l1 - monopolystennek.se/onewebmedia/l1 - monopoly.pdf · – sector regulaon • consump6on...
TRANSCRIPT
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OverviewofIO-partofCourse
• Studyrela6on:Marketstructure=>Marketperformance
– Marketstructure• Concentra6on• Informa6on• Market“rules”(egpricepos6ngvsbargainingvsauc6ons)
– Marketperformance• Efficiency• Splitofsurplus
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OverviewofIO-partofCourse
• Concentra6on– Monopoly(L1)– Oligopoly(L2)– Bargaining(L3)
• Informa6on– Auc6ons(L4)– Adverseselec6on(L5)– MoralHazard&IncompleteContracts(L6)
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RecallPerfectCompe66on
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5
Recall
SRMC
Q
€
p
The Firm in Competitive Equilibrium
P = MC
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6
SRMC
Q
€
p
The Firm in Competitive Equilibrium
Profit
Loss
SRAC
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7
SRMC
Q
€
p
The Firm in Competitive Equilibrium
LRAC
Entry
Exit
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Q
€ The Market in Competitive Equilibrium
Demand
Minimum LRAC
Entry and exit until p = min LRAC
Entry
Exit
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Minimum LRAC
Q
€ The Market in Competitive Equilibrium
Demand
Long run supply
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Recall
• Perfectcompe66on– PRICEdeterminedby(average)cost– QUANTITYdeterminedbydemand(atp=minLRAC)
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Recall• Pharmaceu6cals
– Pricestypicallydifferbetweendifferentcountries• O\enproducedinoneloca6on,eg.India• Transporta6oncostso\ensmall
– Whatcausespricedifferences?Whynotp=c?
• Telecom– Pricepercalldifferfordifferentcustomerinsamemarket
• Customerschoose:“flatrates”vs“pre-paid”– Whypricedifference?Whycomplexity?
• Quickanswer– Ithastodowithalackofcompe66on
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Monopoly
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Monopoly• Defini6on–supplyside
– Onefirmproducingtheproduct– Noclosesubs6tutes– Entrynotpossible
• Defini6on–demandside– Many“small”buyers(consumers,smallfirms)
• Implica6on:Firmcansetpricewithoutthinkingabout– Otherfirms(exis6ngornot)– Individualconsumers
Samereason:Barrierstoentry
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Barrierstoentry• Legal
– PatentstoprotectR&D:pharmaceu6cals(subs6tutes?)– Copyrights:Books(subs6tutes?)– Sectorregula6on
• Consump6oncontrol:liquor• Fiscal:gambling
• Economiesofscale/marketsize– Districthea6nginci6es– Foodretailinginruralareas– Telecomnetworks
• Exclusiveaccesstoessen6alresource– Naturalresource– Exclusivedistribu6onagreement
• Networkeffects– Blocket
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Agenda• Uniformpricing
– Inverseelas6cityrule– Compara6vesta6cs– Welfare
• AdvancedPricing(Pricediscrimina6on)– Pricing-to-Market(3rddegreep.d)[alsoRamseypricing]
– Two-PartTariffs(1stdegreep.d)– Quan6tyDiscounts&Menus(2nddegreep.d)
• Quality– Uniformquality– Qualitydiscrimina6on(versioning)
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UniformPricing
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BasicAssump6ons
• Profitmaximiza6on– Privatelyowned– Noproblemownership-control– Noregula6on
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BasicAssump6ons
• Exogenousdata– Technology: c(q)[Alterna6ve:produc6onfunc6on]– Demand: p(q)[Alterna6ve:directdemand]
• Profit– π(q)=p(q)q–c(q)
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UniformPricing
• Decisionproblemo maxqπ(q)=p(q)q–c(q)
• Firstordercondi6ono p(q)+p’(q)q–c’(q)=0
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UniformPricing
• Decisionproblemo maxqπ(q)=p(q)q–c(q)
• Firstordercondi6ono p(q)+p’(q)q–c’(q)=0
Valueoflastunit Costoflastunit
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UniformPricing
• Decisionproblemo maxqπ(q)=p(q)q–c(q)
• Firstordercondi6ono p(q)+p’(q)q–c’(q)=0
21
reducingrevenuesonallinfra-marginalunitsp´(q)*q
Toselloneunitmore,pricemustbelowered,p´(q)
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UniformPricing
• Decisionproblemo maxqπ(q)=p(q)q–c(q)
• Firstordercondi6ono p(q)+p’(q)q=c’(q)
Marginalrevenue
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Marginalcost
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Loss
UniformPricing
Demand Quan6ty
Price
Δq
Δp
ΔTR≈p*Δq+Δp*q
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MR(q)=p(q)+p’(q)q<p
ΔTR/Δq≈p+(Δp/Δq)*q
Changeinrevenue,whenproducingonemoreunit
Gain
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UniformPricing
Quan6ty
Price Example:LinearDemandp(q)=a–bqMR(q)=p(q)+p’(q)q=(a–bq)–bq=a–2bq
24
a
a/ba/2b
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UniformPricing
Quan6ty
Price
MR
MC
DQ
P
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Characteriza6on:Inverse-Elas6cityRule
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InverseElas6cityRule
• Proposi6on1– Amonopolisthasmoremarketpower,thelesspricesensi9ve
consumersare
• Def:Marketpower– Abilitytosetpriceabovemarginalcostwithoutloosingallcustomers– L=(p–c)/p[Mark-upaspercentageofprice]
• Def:PriceSensi6vity– Willingnesstobuysomethingelsewhenpriceisincreased– Elas6cityofdemand:ε=-(dq/q)/(dp/p)
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InverseElas6cityRule
• Proof
28
!!!
