q PP Q

∂⋅∂

in Eq. (3.20) is the reciprocal of elasticity. That is,

Q PP Q

∂⋅∂ = –

1

pe

By substituting – 1e

for Q PP Q

∂⋅∂

in Eq. (3.20), we get

MR = 11p

Pe

⎛ ⎞−⎜ ⎟

⎝ ⎠…(3.21)

NOTES



Given this relationship between MR and price-elasticity of demand, the decision-markerscan easily know whether it is beneficial to change the price. If e = 1, MR = 0.Therefore, change in price will not cause any change in TR. If e < 1, MR < 0, TRdecreases when price decreases and TR increases when price increases. And, if e > 1,MR > 0, TR increases if price decreases and vice versa.Price Elasticity, AR and MR. Given the Eq. (3.21), price elasticity (ep) can beexpressed in terms of AR and MR. We know that P = AR. So Eq. (3.21) can be writtenas

MR = 11p

ARe

⎛ ⎞−⎜ ⎟

⎝ ⎠

MR = AR – p

ARe

By rearranging the terms, we get

MR – AR = – p

ARe

orMR AR

AR−

= – 1

pe

The reciprocal of this equation gives the measure of elasticity (e), i.e.,

ARMR AR− = – ep

or ep = AR

AR MR−

3.4.6 Determinants of Price Elasticity of DemandWe have noted above that price-elasticity of a product may vary between zero andinfinity. The price-elasticity of a product within this range depends on the followingfactors:

1. Availability of Substitutes. One of the most important determinants ofelasticity of demand for a commodity is the availability of its close substitutes.The higher the degree of closeness of the substitutes, the greater the elasticityof demand for the commodity. For instance, coffee and tea may be consideredas close substitutes for one another. If price of one of these goods increases,the other commodity becomes relatively cheaper. Therefore, consumers buymore of the relatively cheaper good and less of the costlier one, all other thingsremaining the same. The elasticity of demand for both these goods will behigher. Besides, the wider the range of the substitutes, the greater the elasticity.For instance, soaps, toothpastes, cigarettes, etc., are available in differentbrands, each brand being a close substitute for the other. Therefore, the price-elasticity of demand for each brand is much greater than that for the genericcommodity. On the other hand, sugar and salt do not have close substitutesand hence their price-elasticity is lower.

2. Nature of Commodity. The nature of a commodity also affects the price-elasticity of its demand. Commodities can be grouped as luxuries, comfortsand necessities. Demand for luxury goods (e.g., high-price refrigerators, TVsets, cars, decoration items, etc.) is more elastic than the demand for neces-sities and comforts because consumption of luxury goods can be dispensedwith or postponed when their prices rise. On the other hand, consumption ofnecessary goods, (e.g., sugar, clothes, vegetables) cannot be postponed and

Check Your Progress17. Suppose demand function is

given as Q = 100 – 5P. Findthe elasticity of demandbetween price 12 and 10.

18. What is the relationshipbetween price elasticity andtotal revenue?

19. What is the relationshipbetween price elasticity andmarginal revenue?

20. What are the determinants ofprice elasticity of demand?

NOTES



hence their demand is inelastic. Comforts have more elastic demand thannecessities and less elastic than luxuries. Commodities are also categorized asdurable goods and perishable or non-durable goods. Demand for durable goodsis more elastic than that for non-durable goods, because when the price of theformer increases, people either get the old one repaired instead of replacing itor buy a ‘second hand’.

3. Weightage in the total consumption. Another factor that influences theelasticity of demand is the proportion of income which consumers spend on aparticular commodity. If proportion of income spent on a commodity is large, itsdemand will be more elastic and vice versa. Classic examples of suchcommodities are salt, matches, books, pens, toothpastes, etc. These goodsclaim a very small proportion of income. Demand for these goods is generallyinelastic because increase in the price of such goods does not substantiallyaffect the consumer’s budget. Therefore, people continue to purchase almostthe same quantity even when their prices increase.

