chapter 3: d d el i i i demand elasticities

Economics for Managersby Paul Farnhamy

Chapter 3:D d El i i iDemand Elasticities

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Demand ElasticityDemand Elasticity

Demand elasticity shows the percentage change in quantity p g g q ydemanded of a product relative to the percentage change in another

i blvariableThe coefficient represents the pratio of the two percentage changes

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Price Elasticityf D d E tiof Demand Equation

The percentage change in the quantity demanded of a given good relative to a

t h i it ipercentage change in its price

e% ΔQx whereeP =% ΔPx

where

i l ti it f d dΔ = the absolute change eP = price elasticity of demand

Qx= quantity demanded of good X

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Qx= quantity demanded of good X Px= the price of good X

Price Elasticity Price Elasticity Figure 3.1

Measured as a

AP1

movement along a demand curve

B

P1

P2

PP2

0 Q QDemandQ

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Quantity0 Q1 Q2

Price Elasticity and D i i M kiDecision Making

Tells managers what will happen if product prices changep p gHelps firms to develop pricing strategiesstrategiesHelps to develop pricing strategies in the public sectorstrategies in the public sector

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ElasticityElasticity

Elastic demand: change in quantity demanded is greater than the change in priceInelastic demand: change in gquantity demanded is less than the change in priceUnitary elasticity: change in quantity demand is equal to h i i

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change in price

Elasticity andT t l RTotal Revenue

If demand is elastic, higher prices result in lower total revenue. Lower prices result in higher total revenueChanges in price and the resulting total revenue are inversely yproportionate(see Figure 3 2 on next slide)

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(see Figure 3.2 on next slide)

Elastic Demand and T t l RTotal Revenue Figure 3.2

A12

If prices decrease, revenue increases. If prices increaseA

BY

(P1) 10

(P ) 9

If prices increase, revenue decreases.

B

XC(P2) 9 Area X = Q1CBQ2

Area Y = P1ACP2X

Q tit0 2Demand

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Quantity0 2 (Q1)

3 (Q2)

12

Inelastic DemandInelastic Demand

When units are sold at a lower price, the quantity demanded has p , q ynot increased proportionatelyTotal revenue decreasesTotal revenue decreasesChanges in price and the resulting total revenue move in the sametotal revenue move in the same direction(S Fi 3 3 t lid )

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(See Figure 3.3 on next slide)

Inelastic Demand and T t l R Total Revenue Figure 3.3

12If prices decrease, revenue decrease. If prices increaseprices increase, revenue increases.

ABY(P1) 4

(P ) 3

Area X = Q1CBQ2Area Y = P1ACP2

BX

YC

Q tit

(P2) 3

0 8Demand

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Quantity0 8 (Q1)

9 (Q2)

12

Managerial Rule of Thumb: E ti ti P i El ti itEstimating Price Elasticity

Managers can estimate price elasticity by asking customers:

1. What do you currently pay for my product?2. At what price would you stop buying my

product altogether?product altogether?Managers should ask themselves:

1. How much will revenue increase as a result of higher sales?

2 How much will revenue decrease as a

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2. How much will revenue decrease as a result of lower prices for each unit?

Determinants of Price El ti it f D dElasticity of Demand

1. Number of substitute goods2 Percent of a consumer’s income2. Percent of a consumer s income

that is spent on the productTi i d d id ti3. Time period under consideration

4. Nature of the good (durable or g (non-durable)

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Numerical ExamplesNumerical Examples

Demand function• Shows relationship between quantityShows relationship between quantity

demanded and price• Q = 12 – P or P = 12 – Q

Total revenue function• Shows total revenue received byShows total revenue received by

producer as a function of the level of output

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• TR = (P) (Q) = (12 – Q) (Q) = 12Q – Q2

Numerical ExamplesNumerical Examples

Average revenue function: shows how average revenue is related to level of output• AR = TR / Q = [(P) (Q)] / Q = P

Marginal revenue function: shows the additional revenue a producer receives by selling an additional unit of output at different levelsdifferent levels• MR = (ΔTR) / (ΔQ) = (TR2 – TR1) / (Q2 – Q1)

MR = dTR / dQ = 12 2Q

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MR = dTR / dQ = 12 – 2Q

Demand and M i l RMarginal Revenue

Firms are always constrained by demand curveTop half of the demand curve in Figure 3.4 indicates when

l i t t lmanagers lower price, total revenue increasesB tt h lf i di t iBottom half indicates a price decrease causes total revenue to fall

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to fall

Demand and M i l RMarginal Revenue

Figure 3.4

|eP| > 1Demand, marginal

12g

revenue, and total revenue f ti

|eP| = 16 functions are

related6

|eP| < 1Demand

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Marginal Revenue

Quantity0 6 12Demand

The Total Revenue F tiFunction

TotalFigure 3.5

Total Revenue

36

18Total Revenue

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0 126

Extreme Demand CurvesExtreme Demand Curves

Vertical demand curve• Represents perfectly inelastic demandRepresents perfectly inelastic demand• Example might be insulin for diabetics

H i t l d dHorizontal demand curve• Represents perfectly elastic demand• Example would be a bushel of wheat

from an agricultural producer

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Extreme Demand CurvesExtreme Demand Curves

Vertical demand curvePrice

Vertical demand curve

Demand

0Q1 Quantity

PriceHorizontal demand curve

Q1

P1

Price

Demand

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0 Quantity

Elasticities of DemandElasticities of Demand

Income elasticity of demand: percentage change in quantity p g g q ydemanded of a given good relative to percentage change in

iconsumer income• Necessities – elasticity between 0 y

and 1 • Luxuries – elasticity greater than 1

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y g

Managerial Rule of Thumb: C l l ti I El ti itCalculating Income Elasticity

Calculating income elasticity of demand is based on two questions for a consumer:1. What fraction of your total budget1. What fraction of your total budget

do you spend on Product X?2 If you earned a bonus of $10002. If you earned a bonus of $1000,

what part of that bonus would you spend on Product X?

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y p

Elasticities of DemandElasticities of Demand

Cross-price elasticity of demand: measures how demand for Good X

i ith h i th i fvaries with changes in the price of Good Y

S b tit t d h iti• Substitute goods have positive cross elasticity

• Complementary goods have negative• Complementary goods have negative cross elasticity

Defines relevant market in which

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Defines relevant market in which different products compete

Managerial Rule of Thumb: P i El ti it D i i M kiPrice Elasticity Decision Making

Which demand elasticity should be used in making appropriate decisions: the one for the entire product or thethe one for the entire product or the one for the individual producer?

(The answer depends upon how other(The answer depends upon how other firms react to price changes:If we are: monopolistsIf we are: monopolists…Oligopolists…

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Perfect competitors…)

Marketing Literature R di El ti it IRegarding Elasticity Issues

Advertising elasticity of demand: the percentage change in quantity demanded of a good relative to thedemanded of a good relative to the percentage change in advertising dollars spent on that gooddollars spent on that goodMarketing studies

T lli 1988• Tellis, 1988• Sethuraman and Tellis, 1991

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• Hoch, et al, 1995

Summary of Key TermsSummary of Key Terms

Average revenue and average revenue functionCross-price elasticity of demandDemand elasticity yLuxury and necessityM i l d i lMarginal revenue and marginal revenue function

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Summary of Key TermsSummary of Key Terms

P f tl l ti d dPerfectly elastic demandPerfectly inelastic demandPrice elasticity of demandTotal revenue and total revenueTotal revenue and total revenue functionUnitary elasticityUnitary elasticity

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Do you have any Do you have any questions?questions?

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