First!Order!Condition
p q( )+ p ' q( )q− c ' q( ) = 0
Rewrite
p q( )− c ' q( ) = −p ' q( )q ⇔p q( )− c ' q( )
p q( ) = −p ' q( )qp q( )
Thus
L =1
ε q( )
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SecondOrderCondi6on
• Secondordercondi6on: π’’(q)=MR’(q)–MC’(q)<0
– Marginalcostincreasesfasterthanmarginalrevenue[MCcutsMRfrombelow]
– Marginalrevenue[MR’=2p’(q)+p’’(q)q]
• Demandshouldbeconcave,ornotooconvex
– Marginalcost[MC’=c’’]
• Marginalcostshouldbeincreasing,ornotbefallingtooquickly
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Compara6veSta6cs
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Compara6veSta6cs
• Proposi6on2– Anincreaseinmarginalcostleadstoareduc6oninquan6tyandanincreaseinprice
• Simplifica6on– Constantmarginalcost
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Compara6veSta6cs
• Proof:reducedquan6ty
32
!!!
First!order!condition
p q( )+ p ' q( )q−c = 0
Differentiate
2p '+ p ''q( )dq−dc = 0
Rearrange
2p '+ p ''q( )dq = dcdqdc
=1
2p '+ p ''q< 0
where!sign!is!due!to!sosc!(c''!=!0)
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Compara6veSta6cs
• Proof:increasedprice
33
!!!
Demand
p = p q( )
Differentiate
dp = p 'dq
Rearrange
dpdc
= p 'dqdc
> 0
where!sign!is!due!to!downward!sloping!demand
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Compara6veSta6cs
• Passoninmonopoly– Determinedbythecurvatureofdemand
– Lineardemand(p’’=0)=>pass-on=1/2
34
dpdc
= 12+ p''q
p'( ) ∈ 0,∞( )
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Compara6veSta6cs
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Compara6veSta6cs
• Proposi6on3– Anincreaseindemanddoesn’tnecessarilyincreaseprice
• Intui6on– Ifconsumersbecomemorepricesensi6veatsame6me
• Proof– Byexample
• MC=0
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Compara6veSta6cs
37
v1H
v1L
v2H
v2L
Quan6ty
€
• Greenmarket• Highdemand• Elas6cdemand
• Neednotreducepricemuchtosell2ndunit• Op6malprice=v1L
• Redmarket• Lowdemand(Qlowerateveryprice)• Inelas6cdemand
• Needreducepricemuchtosell2ndunit• Op6malprice=v2H>v1L
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Compara6veSta6cs
38
v1H
v1L
v2H
v2L
Quan6ty
€
• Greenmarket• Highdemand• Elas6cdemand
• Neednotreducepricemuchtosell2ndunit• Op6malprice=v1L
• Redmarket• Lowdemand(Qlowerateveryprice)• Inelas6cdemand
• Needreducepricemuchtosell2ndunit• Op6malprice=v2H>v1L
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Compara6veSta6cs
39
v1H
v1L
v2H
v2L
Quan6ty
€
• Greenmarket• Highdemand• Elas6cdemand
• Neednotreducepricemuchtosell2ndunit• Op6malprice=v1L
• Redmarket• Lowdemand(Qlowerateveryprice)• Inelas6cdemand
• Needreducepricemuchtosell2ndunit• Op6malprice=v2H>v1L
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Welfare
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Welfare
• Proposi6on4– Marketpowerimpliestooli{leproduc6onandconsump6on,fromasocialwelfarepointofview
• Def:Socialwelfare– Valueofconsump6on(measuredin€)minuscostofproduc6on
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GCS
Welfare
Quan6ty
Price
42
p
c
GrossConsumerSurplus=Valueofconsump6onin€
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Welfare
Quan6ty
Price
43
p
c
Produc6oncost
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Welfare
Quan6ty
Price
44
p
c
Neteconomicvaluecreatedbymarketin€W=GCS-C
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CS
Welfare
Quan6ty
Price
45
Π
p
c
Distribu6onofsurplusbetween-Consumers(netconsumersurplus)and-Firms(profit)
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CS
Welfare
Quan6ty
Price
46
Π
p
c
Note:MarketisnotefficientSocialvalueofONEextraunit=p–c
Compensa6onprinciple
=-p’q>0
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CS
Welfare
Quan6ty
Price
47
Π
DWL
p
c
Lossofsocialvaluecomparedtomaximum
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CS
Welfare
Quan6ty
Price
48
Π
p
c
Q:Whydoesn’tfirmprodueoneextraunit?
