economics of elasticity

8/17/2019 Economics of Elasticity

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ECONOMICS OF ELASTICITY

Lecturer Ranjita Islam


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INTRODUCTION:

Elasticity is of great importance to business, marketing, and economics. Studies in economics

begin by expressing the importance of the ceteris paribus (translation means all else is held

constant assumption and by focusing on relationships bet!een the possible prices of an itemand the "uantities consumers are !illing and able to purchase at each price# like!ise, the

"uantities suppliers are !illing and able to produce.

Elasticity is one of the most important concepts in neoclassical economic theory. It is useful

for understanding the distribution of !ealth and different types of goods as they relate to

the theory of consumer choice. Elasticity is also crucially important in any discussion

of !elfare distribution, in particular consumer surplus, producer surplus, or go$ernment

surplus.

%he concept of elasticity has an extraordinarily !ide range of applications in economics. In

particular, an understanding of elasticity is fundamental in understanding the response

of supply and demand in a market. Common uses of elasticity including Effect of changing

price on firm re$enue, analysis of incidence of the tax burden and other go$ernment policies,

income elasticity of demand, used as an indicator of industry health, future consumption

patterns and as a guide to firms& in$estment decisions, effect of international trade and terms

of trade effects , analysis of consumption and sa$ing beha$ior, analysis of ad$ertising on

consumer demand for particular goods, etc.

'n the consumer or demand side, students learn $ery early in their course!ork that an

in$erse relationship exists bet!een price and "uantity in accordance !ith the La! ofemand. Relati$ely speaking, smaller amounts are in demand at higher prices and $ice $ersa.

'n the producer or supply side, they learn that a positi$e relationship exists according to the

La! of Supply. )hether one chooses to focus on demand or on supply, elasticity is a concept

that helps us to understand in precise terms exactly ho! much "uantity changes in response

to a price change.

*any students completing and e$aluating introductory courses in economics for non+business

majors find the elasticity topic easy to comprehend. dditionally they report that the topic

makes perfect sense to them and is highly rele$ant to their e$eryday exchanges. Some

commonly used textbooks in economics (rnold, -/# 0uell, -1# *c2onnell 3 4rue,-5# 6arkin, - pro$ide basic topical co$erage, but unfortunately $ery fe! articles found

during a recent search of electronic publications present economic elasticity in a

straightfor!ard manner, !ithout references and narro! application to a specific context.

7urthermore, those contexts usually re"uire readers to ha$e an ad$anced understanding of

economics and other business disciplines.

7rom an economics education perspecti$e, this paper represents one effort to facilitate an

undergraduate student&s understanding of the elasticity concept.


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Central Research Questions

1.0: What is elasticity?

2.0: What is Price lasticity o! De"an#?

2.1: What are the Deter"inants an# in!luences o! it?

$.0: %o& is 'rice elasticity o! #e"an# co"'ute#?

(.0: De"an# cur)e an# elasticity

(.1: What is Per!ectly Inelastic #e"an#?

(.2: What is Inelastic #e"an#?

(.$: What is Unit lastic De"an#?

(.(: What is lastic De"an#?

(.*: What is Per!ectly lastic De"an#?

*.0: What is the relationshi' +et&een 'rice lasticity an# Total Re)enues?

,.0: What are the other #e"an# lasticites?

,.1: Inco"e lasticity

,.2: Cross lasticity

-.0: What is Price lasticity o! u''ly?

/.0: The three ''lications o! De"an# u''ly an# lasticity

/.1: ''lications to a3or cono"ic Issues:

4.0: What are the !!ects o! lasticity?


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cono"ics o! lasticity:

lasticity:

ccording to the dictionary elasticity means8 1. the ability of an object or material to resumeits normal shape after being stretched or compressed# stretching. -. the ability to change and

adapt# adaptability.

4ut in the context of Economics it means something some!hat different. If put simply

lasticity is a measure of ho! much the "uantity demanded of a ser$ice9good changes in

relation to its price, income or supply.

What is it an# ho& it &or5s:

If the "uantity demanded changes a lot !hen prices change a little, a product is said to

be elastic. %his often is the case for products or ser$ices for !hich there are many

alternati$es, or for !hich consumers are relati$ely price sensiti$e. 7or example, if the price of

2ola doubles, the "uantity demanded for 2ola !ill fall !hen consumers s!itch to less+

expensi$e 2ola 4.

