L1 - Monopolystennek.se/onewebmedia/L1 - Monopoly.pdf · – Sector regulaon • Consump6on...

1

Monopoly

Varian Ch. 14

Slides: www.stennek.se/teaching

[email protected]

OverviewofIO-partofCourse

•  Studyrela6on:Marketstructure=>Marketperformance

– Marketstructure•  Concentra6on•  Informa6on•  Market“rules”(egpricepos6ngvsbargainingvsauc6ons)

– Marketperformance•  Efficiency•  Splitofsurplus

2

OverviewofIO-partofCourse

•  Concentra6on– Monopoly(L1)– Oligopoly(L2)– Bargaining(L3)

•  Informa6on– Auc6ons(L4)– Adverseselec6on(L5)– MoralHazard&IncompleteContracts(L6)

3

4

RecallPerfectCompe66on

5

Recall

SRMC

Q

€

p

The Firm in Competitive Equilibrium

P = MC

6

SRMC

Q

€

p


Profit

Loss

SRAC

7

SRMC

Q

€

p


LRAC

Entry

Exit

8

Q

€ The Market in Competitive Equilibrium

Demand

Minimum LRAC

Entry and exit until p = min LRAC

Entry

Exit

9

Minimum LRAC

Q

€ The Market in Competitive Equilibrium

Demand

Long run supply

10

Recall

•  Perfectcompe66on–  PRICEdeterminedby(average)cost–  QUANTITYdeterminedbydemand(atp=minLRAC)

11

Recall•  Pharmaceu6cals

–  Pricestypicallydifferbetweendifferentcountries•  O\enproducedinoneloca6on,eg.India•  Transporta6oncostso\ensmall

–  Whatcausespricedifferences?Whynotp=c?

•  Telecom–  Pricepercalldifferfordifferentcustomerinsamemarket

•  Customerschoose:“flatrates”vs“pre-paid”–  Whypricedifference?Whycomplexity?

•  Quickanswer–  Ithastodowithalackofcompe66on

12

Monopoly

13

Monopoly•  Defini6on–supplyside

– Onefirmproducingtheproduct– Noclosesubs6tutes–  Entrynotpossible

•  Defini6on–demandside– Many“small”buyers(consumers,smallfirms)

•  Implica6on:Firmcansetpricewithoutthinkingabout– Otherfirms(exis6ngornot)–  Individualconsumers

Samereason:Barrierstoentry

Barrierstoentry•  Legal

–  PatentstoprotectR&D:pharmaceu6cals(subs6tutes?)–  Copyrights:Books(subs6tutes?)–  Sectorregula6on

•  Consump6oncontrol:liquor•  Fiscal:gambling

•  Economiesofscale/marketsize–  Districthea6nginci6es–  Foodretailinginruralareas–  Telecomnetworks

•  Exclusiveaccesstoessen6alresource–  Naturalresource–  Exclusivedistribu6onagreement

•  Networkeffects–  Blocket

14

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)

15

UniformPricing

16

BasicAssump6ons

•  Profitmaximiza6on– Privatelyowned– Noproblemownership-control– Noregula6on

17

BasicAssump6ons

•  Exogenousdata– Technology: c(q)[Alterna6ve:produc6onfunc6on]– Demand: p(q)[Alterna6ve:directdemand]

•  Profit– π(q)=p(q)q–c(q)

18

UniformPricing

•  Decisionproblemo maxqπ(q)=p(q)q–c(q)

•  Firstordercondi6ono p(q)+p’(q)q–c’(q)=0

19

UniformPricing



Valueoflastunit Costoflastunit

20

UniformPricing



21

reducingrevenuesonallinfra-marginalunitsp´(q)*q

Toselloneunitmore,pricemustbelowered,p´(q)

UniformPricing


•  Firstordercondi6ono p(q)+p’(q)q=c’(q)

