Revenue(Curves,Calculations&Elasticity)GCEA-LEVEL&IBECONOMICS

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LessonStructure◦Revenue

◦TotalRevenue,MarginalRevenueandAverageRevenue

◦RevenueCurvesunderPerfectandImperfectCompetition

◦PEDanditsrelationshiptorevenuecurves

WhatisPerfectCompetition?

RevenuesUnderPerfectCompetition

PerfectCompetitionAssumptions:

-PriceTaker

-PerfectInformation

-Unlimitednumberofbuyers(consumers)andsellers(firms)

-Homogeneous(Same)Goods

DefinitionsandFormulas

Totalrevenue(TR)ismoneyreceivedbyafirmfromthesaleofgoodsorservices:◦TR=PxQ

Averagerevenue(AR)istotalrevenuedividedbyoutput:◦AR=TR/Q

Marginalrevenueistheadditiontorevenueofsellinganadditionalunitofoutput:◦ΔTR/ΔQ◦whereΔstandsfor“changein”

CalculateQuantity(Output)

Price AverageRevenue

TotalRevenue

MarginalRevenue

0 5 0 0 -

1 5

2 5

3 5

4 5

5 5

6 5

AfirmsellingPlainRavioliisinaperfectlycompetitivemarket,andthepriceofsellingeachravioliisGBP5.

Fillintheblanksfortherestofthetable.

CalculateAfirmsellingPlainRavioliisinaperfectlycompetitivemarket,andthepriceofsellingeachravioliisGBP5.

Fillintheblanksfortherestofthetable.

Quantity(Output)

Price AverageRevenue

TotalRevenue

MarginalRevenue

0 5 0 0 -

1 5 5 5 5

2 5 5 10 5

3 5 5 15 5

4 5 5 20 5

5 5 5 25 5

6 5 5 30 5

ARandMRUnderPerfectCompetition

Price/Revenue

Output0

Thedemandcurveisperfectlyelastic.Why?

-ThefirmmustsellatPasiftheyincreasetheirprice,allconsumerswillbuythesameproductfromotherfirms.Iftheydecreasetheirprice,thefirmwillnotremainprofitableandwillclosedown.

ARandMRUnderPerfectCompetition

D=AR=MR

Price/Revenue

Output0

P=5

Revenueperunit:ARandMR

WhyisARandMRalsohorizontalandequalstodemand?-Asthefirmcannotalterprices,eachadditionalunitproducedissoldatthesameprice.Hence,marginalrevenueisconstantwithincreasingoutput.Becauseofthis,theaveragepricewillalsoremainthesamewhenoutputincreases.

HenceAR=MR=D,andtheareaunderthedemandcurveequatestototalrevenues

HowARandMRRelatestoTR

D=AR=MR

Output0

P=10

Revenueperunit:ARandMR

Output0

TR=100

Q=10

Price/Revenue

Price/Revenue

CanyouplottheTotalRevenuecurve?

HowARandMRRelatestoTR

D=AR=MR

Output0

P=10

Revenueperunit:ARandMR

TR

Output0

Revenueinaggregate:TR

TR=100

Q=10

R=100

Q=10

R=110

Q=11

Price/Revenue

Price/Revenue

RevenuesUnderImperfectCompetition

Underusualcircumstanceswithimperfectcompetition,firmscanchangetheirprices.

Imperfectcompetitionincludesmarketstructureslikemonopoly,oligopoly,monopolisticcompetitionetc.

Whatdoesausualdemandcurvelooklike?

RevenuesUnderImperfectCompetition

D=AR

Output0

Whyisthedemandcurvedownwardsloping?

Price/Revenue

RevenuesUnderImperfectCompetition

D=AR

Output0

Whyisthedemandcurvedownwardsloping?

-Thisisbecauseofthelawofdemand.Whenpricesarehigh,peoplebuyless;whenpricesarelow,peoplebuymore.

Price/Revenue

CalculateMore!Quantity Average

Revenue(P)Total

RevenueMarginalRevenue

0 0 0 -

1 5

2

3

4

5

6

AfirmsellingHomemadeCrabRavioliisinamarketwithimperfectcompetition,andthehighestpriceofbeingabletoselloneravioliisGBP20.

Fillintheblanksfortherestofthetable.

Quantity(Output)

Price TotalRevenue

AverageRevenue

MarginalRevenue

0 22 0 0 -

1 20

2 18

3 16

4 14

5 12

6 10

7 8

CalculateMore!Quantity Average

Revenue(P)Total

RevenueMarginalRevenue

0 0 0 -

1 5 5 5

2 5 10 5

3 5 15 5

4 5 20 5

5 5 25 5

6 5 30 5

Quantity(Output)

Price TotalRevenue

AverageRevenue

MarginalRevenue

0 22 0 0 -

1 20 20 20 20

2 18 36 18 16

3 16 48 16 12

4 14 56 14 8

5 12 60 12 4

6 10 60 10 0

7 8 56 8 -4

AfirmsellingHomemadeCrabRavioliisinamarketwithimperfectcompetition,andthepriceofsellingeachravioliisGBP20.

