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Price elasticity of demandFrom Wikipedia, the free encyclopedia

Not to be confused withPrice elasticity of supply.

PED is derived from the percentage change in quantity (%Qd) and percentage change in price

(%P).

Price elasticity of demand (PED or Ed) is a measure used in economics to show the responsiveness,

orelasticity, of the quantity demanded of a good or service to a change in its price. More precisely, it gives the

percentage change in quantity demanded in response to a one percent change in price (holding constant all the

other determinants of demand, such as income). It was devised byAlfred Marshall.

Price elasticities are almost always negative, although analysts tend to ignore the sign even though this can

lead to ambiguity. Only goods which do not conform to thelaw of demand, such asVeblenandGiffen goods,have a positive PED. In general, the demand for a good is said to be inelastic(or relatively inelastic) when the

PED is less than one (in absolute value): that is, changes in price have a relatively small effect on the quantity

of the good demanded. The demand for a good is said to be elastic(or relatively elastic) when its PED is

greater than one (in absolute value): that is, changes in price have a relatively large effect on the quantity of a

good demanded.
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Revenue is maximised when price is set so that the PED is exactly one. The PED of a good can also be used

to predict theincidence (or "burden") of a taxon that good. Various research methods are used to determine

price elasticity, includingtest markets, analysis of historical sales data andconjoint analysis.

Contents

[hide]

1 Definition

o 1.1 Point-price elasticity

o 1.2 Arc elasticity

2 History

3 Determinants

4 Interpreting values of price elasticity coefficients

5 Effect on total revenue

6 Effect on tax incidence

7 Selected price elasticities

8 See also

9 Notes

10 References

11 External links

[edit]DefinitionPED is a measure of responsiveness of the quantity of a good or service demanded to changes in its

price.[1]

The formula for the coefficient of price elasticity of demand for a good is:[2][3][4]

The above formula usually yields a negative value, due to the inverse nature

of the relationship between price and quantity demanded, as described by the

"law of demand".

[3]

For example, if the price increases by 5% and quantitydemanded decreases by 5%, then the elasticity at the initial price and quantity

= 5%/5% = 1. The only classes of goods which have a PED of greater than

0 areVeblenandGiffengoods.[5]

Because the PED is negative for the vast

majority of goods and services, however, economists often refer to price

elasticity of demand as a positive value (i.e., inabsolute valueterms).[4]
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This measure of elasticity is sometimes referred to as the own-priceelasticity

of demand for a good, i.e., the elasticity of demand with respect to the good's

own price, in order to distinguish it from the elasticity of demand for that good

with respect to the change in the price of some other good, i.e.,

acomplementaryorsubstitute good.[1]The latter type of elasticity measure is

called across-price elasticity of demand.[6][7]

As the difference between the two prices or quantities increases, the accuracy

of the PED given by the formula above decreasesfor a combination of two

reasons. First, the PED for a good is not necessarily constant; as explained

below, PED can vary at different points along thedemand curve, due to its

percentage nature.[8][9]

Elasticity is not the same thing as theslopeof the

demand curve, which is dependent on the units used for both price and

quantity.[10][11]Second, percentage changes are not symmetric; instead,

thepercentage changebetween any two values depends on which one is

chosen as the starting value and which as the ending value. For example, if

quantity demanded increases from10 units to15 units, the percentage

change is 50%, i.e., (15 10) 10 (converted to a percentage). But if quantity

demanded decreases from15 units to10 units, the percentage change is

33.3%, i.e., (10 15) 15.[12][13]

Two alternative elasticity measures avoid or minimise these shortcomings of

the basic elasticity formula: point-price elasticityand arc elasticity.

[edit]Point-price elasticity

One way to avoid the accuracy problem described above is to minimise the

difference between the starting and ending prices and quantities. This is the

approach taken in the definition of point-priceelasticity, which usesdifferential

calculusto calculate the elasticity for an infinitesimal change in price and

quantity at any given point on the demand curve:[14]

In other words, it is equal to the absolute value of the first derivative of

quantity with respect to price (dQd/dP) multiplied by the point's price (P)

divided by its quantity (Qd).[15]
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In terms of partial-differential calculus, point-price elasticity of demand

can be defined as follows:[16]

let be the demand of

goods as a function of parameters price and wealth,

and let be the demand for good . The elasticity of demand

for good with respect to pricepk is

However, the point-price elasticity can be computed only if the

formula for thedemand function,Qd = f(P), is known so its

derivative with respect to price, dQd /dP, can be determined.