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WelfareFormalproofusingquasi-linearu6lity
• Welfare
– Quasi-linearu6lity:U=u(q)+z,whereu’>0,u’’<0
– Demand:u’(q)=p
– Costofproduc6on:c(q)
– W(q)=u(q)–c(q)
• Note– Quasilinearity=>u6litymeasuredinmonetaryunits– Welfare=sumofu6lityandprofit(bothmeasuredinmoney)
49
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Welfare
50
• Equilibrium
– Monopolist’sFOC:u’(qm)+u’’(qm)qm–c’(qm)=0
– Hence:u’(qm)–c’(qm)=-u’’(qm)qm
• Welfareinequilibrium
– W(q)=u(q)–c(q)
– W’(q)=u’(q)–c’(q)
– W’(qm)=u’(qm)–c’(qm)=-u’’(qm)qm>0
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MonopolyPricing• Summary
– Pricenotonlydeterminedbycost.Alsodemandma{ers
– Marketpowerdeterminedbyconsumers’pricesensi6vity
– Highercostsleadstohigherprice
– Higherdemanddoesnotnecessarilyleadtohigherprice,ifpricesensi6vityisincreased
– Thereistooli{leproduc6onandconsump6onundermonopoly
51
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AdvancedPricing(PriceDiscrimina6on)
52
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Pricing-to-Market(3rdDegreeP.D.)
54
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ThirdDegreeP.D.
• Defini6on– Differentprice(ormark-up)indifferentgeographicalmarkets
• Verycommon– Pharmaceu6cals
– Cars– andmostotherthings
55
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• Decisionproblemwith2markets– maxq1,q2π(q1,q2)=p1(q1)q1+p2(q2)q2–c(q1+q2)
• Firstordercondi6ons– pi(qi)+pi’(qi)qi–c=0
• Characteriza6on–
!!Li =
1ε i qi( )
57
ThirdDegreeP.D.
Proposi1on5Pricesdifferbetweencountriesifconsumersdifferinprice-sensi6vity
Now,let’scompare3rddegreeP.Dwithuniformpricing
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ThirdDegreeP.D.
• Uniformpricing(workwithdirectdemand)– maxpπ(p)=[q1(p)+q2(p)](p–c)
• Firstordercondi6on– (q1’+q2’)(p-c)+(q1+q2)=0
• Characteriza6on–
58
!!!L =
1ε1s1+ ε
2s2
!!!!!where!!!!!si =qi
q1+ q
2
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ThirdDegreeP.D.• ThirddegreeP.D.
• Uniformpricing
• Effectonna6onalwelfare– Increasesconsumerwelfareincountrywithelas6cdemand– Reducesconsumerwelfareincountrywithinelas6cdemand
59
!!Li =
1ε i qi( )
!!!L =
1ε1s1+ ε
2s2
!!!!!where!!!!!si =qi
q1+ q
2
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ThirdDegreeP.D.
• Effectonglobalwelfare– Nega6ve
• Inefficientdistribu6onofagivenquan6tyofgoods,MV1≠MV2
– Posi6ve• But,mayincreaseglobalproduc6on,whichwouldbevaluablesinceP>MC
• Neteffectcangoeitherway– Examples
60
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ThirdDegreeP.D.Example1:P.D.goodforwelfare
• Pricediscrimina6on– pA=vA=>qA=xA– pB=vB=>qB=xB
• Uniformpricing– p=vA=>qA=xA– p=vA=>qB=0
• Pricediscrimina6on
– Increasesoutput– Increaseswelfare
(firmprofits)
61
DemandCountryA
DemandCountryB
vA
vB
xA xB
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ThirdDegreeP.D.Example2:P.D.badforwelfare
62
CountryA
vA
CountryB
vB
pA=vADWL
pB=vB
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ThirdDegreeP.D.Example2:P.D.badforwelfare
63
CountryA
vA
CountryB
vB
pA=vADWL
pB=vB
BanningP.D.=>p=vB,ifCountryBmuchbiggerEfficiencyincreases(noDWLincountryA)
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ThirdDegreeP.D.
