Allocation and Distribution under Imperfect

過当競争、垂直統合、内外価格
差：単純絵解経済学*
東大社研セミナー資料, 5.13. 2015
太田浩
青山学院大学名誉教授
*Source: Tohru Wako and Hiroshi Ohta, “Bowley Duopoly under
Vertical Relations,” Pacific Economic Review, forthcoming.
「過当競争」
 「過当競争？」：そのような用語は「経済学にはな
い」(Eleanor Hadley, quoted at AGU, 1960s.)
 But, Japan is different?大学ですら競争は熾烈？；
「国際系」学部もいまや「過当競争」とか。
（「日経新聞」11.18.2014.)
関連文献
 Bowley duopoly model, Wako, et. al.(PER,2015,
forthcoming).
 Cournot unlimited entry models a la McGuire, et.
al. (RIE,2005); Ohta (九大出版,1997); Suzumura,
et. al.(RES,1987); Excess capacity controversies
(1970s).
 Successive monopoly models a la Greenhut, et.al.
(AER,1976); Machlup, et. al. (Economica,1960).
（メガ？過剰？）統合
 「過当競争」がある一方で、メガ統合もある。
(Size, number matters?)
 例：八幡富士（現新日鉄）1970.
 垂直的統合論 a la Greenhut, et. al. (1976,
1979), Abiru, et. al. (1998), et. cet.
内外価格差
 Notorious until 80s, 悪名高い（高かった？）
 An economist’s lament (early 90s?): In Japan
everything is available from all over the world,
but nothing affordable. :( :(
 Ohta (1997) “A successive monopolies model of
the tragedy of mercantilism” (Kyushu U. Press),
followed by McGuire, et .al. (05, RIE,) “Implicit
mercantilism, oligopoly, and trade”.
件の三悪（？）
 名にし負う悪弊（？）
 単純な「絵解経済学」で解釈。
 Excess Competition under Vertical Relations as
Bowley Duopoly vs. Vertical Integration:
Equivalence Theorem?
What’s Bowley Duopoly?
Related Queries






What’s Bowley Duopoly?
Stable equilibrium obtainable?
Under what conditions?
What real world relevance does it have?
What does it matter to, if it does?
Pondering these questions: Primary
objective of present assignment.
Background Literature
 Typical, well-known are Cournot and
Bertrand for duopoly models.
 But Cournot not cool enough until mid-70s for
‘unrealistic’ assumption of quantity-, as
opposed to price-, competition a la Bertrand
 Cournot models, not just duopoly but also
oligopoly, better-received mid-70s, 80s and
thereafter IMHO.
Digression on History of Econ
Thought; Al Chalk. 
 Cournot no classical theory, but
chronologically belongs to classical.
 So, OK for my term paper assignment!
 This is how a dyslexia patient, i.e., HO,
encountered Cournot theory in late 60s,
or before 1971.
Getting Back to Bowley and
Schtackelberg Duopoly
 If Cournot forlorn, Bertrand and
Stackelberg appear lesser known.
 But Bowley is almost totally unknown,
or known notoriously, at best, for its
untenable outcomes, lacking empirical
relevance?
 Does it? Lack empirical relevance?
Bowley Excess Competition:
Empirical Relevance?
 Japan’s frozen food, beer industries: allegedly
engaging in cut-throat competition.
 Question/idea: How do they survive? Rebating
from producers/wholesalers. (Wako, Wako, et al,
2000, 2005.)
 Hypo: Loss incurred from excess competition
among the retailers may be offset by rebating by
wholesalers, to the benefit of all including
consumers enjoying lower prices. 価格破壊？
Viable price destruction?
Related Literatures
 Abiru, M., et al, (1998): On Equilibrium Structures in
Vertical Oligopoly, JEBO.
 Greenhut, M. L., et al.: On Vertically Related Industries,
AER, 1976, 79.
 Itoh,M.(1995): Why are prices high in Japan? (Japanese),
Tokyo: NTT.
 McGuire, M, et. al. (2005): Endogenous Mercantilism,
Oligopoly, and Trade, RIE.
 大橋弘等 (2010): 「八幡富士合併の定量的評価」 RIETI
Discussion Paper（キーワード：競争回復措置、競争制限
効果、生産性向上効果）
To Be Considered, In What
Follows, Are:
 Simple Monopoly: Demand and AR Conceptually
Distinguished. (Demand shows the consumer behavior,
which is relevant to the seller insofar as it can be viewed
as an AR curve.)
 Successive Monopoly: Vertically related monopolies, as
distinguished from either monopsony or even bilateral
monopoly: most realistic case, but least discussed.
 Alternative Successive Oligopoly Models of a
Monopolist Upstream along with:
 a) Leader-Follower Stackelberg Duopoly Downstream.
 b) Leader-Leader Bowley Duopoly Downstream.
Simple Account of
Simple Monopoly: SM
 As a starter, consider SM facing market
demand MD. Then related optimal solutions
are given as follows.
MD: p = 1 - Q
CS*
p*=1/2
CS*=1/8
*=1/4
(MC=0 assumed)
*
Q*=1/2
Successive Monopoly:
Retailer Downstream
 Consider a monopolistic retailer downstream.
MD gives his AR denoted by ARR.
 ARR is his net retail price pR, net of purchase
price pW from the wholesaler upstream, as a
function of qR supplied: pR = (1-pW)-qR.
 This ARR in turn yields MRR= 1-pW-2qR.
 To be equated, for FOC, to MC(=0).
 FOC, MRR=MC=0, yields qR*=(1-pW)/2, i.e.,
half the net reservation price.
Successive Monopoly:
Wholesaler Upstream
 Retiler’s best response, of qR*=(1-pW)/2,
yields wholesaler’s ARW: pW=1- 2qW,
(qW=qR).
 Related MRW=1-4q .
 To be equated, for FOC, to MC=0.
The Upshot?
 Upshot: q*=1/4, q*(= qW*=qR*) produced,
sold at the wholesale market at:
 pW*=1/2, at which price the retailer buys,
and sells, at the final retail market at:
pR*=3/4.
 This is given by equating the retailer’s
MR =1-2qR*=pW*(=1/2) to get qR*=1/4,
then pR*=1-qR*.
Successive Monopoly in a Nutshell:
SM vs. SSM
Simple Monopoly SM:
ARSM: p=1  q
MRSM: p=1  2q
pR*=3/4

