Bilateral Market Power & Bargaining

1

Bilateral Market Power & Bargaining

Johan Stennek

Don’tneedtoknowappendixesinlecturenotes

BilateralMarketPowerExample:FoodRetailing

4

Food Retailing •  Food retailers are huge

!

The!world’s!largest!food!retailers!in!2003!

Company! Food!Sales!(US$mn)!

Wal$Mart( 121(566(

Carrefour( 77(330(

Ahold( 72(414(

Tesco( 40(907(

Kroger( 39(320(

Rewe( 36(483(

Aldi( 36(189(

Ito$Yokado( 35(812(

Metro(Group(ITM( 34(700((

½ Swedish GDP

5

Food Retailing •  Retail markets are highly concentrated

Tabell&1a.&Dagligvarukedjornas&andel&av&den&svenska&marknaden&Kedja& Butiker&

(antal)&Butiksyta&(kvm)&

Omsättning&(miljarder&kr)&

Axfood& 803&(24%)&

625&855&(18%)&

34,6&&&&&&&&&(18%)&

Bergendahls& 229&(7%)&

328&196&(10%)&

13,6&(7%)&

Coop& 730&(22%)&

983&255&(29%)&

41,4&(21%)&

ICA& 1&379&(41%)&

1&240&602&(36%)&

96,6&(50%)&

Lidl& 146&(4%)&

170&767&(5%)&

5,2&&&&&&&&&(3%)&

Netto& 105&(3%)&

70&603&(2%)&

3,0&(2%)&

&

6

Food Retailing

•  Food manufacturers – Some are huge:

•  Kraft Food, Nestle, Scan •  Annual sales tenth of billions of Euros

– Some are tiny: •  local cheese

7

Food Retailing •  Mutual dependence

– Some brands = Must have •  ICA “must” sell Coke •  Otherwise families would shop at Coop

– Some retailers = Must channel •  Coke “must” sell via ICA to be active in Sweden •  Probably large share of Coke’s sales in Sweden

– Both would lose if ICA would not sell Coke

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Food Retailing •  Mutual dependence

– Manufacturers cannot dictate wholesale prices – Retailers cannot dictate wholesale prices

•  Thus – They have to negotiate and agree

•  In particular – Also retailers have market power

= buyer power

9

Food Retailing •  Large retailers pay lower prices

(= more buyer power) Retailer( Market(Share(

(CC#Table#5:3,#p.#44)#

Price(

(CC#Table#5,#p.#435)#

Tesco# 24.6# 100.0#

Sainsbury# 20.7# 101.6#

Asda# 13.4# 102.3#

Somerfield# 8.5# 103.0#

Safeway# 12.5# 103.1#

Morrison# 4.3# 104.6#

Iceland# 0.1# 105.3#

Waitrose# 3.3# 109.4#

Booth# 0.1# 109.5#

Netto# 0.5# 110.1#

Budgens# 0.4# 111.1#

#

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Food Retailing

•  Questions – How analyze bargaining in intermediate goods

markets?

– Why do large buyers get better prices?

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Other examples

•  Labor markets – Vårdförbundet vs Landsting

•  Relation-specific investments – Car manufacturers vs producers of parts

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Bilateral Monopoly

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BilateralMonopoly

•  Bilateral monopoly

–  One Seller: MC(q) = inverse supply if price taker

–  One Buyer: MV(q) = inverse demand if price taker

q

€

MC(q)

MV(q)

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Bilateral Monopoly Intuitive Analysis

•  Efficient quantity – Complete information – Maximize the surplus

to be shared

q

€

MC(q)

MV(q) q*

S*

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Bilateral Monopoly Intuitive Analysis

•  Efficient quantity – Complete information – Maximize the surplus

to be shared

q

€

MC(q)

MV(q) q*

S*

Efficiency from the point of view of the two firms = Same quantity as a vertically integrated firm would choose

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BilateralMonopolyIntuiHveAnalysis

•  Problem

–  But what price?