• Proposi6on6– 3rddegreeP.D.
• Reducesglobalwelfareifaggregateoutputisreduced• Increasesglobalwelfareifweightedsumofoutputsisincreased
• Proof– SeeVarian(orblueslides)
• Assume– Constantmarginalcost– Quasi-linearu6lity
64
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ThirdDegreeP.D.
65
Considertheeffectofapricereduc6oninonecountry- p0èp1- q0èq1
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ThirdDegreeP.D.
66
Considertheeffectofapricereduc6oninonecountry- p0èp1- q0èq1
- Ouraimistomeasurethechangeinu6lityinthiscountry:Δu- WewillfindupperandlowerboundforΔu
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ThirdDegreeP.D.
67
!!!
Upper!BoundConcavity!of!utility
u q1( ) ≤ u q0( )+u ' q0( ) q1 − q0( )Rearrange
u q1( )−u q0( ) ≤ u ' q0( ) q1 − q0( )Utility!max!(p=u')
u q1( )−u q0( ) ≤ p0 q1 − q0( )Δu ≤ p0Δq
q1q0
u(q0)
u(q1)
Considertheeffectofapricereduc6oninonecountry- p0èp1- q0èq1
Sameistrueforpriceincrease
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ThirdDegreeP.D.
68
!!!
Lower!BoundConcavity!of!utility
u q0( ) ≤ u q1( )+u ' q1( ) q0 − q1( )Rearrange
u q1( )−u q0( ) ≥ u ' q1( ) q1 − q0( )Utility!max
u q1( )−u q0( ) ≥ p1 q1 − q0( )Δu ≥ p1Δq
q1q0
u(q0)
u(q1)
Considertheeffectofapricereduc6oninonecountry- p0èp1- q0èq1
Sameistrueforpriceincrease
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ThirdDegreeP.D.
• Thus– Considerachangeinpricefromp0top1andtheassociatedchangeinquan6tyΔq.Then:
– ΔUisunder(over)es6matedifwelookatmarketvalueofΔqinold(new)prices
69
!!p1Δq ≤ Δu ≤ p0Δq
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ThirdDegreeP.D.
70!!!
Global!welfareW qA
0 ,qB0( ) =uA qA
0( )+uB qB0( )−c qA
0 +qB0( )
W qA1 ,qB
1( ) =uA qA1( )+uB qB
1( )−c qA1 +qB
1( )
ConcavityΔW ≤ p0ΔqA + p
0ΔqB −c ΔqA +ΔqB$%
&'
ΔW ≥ pA1ΔqA + pB
1ΔqB −c ΔqA +ΔqB$%
&'
RearrangeΔW ≤ p0 −c( ) ΔqA +ΔqB
$%
&'
ΔW ≥ pA1 −c( )ΔqA
(−)
+ pB1 −c( )ΔqB
(+)
Effectofinterna6onalpricediscrimina6on(betweencountryAandB)
!!!
pA1 > p0 !!!⇒ !!!!!qA
1 < qA0
pB1 < p0 !!!⇒ !!!!!qB
1 > qB0
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ThirdDegreeP.D.
71!!!
Global!welfareW qA
0 ,qB0( ) =uA qA
0( )+uB qB0( )−c qA
0 +qB0( )
W qA1 ,qB
1( ) =uA qA1( )+uB qB
1( )−c qA1 +qB
1( )
ConcavityΔW ≤ p0ΔqA + p
0ΔqB −c ΔqA +ΔqB$%
&'
ΔW ≥ pA1ΔqA + pB
1ΔqB −c ΔqA +ΔqB$%
&'
RearrangeΔW ≤ p0 −c( ) ΔqA +ΔqB
$%
&'
ΔW ≥ pA1 −c( )ΔqA
(−)
+ pB1 −c( )ΔqB
(+)
Effectofinterna6onalpricediscrimina6on(betweencountryAandB)
!!!
pA1 > p0 !!!⇒ !!!!!qA
1 < qA0
pB1 < p0 !!!⇒ !!!!!qB
1 > qB0
Ifglobaloutputreduced,welfareisreduced
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ThirdDegreeP.D.
72!!!