[edit]Arc elasticity

A second solution to the asymmetry problem of having a PED

dependent on which of the two given points on a demand curve is

chosen as the "original" point and which as the "new" one is to

compute the percentage change in P and Q relative to

the averageof the two prices and the averageof the two quantities,

rather than just the change relative to one point or the other. Loosely

speaking, this gives an "average" elasticity for the section of the

actual demand curvei.e., the arcof the curvebetween the two

points. As a result, this measure is known as thearc elasticity, in this

case with respect to the price of the good. The arc elasticity is

defined mathematically as:[13][17][18]

This method for computing the price elasticity is also known as

the "midpoints formula", because the average price and average

quantity are the coordinates of the midpoint of the straight line

between the two given points.[12][18]

However, because this

formula implicitly assumes the section of the demand curve

between those points is linear, the greater the curvature of the

actual demand curve is over that range, the worse this

approximation of its elasticity will be.[17][19]

[edit]History
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The illustration that accompanied Marshall's original

definition of PED, the ratio of PT to Pt

Together with the concept of an economic "elasticity"

coefficient,Alfred Marshallis credited with defining PED

("elasticity of demand") in his bookPrinciples of Economics,

published in 1890.[20]

He described it thus: "And we may say

generally: the elasticity (or responsiveness) of demand in a

market is great or small according as the amount demanded

increases much or little for a given fall in price, and diminishes

much or little for a given rise in price".[21]

He reasons this since

"the only universal law as to a person's desire for a commodity

is that it diminishes... but this diminution may be slow or rapid. If

it is slow... a small fall in price will cause a comparatively large

increase in his purchases. But if it is rapid, a small fall in price

will cause only a very small increase in his purchases. In the

former case... the elasticity of his wants, we may say, is great. In

the latter case... the elasticity of his demand is

small."[22]

Mathematically, the Marshallian PED was based on a

point-price definition, using differential calculus to calculate

elasticities.[23]

[edit]DeterminantsThe overriding factor in determining PED is the willingness and

ability of consumers after a price change to postpone immediate

consumption decisions concerning the good and to search for

substitutes ("wait and look").[24]

A number of factors can thus

affect the elasticity of demand for a good:[25]
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Availability ofsubstitute goods: the more and closer the

substitutes available, the higher the elasticity is likely to be,

as people can easily switch from one good to another if an

even minor price change is made;[25][26][27]

There is a strong

substitution effect.[28]If no close substitutes are available the

substitution of effect will be small and the demand

inelastic.[29]

Breadth of definition of a good: the broader the

definition of a good (or service), the lower the elasticity.

For example, Company X's fish and chips would tend to

have a relatively high elasticity of demand if a

significant number of substitutes are available, whereas

food in general would have an extremely low elasticityof demand because no substitutes exist.

[30]

Percentage of income: the higher the percentage of the

consumer's income that the product's price represents, the

higher the elasticity tends to be, as people will pay more

attention when purchasing the good because of its

cost;[25][26]

The income effect is substantial.[31]

When the

goods represent only a negligible portion of the budget the

income effect will be insignificant and demand inelastic,[32]

Necessity: the more necessary a good is, the lower the

elasticity, as people will attempt to buy it no matter the

price, such as the case ofinsulinfor those that need it.[10][26]

Duration: for most goods, the longer a price change holds,

the higher the elasticity is likely to be, as more and more

consumers find they have the time and inclination to search

for substitutes.[25][27]

When fuel prices increase suddenly, for

instance, consumers may still fill up their empty tanks in the

short run, but when prices remain high over several years,

more consumers will reduce their demand for fuel by

switching tocarpoolingor public transportation, investing in

vehicles with greaterfuel economyor taking other

measures.[26]

This does not hold forconsumer

durablessuch as the cars themselves, however; eventually,
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it may become necessary for consumers to replace their

present cars, so one would expect demand to be less

elastic.[26]

Brand loyalty: an attachment to a certain brandeither out

of tradition or because of proprietary barrierscan override

sensitivity to price changes, resulting in more inelastic

demand.[30][33]