Marginalrevenue

22

Marginalcost

Loss

UniformPricing

Demand Quan6ty

Price

Δq

Δp

ΔTR≈p*Δq+Δp*q

23

MR(q)=p(q)+p’(q)q<p

ΔTR/Δq≈p+(Δp/Δq)*q

Changeinrevenue,whenproducingonemoreunit

Gain

UniformPricing

Quan6ty

Price Example:LinearDemandp(q)=a–bqMR(q)=p(q)+p’(q)q=(a–bq)–bq=a–2bq

24

a

a/ba/2b

UniformPricing

Quan6ty

Price

MR

MC

DQ

P

25

Characteriza6on:Inverse-Elas6cityRule

26

InverseElas6cityRule

•  Proposi6on1–  Amonopolisthasmoremarketpower,thelesspricesensi9ve

consumersare

•  Def:Marketpower–  Abilitytosetpriceabovemarginalcostwithoutloosingallcustomers–  L=(p–c)/p[Mark-upaspercentageofprice]

•  Def:PriceSensi6vity–  Willingnesstobuysomethingelsewhenpriceisincreased–  Elas6cityofdemand:ε=-(dq/q)/(dp/p)

27

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( )

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

29

Compara6veSta6cs

30

Compara6veSta6cs

•  Proposi6on2– Anincreaseinmarginalcostleadstoareduc6oninquan6tyandanincreaseinprice

•  Simplifica6on– Constantmarginalcost

31

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)

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

Compara6veSta6cs

•  Passoninmonopoly–  Determinedbythecurvatureofdemand

–  Lineardemand(p’’=0)=>pass-on=1/2

34

dpdc

= 12+ p''q

p'( ) ∈ 0,∞( )

Compara6veSta6cs

35

Compara6veSta6cs

•  Proposi6on3– Anincreaseindemanddoesn’tnecessarilyincreaseprice

•  Intui6on–  Ifconsumersbecomemorepricesensi6veatsame6me

•  Proof–  Byexample

•  MC=0

36

Compara6veSta6cs

37

v1H

v1L

v2H

v2L

Quan6ty

€

•  Greenmarket•  Highdemand•  Elas6cdemand

•  Neednotreducepricemuchtosell2ndunit•  Op6malprice=v1L

•  Redmarket•  Lowdemand(Qlowerateveryprice)•  Inelas6cdemand

•  Needreducepricemuchtosell2ndunit•  Op6malprice=v2H>v1L

Compara6veSta6cs

38

v1H

v1L

v2H

v2L

Quan6ty

€





Compara6veSta6cs

39

v1H

v1L

v2H

v2L

Quan6ty

€





Welfare

40

Welfare

•  Proposi6on4– Marketpowerimpliestooli{leproduc6onandconsump6on,fromasocialwelfarepointofview

•  Def:Socialwelfare– Valueofconsump6on(measuredin€)minuscostofproduc6on

41

GCS

Welfare

Quan6ty

Price

42

p

c

GrossConsumerSurplus=Valueofconsump6onin€

Welfare

Quan6ty

Price

43

p

c

Produc6oncost

Welfare

Quan6ty

Price

44

p

c

Neteconomicvaluecreatedbymarketin€W=GCS-C

CS

Welfare

Quan6ty

Price

45

Π

p

c

Distribu6onofsurplusbetween-Consumers(netconsumersurplus)and-Firms(profit)

CS

Welfare

Quan6ty

Price

46

Π

p

c

Note:MarketisnotefficientSocialvalueofONEextraunit=p–c

Compensa6onprinciple

=-p’q>0

CS

Welfare

Quan6ty

Price

47

Π

DWL

p

c

Lossofsocialvaluecomparedtomaximum

CS

Welfare

Quan6ty

Price

48

Π

p

c

Q:Whydoesn’tfirmprodueoneextraunit?

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

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

MonopolyPricing•  Summary

–  Pricenotonlydeterminedbycost.Alsodemandma{ers

– Marketpowerdeterminedbyconsumers’pricesensi6vity

–  Highercostsleadstohigherprice

–  Higherdemanddoesnotnecessarilyleadtohigherprice,ifpricesensi6vityisincreased

–  Thereistooli{leproduc6onandconsump6onundermonopoly

51

AdvancedPricing(PriceDiscrimina6on)

52

Pricing-to-Market(3rdDegreeP.D.)

54

ThirdDegreeP.D.

•  Defini6on– Differentprice(ormark-up)indifferentgeographicalmarkets

•  Verycommon–  Pharmaceu6cals

–  Cars–  andmostotherthings

55

•  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

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

ThirdDegreeP.D.•  ThirddegreeP.D.