)hen there is a small change in demand !hen prices change a lot, the product is said to be

inelastic. %he most famous example of relati$ely inelastic demand is that for gasoline. s the

price of gasoline increases, the "uantity demanded doesn&t decrease all that much. %his is

because there are $ery fe! good substitutes for gasoline and consumers are still !illing to

buy it e$en at relati$ely high prices.

Why it is i"'ortant:

Elasticity is important because it describes the fundamental relationship bet!een the price of

a good and the demand for that good. lastic goods and ser$ices generally ha$e plenty of

substitutes. s an elastic ser$ice9good&s price increases, the "uantity demanded of that good

can drop fast. Example of elastic goods and ser$ices include furniture, motor $ehicles,

instrument engineering products, professional ser$ices, and transportation ser$ices.

Inelastic goods ha$e fe!er substitutes and price change doesn&t affect "uantity demanded as

much. Some inelastic goods include gas, electricity, !ater, drinks, clothing, tobacco, food,and oil.

Price lasticity o! De"an#:

6rice elasticity of demand is basically a measure of ho! much the "uantity demanded of agood responds to a change in the price of that good, computed as the percentage change in

"uantity demanded di$ided by the percentage change in price.


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6rice elasticity of demand (6E or Ed is a measure used in economics to sho! the

responsi$eness, or elasticity, of the "uantity demanded of a good or ser$ice to a change in its

price. *ore precisely, it gi$es the percentage change in "uantity demanded in response to a

one percent change in price (holding constant all the other determinants of demand, such as

income. It !as de$ised by lfred *arshall.

6rice elasticities are almost al!ays negati$e, although analysts tend to ignore the sign e$en

though this can lead to ambiguity. 'nly goods !hich do not conform to the la! of demand,

such as :eblen and 0iffen goods, ha$e a positi$e 6E. In general, the demand for a good is

said to be inelastic (or relati$ely inelastic !hen the 6E is less than one (in absolute $alue8

that is, changes in price ha$e a relati$ely small effect on the "uantity of the good demanded.

%he demand for a good is said to be elastic (or relati$ely elastic !hen its 6E is greater than

one (in absolute $alue8 that is, changes in price ha$e a relati$ely large effect on the "uantity

of a good demanded.

Re$enue is maximi;ed !hen price is set so that the 6E is exactly one. %he 6E of a good

can also be used to predict the incidence (or


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than broadly defined markets because it is easier to find close substitutes for narro!ly defined

goods. 7or example, food, a broad category, has a fairly inelastic demand because there are

no good substitutes for food. Ice cream, a narro!er category, has a more elastic demand

because it is easy to substitute other desserts for ice cream. :anilla ice cream, a $ery narro!

category, has a $ery elastic demand because other fla$ors of ice cream are almost perfectsubstitutes for $anilla.

%ime ?ori;on: 0oods tend to ha$e more elastic demand o$er longer time hori;ons. )hen the

price of gasoline rises, the "uantity of gasoline demanded falls only slightly in the first fe!

months. '$er time, ho!e$er, people buy more fuel efficient cars, s!itch to public

transportation, and mo$e closer to !here they !ork.

Calculation o! Price lasticity o! De"an#:

6E is a measure of the sensiti$ity (or responsi$eness of the "uantity of a good or ser$ice

demanded to changes in its price. %he formula for the coefficient of price elasticity of

demand for a good is8

Q

P P

2− P

1

(¿¿2+ P1)/2Q

2−Q

1

(¿¿2+Q1)/2¿

Ed= Relative Change∈Quantity Demanded

Relative Change∈ Price =

Δ Quantity Average Quantity

Δ Price

Average Price

=¿

Ed=Change∈quality demanded

Change∈ price

%he price elasticity of demand is commonly di$ided into one of fi$e elasticity alternati$es#

perfectly elastic, relati$ely elastic, unit elastic, relati$ely inelastic, and perfectly inelastic,

depending on the relati$e response of "uantity to price. %hese fi$e alternati$es form a

continuum of possibilities.

%he chart displays fi$e alternati$es based on the coefficient of elasticity. %he negati$e $alue

obtained !hen calculating the price elasticity of demand is ignored. %his formula usuallyyields a negati$e $alue, due to the in$erse nature of the relationship bet!een price and


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"uantity demanded, as described by the


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greater the price elasticity of demand. %he steeper the demand cur$e that passes through a

gi$en point, the smaller the price elasticity of demand.