4. Time factor in adjustment of consumption pattern. Price-elasticity ofdemand depends also on the time consumers need to adjust their consumptionpattern to a new price: the longer the time allowed, the greater the elasticity.The reason is that over a period of time, consumers are able to adjust theirexpenditure pattern to price changes. For instance, if the price of TV sets isdecreased, demand will not increase immediately unless people possess excesspurchasing power. But over time, people may be able to adjust theirexpenditure pattern so that they can buy a TV set at a lower (new) price.Consider another example. If price of petrol is reduced, the demand for petrolis unlikely to increase significantly. Over time, however, people may beencouraged by low petrol prices to buy automobiles resulting in a significantrise in demand for petrol.

5. Range of commodity use. The range of uses of a commodity also influencesthe price-desticity its demand. The wider the range of the uses of a product,the higher the elasticity of demand for the decrease in price. As the price ofa multi-use commodity decreases, people extend their consumption to its otheruses. Therefore, the demand for such a commodity generally increases morethan the proportionate increase in its price. For instance, milk can be taken asit is and in the form of curd, cheese, ghee and butter-milk. The demand formilk will therefore be highly elastic for decrease in price. Similarly, electricitycan be used for lighting, cooking, heating and for industrial purposes. There-fore, demand for electricity has a greater elasticity.However, for the increase in price, the commodity has a lower elasticitybecause the consumption of a normal good cannot be cut down substantiallybeyond a point when the price of the commodity increases.

6. Proportion of market supplied. The elasticity of market demand alsodepends on the proportion of the market supplied at the ruling price. If lessthan half of the market is supplied at the ruling price, price-elasticity ofdemand will be higher than 1 and if more than half of the market is suppliede < 1. That is, the demand curve is more elastic over the upper half than overthe lower half.

3.4.7 Cross-Elasticity of DemandThe cross-elasticity is the measure of responsiveness of demand for a commodity to thechanges in the price of its substitutes and complementary goods. For instance,cross-elasticity of demand for tea is the percentage change in its quantity demandedwith respect to the change in the price of its substitute, coffee. The formula for

NOTES



measuring cross-elasticity of demand for tea (et,c) and the same for coffee (ec,t) is givenbelow.

et,c = Percentage change in demand for tea ( )Percentage change in price of coffee ( )

t

c

QP

= .c t

t c

P QQ P

ΔΔ

…(3.22)

and ec,t = .t c

c t

P QQ P

ΔΔ

…(3.23)

The same formula is used to measure the cross-elasticity of demand for a good withrespect to a change in the price of its complementary goods. Electricity to electricalgadgets, petrol to automobile, butter to bread, sugar and milk to tea and coffee, are theexamples of complementary goods.It is important to note that when two goods are substitutes for one another, their demandhas positive cross-elasticity because increase in the price of one increases the demandfor the other. And, the demand for complementary goods has negative cross-elasticity,because increase in the price of a good decreases the demand for its complementarygoods.Uses of Cross-Elasticity. An important use of cross-elasticity is that it is used to definesubstitute goods. If cross-elasticity between two goods is positive, the two goods maybe considered as substitutes of one another. Also, the greater the cross-elasticity, thecloser the substitute. Similarly, if cross-elasticity of demand for two related goods isnegative, the two may be considered as complementary of one another: the higher thenegative cross-elasticity, the higher the degree of complementarity.The concept of cross-elasticity is of vital importance in changing price of productshaving substitutes and complementary goods. If cross-elasticity in response to the priceof substitutes is greater than one, it would be inadvisable to increase the price; rather,reducing the price may prove beneficial. In case of complementary goods also, reducingthe price may be helpful in maintaining the demand in case the price of thecomplementary good is rising. Besides, if accurate measures of cross-elasticities areavailable, the firm can forecast the demand for its product and can adopt necessarysafeguards against fluctuating price of substitutes and complements.

