revenue (curves, calculations & elasticity)
TRANSCRIPT
Revenue(Curves,Calculations&Elasticity)GCEA-LEVEL&IBECONOMICS
VisitusatWeAreQurious.com/Economicsfornotes,pastpapers,tutoringandmore!©2020QuriousEducationLtd.AllRightsReserved.
LessonStructure◦Revenue
◦TotalRevenue,MarginalRevenueandAverageRevenue
◦RevenueCurvesunderPerfectandImperfectCompetition
◦PEDanditsrelationshiptorevenuecurves
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?
-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
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?
VisitUs
Toview/downloadmoreEconomicsresources,visituswiththeseclickablebuttons:
A-Level/IBEconomicsNotes&Questionsby
Topic
A-LevelEconomicsPast-Papers(Edexcel)
A-LevelEconomicsPast-Papers(AQA)