Product Diversification, Entry

Endogenous Flexibility in
Flexible Manufacturing System
(FMS)
Joint work with Daisuke Shimizu
Oligopoly Theory
1
Plan of the presentation
(1) Rough sketch of the model and results
(2) Background
(2a)Production substitution and R&D
(2b)Overview of spatial competition
(3) Non-spatial interpretation of delivered pricing
model
(4) Explanation of related works
(5) Formal explanation of our model
(6) Results and implications
Oligopoly Theory
2
Flexible Manufacturing
System (FMS)
FMS:多品種少量生産
需要に応じて柔軟に生産する種類を切り替え、各
製品の生産量を柔軟に量を変える
⇔フォードシステム:少品種大量生産
Oligopoly Theory
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Rough sketch of the model
duopoly, delivered pricing model (shipping model),
exogenous locations, Cournot competition, linear
transport cost
In the first stage firms choose the level of transport
cost.
In the second stage firms face Cournot competition.
Our main concerns: Relationship between
equilibrium and efficient levels of
transport cost.
Oligopoly Theory
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Result
Equilibrium level of transport cost is lower than
socially efficient level.
The level of transport cost corresponds to the
degree of flexibility in manufacturing system
Eaton and Schmitt (1994)
→Firms adopt too flexible system from the
normative viewpoint
Oligopoly Theory
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Welfare-improving production
substitution
・限界費用の低い企業の生産量が増えて限界費
用の高い企業の生産量が減る
→全体の生産費用が節約されて経済厚生が改善
する
Oligopoly Theory
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Welfare-improving production
substitution
企
業
2
の
生
企業1の
産
量 反応曲線
0
Oligopoly Theory
変化後の
企業1の
反応曲線
企業2の
反応曲線
企業1の生産量
7
Welfare-reducing production
substitution
企業1の
反応曲線
企
業
2
の
生
産
量
変化前の
企業2の
反応曲線
変化後の
企業2の
反応曲線
0
Oligopoly Theory
企業1の生産量
8
Two Models of Spatial
Competition
(1) Mill Pricing Model (Shopping Model)
Consumers pay the transport costs. Consumers go
to the firm's shop.
(2) Delivered Pricing Model (Shipping Model,
Spatial Price Discrimination Model)
Firms pay the transport costs. Firms bring the
goods to the markets.
Oligopoly Theory
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Mill Pricing Model
(Shopping Model)
長岡京
河原町
高槻
梅田
茨木
淡路
Oligopoly Theory
10
Delivered Pricing Model (Shipping
Model, Spatial Price Discrimination
Model)
北海道
東北
九州
Oligopoly Theory
関西
東海
関東
11
Hamilton, Thisse, and Weskamp
(1989)
duopoly, delivered pricing model,
linear transport cost, linear demand at
point, Hotelling–type linear city
each
In the first stage firms choose their locations
In the second stage firms face Bertrand or
Cournot competition
Oligopoly Theory
12
Bertrand
Firm 1
0
Oligopoly Theory
1/4
Firm 2
3/4
1
13
Cournot
Firm 2
Firm 1
0
Oligopoly Theory
1/2
1
14
Pal (1998)
duopoly, delivered pricing model,
linear transport cost, linear demand at
each point, Salop–type circular markets
In the first stage firms choose their
locations
In the second stage firms face Cournot
competition
Oligopoly Theory
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Cournot
Firm 1
0
1/2
Firm 2
Oligopoly Theory
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Shipping modelのその他の研究
Oligopoly:
Anderson and Neven(1991), Matsushima
(2001),Shimizu and Matsumura (2003), Gupta et
al (2004), Matsumura, Ohkawa, and Shimizu
(2005)
Welfare:
Matsumura and Shimizu (2005a, 2005b)
Oligopoly Theory
17
Shipping modelのその他の研究
General Transport Costs:
Gupta (2004), Matsumura and Shimizu (2006)
Mixed Strategy Equilibria:
Matsumura and Shimizu (2008)
Product Differentiation:
Shimizu (2002), Yu and Lai (2003)
Oligopoly Theory
18
Shipping modelのその他の研究
Multi Plants:
Chamorro-Rivas (2000), Pal and Sarkar (2002)
Different Production Costs across locations
Mayer (2000)
Oligopoly Theory
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Shipping modelのapplications
FMS:
Anderson and de Palma (1998),
Eaton and Schmitt(1994), Norman and Thisse(1999).
Antitrust
Gupta, Kats, and Pal(1995), Matsumura(2003,2004),
Matsumura and Matsushima (2005) ,Matsumura and
Okamura (2006)
Mixed Oligopoly
Matsushima and Matsumura (2003, 2006)
Oligopoly Theory
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Spatial Interpretation of Shipping
Model
Firm 1
Market A
Oligopoly Theory
Firm 2
Market B
21
Non Spatial Interpretation of
Shipping Model: Technological
Choice (Matsumura (2004))
Firm 1
Firm 2
Market A:
Market B:
Small Car
Large Car
Oligopoly Theory
22
Non Spatial Interpretation of
Shipping Model: FMS Eaton
and Schmitt (1994)
Variant (firm 2)
Firm 1
Base Product (firm 1)
Oligopoly Theory
Base Product (firm 2)
Firm 2
Variant (firm 1)
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Röller and Tombak (1990)
duopoly, 2 markets, linear demand at
each point
In the first stage firms choose whether or
not to adopt FMS. If a firm supplies for
both markets iff it adopt FMS.