3.4.8 Income-Elasticity of DemandApart from the price of a product and its substitutes, consumer’s income is anotherbasic determinant of demand for a product. As noted earlier, the relationship betweenquantity demanded and income is of positive nature, unlike the negative price-demandrelationship. The demand for goods and services increases with increase in consumer’sincome and vice-versa. The responsiveness of demand to the changes in income is knownas income-elasticity of demand.Income-elasticity of demand for a product, say X, (i.e., ey) may be defined as:

ey =

q

q q

q

XX XY

Y X YY

Δ

Δ= ⋅

Δ Δ …(3.24)

(where Xq = quantity of X demanded; Y = disposable income; ΔXq = change in quantityof X demanded; and ΔY = change in income)Obviously, the formula for measuring income-elasticity of demand is the same as thatfor measuring the price-elasticity. The only change in the formula is that the variable

NOTES



‘income’ (Y) is substituted for the variable ‘price’ (P). Here, income refers to thedisposable income, i.e., income net of taxes. All other formulae for measuring price-elasticities may by adopted to measure the income-elasticities, keeping in mind thedifference between them and the purpose of measuring income-elasticity.Unlike price-elasticity of demand, which is always negative9, income-elasticity ofdemand is always positive10 because of a positive relationship between income andquantity demanded of a product. But there is an exception to this rule. Income-elasticityof demand for an inferior good is negative, because of the inverse substitution effect.The demand for inferior goods decreases with increase in consumer’s income and vise-versa. The reason is that when income increases, consumers switch over to theconsumption of superior substitutes, i.e., they substitute superior goods for inferiorones. For instance, when income rises, people prefer to buy more of rice and wheat andless of inferior foodgrains; buy more of meat and less of potato, and travel more byplane and less by train.Nature of commodity and income-elasticity. For all normal goods, income-elasticityis positive though the degree of elasticity varies in accordance with the nature ofcommodities. Consumer goods of the three categories, viz., necessities, comforts andluxuries have different elasticities. The general pattern of income-elasticities of differentgoods for increase in income and their effect on sales are given in Table 3.4.

Table 3.4: Income-Elasticities

Consumer goods Co-efficient of Effect on Saleincome-elasticity

1. Essential goods Less than one (ey < 1) Less than proportionatechange in sale

2. Comforts Almost equal to unity Almost proportionate(ey ≅ 1) change in sale

3. Luxuries Greater than unity More than proportionate(ey > 1) increase in sale

The income-elasticity of demand for different categories of goods may, however, varyfrom household to household and from time to time, depending on the choice andpreference of the consumers, levels of consumption and income, and their susceptibilityto ‘demonstration effect’. The other factor which may cause deviation from the generalpattern of income-elasticities is the frequency of increase in income. If frequency of risein income is high, income-elasticities will conform to the general pattern.Uses of Income-elasticity in Business Decisions. While price and cross elasticities areof greater significance in the pricing of a product aimed at maximizing the total revenuein the short period, income-elasticity of a product is of a greater significancein production planning and management in the long run, particularly during theperiod of a business cycle. The concept of income-elasticity can be used in estimatingfuture demand provided that the rate of increase in income and income-elasticity ofdemand for the products are known. The knowledge of income elasticity can thus beuseful in forecasting demand, when a change in personal incomes is expected, otherthings remaining the same. It also helps in avoiding over-production or under-production.In forecasting demand, however, only the relevant concept of income and data shouldbe used. It is generally believed that the demand for goods and services increases withincrease in GNP depending on the marginal propensity to consume. This may be truein the context of aggregate national demand, but not necessarily for a particular product.It is quite likely that increase in GNP flows to a section of consumers who do not, orare not in a position to, consume the product in which a businessman is interested. Forinstance, if the major proportion of incremental GNP goes to those who can afford a

NOTES



car, the growth rate in GNP should not be used to calculate income-elasticity of demandfor bicycles. Therefore, the income of only a relevant class or income-group should beused. Similarly, where the product is of a regional nature, or if there is a regional divisionof market between the producers, the income of only the relevant region should be usedin forecasting the demand.The concept of income-elasticity may also be used to define the ‘normal’ and ‘inferior’goods. The goods whose income-elasticity is positive for all levels of income are termed‘normal goods’. On the other hand, goods whose income-elasticities are negative beyonda certain level of income are termed ‘inferior goods’.