Global!welfareW qA
0 ,qB0( ) =uA qA
0( )+uB qB0( )−c qA
0 +qB0( )
W qA1 ,qB
1( ) =uA qA1( )+uB qB
1( )−c qA1 +qB
1( )
ConcavityΔW ≤ p0ΔqA + p
0ΔqB −c ΔqA +ΔqB$%
&'
ΔW ≥ pA1ΔqA + pB
1ΔqB −c ΔqA +ΔqB$%
&'
RearrangeΔW ≤ p0 −c( ) ΔqA +ΔqB
$%
&'
ΔW ≥ pA1 −c( )ΔqA
(−)
+ pB1 −c( )ΔqB
(+)
Effectofinterna6onalpricediscrimina6on(betweencountryAandB)
!!!
pA1 > p0 !!!⇒ !!!!!qA
1 < qA0
pB1 < p0 !!!⇒ !!!!!qB
1 > qB0
Anincreaseinglobalproduc6onisnotsufficienttoguaranteeincreasedwelfareRecallpA>pB
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RamseyPricing(notinVarian)
73
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RamseyPricing
• BasicIdea
– CompaniesmustearnprofittofinanceR&Dinvestments
– Cannottaxothermarkets
– Priceabovecost=>DWL
– TominimizeDWL=>– Pricesensi6veconsumersshouldpaylowprice– Priceinsensi6veconsumersshouldpayhighprice
74
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RamseyPricing• Aim:Maximizeglobalwelfare
(2countries)
75
W = CS +π∑= QA z( )dz
pA
∞
∫ + QB z( )dzpB
∞
∫ + pA − c( ) ⋅QA pA( ) + pB − c( ) ⋅QB pB( )⎡⎣ ⎤⎦
QA(p)
p
Q
pA
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RamseyPricing
• Aim:Maximizeglobalconsumersurplus(2countries)
• Constraint:Firmearnssufficientprofit
76
!π = pA − c( )QA pA( ) + pB − c( )QB pB( )
W = QA z( )dzpA
∞
∫ + QB z( )dzpB
∞
∫ + pA − c( ) ⋅QA pA( ) + pB − c( ) ⋅QB pB( )⎡⎣ ⎤⎦
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RamseyPricing
77
Lagrangian
L = QA z( )dzpA
∞
∫ + QB z( )dzpB
∞
∫ + pA − c( ) ⋅QA pA( ) + pB − c( ) ⋅QB pB( )⎡⎣ ⎤⎦ −
+ µ pA − c( )QA pA( ) + pB − c( )QB pB( )− !π⎡⎣ ⎤⎦
First order condition
∂L∂pi
= −Qi + 1+ µ( ) Qi + pi − c( ) dQi
dpi
⎡
⎣⎢
⎤
⎦⎥ = 0
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RamseyPricing
78
Lagrangian
L = QA z( )dzpA
∞
∫ + QB z( )dzpB
∞
∫ + pA − c( ) ⋅QA pA( ) + pB − c( ) ⋅QB pB( )⎡⎣ ⎤⎦ −
+ µ pA − c( )QA pA( ) + pB − c( )QB pB( )− !π⎡⎣ ⎤⎦
First order condition
∂L∂pi
= −Qi + 1+ µ( ) Qi + pi − c( ) dQi
dpi
⎡
⎣⎢
⎤
⎦⎥ = 0
Recallhowtotakederiva6veswithrespecttolimitsofintegra6on
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RamseyPricing
79
First order condition
∂L∂pi
= −Qi + 1+ µ( ) Qi + pi − c( ) dQi
dpi
⎡
⎣⎢
⎤
⎦⎥ = 0
Rewrite
−1+ 1+ µ( ) 1+ pi − cpi
⎛⎝⎜
⎞⎠⎟dQi
dpipiQi
⎡
⎣⎢
⎤
⎦⎥ = 0
pi − cpi
= − 1dQi
dpipiQi
⋅ µ1+ µ
pi − cpi
= 1ε i⋅ µ
1+µ( )
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RamseyPricing
• Conclusion– Markupspropor6onaltodemandelas6city– Monopolistsetscorrect“rela6veprices”– Butthelevelistypicallytoohigh
80
Ramsey rulepi − cpi
= 1ε i⋅ µ
1+µ( ) ( µ1+µ <1)
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ThirdDegreeP.D.
• Are price differences good?– Not necessarily, but– Yes, if output expanded a lot– Yes, if necessary to finance R&D
(Ramesey pricing)– Yes, can be fair
83
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Two-PartTariffs(1stDegreeP.D.)