•  Only restrictions

–  Seller must cover his costs, C(q*)

–  Buyer must not pay more than wtp,

V(q*)

=> Any split of S* = V(q*) – C(q*) seems reasonable

q

€

MC(q)

MV(q)q*

S*

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BilateralMonopolyIntuiHveAnalysis

•  Note –  If someone demands “too much”

–  The other side will reject and make a counter-offer

•  Problem –  Haggling could go on forever

–  Gains from trade delayed

•  Thus –  Both sides have incentive to be reasonable

–  Party with less aversion to delay has strategic advantage

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BilateralMonopolyDefiniHons

•  Definitions

–  Efficient quantity: q*

–  Walrasian price: pw

–  Maximum bilateral surplus: S*

q

€

MC(q)

MV(q)q*

pw S*

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BilateralMonopoly

•  First important insight: –  Contract must specify both price and

quantity, (p, q)

–  Q: Why?

–  Otherwise inefficiency (If p > pw then q < q*)

q

€

MC(q)

MV(q)q*

pw S*

ExtensiveFormBargainingUlHmatumbargaining

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UlHmatumbargaining

•  One round of negotiations –  One party, say seller, gets to propose a contract (p, q)

–  Other party, say buyer, can accept or reject

•  Outcome –  If (p, q) accepted, it is implemented

–  Otherwise game ends without agreement

•  Payoffs –  Buyer: V(q) – p q if agreement, zero otherwise

–  Seller: p q – C(q) if agreement, zero otherwise

•  Perfect information –  Backwards induction

Solvethisgamenow!

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UlHmatumbargaining

•  Time 2

–  Buyer accepts proposed contract (p, q) iff V(q) – p q ≥ 0

•  Time 1

–  Seller: maxp,q p q – C(q) such that V(q) – p q ≥ 0

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UlHmatumbargaining

max p,q p q – C(q)

st : V (q) – p q ≥ 0

Must set p such that: p ⋅q = V (q)

maxq V (q) – C(q)

Must set q such that: MV q( ) = MC(q)

Sellertakeswholesurplus

EfficientquanHty

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UlHmatumbargaining

•  SPE of ultimatum bargaining game

–  Unique equilibrium

–  There is agreement

–  Efficient quantity

–  Proposer takes the whole (maximal) surplus

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UlHmatumbargaining

•  Assume rest of lecture –  Always efficient quantity

–  Surplus = 1

–  Player S gets share πS

–  Player B gets share πB = 1 – πS

•  Ultimatum game

–  πS = 1

–  πB = 0

Tworounds(T=2)

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Tworounds(T=2)

•  Alternating offers

•  Players are impatient

–  For B: €1 in period 2 is equally good as €δB in period 1

–  Where δB, δS < 1 are discount factors

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Tworounds(T=2)

•  Period 1 –  B proposes

–  S accepts or rejects

•  Period 2 (in case S rejected)

–  S proposes

–  B accepts or rejects

•  Perfect information => Use BI

Solvethisgamenow!

π BT ,π S

T( )

π BT −1,π S

T −1( )

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Tworounds

•  Period T = 2 (S bids) (in case S rejected) –  B accepts iff:

–  S proposes:

•  Period T-1 = 1 (B bids) –  S accepts iff:

–  B proposes:

•  Note –  S willing to reduce his share to get an early agreement

–  Both players get part of surplus

–  B’s share determined by S’s impatience. If S very patient πS≈1

π BT ≥ 0

π BT = 0 π S

T = 1

π ST −1 ≥ δSπ S

T = δS < 1

π BT −1 = 1− δS > 0 π S

T −1 = δS

Trounds

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T rounds

•  Model

–  Large number of periods, T

–  Buyer and seller take turns to make offer

–  Common discount factor δ = δB = δS

–  Subgame perfect equilibrium (ie start analysis in last period)

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T rounds

Time Bidder πB πS Resp. T S ? ? ?

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T rounds

Time Bidder πB πS Resp. T S 0 1 yes

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T rounds


T-1 B ? ? ?