MD
R
pW*=2/4
 W
MRSM
= ARW
q*SSM=1/4
SS Monopoly SSM:
MRSM =ARW: p=1  2q
MRW: p=1  4q
CS*SSM=1/32;CS*SM=4/32
*SSM=1/8+1/16; *SM=4/16
The Nature of Successive Monopoly,
Merger Incentives Thereof, or?
 Negative welfare effects of vertically
related market structures; prices to go up,
profits to go down, consumer surplus to go
down, so does social welfare.
 Monopolist upstream has incentives to
contrive downstream monopoly or
oligopolies to either merge with him (a la
GO) vertically, … Or?
Excess Rivalry Downstream
 Or play cut-throat competition
horizontally (present model of excess
comp downstream).
 The latter case may require upstream
leadership, say, with rebating
downstream ex post, so that they all
benefit, including consumers.
Roundabout Vertical Effects of
Distribution: A Digression?
 Japan’s distribution system（流通）, called the
dark continent, notorious for its innumerable
roundabout vertically related sub-sectors.
 Related observations or stylized facts on domestic
prices relative to the prices abroad preceding the
last 2 decades and a half: STAGGERING 内外価
格差. Cf. Itoh (95).
 Also observed, last (lost?) quarter century, are:
価格破壊.
 So, may call for Bowley duopoly. maybe realistic.
価格破壊, How it works
 Two ways: One by voluntary merger (a la GO.
cf. Volks steak episode?)
 The other way, on the contrary, is via cut-throat
competition (a la Bowley).
 Either way will work, provided that the market
is let alone with freedom: to compete or not to
compete? More Lionel Robbins’ donkey
question than Shakespearian,…, to be or not to
be?
Getting Back to the Vertical Effects of
Successive Monopoly Reversely:
Introducing Horizontal Rivalry
 Consider two alternative modes of rivalry
downstream: Stackelberg and Bowley.
 The former defined as a leader-follower duopoly,
and the latter a leader-leader duopoly.
 Which is better?
 Intuitively the former: the leader-follower must be
preferred to the leader-leader duopoly? A tiny profit
remaining even to a follower better than none under
excess rivalry. Right? No. Why not?
 Producer upstream has incentives to compensate
retailers’ profits forgone from excess rivalry.
Stackelberg Leader-Follower
Duopoly Outcomes
 Given the MD, Stackelberg output qS,
retatil price pRS, and wholesale price pWS
in equilibrium are:
q
S*
= 3 /8 (> 2 /8)
RS*
= 5 /8 (< 6 /8)
WS*
= 1/2
p
p
Stackelberg Leader-Follower
Duopoly Downstream;
Monopoly Upstream
p*
pw*
p*=5/8
pw*=1/2
l*=2/64 f*
Rebf
MD
Df
ql*
qs*
=2/8
=3/8
4/8
ql*
qf*
Bowley Leader-Leader Duopoly Downstream;
Monopoly Upstream
SW=(8+4)/64
RebateSW=1/64
BW=(8+8)/64
RebateBW=4/64
Net BW>NetSW
pR*= pW* Rebate
p*
pw*
MD
=1/2
ql*
ql*
q*
=2/8
=2/4
Without
Rebates
Stackelberg/Bowley:
Outcomes for Wholesaler
S=(8+4)/64
RebateS=1/64
B=(8+8)/64 > S
RebateB=4/64 > RebateS
Net B >Net S. This is because of
increasing-sales-proceed effects of
greater competition downstream.
Stackelberg/Bowley:
Outcomes for Retailers
 Retailers downstream are guaranteed
the same profits via rebating regardless
of their choice of competitive modes.
 So, retailers are indifferent to choose
either a Stackelberg leader-follower,
or Bowley leader position.
The Wholesaler Incentive
 The wholesaler upstream wishes the retailers
to choose a unique mode, i.e., Bowley mode,
for the largest own profit while fully
compensating the retailers loss from leaderleader excess competition.
 So, he does have an incentive to contrive
Bowley competition downstream by
providing an extra amount of rebate (up to
1/16) to entice retailers to play excess rivalry
or to practice marginal cost pricing.
Conclusions
 Consider related industries with a wholesaler
upstream and duopolistic retailers downstream.
 Then leader-leader Bowley rivalry is doomed to
excess competition; both leaders’ profits forgone.
 But if fully compensated or contrived by the
monopolist upstream, it will yield an optimal
outcome for all, including the monopolist, retailers,
and the consumers. (Thanks to the price effect.)
 Equivalence Hypo?: Horizontal excess competition
under vertical relations equivalent to vertical
integration a la GO (1976). Deserve Anti-Trust
accusations anyway? In defense of monopoly
upstream (or a la R. Z. McKenzie?)
付録: Implicit Mercantilism, Oligopoly, Trade, Revisited
MO (RIE, 05)

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