84
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Two-PartTariffs• Examples
• Telecom(flatrate)– Highmonthlyfee– Cheapcalls
• Amusementparks– Highentryfee– Lowpriceperride
• Smorgasbord– Highentryfee– Eatasmuchasyouwant
• Apple– Noprofitonsalesofsongs(iTunes)– HighprofitonsalesofiPods
85
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Two-PartTariffs
• Q:Whydofirmusetwo-parttariffs?• monthlyfee&pricepercall
86
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Two-PartTariffs
• Simplifica6ons• Allconsumersiden6cal• Quasi-linearu6lity• Constantmarginalcost
87
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Two-PartTariffs
• Two-parttariff• p=priceperunit• F=fixedfee(“permonth”)
• Profit– π=pq(p)+F–cq(p)
88
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Two-PartTariffs
• Maximumentryfee–
• Thus– π=pq(p)+CS(p)–cq(p)
89
!!F =CS p( ) = q(z)
p
∞
∫ dzp
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Two-PartTariffs
• Profit–
• Firstordercondi6on–
90
!!
π p p( ) = q p( )+ p ⋅q' p( )+CS ' p( )− c ⋅q' p( )
π p p( ) = q+ p ⋅q'−q− c ⋅q'
π p p( ) = p− c⎡⎣ ⎤⎦q' p( ) ⇒ p = c
!π p( ) = p ⋅q p( )+CS p( )− c ⋅q p( )
p
q
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Two-PartTariffs
• Conclusions– Paretoefficientquan6ty[sincep=c]
– Monopolisttakesthewholesurplus[sinceF=CS(c)]
91
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Two-PartTariffs
• Alterna6vewaytoimplement– Adjust“packagesize”:sellqunitsatpricer
92
r
q
No6ce:Op6malcontracthastwoparts- Entryfee+usagefee,or- Quan6ty+price
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SecondDegreeP.D.“menupricing”
96
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SecondDegreeP.D.
• Example1– Mobilephonesubscrip6ons
• Example2– Quan6tydiscounts
• take3payfor2,or• Take1payfor1
98
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SecondDegreeP.D.GraphicalTreatment
99
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SecondDegreeP.D.
• Assume– Twoconsumers
• Highdemand• Lowdemand
– Firmcannottellwhoiswho– Zeromarginalcost
100
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SecondDegreeP.D.
101
Quan6ty
DHDL
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SecondDegreeP.D.
102
A
B
C
Quan6ty
Monopolist’sfirstbestEfficientquan66es q*Lq*H
Fullrentextrac6on r*L=Ar*H=A+B+C
q*L q*H
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SecondDegreeP.D.
103
A
B
C
Quan6ty
ProblemH-consumerswillmimicL:Buyq*LPayACS=B
q*L q*H
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SecondDegreeP.D.
104
A
B
C
Quan6tyq*L q*H
Solu6on1–LeaveHwithsurplusSellq*Lq*HOnlychargerL=ArH=A+C
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SecondDegreeP.D.
105
A
B
C
Quan6ty
Solu6on2–DistortL’sconsump6onReduc6oninrL=Aissmall(second-ordereffect)IncreaseinrH=A+Cislarge
qL q*H
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SecondDegreeP.D.
106
Intui6onReducingqLsomewhatdoesma{ermuchforL(secondordereffect),needonlyreducepriceali{leButforH,thevalueoftheL-packageisreducedalot,sinceitalreadyhastoofewunits.Thus,increasepriceofH-packagealot.
A
B
C
Quan6tyqL q*H
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SecondDegreeP.D.
• Conclusion
– H-consumers• Efficientquan6ty• Surplus(tohindermimicking)
– L-consumers• Nosurplus• Consumetooli{le(tomaketheirofferlessa{rac6vetoH)
107
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SecondDegreeP.D.
• Comment
– Menuofp/q-contractscanbeimplementedbyamenuoftwo-parttariffs
– Menusentailquan6tydiscounts(=pricediscrimina6on)
108
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SecondDegreeP.D.Themath
109
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SecondDegreeP.D.
• Assumequasi-linearpreferences– U6lity:U(q,y)=u(q)+y– Budget:I=r*q+y– Subs6tute:U(q,I–r*q)=I+u(q)–r*q
110
U6litymeasuredinmonetaryterms-u(q)=WTPforqunitsofthegood
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SecondDegreeP.D.
• Twotypesofconsumers– uL(q)anduH(q)
• “Singlecrossing”– u’H(q)>u’L(q)forallq– ThisalsoimpliesuH(q)>uL(q)
111
Quasi-linearpreferences
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SecondDegreeP.D.
• Menuofprice/quan6ty-contracts– (rL,qL)and(rH,qH)
• Restric6ons– Buyingisvoluntary– Consumerscanchosewhichcontracttheywant
112
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SecondDegreeP.D.