35

T rounds


T-1 B rest δ yes

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T rounds


T-1 B 1-δ δ yes

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T rounds


T-1 B 1-δ δ yes T-2 S ? ? ?

38

T rounds


T-1 B 1-δ δ yes T-2 S δ(1-δ) rest yes

39

T rounds


T-1 B 1-δ δ yes T-2 S δ(1-δ) 1-δ(1-δ) yes

40

T rounds


T-1 B 1-δ δ yes T-2 S δ(1-δ) 1-δ(1-δ) yes

multiply

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T rounds


T-1 B 1-δ δ yes T-2 S δ-δ2 1-δ+δ2 yes

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T rounds


T-1 B 1-δ δ yes T-2 S δ-δ2 1-δ+δ2 yes T-3 B ? ? ?

43

T rounds


T-1 B 1-δ δ yes T-2 S δ-δ2 1-δ+δ2 yes T-3 B rest δ(1-δ+δ2) yes

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T rounds


T-1 B 1-δ δ yes T-2 S δ-δ2 1-δ+δ2 yes T-3 B 1-δ(1-δ+δ2) δ(1-δ+δ2) yes

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T rounds


T-1 B 1-δ δ yes T-2 S δ-δ2 1-δ+δ2 yes T-3 B 1-δ+δ2-δ3 δ-δ2+δ3 yes

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T rounds


T-1 B 1-δ δ yes T-2 S δ-δ2 1-δ+δ2 yes T-3 B 1-δ+δ2-δ3 δ-δ2+δ3 yes T-4 S δ(1-δ+δ2-δ3) rest yes

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T rounds


T-1 B 1-δ δ yes T-2 S δ-δ2 1-δ+δ2 yes T-3 B 1-δ+δ2-δ3 δ-δ2+δ3 yes T-4 S δ(1-δ+δ2-δ3) 1-δ(1-δ+δ2-δ3) yes

48

T rounds


T-1 B 1-δ δ yes T-2 S δ-δ2 1-δ+δ2 yes T-3 B 1-δ+δ2-δ3 δ-δ2+δ3 yes T-4 S δ-δ2+δ3-δ4 1-δ+δ2-δ3+δ4 yes

49

T rounds


T-1 B 1-δ δ yes T-2 S δ-δ2 1-δ+δ2 yes T-3 B 1-δ+δ2-δ3 δ-δ2+δ3 yes T-4 S δ-δ2+δ3-δ4 1-δ+δ2-δ3+δ4 yes … … … … … 1 S δ-δ2+δ3-δ4+…-δT-1 1-δ+δ2-δ3+δ4-…+δT-1 yes

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T rounds


T-1 B 1-δ δ yes T-2 S δ-δ2 1-δ+δ2 yes T-3 B 1-δ+δ2-δ3 δ-δ2+δ3 yes T-4 S δ-δ2+δ3-δ4 1-δ+δ2-δ3+δ4 yes … … … … … 1 S δ-δ2+δ3-δ4+…-δT-1 1-δ+δ2-δ3+δ4-…+δT-1 yes

π B = δ − δ 2 + δ 3 − δ 4 + ...− δ T −1

π S = 1− δ + δ 2 − δ 3 + δ 4 − ...+ δ T −1

51

T rounds

Geometric seriesπ B = δ − δ 2 + δ 3 − δ 4 + ...− δ T −1

π S = 1− δ + δ 2 − δ 3 + δ 4 − ...+ δ T −1

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T rounds

S's shareπ S = 1− δ + δ 2 − δ 3 + δ 4 − ...+ δ T −1

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T rounds


Multiplyδπ S = δ − δ 2 + δ 3 − δ 4 + δ 5 − ...+ δ T

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T rounds



Addπ S + δπ S = 1+ δ T

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T rounds



Addπ S + δπ S = 1+ δ T

Solve

π S =1+ δ T

1+ δ

56

T rounds

Equilibrium shares with T periods

π S =1

1+ δ1+ δ T( )

π B =δ

1+ δ1− δ T −1( )