3.4.9 Advertisement or Promotional Elasticity of SalesThe expenditure on advertisement and on other sales-promotion activities does help inpromoting sales, but not in the same degree at all levels of the total sales. The conceptof advertisement elasticity is useful in determining the optimum level of advertisementexpenditure. The concept of advertisement-elasticity assumes a greater significance indeciding on advertisement expenditure, particularly when the government imposesrestriction on advertisement cost or there is competitive advertising by the rival firms.Advertisement-elasticity (eA) of sales may be defined as

eA = S/S S AA/A A S

Δ Δ= ⋅

Δ Δ

where S = sales; ΔS = increase in sales; A = initial advertisement cost, and ΔA =additional expenditure on advertisement.

Interpretation of advertisement-elasticity. The advertisement elasticity of salesvaries between eA = 0 and eA = •. Interpretation of some measures of advertisingelasticity is given below.

Elasticities InterpretationeA = 0 Sales do not respond to the advertisement expenditure.

eA > 0 but < 1 Increase in total sales is less than proportionate to the increase inadvertisement expenditure.

eA = 1 Sales increase in proportion to the increase in expenditure onadvertisement.

eA > Sales increase at a higher rate than the rate of increase of adver-tisement expenditure.

Determinants of advertisement-elasticity. Some of the important factors whichdetermine advertisement elasticity are the following:

(i) The level of total sales. In the initial stages of sale of a product, particularlyof one which is newly introduced in the market, the advertisement-elasticity isgreater than unity. As sales increase, the elasticity decreases. For instance, afterthe potential market is supplied, the function of advertisement is to createadditional demand by attracting more consumers to the product, particularlythose who are slow in adjusting their consumption expenditure to provide fornew commodities. Therefore, demand increases at a rate lower than the rateof increase in advertisement expenditure.

(ii) Advertisement by rival firms. In a highly competitive market, theeffectiveness of advertisement by a firm is also determined by the relativeeffectiveness of advertisement by the rival firms.

(iii) Cumulative effect of past advertisement. In case expenditure incurred onadvertisement in the initial stages is not adequate enough to be effective,elasticity may be very low. But over time, additional doses of advertisement

Check Your Progress21. What is meant by cross

elasticity of demand? Write theformula for measuring crosselasticity.

22. What are the uses of crosselasticity in business decision-making?

23. What factors affect theadvertisement-elasticity ofdemand?

24. How is price expectationrelated to demand elasticity?

NOTES



expenditure may have a cumulative effect on the promotion of sales andadvertising elasticity may increase considerably.

(iv) Other factors. Advertisement elasticity is also affected by other factors affectingthe demand for a product, e.g., change in products’ price, consumer’s income,growth of substitutes and their prices.

3.4.10 Elasticity of Price-ExpectationsSometimes, mainly during the period of price fluctuations, consumer’s priceexpectations play a much more important role in determining demand for a commoditythan any other factor. The concept of price-expectation-elasticity was devised andpopularised by J.R. Hicks in 1939. The price-expectation-elasticity refers to the expectedchange in future price as a result of change in current prices of a product. The elasticityof price-expectation is defined and measured by the formula given below.

ex = //

f f f c

c c c f

P P P PP P P P

Δ Δ= ⋅

Δ Δ…(3.25)

where Pc and Pf are current and future prices, respectively.The coefficient ex gives the measure of expected percentage change in future price asa result of 1 per cent change in present price. If ex > 1, it indicates that future changein price will be greater than the present change in price, and vice versa. If ex = 1, itindicates that the future change in price will be equal to the change in the current price.The concept of elasticity of price-expectation is very useful in formulating future pricingpolicy. For example, if ex > 1, it indicates that sellers will be able to sell more in thefuture at higher prices. Thus, businessmen may accordingly determine their futurepricing policy.