%he price elasticity of demand determines !hether the demand cur$e is steep or flat.

Per!ectly Inelastic #e"an#:

Per!ectly inelastic means that "uantity demanded or supplied is unaffected by any change in

price. In other !ords, the "uantity is essentially fixed. It does not matter ho! much price

changes, "uantity does not budge. Per!ectly inelastic #e"an# occurs !hen buyers ha$e no

choice in the consumption of a good.

Elasticity e"uals to

7or example8 Essential medications.

Inelastic #e"an#:


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If the price increase had no impact !hatsoe$er on the "uantity demanded, the medication

!ould be considered perfectly inelastic. Economics textbooks depict the demand cur$e for a

perfectly inelastic good as a $ertical line, because the "uantity demanded is the same at any

price.

E %he most famous and simple example of relati$ely inelastic #e"an# is that for gasoline.

s the price of gasoline increases, the "uantity demanded doesn&t decrease all that much. %his

is because there are $ery fe! good substitutes for gasoline and consumers are still !illing to

buy it e$en at relati$ely high prices

Elasticity is less than C

Unit lastic De"an#:

Fnit elastic demand describes a supply or demand cur$e !hich is perfectly responsi$e to

changes in price. %hat is, the "uantity supplied or demanded changes according to the same

percentage as the change in price. cur$e !ith an elasticity of C is unit elastic.

lastic De"an#:


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If the $alue obtained by the formula is greater than C, demand is said to be elastic, because

demand expands more than the price.

Per!ectly lastic De"an#:

If demand is perfectly elastic, it means that at a certain price demand is infinite ( good !ith

a $ery high elasticity of demand. In other !ords if a firm increased price by C@, it !ould see

all its demand e$aporate. If demand is perfectly elastic, then demand !ill be hori;ontal.

Elasticity e"uals to infinity.

The relationshi' +et&een Total re)enue an# Price

elasticity:

Total re)enue is calculated as the "uantity of a good sold multiplied by its price. It is ameasure of ho! much money a company makes from selling its product, before any costs are


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considered. 'b$iously, the goal of a company is to maximi;e profits, and one !ay to do this

is by increasing total re$enue. %he company can increase its total re$enue by selling more

items or by raising the price.

6rice elasticity of demand and total re$enue are closely interrelated because they deal !ith

the same t!o $ariables, 6 and G. If your product has elastic demand, you can increase your

re$enue by decreasing the price of that good. 6 !ill decrease, but G !ill increase at a greater

rate, thus increasing total re$enue. If the product is inelastic, then you can actually raise

prices, sell slightly less of that item but make higher re$enue. s a result, it is important for

management to kno! !hether its product has inelastic or elastic demand.

Other De"an# lasticities:

Inco"e lasticity:

In economics, income elasticity of demand measures the responsi$eness of the demand for agood to a change in the income of the people demanding the good, holding all prices

constant. It is calculated as the ratio of the percentage change in demand to the percentage

change in income. Income elasticity of demand measures the relationship bet!een a change

in "uantity demanded and a change in income. %he basic formula for calculating the

coefficient of income elasticity is8

Ed=Change∈quantity demanded

Change∈real income


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=ormal goods ha$e a positi$e income elasticity of demand so as income rise more is demand

at each price le$el. )e make a distinction bet!een normal necessities and normal luxuries

(both ha$e a positi$e coefficient of income elasticity.

=ecessities ha$e an income elasticity of demand of bet!een and HC. emand rises !ith

income, but less than proportionately. 'ften this is because !e ha$e a limited need to

consume additional "uantities of necessary goods as our real li$ing standards rise. %he class

examples of this !ould be the demand for fresh $egetables, toothpaste and ne!spapers.

emand is not $ery sensiti$e at all to fluctuations in income in this sense total market

demand is relati$ely stable follo!ing changes in the !ider economic (business cycle.

Luxuries on the other hand are said to ha$e an income elasticity of demand HC. (emand

rises more than proportionate to a change in income. Luxuries are items !e can (and often

do manage to do !ithout during periods of belo! a$erage income and falling consumer

confidence. )hen incomes are rising strongly and consumers ha$e the confidence to go

ahead !ith Jbig+ticketK items of spending, so the demand for luxury goods !ill gro!.

2on$ersely in a recession or economic slo!do!n, these items of discretionary spending

might be the first $ictims of decisions by consumers to rein in their spending and rebuild

sa$ings and household financial balance sheets.