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T rounds


π S =1

1+ δ1+ δ T( )

π B =δ

1+ δ1− δ T −1( )

S has advantage of making last bid1+ δ T > 1− δ T −1

To confirm this, solve model where -  B makes last bid -  S makes first bid

58

T rounds


π S =1

1+ δ1+ δ T( )

π B =δ

1+ δ1− δ T −1( )

S has advantage of making last bid1+ δ T > 1− δ T −1 Disappears if T very large

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T rounds

Equilibrium shares with T ≈ ∞ periods

π S =1

1+ δ

π B =δ

1+ δ

S has advantage of making first bid1

1+ δ>

δ1+ δ

To confirm this, solve model where -  B makes first bid

60

T rounds


π S =1

1+ δ

π B =δ

1+ δ


1+ δ>

δ1+ δ

To confirm this, solve model where -  B makes first bid

61

T rounds


π S =1

1+ δ

π B =δ

1+ δ


1+ δ>

δ1+ δ

First bidder’s advantage disappears if δ ≈ 1

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T rounds

Equilibrium shares with T ≈ ∞ periods and very patient players (δ ≈ 1)

π S =12

π B =12

63

Difference in Patience

Equilibrium shares with T ≈ ∞ periods and different discount factors

π S =1− δB

1− δSδB

π B =1− δS

1− δSδB

δB

(Easy to show using same method as above)

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Difference in Patience

•  Recall –  ri = continous-time discount factor

–  Δ = length of time period

•  Then, as Δ è 0:

– 

–  Using l’Hopital’s rule

δ i = e−riΔ

π S =1− δB

1− δSδB

≈rB

rS + rB

65

Extensive form bargaining

•  Conclusions

–  Exists unique equilibrium (SPE)

–  There is agreement

–  Agreement is immediate

–  Efficient agreement (here: quantity)

–  Split of surplus (price) determined by relative patience •  Right to propose in last round gives advantage (T < ∞)

•  Right to propose in first round gives advantage (δ < 1)

66

Implications for Bilateral Monopoly

67


•  Equal splitting

ΠS = ΠB

p ⋅q − C q( ) = V q( ) − p ⋅q

2 ⋅ p ⋅q = V q( ) + C q( )

p = 12V q( )q

+C q( )q

⎡

⎣⎢

⎤

⎦⎥

68



ΠS = ΠB

p ⋅q − C q( ) = V q( ) − p ⋅q

2 ⋅ p ⋅q = V q( ) + C q( )

p = 12V q( )q

+C q( )q

⎡

⎣⎢

⎤

⎦⎥

Retailer’s average revenues

69



ΠS = ΠB

p ⋅q − C q( ) = V q( ) − p ⋅q

2 ⋅ p ⋅q = V q( ) + C q( )

p = 12V q( )q

+C q( )q

⎡

⎣⎢

⎤

⎦⎥

Manufacturer’s average costs

70



ΠS = ΠB

p ⋅q − C q( ) = V q( ) − p ⋅q

2 ⋅ p ⋅q = V q( ) + C q( )

p = 12V q( )q

+C q( )q

⎡

⎣⎢

⎤

⎦⎥

The firms share the Retailer’s revenues

and the Manufacturer’s costs

equally

71

Nash Bargaining Solution -- A Reduced Form Model

72

Nash Bargaining Solution

•  Extensive form bargaining model –  Intuitive

–  But tedious

•  Nash bargaining solution –  Less intuitive

–  But easier to find the same outcome

73


•  Three steps 1.  Describe bargaining situation

2.  Define Nash product

3.  Maximize Nash product

74


•  Step 1: Describe bargaining situation 1.  Who are the two players?

2.  What contracts can they agree upon?

3.  What payoff would they get from every possible contract?

4.  What payoff do they have before agreement?

5.  What is their relative patience (= bargaining power)

75

Nash Bargaining Solution Example 1: Bilateral monopoly

•  Step 1: Describe the bargaining situation –  Players: Manufacturer and Retailer

–  Contracts: (T, q)

–  Payoffs: •  Retailer:

•  Manufacturer:

–  Payoff if there is no agreement (while negotiating) •  Retailer:


–  Same patience => same bargaining power

!π R = 0

!πM = 0

π R T ,q( ) = V q( ) − TπM T ,q( ) = T − C q( )

T = total price for q units.