•  Uniformpricing

•  Effectonna6onalwelfare–  Increasesconsumerwelfareincountrywithelas6cdemand–  Reducesconsumerwelfareincountrywithinelas6cdemand

59

!!Li =

1ε i qi( )

!!!L =

1ε1s1+ ε

2s2

!!!!!where!!!!!si =qi

q1+ q

2

ThirdDegreeP.D.

•  Effectonglobalwelfare– Nega6ve

•  Inefficientdistribu6onofagivenquan6tyofgoods,MV1≠MV2

– Posi6ve•  But,mayincreaseglobalproduc6on,whichwouldbevaluablesinceP>MC

•  Neteffectcangoeitherway– Examples

60

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

ThirdDegreeP.D.Example2:P.D.badforwelfare

62

CountryA

vA

CountryB

vB

pA=vADWL

pB=vB

ThirdDegreeP.D.Example2:P.D.badforwelfare

63

CountryA

vA

CountryB

vB

pA=vADWL

pB=vB

BanningP.D.=>p=vB,ifCountryBmuchbiggerEfficiencyincreases(noDWLincountryA)

ThirdDegreeP.D.

•  Proposi6on6–  3rddegreeP.D.

•  Reducesglobalwelfareifaggregateoutputisreduced•  Increasesglobalwelfareifweightedsumofoutputsisincreased

•  Proof–  SeeVarian(orblueslides)

•  Assume–  Constantmarginalcost–  Quasi-linearu6lity

64

ThirdDegreeP.D.

65

Considertheeffectofapricereduc6oninonecountry- p0èp1- q0èq1

ThirdDegreeP.D.

66


- Ouraimistomeasurethechangeinu6lityinthiscountry:Δu- WewillfindupperandlowerboundforΔu

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)


Sameistrueforpriceincrease

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)


Sameistrueforpriceincrease

ThirdDegreeP.D.

•  Thus– Considerachangeinpricefromp0top1andtheassociatedchangeinquan6tyΔq.Then:

– ΔUisunder(over)es6matedifwelookatmarketvalueofΔqinold(new)prices

69

!!p1Δq ≤ Δu ≤ p0Δq

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


&'

RearrangeΔW ≤ p0 −c( ) ΔqA +ΔqB

$%

&'

ΔW ≥ pA1 −c( )ΔqA

(−)

+ pB1 −c( )ΔqB

(+)

Effectofinterna6onalpricediscrimina6on(betweencountryAandB)

!!!

pA1 > p0 !!!⇒ !!!!!qA

1 < qA0

pB1 < p0 !!!⇒ !!!!!qB

1 > qB0

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( )



&'



&'


$%

&'


(−)

+ pB1 −c( )ΔqB

(+)


!!!

pA1 > p0 !!!⇒ !!!!!qA

1 < qA0

pB1 < p0 !!!⇒ !!!!!qB

1 > qB0

Ifglobaloutputreduced,welfareisreduced

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( )



&'



&'


$%

&'


(−)

+ pB1 −c( )ΔqB

(+)


!!!

pA1 > p0 !!!⇒ !!!!!qA

1 < qA0

pB1 < p0 !!!⇒ !!!!!qB

1 > qB0

Anincreaseinglobalproduc6onisnotsufficienttoguaranteeincreasedwelfareRecallpA>pB

RamseyPricing(notinVarian)

73

RamseyPricing

•  BasicIdea

–  CompaniesmustearnprofittofinanceR&Dinvestments

–  Cannottaxothermarkets

–  Priceabovecost=>DWL

–  TominimizeDWL=>–  Pricesensi6veconsumersshouldpaylowprice–  Priceinsensi6veconsumersshouldpayhighprice

74

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

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( )⎡⎣ ⎤⎦

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

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⎡⎣ ⎤⎦


∂L∂pi

= −Qi + 1+ µ( ) Qi + pi − c( ) dQi

dpi

⎡

⎣⎢

⎤

⎦⎥ = 0

Recallhowtotakederiva6veswithrespecttolimitsofintegra6on

RamseyPricing

79


∂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( )

RamseyPricing

•  Conclusion–  Markupspropor6onaltodemandelas6city–  Monopolistsetscorrect“rela6veprices”–  Butthelevelistypicallytoohigh

80

Ramsey rulepi − cpi

= 1ε i⋅ µ

1+µ( ) ( µ1+µ <1)

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

Two-PartTariffs(1stDegreeP.D.)