In other !ords8

positi$e sign denotes a normal good

negati$e sign denotes an inferior good

%he income elasticity of demand for a product !ill also change o$er time M the $ast

majority of products ha$e a finite life+cycle. 2onsumer perceptions of the $alue and

desirability of a good or ser$ice !ill be influenced not just by their o!n experiences


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of consuming it (and the feedback from other purchasers but also the appearance of

ne! products onto the market. 2onsider the income elasticity of demand for flat+

screen color tele$isions as the market for plasma screens de$elops and the income

elasticity of demand for %: ser$ices pro$ided through satellite dishes set against the

gro!ing a$ailability and falling cost (in nominal and real terms and integrated digitaltele$isions.

Cross lasticity:

In economics, the cross elasticity of demand or cross+price elasticity of demand

measures the responsi$eness of the demand for a good to a change in the price of

another good. It is measured as the percentage change in demand for the first good

that occurs in response to a percentage change in price of the second good.

7or example, the t!o goods, fuel and cars (consists of fuel consumption, are

complements# that is, one is used !ith the other. In these cases the cross elasticity of

demand !ill be negati$e, as sho!n by the decrease in demand for cars !hen the price

of fuel increased. )here the t!o goods are substituting the cross elasticity of demand

!ill be positi$e, so that as the price of one goes up the demand of the other !ill

increase. 7or example, in response to an increase in the price of carbonated soft

drinks, the demand for non+carbonated soft drinks !ill rise. In the case of perfect

substitutes, the cross elasticity of demand is e"ual to positi$e infinity. )here the t!o

goods are independent, or, as described in consumer theory, if a good is independent

in demand then the demand of that good is independent of the "uantity consumed of

all other goods a$ailable to the consumer, the cross elasticity of demand !ill be ;ero8as the price of one good changes, there !ill be no change in demand for the other

good.

It is basically, a measure of ho! much the "uantity demanded of one good responds to

a change in the price of another good, computed as the percentage change in "uantity

demanded of the first good di$ided by the percentage change in price of the second

good

Price lasticity o! u''ly:

6rice elasticity of supply (6ES measures the responsi$eness of "uantity supplied to a change

in price. It is necessary for a firm to kno! ho! "uickly, and effecti$ely, it can respond to

changing market conditions, especially to price changes. %he follo!ing e"uation can be used

to calculate 6ES.

4asically the 6rice Elasticity of Supply measures the rate of response of "uantity demand due

to a price change. )e calculate the 6rice Elasticity of Supply by the formula8


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6EoS A (@ 2hange in Guantity Supplied(@ 2hange in 6rice

Inter'retation o! the Price lasticity o! u''ly

%he price elasticity of supply is used to see ho! sensiti$e the supply of a good is to a price

change. %he higher the price elasticity, the more sensiti$e producers and sellers are to price

changes. $ery high price elasticity suggests that !hen the price of a good goes up, sellers

!ill supply a great deal less of the good and !hen the price of that good goes do!n, sellers

!ill supply a great deal more. $ery lo! price elasticity implies just the opposite, that

changes in price ha$e little influence on supply.

'ften you&ll ha$e the follo! up "uestion


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Ti"e 'erio# an# 'ro#uction s'ee#8

Supply is more price elastic the longer the time period that a firm is allo!ed to adjust

its production le$els. In some agricultural markets the momentary supply is fixed and

is determined mainly by planting decisions made months before, and also climatic

conditions, !hich affect the production yield. In contrast the supply of milk is price

elastic because of a short time span from co!s producing milk and products reaching

the market place.

Three ''lications o! De"an# u''ly an# lasticity:

2an good ne!s for farming be bad ne!s for farmers )hy did '6E2 fail to keep the

price of oil light oes drug interdiction increase or decrease drug related crime t

first, these "uestions might seem to ha$e little in common. et all three "uestions are

about markets, and all markets are subject to the forces of supply and demand. ?ereare applying the $ersatile tools of supply demand and elasticity to ans!er these

seemingly complex "uestions.

2an good ne!s for farming be bad ne!s for farmers )hat happens to !heat farmers

and the market for !heat !hen uni$ersity agronomics disco$er a ne! !heat hybrid

that is more producti$e than existing $arieties 7irst !e examine !hether the supply

or demand cur$e shifts. Second, !e consider !hich direction the cur$e shifts. %hird,

!e use the supply and demand diagram to see ho! the market e"uilibrium changes.