76


•  Step 2: Set up Nash product

N T ,q( ) = π R T ,q( ) − !π R⎡⎣ ⎤⎦ ⋅ πM T ,q( ) − !πM⎡⎣ ⎤⎦

Retailer’s profit from contract Manufacturer’s profit from contract

77




Retailer’s extra profit from contract Manufacturer’s extra profit from contract

78




Nash product - Product of payoff increases

Depends on contract

79




Claim: The contract (T, q) maximizing N is the same contract that the parties would agree upon in an extensive form bargaining game!

80




N T ,q( ) = V q( ) − T⎡⎣ ⎤⎦ ⋅ T − C q( )⎡⎣ ⎤⎦

81


•  Maximize Nash product

N T ,q( ) = V q( ) − T⎡⎣ ⎤⎦ ⋅ T − C q( )⎡⎣ ⎤⎦

∂N∂T

= − T − C q( )⎡⎣ ⎤⎦ + V q( ) − T⎡⎣ ⎤⎦ = 0 ⇒ T = 12 V q( ) + C q( )⎡⎣ ⎤⎦

⇒ p = 12V q( )q

+C q( )q

⎡

⎣⎢

⎤

⎦⎥

Equal profits = Equal split of surplus

82



N T ,q( ) = V q( ) − T⎡⎣ ⎤⎦ ⋅ T − C q( )⎡⎣ ⎤⎦

∂N∂T

= − T − C q( )⎡⎣ ⎤⎦ + V q( ) − T⎡⎣ ⎤⎦ = 0 ⇒ T = 12 V q( ) + C q( )⎡⎣ ⎤⎦

⇒ p = 12V q( )q

+C q( )q

⎡

⎣⎢

⎤

⎦⎥

83



N T ,q( ) = V q( ) − T⎡⎣ ⎤⎦ ⋅ T − C q( )⎡⎣ ⎤⎦

∂N∂T

= − T − C q( )⎡⎣ ⎤⎦ + V q( ) − T⎡⎣ ⎤⎦ = 0 ⇒ T = 12 V q( ) + C q( )⎡⎣ ⎤⎦

⇒ p = 12V q( )q

+C q( )q

⎡

⎣⎢

⎤

⎦⎥

Convert to price per unit.

84



N T ,q( ) = V q( ) − T⎡⎣ ⎤⎦ ⋅ T − C q( )⎡⎣ ⎤⎦

∂N∂T

= − T − C q( )⎡⎣ ⎤⎦ + V q( ) − T⎡⎣ ⎤⎦ = 0

∂N∂q

= V ' q( ) ⋅ T − C q( )⎡⎣ ⎤⎦ − C ' q( ) ⋅ V q( ) − T⎡⎣ ⎤⎦ = 0 ⇒ V ' q( ) = C ' q( )

85



N T ,q( ) = V q( ) − T⎡⎣ ⎤⎦ ⋅ T − C q( )⎡⎣ ⎤⎦

∂N∂T

= − T − C q( )⎡⎣ ⎤⎦ + V q( ) − T⎡⎣ ⎤⎦ = 0

∂N∂q

= V ' q( ) ⋅ T − C q( )⎡⎣ ⎤⎦ − C ' q( ) ⋅ V q( ) − T⎡⎣ ⎤⎦ = 0 ⇒ V ' q( ) = C ' q( )