• Individualra6onality– uL(qL)≥rL(IRL)– uH(qH)≥rH(IRH)
113
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SecondDegreeP.D.
• Incen6vecompa6bility
– uL(qL)-rL≥uL(qH)–rH(ICL)– uH(qH)-rH≥uH(qL)-rL(ICH)
114
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SecondDegreeP.D.
• ConsumerL
– rL≤uL(qL)(IRL)
– rL≤uL(qL)–uL(qH)+rH(ICL)
• ConsumerH
– rH≤uH(qH)(IRH)
– rH≤uH(qH)–uH(qL)+rL(ICH)
115
• Claim1
– Exactlyoneconstraintbindsforeachtype
• Proof
• WantrLtobehigh
• IncreasingrLmakesICHeasiertosa6sfy
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SecondDegreeP.D.
116
• Claim2
– ICHbinds
• Proof
• Assumeopposite(IRHbinds)
• rH=uH(qH)
• ConsiderICH• uH(qH)-rH≥uH(qL)-rL
• 0≥uH(qL)–rL
• uH(qL)≤rL
• SinceuL(q)<uH(q)
• uL(qL)<rL
• ContradictsIRL
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SecondDegreeP.D.
117
Claim3IRL binds
ProofAssumeopposite(ICL binds)
uL qL( )−uL qH( ) = rL − rH
RecallICH
uH qL( )−uH qH( ) = rL − rH
Combine
uL qL( )−uL qH( ) =uH qL( )−uH qH( )uL' z( )
qH
qL∫ dz = uH' z( )
qH
qL∫ dz violatinguL' z( ) <uH' z( )
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SecondDegreeP.D.
• Conclusions• rL=uL(qL)(IRL)• rH–rL=uH(qH)-uH(qL)(ICH)
• Inwords– Low-demandconsumerschargedwillingness-to-pay– High-demandconsumerschargednottomimic
• Note– TheextrapriceforqH(rela6vetoqL)isH’svalua6onoftheextraunits
118
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SecondDegreeP.D.
• Note:Hgetsasurplus• Proof:
– RecallICH• uH(qH)–rH=uH(qL)–rL
– UseIRL:rL=uL(qL)• uH(qH)–rH=uH(qL)–uL(qL)>0
119
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SecondDegreeP.D.
• Thus• uL(qL)-rL=0(IRL)• uH(qH)–rH=uH(qL)–uL(qL)>0(ICH)
• Inwords– Learnsnosurplus
– Hearnsasurplus(“informa6onrent”)
– Informa6onrentisdeterminedbyqL
• AhighqLincreasesH’sincen6vetomimicL
120
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SecondDegreeP.D.
• Monopolist’sdecisionproblem– maxrL,qL,rH,qHπ=[rL–cqL]+[rH–cqH]
– subjectto• rL=uL(qL)(IRL)• rH=uH(qH)-uH(qL)+rL(ICH)
121
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SecondDegreeP.D.
122
• Monopolist’sdecisionproblem– maxrL,qL,rH,qHπ=[rL–cqL]+[rH–cqH]
– subjectto• rL=uL(qL)(IRL)• rH=uH(qH)-uH(qL)+rL(ICH)
• Subs6tute– maxqL,qHπ=[uL(qL)–cqL]+[uH(qH)–cqH]-[uH(qL)-uL(qL)]
SocialWelfareH’sInforma6onrent
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SecondDegreeP.D.
123
Hconsumesefficientquan1ty
Lconsumestooli;leTomakecontractlessa{rac6vetoH
>0
• Monopolist’sdecisionproblem– maxqL,qHπ=[uL(qL)–cqL]+[uH(qH)–cqH]-[uH(qL)-uL(qL)]
• Firstordercondi6ons(qLandqH)– u’H(qH)–c=0
– u’L(qL)–c–[u’H(qL)-u’L(qL)]=0
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SecondDegreeP.D.
• Conclusion
– H-consumers• Efficientquan6ty• Surplus(tohindermimicking)
– L-consumers• Nosurplus• Consumetooli{le(tomaketheirofferlessa{rac6vetoH)
124
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SecondDegreeP.D.
• Welfare(tenta6ve)
– P/Q-contractsandtwo-parttariffstendtoincreasesocialwelfarerela6vetouniformpricing
– Monopolistcaptureslargershareofsurplus
125
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Quality
126
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127
Quality• Trade-off
– Morecostlytoproduce
– Customerswillingtopaymore
• Problem
– Onlyonequality– Differentconsumersvaluethequalityincreasedifferently
– Howdoyoudecide?