3.4.11 Some Estimates of Demand ElasticitiesIn this section, we present a summary of some estimates of demand elasticities, madein the United States and Britain.

Table 3.5: Price Elasticities of Demand for Selected Products in the US

Commodity Price elasticity of Incomedemand elasticities

Tomatoes 4.60 —Restaurant meals 1.63 1.40Glassware 1.34 —Taxi Service 1.24 —Radio & TV Service 1.19 —Furniture 1.01 1.48Housing 1.00 —Alcohol 0.92 1.54Movies 0.87 —Foreign Air Travel 0.77 —Shoes 0.70 1.40Auto Repair 0.36 —Medical Insurance 0.31 0.92Gasoline and oil 0.14 0.48Owner Occupied Housing — 1.49

Source: H. Houthakker and L.D. Taylor, Consumer Demand in the United States: Analysis andProjections, Mass., Harvard University Press, 2nd Edn. quoted from Mansfield, E., op. cit.

NOTES



Table 3.6: Price Elasticities of Demand for Car Models

1. Chevrolet ImpalaRelative price elasticity – 14.79Cross-elasticity w.r.t.

Pontiac Catalina 19.302. Pontiac Catalina

Relative price elasticity – 16.99Cross elasticity w.r.t.

Chavrolet Impala 5.093. Plymouth Fury

Relative price elasticity – 4.59Cross elasticity w.r.t.

Chevrolet Impala 4.22Pontiac Catalina 0.49Ford Calaxy 6.82

Source : F.O. Irvine, Jr., “Demand Equations for Individual New Car Models Estimated Using TransitionPrices with Implications for Regulatory Issues.” South Eco. Jl., (4.9), January 1983.

Table 3.7: Demand Elasticities of Electricity

Variable Residential Commercial Industrialuse use use

Electricity price – 0.794 – 0.916 – 1.404Per capita income 0.714 1.249 – 0.450Price of natural gas 0.159 – 0.193 – 0.293

Source : R. Halvorsen “Demand for Electricity Energy in the United States,” South Eco. Jl., (43), April1976.

Table 3.8: Price and Income Elasticities of Some Selected Consumer Goods in Britain

Consumer Goods Price IncomeElasticity Elasticity

Food 0.00 0.21Clothing 0.92 2.00Housing 0.31 0.03Fuel 0.28 1.67Drinks and Tobacco 0.60 1.22Transport and Communication 1.21 1.23

Source : Deaton and Muellbauer, 1980

3.5 SUMMARY

• This unit deals with market demand and demand elasticities.• Market demand is defined as sum of individual demand for a product at a given

price per unit of time.• Market demand is generally classified as (i) short-term demand and (ii) long-term

demand. Short-term demand is linked to only the price of the product whereaslong-term demand is assessed on the basis of all other determinants of demand.

• The long-term determinants of demand include (i) price of the product,(ii) consumer’s income, (iii) prices of the substitute and complementary goods,(iv) taste and preferences, (v) advertisement, (vi) price expectations, (vii) consumercredit facilities, (viii) demonstration effects, and (ix) population.

• The nature and extent of relationship between demand for a product and itsdeterminants are expressed through a demand function. For example, the relationship

NOTES



between price and demand is expressed as Q = A – bP. Here, the minus sign showsthe nature and ‘b’ gives the extent of relationship.

• Elasticity is an important concept used in business decision-making, especially inregard to changing the price, all other factors remaining constant.

• Elasticity of demand is the degree of responsiveness of demand to change in itsdeterminants. The formula for estimating price elasticity of demand is given as

Price Elasticity (ep) = 0

0.

PQP Q

ΔΔ

, where P0 is original price and Q0 is original quantity

demanded.