Efficiency

86


•  Conclusion –  Maximizing Nash product is easy way to find equilibrium

–  Efficient quantity

–  Price splits surplus equally

87


•  With different bargaining power

N T ,q( ) = π R T ,q( )− !π R⎡⎣ ⎤⎦β⋅ πM T ,q( )− !πM⎡⎣ ⎤⎦

1−β

Exponents determined by relative patience

88

Nash Bargaining Solution Example 2: Bilateral oligopoly with two retailers

Manufacturer

Retailer 1 Retailer 2

Consumers Consumers

89


Manufacturer


Consumers Consumers

π1 T1,q1( ) = V q1( ) − T1 π 2 T2 ,q2( ) = V q2( ) − T2

Retailers independent

90


Manufacturer


Consumers Consumers

π1 T1,q1( ) = V q1( ) − T1 π 2 T2 ,q2( ) = V q2( ) − T2

πM T1,T2 ,q1,q2( ) = T1 + T2 − C q1 + q2( )

91


•  Step 1: Describe one of the bargaining situations –  Contracts: (T1, q1)

92





π1 T1,q1( ) = V q1( ) − T1πM T1,T2 ,q1,q2( ) = T1 + T2 − C q1 + q2( )

93





–  Payoff if no agreement •  Retailer:

•  Manufacturer: !π1 = 0

!πM = T2 − C q2( )


Manufacturer only supplies other retailer

94





–  Payoff while negotiating •  Retailer:


–  Same patience => same bargaining power

!π1 = 0

!πM = T2 − C q2( )


Manufacturer only supplies other retailer

95



N T1,q1( ) = π R T1,q1( ) − !π R⎡⎣ ⎤⎦ ⋅ πM T1,T2 ,q1,q2( ) − !πM⎡⎣ ⎤⎦

N T1,q1( ) = V q1( ) − T1⎡⎣ ⎤⎦ ⋅ T1 + T2 − C q1 + q2( ){ } − T2 − C q2( ){ }⎡⎣ ⎤⎦

N T1,q1( ) = V q1( ) − T1⎡⎣ ⎤⎦ ⋅ T1 − C q1 + q2( ) − C q2( ){ }⎡⎣ ⎤⎦

Incremental cost

96




N T1,q1( ) = V q1( ) − T1⎡⎣ ⎤⎦ ⋅ T1 + T2 − C q1 + q2( ){ } − T2 − C q2( ){ }⎡⎣ ⎤⎦

N T1,q1( ) = V q1( ) − T1⎡⎣ ⎤⎦ ⋅ T1 − C q1 + q2( ) − C q2( ){ }⎡⎣ ⎤⎦

Incremental cost

97




N T1,q1( ) = V q1( ) − T1⎡⎣ ⎤⎦ ⋅ T1 + T2 − C q1 + q2( ){ } − T2 − C q2( ){ }⎡⎣ ⎤⎦

N T1,q1( ) = V q1( ) − T1⎡⎣ ⎤⎦ ⋅ T1 − C q1 + q2( ) − C q2( ){ }⎡⎣ ⎤⎦

Incremental cost

98




N T1,q1( ) = V q1( ) − T1⎡⎣ ⎤⎦ ⋅ T1 + T2 − C q1 + q2( ){ } − T2 − C q2( ){ }⎡⎣ ⎤⎦

N T1,q1( ) = V q1( ) − T1⎡⎣ ⎤⎦ ⋅ T1 − C q1 + q2( ) − C q2( ){ }⎡⎣ ⎤⎦

Incremental cost

99



N T1,q1( ) = V q1( ) − T1⎡⎣ ⎤⎦ ⋅ T1 − C q1 + q2( ) − C q2( ){ }⎡⎣ ⎤⎦

∂N∂T1

= T1 − C q1 + q2( ) − C q2( ){ }⎡⎣ ⎤⎦ − V q1( ) − T1⎡⎣ ⎤⎦ = 0

⇒ T1 = 12 V q1( ) + C q1 + q2( ) − C q2( ){ }⎡⎣ ⎤⎦

⇒ p1 = 12

V q1( )q1

+C q1 + q2( ) − C q2( )

q1

⎡

⎣⎢

⎤

⎦⎥

Average incremental cost

100


p1 = 12 6 +

C q1 + q2( )−C q2( )q1

⎡

⎣⎢

⎤

⎦⎥

Example -  V(q) = 6 q -  C(q) = ½ q2

0 1 2 3 4 5 6 7 8 9 10

10

0

1

2

3

4

5

6

7

8

9

Quantity

€

MC(q)