Who pays: where the purchaser does not directly pay for

the good they consume, such as with corporate expense

accounts, demand is likely to be more inelastic.[33]

[edit]Interpreting values of priceelasticity coefficients

Perfectly inelastic demand[10]

Perfectly elastic demand[10]
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Elasticities of demand are interpreted as follows:[10]

Value Descriptive Terms

Ed = 0 Perfectly inelastic demand

- 1 < Ed < 0 Inelastic or relatively inelastic demand

Ed = - 1Unit elastic, unit elasticity, unitary elasticity, or unitarily elastic

demand

- < Ed < -1

Elastic or relatively elastic demand

Ed = - Perfectly elastic demand

A decrease in the price of a good normally results in an increase

in the quantity demanded by consumers because of thelaw of

demand, and conversely, quantity demanded decreases when

price rises. As summarized in the table above, the PED for a

good or service is referred to by different descriptive terms

depending on whether the elasticity coefficient is greater than,

equal to, or less than 1. That is, the demand for a good is

called:

relatively inelasticwhen the percentage change in quantity

demanded is less thanthe percentage change in price (so

that Ed > - 1);

unit elastic, unit elasticity, unitary elasticity, or unitarily

elasticdemand when the percentage change in quantity

demanded is equal tothe percentage change in price (so

that Ed = - 1); and
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relatively elasticwhen the percentage change in quantity

demanded is greater thanthe percentage change in price

(so that Ed < - 1).[10]

As the two accompanying diagrams show, perfectly

elasticdemand is represented graphically as a horizontal line,

and perfectly inelasticdemand as a vertical line. These are

the onlycases in which the PED and the slope of the demand

curve (P/Q) are bothconstant, as well as the onlycases in

which the PED is determined solely by the slope of the demand

curve (or more precisely, by the inverseof that slope).[10]

[edit]Effect on total revenue

See also:Total revenue test

A set of graphs shows the relationship between

demand and total revenue (TR) for a linear demandcurve. As price decreases in the elastic range, TR

increases, but in the inelastic range, TR decreases.

TR is maximised at the quantity where PED = 1.
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A firm considering a price change must know what effect the

change in price will have on total revenue. Generally any

change in price will have two effects:[34]

the price effect: an increase in unit price will tend to

increase revenue, while a decrease in price will tend to

decrease revenue.

the quantity effect: an increase in unit price will tend to lead

to fewer units sold, while a decrease in unit price will tend to

lead to more units sold.

Because of the inverse nature of the relationship between price

and quantity demanded (i.e., the law of demand), the two effects

affect total revenue in opposite directions. But in determiningwhether to increase or decrease prices, a firm needs to know

what the net effect will be. Elasticity provides the answer: The

percentage change in total revenue is equal to the percentage

change in quantity demanded plus the percentage change in

price. (One change will be positive, the other negative.)[35]

As a result, the relationship between PED and total revenue can

be described for any good:[36][37]

When the price elasticity of demand for agoodis perfectly

inelastic(Ed = 0), changes in the price do not affect the

quantity demanded for the good; raising prices will cause

total revenue to increase.

When the price elasticity of demand for a good is relatively

inelastic(-1 < Ed < 0), the percentage change in quantity

demanded is smaller than that in price. Hence, when the

price is raised, the total revenue rises, and vice versa.

When the price elasticity of demand for a good is unit (or

unitary) elastic(Ed = -1), the percentage change in quantity

is equal to that in price, so a change in price will not affect

total revenue.

When the price elasticity of demand for a good is relatively

elastic( - < Ed < -1), the percentage change in quantity
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demanded is greater than that in price. Hence, when the

price is raised, the total revenue falls, and vice versa.

When the price elasticity of demand for a good is perfectly

elastic(Edis ), any increase in the price, no matter how

small, will cause demand for the good to drop to zero.

Hence, when the price is raised, the total revenue falls to

zero.

Hence, as the accompanying diagram shows, total revenue is

maximized at the combination of price and quantity demanded

where the elasticity of demand is unitary.[37]

It is important to realize that price-elasticity of demand

is notnecessarily constant over all price ranges. The linear

demand curve in the accompanying diagram illustrates that

changes in price also change the elasticity: the price elasticity is

different at every point on the curve.

[edit]Effect on tax incidence

When demand is more elastic than supply, producers

will bear a greater proportion of the tax burden than

consumers will.