Fillintheblanksfortherestofthetable.

RevenuesUnderImperfectCompetition

Output0

LetusplottheARandMRcurvesonthesamediagram.

Price/Revenue

RevenuesUnderImperfectCompetition

D=AR

Output0

WhyistheARalsodownwardslopingandequaltoDemand?

-TheDemandCurveissimplythepricegivendifferentlevelsofoutput.IfAR=Pfordifferentlevelsofoutput,thenitmustequaltodemand.

Mathematically:AR=TR/QAR=PxQ/Q(becauseTR=PxQ)AR=P

Price/Revenue

RevenuesUnderImperfectCompetition

D=AR

Output0

WhyistheMRtwiceassteepastheAR?

- Thisisbecausewhenthefirmreducesprice,itneedstodecreaseitforallunitsofoutput.Thismeansthelossinmarginalrevenuewhendecreasingoutputismuchhigherthanthereductioninaveragerevenue.Youcanalsoseethisinthedata.

Price/Revenue

MR

MathematicalProof:https://warwickeconomics.wordpress.com/2015/02/26/why-is-the-slope-of-mr-twice-than-that-of-ar-assuming-that-the-ar-curve-is-linear/

RevenuesUnderImperfectCompetition

Output0

PlottheARandMRcurvesonthisdiagram.

Afterwards,let’salsoplotthetotalrevenuecurvehere.

Price/Revenue

RevenuesUnderImperfectCompetition

TR

Output0

D=AR

Output0MR

Price/Revenue

Price/Revenue

WhyistheTRshapedlikethis?

- MRmeanstheamountofrevenueearnedforthenextunitofoutput.Hence,aslongasMRremainstobeapositivenumber,TRwillincrease.

- TRismaximizedwhenMR=0- Similarly,whenMRbecomesnegative

(i.e.lossofrevenuewhenproducingonemoreoutput)thenTRwilldecrease

ElasticityUnderImperfectCompetition

D=AR

Output0

Elastic

Inelastic

Unitaryelasticity

Perfectly

Elastic=∞

Perfectlyinelastic=0

Price/Revenue

Theupperpartsofthedemand/revenuecurveisPEDelastic;themiddlepartisunitarilyelastic;andthelowerpartsPEDinelastic.(Nottobeconfusedwiththesteepness)

WhatdoImean?

ElasticityUnderImperfectCompetition

D=AR

Output0

Elastic

Inelastic

Unitaryelasticity

Perfectly

Elastic=∞

Perfectlyinelastic=0

Price/Revenue

PED=%ΔQd/%ΔP

Athigherlevelsofthecurve,%changeinquantitygoingfrom1to2is+100%

%changeinpricegoingfrom20to18is-10%

PED=100%/10%=10...Veryelastic!

12

20

18

ElasticityUnderImperfectCompetition

D=AR

Output0

Elastic

Inelastic

Unitaryelasticity

Perfectly

Elastic=∞

Perfectlyinelastic=0

Price/Revenue

PED=%ΔQd/%ΔP

Athigherlevelsofthecurve,%changeinquantitygoingfrom8to9is+12.5%

%changeinpricegoingfrom4to2is-50%

PED=12.5%/50%=0.25...Veryinelastic!

4

2

89

RevenuesUnderImperfectCompetition

TR

Output0

Price/Revenue

Price/Revenue

AsMRistwiceassteepasAR,theoutputwhereMR=0isalsothemiddleofthedemand/revenuecurve.

RememberthetheoryofPED?Italsoapplieshere.

-IfPEDiselasticathigherportionsoftherevenue/demandcurve,adecreaseinpricewillresultinhighertotalrevenues.

-IfPEDisinelasticatlowerportionsoftherevenue/demandcurve,anincreaseinpricewillresultinhighertotalrevenues.

D=AR

Output0

Elastic

Inelastic

Unitaryelasticity

Perfectly

Elastic=∞

Perfectlyinelastic=0

MR

QuickQuestions

- Whatdoesthemarginalrevenuecurveofaperfectlycompetitivemarketlooklike?Why?

- Whatdoestheaveragerevenuecurveofanimperfectlycompetitivemarketlooklike?Why?

- WhatistherelationshipbetweenARandMRinanimperfectlycompetitivemarket?

- Whenistotalrevenuemaximizedinanimperfectlycompetitivemarket?

- Whichpartsofthedemandcurveiselastic,inelasticandunitaryelastic?

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