• Income Elasticity (ey) = 0

0.YQ

Y QΔΔ

, where Y = Consumer’s income

• Cross Elasticity ( )pse = 0

0. S

S

PQP QΔΔ

, where Ps = Price of substitute good

• Elasticity (ea) = 0

0.

AQA Q

ΔΔ

, where A = Advertise expenditure

• Price Expectation Elasticity (epx) = .f c

c f

P PP P

Δ

Δ, where subscripts c and f indicate

current and future prices respectively.

3.6 ANSWERS TO ‘CHECK YOUR PROGRESS’

1. Market demand is defined as the sum of individual demands for a product per unitof time given the price.

2. Autonomous demand is one that arises due to biological or physical need or desireto consume a product whereas derived demand arises due to consumption or useof some other goods, e.g., demand for petrol arises due to the use of automobiles.Demand for petrol is a derived demand.

3. Consumer durables are those which are used over time, e.g., clothes, house, car,etc. Non-durable goods are those which can be consumed only once, e.g., fooditems, travel tickets, and petrol, etc.

4. Short-term demands are those which exist in a short period, e.g., demand for NewYear Greeting cards, crackers for Deepawali, fashion goods, umbrellas etc. Long-term demands are those which last for a long period.

5. The determinants of demand for a product are (i) price of the product, (ii) price ofits substitutes and complements, (iii) consumer’s income, (iv) taste andpreferences, (v) advertisement, (vi) price expectations, (vii) number of consumers,(viii) demonstration effect, and (ix) availability of consumer credit.

6. The change in the price of a product changes demand of substitutes in the samedirection. For example, when price of coffee increases, demand for tea—a substituteof coffee—increases and vice-versa.

7. When consumer’s income increases, the demand for inferior goods decreases.For example, when income increases demand for jwar and bajra (inferior food-grains) decreases and for cheaper goods decreases.

8. When consumers imitate consumption of superior sections of the society, this iscalled demonstration effect.

9. A demand function demand for a product and its determinants. A short-run demandfunction links demand for a product to its price, assuming other determinants toremain constant. The short-run demand function is written asD = f (P).

10. A linear demand function shows a constant relationship between demand for aproduct and its changing price. It is expressed as D – a – bP. Here ‘b’ shows the

NOTES



constant relation between D and P. If relation between demand and price keepschanging, it produces a non-linear demand function.

11. Given demand function as D = 50 – 2P, quantity demanded at P = 10 equalsD = 50 – 2 × 10 = 30.

12. A multi-variate demand function includes all determinants of demand written as Dx= f (Px, Ps, I, T, A, C …….) where Px = Price of good X, Ps = price of substitute,I = income, T = taste, A = advertisement, and C = consumer credit. Its significancelies in that it gives the nature and extent of relation between demand and itsdeterminants.

13. Elasticity of demand is the responsiveness of demand to change in its determinants.For example, price elasticity of demand is the measure of the degree ofresponsiveness of demand to change in price.

14. Price elasticity of demand is measured by the following formula:

(ep) = 0

0.

PQP Q

ΔΔ

.

15. If price elasticity coefficient is 1.5, it means that if price change by one percent,demand changes by 1.5 percent.

16. Point elasticity is the measure of elasticity of demand curve whereas arc elasticityis the measure of elasticity between any two points on the demand curve.

17. Given the demand function Q = 100–5P, if P =10, then Q = 100–5(10) = 50 and atP =12, Q = 100–5(12) = 40.If price decreases from 12 to 10, then ΔP = 2 and ΔQ = 40–50 = –10. Thus,

(ep) = – 0

0.

PQP Q

ΔΔ =

10 10.2 40 = 1.25.

18. If e =1, total revenue does not change total revenue with change in price; if e < 1,increase in price increases total revenue and decrease in price decrease total revenue;and if e > 1, increasing price decrease total revenue and decreasing price increasestotal revenue.