Main article:tax incidence

PEDs, in combination withprice elasticity of supply(PES), can

be used to assess where the incidence (or "burden") of a per-

unit tax is falling or to predict where it will fall if the tax is

imposed. For example, when demand is perfectly inelastic, by

definition consumers have no alternative to purchasing the good

or service if the price increases, so the quantity demanded
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12/13

would remain constant. Hence, suppliers can increase the price

by the full amount of the tax, and the consumer would end up

paying the entirety. In the opposite case, when demand

isperfectly elastic, by definition consumers have an infinite ability

to switch to alternatives if the price increases, so they would

stop buying the good or service in question completely

quantity demanded would fall to zero. As a result, firms cannot

pass on any part of the tax by raising prices, so they would be

forced to pay all of it themselves.[38]

In practice, demand is likely to be only relativelyelastic or

relatively inelastic, that is, somewhere between the extreme

cases of perfect elasticity or inelasticity. More generally, then,

the higherthe elasticity of demand compared to PES, the

heavier the burden on producers; conversely, the

more inelasticthe demand compared to PES, the heavier the

burden on consumers. The general principle is that the party

(i.e., consumers or producers) that has feweropportunities to

avoid the tax by switching to alternatives will bear

the greaterproportion of the tax burden.[38]

[edit]Selected price elasticities

Various research methods are used to calculate price elasticities

in real life, including analysis of historic sales data, both public

and private, and use of present-day surveys of customers'

preferences to build uptest marketscapable of modelling such

changes. Alternatively,conjoint analysis(a ranking of users'

preferences which can then be statistically analysed) may be

used.[39]

Though PEDs for most demand schedules vary depending on

price, they can be modeled assuming constant

elasticity.[40]

Using this method, the PEDs for various goods

intended to act as examples of the theory described aboveare

as follows. For suggestions on why these goods and services

may have the PED shown, see the above section on

determinants of price elasticity.
http://en.wikipedia.org/wiki/Price_elasticity_of_demand#cite_note-wall57-37http://en.wikipedia.org/wiki/Price_elasticity_of_demand#cite_note-wall57-37http://en.wikipedia.org/wiki/Price_elasticity_of_demand#cite_note-wall57-37http://en.wikipedia.org/wiki/Price_elasticity_of_demand#cite_note-wall57-37http://en.wikipedia.org/wiki/Price_elasticity_of_demand#cite_note-wall57-37http://en.wikipedia.org/wiki/Price_elasticity_of_demand#cite_note-wall57-37http://en.wikipedia.org/w/index.php?title=Price_elasticity_of_demand&action=edit&section=9http://en.wikipedia.org/w/index.php?title=Price_elasticity_of_demand&action=edit&section=9http://en.wikipedia.org/w/index.php?title=Price_elasticity_of_demand&action=edit&section=9http://en.wikipedia.org/wiki/Marketing_researchhttp://en.wikipedia.org/wiki/Marketing_researchhttp://en.wikipedia.org/wiki/Marketing_researchhttp://en.wikipedia.org/wiki/Conjoint_analysishttp://en.wikipedia.org/wiki/Conjoint_analysishttp://en.wikipedia.org/wiki/Conjoint_analysishttp://en.wikipedia.org/wiki/Price_elasticity_of_demand#cite_note-38http://en.wikipedia.org/wiki/Price_elasticity_of_demand#cite_note-38http://en.wikipedia.org/wiki/Price_elasticity_of_demand#cite_note-38http://en.wikipedia.org/wiki/Price_elasticity_of_demand#cite_note-39http://en.wikipedia.org/wiki/Price_elasticity_of_demand#cite_note-39http://en.wikipedia.org/wiki/Price_elasticity_of_demand#cite_note-39http://en.wikipedia.org/wiki/Price_elasticity_of_demand#cite_note-39http://en.wikipedia.org/wiki/Price_elasticity_of_demand#cite_note-38http://en.wikipedia.org/wiki/Conjoint_analysishttp://en.wikipedia.org/wiki/Marketing_researchhttp://en.wikipedia.org/w/index.php?title=Price_elasticity_of_demand&action=edit&section=9http://en.wikipedia.org/wiki/Price_elasticity_of_demand#cite_note-wall57-37http://en.wikipedia.org/wiki/Price_elasticity_of_demand#cite_note-wall57-37


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