84

Two-PartTariffs•  Examples

•  Telecom(flatrate)–  Highmonthlyfee–  Cheapcalls

•  Amusementparks–  Highentryfee–  Lowpriceperride

•  Smorgasbord–  Highentryfee–  Eatasmuchasyouwant

•  Apple–  Noprofitonsalesofsongs(iTunes)–  HighprofitonsalesofiPods

85

Two-PartTariffs

•  Q:Whydofirmusetwo-parttariffs?•  monthlyfee&pricepercall

86

Two-PartTariffs

•  Simplifica6ons•  Allconsumersiden6cal•  Quasi-linearu6lity•  Constantmarginalcost

87

Two-PartTariffs

•  Two-parttariff•  p=priceperunit•  F=fixedfee(“permonth”)

•  Profit–  π=pq(p)+F–cq(p)

88

Two-PartTariffs

•  Maximumentryfee– 

•  Thus–  π=pq(p)+CS(p)–cq(p)

89

!!F =CS p( ) = q(z)

p

∞

∫ dzp

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

Two-PartTariffs

•  Conclusions– Paretoefficientquan6ty[sincep=c]

– Monopolisttakesthewholesurplus[sinceF=CS(c)]

91

Two-PartTariffs

•  Alterna6vewaytoimplement– Adjust“packagesize”:sellqunitsatpricer

92

r

q

No6ce:Op6malcontracthastwoparts-  Entryfee+usagefee,or-  Quan6ty+price

SecondDegreeP.D.“menupricing”

96

SecondDegreeP.D.

•  Example1– Mobilephonesubscrip6ons

•  Example2– Quan6tydiscounts

•  take3payfor2,or•  Take1payfor1

98

SecondDegreeP.D.GraphicalTreatment

99

SecondDegreeP.D.

•  Assume– Twoconsumers

•  Highdemand•  Lowdemand

– Firmcannottellwhoiswho– Zeromarginalcost

100

SecondDegreeP.D.

101

Quan6ty

DHDL

SecondDegreeP.D.

102

A

B

C

Quan6ty

Monopolist’sfirstbestEfficientquan66es q*Lq*H

Fullrentextrac6on r*L=Ar*H=A+B+C

q*L q*H

SecondDegreeP.D.

103

A

B

C

Quan6ty

ProblemH-consumerswillmimicL:Buyq*LPayACS=B

q*L q*H

SecondDegreeP.D.

104

A

B

C

Quan6tyq*L q*H

Solu6on1–LeaveHwithsurplusSellq*Lq*HOnlychargerL=ArH=A+C

SecondDegreeP.D.

105

A

B

C

Quan6ty

Solu6on2–DistortL’sconsump6onReduc6oninrL=Aissmall(second-ordereffect)IncreaseinrH=A+Cislarge

qL q*H

SecondDegreeP.D.

106

Intui6onReducingqLsomewhatdoesma{ermuchforL(secondordereffect),needonlyreducepriceali{leButforH,thevalueoftheL-packageisreducedalot,sinceitalreadyhastoofewunits.Thus,increasepriceofH-packagealot.

A

B

C

Quan6tyqL q*H

SecondDegreeP.D.

•  Conclusion

– H-consumers•  Efficientquan6ty•  Surplus(tohindermimicking)

–  L-consumers•  Nosurplus•  Consumetooli{le(tomaketheirofferlessa{rac6vetoH)

107

SecondDegreeP.D.

•  Comment

– Menuofp/q-contractscanbeimplementedbyamenuoftwo-parttariffs

– Menusentailquan6tydiscounts(=pricediscrimina6on)

108

SecondDegreeP.D.Themath

109

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

SecondDegreeP.D.

•  Twotypesofconsumers– uL(q)anduH(q)

•  “Singlecrossing”– u’H(q)>u’L(q)forallq– ThisalsoimpliesuH(q)>uL(q)

111

Quasi-linearpreferences

SecondDegreeP.D.