In this case, the disco$ery of the ne! hybrid affects the supply cur$e. 4ecause the

hybrid increases the amount of !heat that can be produced in each acre of land

farmers are no! !illing to supply more !heat at any gi$en price. In other !ords, the

supply cur$e shifts tot e right. %he demand cur$e remains the same because

consumers> desire to buy !heat products at any gi$en price are not affected by the

introduction of a ne! hybrid. 7igure sho!s an example of such a change. )hen the

supply cur$e shifts from SC to S- the "uantity of !heat sold increases from C to

CC, and the price of !heat falls from NP to N-.

oes this disco$ery make farmers better off s a first cut to ans!ering this "uestion,

consider !hat happens to the total re$enue recei$ed by farmers. 7armer>s totalre$enue is 6 T G the price of the !heat times the "uantity sold. %he disco$ery affects

farmers n t!o conflicting !ays. %he hybrid allo!s farmers to produce more !heat (G

rises but no! each bushel of !heat sells for less (6 falls.

)hether total re$enue rises or falls depends on the elasticity of demand. In practice,

the demand or basic foodstuffs such as !heat is usually inelastic because these items

are relati$ely inexpensi$e and ha$e fe! good substitutes. )hen the demand cur$e is

inelastic as it in the figure, decrease in price cause total re$enue to fall. ou can see

this in the figure. %he price of !heat falls substantially !hereas the "uantity of !heat

sold rises only slightly. %otal re$enue falls from NP to N--. %hus, the disco$ery ofthe ne! hybrid lo!ers the total farmers recei$e for the sale of their crops.


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''lications to a3or cono"ic Issues:

♦ 'ne of the most fruitful arenas for application of supply+and+demand analysis

is agriculture. Impro$ements in agricultural technology mean that supply

increases greatly, !hile demand for food rises less than proportionately !ithincome. ?ence free+market prices for foodstuffs tend to fall. =o !onder

go$ernments ha$e adopted a $ariety of programs, like crop restrictions, to

prop up farm incomes.

♦ commodity tax shifts the supply+and+demand e"uilibrium. %he tax&s

incidence (or impact on incomes !ill fall more hea$ily on consumers than on

producers to the degree that the demand is inelastic relati$e to supply.

♦ 0o$ernments occasionally interfere !ith the !orkings of competiti$e markets

by setting maximum ceilings or minimum floors on prices. In such situations,

"uantity supplied need no longer e"ual "uantity demanded# ceilings lead to

excess demand, !hile floors lead to excess supply. Sometimes, the

interference may raise the incomes of a particular group, as in the case of

farmers or lo!+skilled !orkers. 'ften, distortions and inefficiencies result.

lasticity in the real &orl#:

)e&$e seen ho! elasticity can affect changes in price and "uantity in a market

economy on a graph, but do this actually happen in the real !orld )hile it is

unlikely that demand for $ery many goods is perfectly elastic or perfectlyinelastic, economists recogni;e that demand for certain goods !ill be more

elastic than others, and demand for certain goods !ill be less elastic. So, !hile

the extreme cases are pretty rare, elasticity still has some effect o$er market

beha$ior.0oods !ith $ery elastic demand tend to be non+necessary goods, or goods that

can be easily substituted for by other goods. )hen the prices of these goods

go up, consumers !ill either decide they don&t really need the goods, and !on&t

buy any, or they !ill begin to substitute a!ay from the goods, buying more of

the cheaper substitutes. 'ne possible example of a non+essential good might

be candy. It is not an essential good, and if the price !ere to double, demand

!ould probably fall a good deal as consumers decide they don&t really need to

eat candy, especially since it costs so much money. n easily substituted good

might be cola. If the price of one brand of cola increases, demand !ill drop

"uickly as consumers decide to buy a competing brand, !hose price has

stayed the same.0oods !ith $ery inelastic demand tend to be goods !ith no easy substitutes, or

essential goods that consumers cannot do !ithout. 7or these goods, e$en !hen

the price increases, demand stays relati$ely steady, because consumers ha$e

no other options, and feel that they still need to buy the same amount of goods.In the short run, gasoline could be considered an inelastic good, since it is


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difficult to completely alter transportation patterns in an immediate response

to changes in gasoline prices. ('$er the long run, ho!e$er, consumers may

change their habits and decrease their consumption of gasoline, using public

transportation or carpools, once they reali;e that their costs ha$e increased

permanently. nother example might be staple foods. )hile luxury itemssuch as ca$iar or 4elgian chocolates aren&t essential to our diet, basics such as

bread, pasta, and rice are relati$ely indispensable. In other !ords, an increase

in price !ould ha$e less effect on the consumption of staple foods than it

!ould ha$e on luxury foods.