MV(q)

Average incremental cost

101


0 1 2 3 4 5 6 7 8 9 10

10

0

1

2

3

4

5

6

7

8

9

Quantity

€

MC(q)

MV(q)

Incremental Cost

Units sold to other firm

Retailer 1buys 4 units

Example - Retailer 1 buys 4 units - Retailer 2 buys 2 units

p1 = 12 6 +

C q1 + q2( )−C q2( )q1

⎡

⎣⎢

⎤

⎦⎥ = 1

2 6 +164

⎡⎣⎢

⎤⎦⎥= 5

102

•  Compare prices when retailer 1 buys more than 2


•  Average incremental cost is lower for supplying 1!

103


0 1 2 3 4 5 6 7 8 9 10

10

0

1

2

3

4

5

6

7

8

9

Quantity

€

MC(q)

MV(q)

Incremental Cost



0 1 2 3 4 5 6 7 8 9 10

10

0

1

2

3

4

5

6

7

8

9

Quantity

€

MC(q)

MV(q)

Incremental Cost



•  Retailer 1 will pay a lower price per unit

104


0 1 2 3 4 5 6 7 8 9 10

10

0

1

2

3

4

5

6

7

8

9

Quantity

€

MC(q)

MV(q)

Incremental Cost



0 1 2 3 4 5 6 7 8 9 10

10

0

1

2

3

4

5

6

7

8

9

Quantity

€

MC(q)

MV(q)

Incremental Cost



105


0 1 2 3 4 5 6 7 8 9 10

10

0

1

2

3

4

5

6

7

8

9

Quantity

€

MC(q)

MV(q)

Incremental Cost



0 1 2 3 4 5 6 7 8 9 10

10

0

1

2

3

4

5

6

7

8

9

Quantity

€

MC(q)

MV(q)

Incremental Cost



p1 = 12 6 +

C q1 + q2( )−C q2( )q1

⎡

⎣⎢

⎤

⎦⎥ = 1

2 6 +12 ⋅36 − 1

2 ⋅44

⎡⎣⎢

⎤⎦⎥= 1

2 6 +164

⎡⎣⎢

⎤⎦⎥= 5 p2 = 1

2 6 +C q1 + q2( )−C q1( )

q1

⎡

⎣⎢

⎤

⎦⎥ = 1

2 6 +12 ⋅36 − 1

2 ⋅162

⎡⎣⎢

⎤⎦⎥= 1

2 6 +102

⎡⎣⎢

⎤⎦⎥= 5.5

106



N T1,q1( ) = V q1( ) − T1⎡⎣ ⎤⎦ ⋅ T1 − C q1 + q2( ) − C q2( ){ }⎡⎣ ⎤⎦

∂N∂q1

= V ' q1( ) ⋅ T1 − C q1 + q2( ) − C q2( ){ }⎡⎣ ⎤⎦ + C ' q1 + q2( ) ⋅ V q1( ) − T1⎡⎣ ⎤⎦ = 0

⇒ V ' q1( ) = C ' q1 + q2( )

Bilateral Efficiency

107



V ' q1( ) = C ' q1 + q2( )

V ' q2( ) = C ' q1 + q2( )

⎫

⎬⎪⎪

⎭⎪⎪

⇒V ' q1( ) = V ' q2( )

Bilateral efficiency 1

Bilateral efficiency 2

108



V ' q1( ) = C ' q1 + q2( )

V ' q2( ) = C ' q1 + q2( )

⎫

⎬⎪⎪

⎭⎪⎪

⇒V ' q1( ) = V ' q2( )

Overall market efficiency - Efficient distribution of goods

109

•  Conclusions –  Prices of homogenous goods may differ

•  Quantity discounts if producer has increasing MC

–  Market with bilateral market power may be efficient


Documents

Bilateral Market Power & Bargaining