• Intui6vesolu6on
– Lookatsomeaverageoverconsumers
• But,no…– Thatis(unfortunately)notwhatfirmsdo
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128
Quality
• Monopolist’schoiceofquality– Theinfra-marginalconsumersdonotma{er
• Theybuythegoodevenifpriceisincreasedorqualityisreducedali{le
– Themarginalconsumerdecides
• Marginalconsumer=personwhoisindifferentbetweenbuyingandnot
• Intui6on:Quality↑⇒WTPmarginalconsumer↑⇔P↑
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129
Quality
• Socialwelfare
– Averageconsumershoulddecide
• Inefficiency
– Under-provision
– Over-provision
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Quality• Consumeru6lity
– Quasi-linear:U=u(q,y)+z• q=quan6ty;y=quality;z=othergoods
• Demand– p=p(q,y)=u’(q,y)
• Grossconsumersurplus–
130
!!u(q,y)= p(s,y)ds
0
q
∫q
p(q,y)
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Quality
• Socialop6mum
131
Socialwelfare
w(q,y)=u(q,y)− c(q,y)= p(s,y)ds0
q
∫ − c(q,y)
Marginalvalueofquality
wy (q,y)= py (s,y)ds0
q
∫ − cy (q,y)
Rewrite
wy (q,y)=1q
py (s,y)ds0
q
∫⎡
⎣⎢
⎤
⎦⎥⋅q − cy (q,y)
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Quality
• Socialop6mum
132
Socialwelfare
w(q,y)=u(q,y)− c(q,y)= p(s,y)ds0
q
∫ − c(q,y)
Marginalvalueofquality
wy (q,y)= py (s,y)ds0
q
∫ − cy (q,y)
Rewrite
wy (q,y)=1q
py (s,y)ds0
q
∫⎡
⎣⎢
⎤
⎦⎥⋅q − cy (q,y)
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Quality
• Socialop6mum
133
Marginalvalueofincreasedquality
Socialwelfare
w(q,y)=u(q,y)− c(q,y)= p(s,y)ds0
q
∫ − c(q,y)
Marginalvalueofquality
wy (q,y)= py (s,y)ds0
q
∫ − cy (q,y)
Rewrite
wy (q,y)=1q
py (s,y)ds0
q
∫⎡
⎣⎢
⎤
⎦⎥⋅q − cy (q,y)
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Quality
• Socialop6mum
134
Marginalvalueofincreasedquality…......averageoverallunits
Socialwelfare
w(q,y)=u(q,y)− c(q,y)= p(s,y)ds0
q
∫ − c(q,y)
Marginalvalueofquality
wy (q,y)= py (s,y)ds0
q
∫ − cy (q,y)
Rewrite
wy (q,y)=1q
py (s,y)ds0
q
∫⎡
⎣⎢
⎤
⎦⎥⋅q − cy (q,y)
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Quality
• Monopoly
135
Marginalvalueofincreasedquality…....oflastunit
Profitπ (q,y)= p(q,y)⋅q− c(q,y)
FOCforqualityπ y (q,y)= py (q,y)⋅q− cy (q,y)
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Quality
• Under-provision–Anexample
– Unitdemand– Normalgood
• HighincomepeoplehavehighWTP• Marginalconsumerhaslowerincomethaninfra-marginalconsumers
– Quality=normal• Low-incomepeople(=marginalconsumer)haslowerWTPforqualityimprovementthanhigh-incomepeople(=inframarginalconsumer)
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Quality Discrimination
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Quality Discrimination
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Ques6onWhyopencarriagesin3rdclass?
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QualityDiscrimina6on
“Itisnotbecauseofthefewthousandfrancswhichwouldhavetobespenttoputaroofoverthethird-classcarriageortoupholsterthethird-classseatsthatsomecompanyorotherhasopencarriageswithwoodenbenches…
Whatthecompanyistryingtodoispreventthepassengerswhocanpaythesecond-classfarefromtravelingthirdclass;
ithitsthepoor,notbecauseitwantstohurtthem,buttofrightentherich…
Anditisagainforthesamereasonthatthecompanies,havingprovedalmostcrueltothethird-classpassengersandmeantothesecond-classones,becomelavishindealingwithfirst-classcustomers.Havingrefusedthepoorwhatisnecessary,theygivetherichwhatissuperfluous.”
JulesDupuit,ca1860.
139
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Adverse Selection and Screening • Telecom pricing
– Menu of two-part tariffs
• Software – Disable features = quality discrimination
• Insurance markets – Deductibles: Only those who know they have low
risk take them, and get lower price on the risk they sell
• Credit markets – Entrepreneurs risking their own fortunes get better
price
140