•  Menuofprice/quan6ty-contracts–  (rL,qL)and(rH,qH)

•  Restric6ons– Buyingisvoluntary– Consumerscanchosewhichcontracttheywant

112

SecondDegreeP.D.

•  Individualra6onality– uL(qL)≥rL(IRL)– uH(qH)≥rH(IRH)

113

SecondDegreeP.D.

•  Incen6vecompa6bility

– uL(qL)-rL≥uL(qH)–rH(ICL)– uH(qH)-rH≥uH(qL)-rL(ICH)

114

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

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

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( )

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

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

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

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

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

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

SecondDegreeP.D.

•  Conclusion

– H-consumers•  Efficientquan6ty•  Surplus(tohindermimicking)

–  L-consumers•  Nosurplus•  Consumetooli{le(tomaketheirofferlessa{rac6vetoH)

124

SecondDegreeP.D.

•  Welfare(tenta6ve)

– P/Q-contractsandtwo-parttariffstendtoincreasesocialwelfarerela6vetouniformpricing

– Monopolistcaptureslargershareofsurplus

125

Quality

126

127

Quality•  Trade-off

–  Morecostlytoproduce

–  Customerswillingtopaymore

•  Problem

–  Onlyonequality–  Differentconsumersvaluethequalityincreasedifferently

–  Howdoyoudecide?

•  Intui6vesolu6on

–  Lookatsomeaverageoverconsumers

•  But,no…–  Thatis(unfortunately)notwhatfirmsdo

128

Quality

•  Monopolist’schoiceofquality–  Theinfra-marginalconsumersdonotma{er

•  Theybuythegoodevenifpriceisincreasedorqualityisreducedali{le

–  Themarginalconsumerdecides

•  Marginalconsumer=personwhoisindifferentbetweenbuyingandnot

•  Intui6on:Quality↑⇒WTPmarginalconsumer↑⇔P↑

129

Quality

•  Socialwelfare

–  Averageconsumershoulddecide

•  Inefficiency

–  Under-provision

–  Over-provision

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)

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)

Quality

•  Socialop6mum

132

Socialwelfare


q

∫ − c(q,y)



q

∫ − cy (q,y)

Rewrite

wy (q,y)=1q

py (s,y)ds0

q

∫⎡

⎣⎢

⎤

⎦⎥⋅q − cy (q,y)

Quality

•  Socialop6mum

133

Marginalvalueofincreasedquality

Socialwelfare


q

∫ − c(q,y)



q

∫ − cy (q,y)

Rewrite

wy (q,y)=1q

py (s,y)ds0

q

∫⎡

⎣⎢

⎤

⎦⎥⋅q − cy (q,y)

Quality

•  Socialop6mum

134

Marginalvalueofincreasedquality…......averageoverallunits

Socialwelfare


q

∫ − c(q,y)



q

∫ − cy (q,y)

Rewrite

wy (q,y)=1q

py (s,y)ds0

q

∫⎡

⎣⎢

⎤

⎦⎥⋅q − cy (q,y)

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)

136

Quality

•  Under-provision–Anexample

–  Unitdemand–  Normalgood

•  HighincomepeoplehavehighWTP•  Marginalconsumerhaslowerincomethaninfra-marginalconsumers

–  Quality=normal•  Low-incomepeople(=marginalconsumer)haslowerWTPforqualityimprovementthanhigh-incomepeople(=inframarginalconsumer)

Quality Discrimination

Quality Discrimination

138

Ques6onWhyopencarriagesin3rdclass?

QualityDiscrimina6on

“Itisnotbecauseofthefewthousandfrancswhichwouldhavetobespenttoputaroofoverthethird-classcarriageortoupholsterthethird-classseatsthatsomecompanyorotherhasopencarriageswithwoodenbenches…

Whatthecompanyistryingtodoispreventthepassengerswhocanpaythesecond-classfarefromtravelingthirdclass;

ithitsthepoor,notbecauseitwantstohurtthem,buttofrightentherich…

Anditisagainforthesamereasonthatthecompanies,havingprovedalmostcrueltothethird-classpassengersandmeantothesecond-classones,becomelavishindealingwithfirst-classcustomers.Havingrefusedthepoorwhatisnecessary,theygivetherichwhatissuperfluous.”

JulesDupuit,ca1860.

139

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

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