Po&er!ul !!ects o! lasticity:

*any real estate markets are affected by an aspect of consumer beha$ior U

and sometimes supplier beha$ior U that in$ol$es people making rapid, oftenunexpected, responses to situations they !ant to a$oid. I call this the elastic

adjustment factor. It affects !hat people do in housing and office markets.%he most common elastic adjustment occurs in rental housing markets during

economic slo!do!ns. *any renters li$ing alone during prosperity can no

longer afford to do so !hen economic ad$ersity strikes U so they double up,

or return to their parents& homes. %his causes a bigger drop in demand for total

rental units during recessions than may be justified by demographic factors or

the shrinkage of a$ailable jobs alone.6oor households immigrating to the Fnited States into high+cost housing also

make similar adjustments. 2alifornia has the highest housing costs in thenation, yet it recei$es more poor immigrants than any other state. ?o! can

they afford to li$e in 2alifornia&s expensi$e units %hey double up, !ith

multiple families li$ing in a unit designed U and legally limited to U one

family.%hat is !hy Southern 2alifornia has more illegally o$ercro!ded units than

any other place in the nation. Such beha$ior also occurs in large cities that

recei$ed many poor immigrants in the COOs.%he arri$al of such ne!comers has stimulated housing markets in cities

ranging from =e! ork to 2hicago to 7resno, 2alif. 4ut housing demand

often does not rise nearly as much as the number of ne! immigrant

households because so many are sharing accommodations. In addition, many

poor immigrants from abroad are no! mo$ing directly into older suburbs, as

in rlington 2ounty, :a.'art"ent ector Isn;t lone

Elastic adjustment also is pre$alent in the office sector, !here tenants are

marketing excess space that they no longer need or can afford. Some industry

obser$ers estimate that nearly C/@ of all office space on the market today is

sublease space. )hen the market softened, experts& difficulty in projecting just

ho! large an elastic adjustment !ould take place in the office sector led many


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of them to underestimate the real $acancy rate by considering only unrented

space.'ne result of elastic adjustments is that economic forecasts regarding housing

and office occupancy or beha$ior are often mistaken because they do not

allo! for such adjustments.7or example, many belie$e that high housing prices ha$e led to a housing

price bubble that !ill soon burst and be follo!ed by plunging housing $alues

because !e are no! in a period of economic !eakness.4ut this forecast does not take into account the ability of existing homeo!ners

to elastically adjust to declines in market demand. 7aced !ith the prospect of

selling their homes at reduced pricing le$els in a sluggish economy, most

homeo!ners !ill likely !ait until market conditions impro$e before putting

their house on the block. %his ability of homeo!ners to hold out for their

desired price keeps home $alues from plunging e$en during periods of

d!indling demand.%i7h


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Conclusion

Elasticity is one of the most important concepts in neoclassical economic

theory. It is useful for understanding the distribution of !ealth and

different types of goods as they relate to the theory of consumer choice. =ot

only that, ha$ing a good grasp on it helps us understand ho! the economy and

market !orks and ho! it can be affected by simplest of things.


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Re!erences:

♦ en.!ikipedia.org9!iki9elasticity

♦ https899!!!.economicshelp.org9blog9CC59economics9perfectly+

elastic+demand9

♦ http899!!!.enotes.com9research+starters9elasticity

♦ http899!!!.in$estingans!ers.com9financial+

dictionary9economics9elasticity+-51P

♦ http899!!!.in$estopedia.com9terms9e9inelastic.asp

♦ http899smallbusiness.chron.com9relationship+bet!een+price+

elasticity+total+re$enue+-V/VV.html

♦ http899economics.about.com9cs9micfrohelp9a9priceelasticity.htm

♦ http899!!!.citeman.com9CVV1+three+applications+of+supply+

demand+and+elasticity.html

♦ http899!!!.sparknotes.com9economics9micro9elasticity9section-.

rhtml

♦ http899nreionline.com9commentary9po!erful+effects+elasticity

♦ http899!!!.sparknotes.com9economics9micro9elasticity9section-


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economics of elasticity

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