19. The relationship between price elasticity and marginal revenue (MR) is given bythe following rules

11p

MR Pe

⎛ ⎞= −⎜ ⎟

⎝ ⎠.

20. Price elasticity of demand depends on (i) nature of commodity, (ii) availability ofsubstitute, (iii) percentage of expenditure to total income, (iv) number of com-modity use, and (v) time required for adjustment in consumption.

21. Cross elasticity of demand is the elasticity of demand in respect of price of thesubstitute good. Suppose X and Y are two substitute goods, then

(eps) = . y

y x

PQP QΔΔ

.

22. Cross elasticity of demand is used in assessing the change in demand for a productdue to change in the price of substitute.

23. Advertisement elasticity depends on (i) the total sales, (ii) advertisement by rivalfirms, (iii) cumulative effect of past advertisement.

24. When people expect prices to decrease price elasticity becomes lower. So is thecase with expectation of rising prices because people tend to buy more even ifprices are raised.

NOTES


Analysis of Market Demand andDemand Elasticities3.7 EXERCISES AND QUESTIONS

1. What are the determinants of market demand for a commodity? How do the changesin the following factors affect the demand for a commodity?(a) Price, (b) Income,(c) Price of the substitute, (d) Advertisement, and(e) Population.Also describe the nature of relationship between demand for a product and thesefactors. (Consider one factor at a time assuming other factors remain constant).

2. Distinguish between: (i) demand function and demand schedule, (ii) individualdemand and market demand, and (iii) demand for normal goods and inferior goods.

3. Define and distinguish between:(a) Arc elasticity and point elasticity,(b) Price elasticity and cross-elasticity, and(c) Income elasticity and price elasticity.

4. When prices of both substitutes and complements of a commodity, say X, rise, whathappens to the demand for X : (a) rises, (b) falls, (c) remains constant, or (d) allof the above possibilities exist?

5. List the major purposes of demand analysis from the standpoint of management. Canmanagement manipulate all the variables which affect demand?

6. (a) Distinguish between linear and non-linear demand functions.(b) What is the difference between the following demand functions?

(i) Qx = 1 – 5 Px; (ii) Qx = 100 – 2P2x

(iii) Qx = Ap–b and (iv) Qx = (a/p + c) – b7. What is meant by demand schedule, demand curve and demand function? Show

how market demand is calculated from individual demand curves.8. Which of the following commodities has the most inelastic demand and why?

(a) Soap, (b) Salt, (c) Penicillin, (d) Cigarettes and (e) Ice-cream.9. Explain the following concepts separately:

(i) Income elasticity of demand,(ii) Price elasticity of demand, and(iii) Elasticity of price expectations.What useful information do these concepts of elasticity provide to management?

10. Given the demand function: Qd = 12 – P

(a) find the demand and marginal revenue schedules,(b) plot the AR and MR schedules,(c) find marginal revenue when P = 10, 6 and 2, and(d) estimate the elasticity coefficient of the demand curve, when the total revenue

is at the maximum.11. Define elasticity of price expectation (Ee). In the context of an environment of

business recession, state briefly the implication of:(i) Ee > 1, (ii) Ee = 1, (iii) 0 < Ee > 1, (iv) Ee = 0 and (v) Ee < 0.

12. A publishing company plans to publish a book. It finds from the sales data of otherpublishers of similar books that the demand function for the book can be expressedas Q = 5000 – 5P. Find out:(a) Demand schedule and demand curve,(b) Number of books sold when P = Rs. 25,

NOTES



(c) Price for selling 2500 copies,(d) Price for zero sales,(e) Point-elasticity of demand at price Rs. 20, and(f) Arc elasticity for a fall in price from Rs. 25 to Rs. 20 and for a rise in price

from Rs. 20 to Rs. 25.13. Suppose the demand function for a product is given as Q = 500 – 5P. Find out:

(i) Quantity demanded at price Rs. 15,(ii) Price to sell 200 units,

(iii) Price for zero demand, and(iv) Quantity demanded at zero price.