In the second stage firms face Cournot
competition
→Private incentives for adopting FMS is
too small from the normative viewpoint
Oligopoly Theory
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Intuition
双方がFMSを選ばないと双方が単一市場で独占
になる。
FMSを選ぶと競争が起こる
→消費者の利益が増える
→これを企業は考慮しないのでFMSを導入する
誘因は過小。
Oligopoly Theory
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Röller and Tombak (1990)への疑問
Röller and Tombak (1990) あるいは他の多くの研
究が指摘しているとおり現在ではほとんどの企業が
何らかの形でFMSを導入している。
→incentiveは過小なのだけれどしかしそれでも浸
透してしまった、と考えるのは自然か?
→既に(程度はともかくとして)浸透したシステムの
導入のincentiveを今更議論してもしょうがない(もち
ろん彼らが論文を書いた時点では意味があった)。
Oligopoly Theory
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この論文がやったこと
・FMSを入れるか入れないかというall or
nothingの選択ではなく、FMSが導入されるこ
とを前提として、そのflexibility を内生化する。
・flexibilityの程度が過小なのか過大なのかを
分析する。
・flexibilityの程度に依らず競争が起こってい
る事を前提とする(当然競争の程度は変わる
が)。
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The Model
・exogenous locations(内生化しても同じ)
・circular-markets
・linear transport cost
・linear demand
In the first stage each firm chooses t (unit
transport cost).
In the second stage firms face Cournot
competition
Oligopoly Theory
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Notations
Ii(ti): Investment Cost
x∈(0,1): location
qi: Firm i‘s output Q: Total output
ci(ti) : Firm i's production cost
p(Q)=A-Q: demand function
πi: Firm i‘s profit Π: total profits
CS: Consumer surplus W: social surplus
tE: equilibrium level of t tW: optimal level of t
(for W) tC: optimal level of t (for CS)
tP: optimal level of t (for producer surplus)
Oligopoly Theory
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Two Models
Model 1
Flexibility increases
→Fixed Investment cost I(T) increases
Model 2
Flexibility increases
→Variable production cost c(T)
increases
Oligopoly Theory
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Model 1
t
0
Oligopoly Theory
固定費を投入してflexibilityを確保
I(固定費用)
31
Model 2
base productの競争力を弱めてflexibilityを上げる
t
base productの生産
に高い競争力
高いflexibility
0
c(可変費用)
Oligopoly Theory
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Results
Propositions 1 and 2 (Model 1)
tC<tE tP>tE
tW>tE
Propositions 3 and 4 (Model 2)
tC<tE tP>tE
tW>tE
⇒Flexibilityをあげるprivate incentiveは大きす
ぎる
⇒過大なflexibility
Oligopoly Theory
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Intuition(model 1, tC<tE )
Market A
Market B
t+c
c
Firm 1
t+c
c
Firm 2
tが下がる→競争が激化する→消費者余剰が増える
企業はこの効果を考えずにtを決めるので
(消費者余剰最大化の観点からは)tが過大になる
Oligopoly Theory
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Intuition(model 1, tP>tE )
Market A
Market B
t+c
c
t+c
c
Firm 2
Firm 1
tが下がる→競争が激化し、Market A(B)での企業1(2)の
利潤が減る
企業2(1)はこの効果を考えずにtを決めるので
(生産者余剰最大化の観点からは)tが過小になる
Oligopoly Theory
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Intuition (model 1,
W
E
t >t
)
Market B
Market A
t+c
c
Firm 1
c
t+c
Firm 2
tが下がる→Market A(B)での企業1(2)から企業2(1)
への生産代替が起こる→費用の低い(高い)企業の生
産量が減り(増え)生産費用が増加→経済厚生悪化
企業1(2)はこの効果を考えずにtを決めるので
(総余剰最大化の観点からは)tが過小になる
Oligopoly Theory
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Intuition (model 2, tW>tE )
Market A
Market B
t+c(t)
c(t)
c(t)
Firm 1
t+c(t)
Firm 2
tが下がる→Market A(B)での企業1(2)から企業2(1)へ
の生産代替→経済厚生悪化(model 1と同じ)
企業1(2)はこの効果を考えずにtを決めるので
(総余剰最大化の観点からは)tが過小になる
Oligopoly Theory
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Intuition (model 2, tC<tE )
Market A
Market B
t+c(t)
c(t)
Firm 1
t+c(t)
c(t)
Firm 2
市場Aの価格、CSはc(企業1の限界費用)+(c+t)(企業2
の限界費用)に依存→2c+tが最小のときCSが最大
企業1が市場AでのMCと市場BでのMCの和を最小化す
ればtC=tEとなる。しかし企業1は2c+tを最小化するtでは
なくそれよりも大きなtを選ぶ~Market Aでの企業1の生
産量の方が大きいからMarket Aでの費用をより重視する
Oligopoly Theory
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Why do Röller and Tombak
(1990) obtain the opposite
result?
In their model, t changes from ∞ to 0 when firms
adopt FMS.
→Welfare-reducing production substitution never
occurs.
Oligopoly Theory
39
まとめ
・不完全競争市場では自分の得意な財への特化の
程度が過小になる
・しかしこの均衡状態は消費者の利益の観点から
すると望ましい
Oligopoly Theory
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Extensions
もし自由参入にしたら?
→tをあげる→企業の利潤が増える→企業の参入が増
える→過剰参入の弊害が激化
⇒tをあげることのwelfare gainは長期の方が小さい
もし混合寡占にしたら?
公企業は私企業よりflexibilityを高める誘因がより大
きい
→でも民営化すると全体のflexibilityはあがる
Oligopoly Theory
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