14. Which of the following statements is true ?(i) If price elasticity = 1, MR = 0

(ii) If price elasticity > 1, MR > 0(iii) If price elasticity < 1, MR < 0 (Ans. All Three)

15. Suppose individual demand schedules for A, B and C are given as follows:Price A’s B’s C’s(Rs.) demand demand demand

5 80 40 2010 40 20 1015 20 10 520 10 5 025 0 0 0

Find (i) market demand schedule,(ii) market demand curve,

(iii) elasticity when price falls from Rs. 15 to Rs. 10, and(iv) elasticity when price rises from Rs. 10 to Rs. 15.

3.8 FURTHER READING

Baumol, William J. Economic Theory and Operations Analysis, Prentice-Hall of IndiaPvt. Ltd., New Delhi, 1985.Bilas, Richard, A., Microeconomic Theory, McGraw-Hill, New York, 1971.Brigham, Eugene F. and James L. Pappas, Managerial Economics, Dryden Press,Hinsdale, Illinois (latest edition).Douglas, Evans J., Managerial Economics: Theory and Practice and Problems,Prentice-Hall Inc., New Jersey.Ferguson, C.E., Microeconomics Theory, Richard D. Irwin, Home Wood, Ill.Leftwich, Richard H., The Price System and Resource Allocation, Dryden Press,Hinsdale, Ill.Mansfield, Edwin, Microeconomics: Theory and Application, W.W. Norton, New York.Nicholson, Walter, Intermediate Microeconomics and Its Application, Dryden Press,Hinsdale.Spencer, Milton H., Managerial Economics, Richard D. Irwin, Home-wood Ill.Watson, Donald S., Price Theory and Its Uses, Houghton Mifflin, Boston. Price Theoryin Action, Houghton Miffln, Boston.Webb, Samuel C., Managerial Economics, Houghton Mifflin, Boston.

NOTES



References1. Named after 19th century German Statistician, Christian Lorenz Ernst Engel.2. For details see, Harvey Leibenstein, “Bandwagon, Snob, and Veblen Effect in the

Theory of Consumer’s Demand”, Qly. Jl. Of Eco., 65 (May 1950).3. Sellers provide ‘buy now pay later’ facility.4. ΔD/ΔP is, in fact, reciprocal of the slope of a linear demand curve.5. For example, Phillip L. Paalberg and Robert Thompson have estimated the US

demand function for wheat as follow. Qw = 87.9041 – 0.0924 Pw where Qw =demand for wheat and Pw is wheat price (See their paper “ Interrelated Productsand the Effects of an Import Tariffs” in Agri. Eco. Res., 32, (October 1980).Quoted in J.R. Davis and Seemon Chang. Principles Managerial Economics,Prentice-Hall, 1968, p. 13.

6. Edwin Mansfield, op. cit., p. 52.7. The elasticity formula is derived as follows:

1 2

1 1 1

1 2 1

11

100

100p

Q Q QQ Q PQe P P P P Q

PP

− Δ×

Δ= = = ⋅

− Δ Δ×

where P1 is old price, P2 is new price Q1 is quantity demanded at P1 and Q2 isquantity demanded at P2.

8. Price-elasticity of demand calculated without a minus sign will always be a negativevalue because either DP or DQ will carry a negative sing due to inverse relationshipbetween price and quantity demanded. This gives a negative value of elasticitywhereas in the concept of elasticity, a negative value has no meaningfulinterpretation expect that it indicates inverse relationship between P and Q. Thenegative elasticity coefficient is rather misleading. The ‘minus’ sign is, therefore,inserted as a matter of ‘linguistic’ convenience, to make the coefficient of elasticitynon-negative. Sometimes, ‘it is also advised to ignore the negative sing in thenumerator and denominator of the elasticity formula. The elasticity in Eq. (4.9)ignores the negative sign.

9. Except in case of Giffen’s goods.10. With an exception of inferior goods.

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