Beyond Excess Competition: A New Theory of Implicit Mercantilism
By Hiroshi Ohta (AGU) and Martin McGuire (UCI)
Prepared for the 2015 Annual Meetings of the Regional Science International, Japan,Okayama University

ABSTRACT:

Industrial Organization’s familiar Chamberlinean tangency equilibrium has been characterized
as generating “excess capacity” in the product-industry, and the behavior of individual firms,
therefore, is often described as “excess competition.” Adopting this terminology, excesscompetition in the presence of mergers and international price discrepancies, is often
characteristic of developing economies like Japan was in the last-half century. Although suchphenomena might seem unconnected, we show how a simple Cournot oligopoly model can giverise to them all at once. Moreover, we show that industries of a mercantile economy assumed to
face a competitive world market, can generate more than the ordinary “excess” entry of
Chamberlin, going beyond that familiar benchmark and characterized by an off-tangency
equilibrium. We name this feature “super-excess” entry, and we show that it eliminates ordinary“excess capacity,” and that it generates economic efficiency compatible with welfaremaximization.

Keywords: implicit mercantilism, Cournot unlimited entry, excess completion, super-excesscompetition* Collaboration is under way with Martin McGuire (UCI).
Introduction.
McGuire-Ohta (MO, 2005) shows how a developing economy could evolve to produce“implicit mercantilism.” Free unlimited entry, when combined with competitive behavior indeveloped countries, generates distinct stages of mercantilism hitherto unrecognized in theliterature. As the production costs and techniques of the mercantile society converge to worldstandards, its citizens will first lose from this progress, but later to gain. Both effects are due tocertain relationships between home prices and world prices, identified by MO (2005).
Modern endogenous dumping can thus yield super-excess competition, yet no excess
capacity, and hence can benefit all. To reiterate suppose that the so-called excess competitionand excess capacity are mutually defined and identified by the Chamberlinean tangency point1

(Ohta, 1977). Then, modern oligopolistic dumping can restore efficiency, not by limiting entry,
but instead by allowing unlimited super-excess entry, which will end up endogenously in
off-Chamberlinean tangency equilibrium. The upshot benefits all with productive efficiency
restored and welfare maximized.
Section 1 reviews alternative definitions/theories of ‘excess competition.’ As a reference
departure point for a desirable ‘excess competition,’ Section 2 presents a basic model ofsuccessive monopolies as a departure point for Section 3. It discusses what Wako-Ohta (2015)
calls excess competition under ‘vertical relations’ and also a ‘win-win-win’ game. But it falls
short of genuine perfect competition throughout all the vertically related markets considered.
For this particular reason Section 4 revisits McGuire-Ohta (2005) as a theory of endogenous
mercantilism that yields perfect competition outcmes.
Section 1. Alternative Definitions/Theories of ‘Excess Competition’The first, classic definition of excess competition is given as a state of equilibrium under
Chamberlinean monopolistic competition. This state is given by, identified at, the familiar
Chamberlinean tangency equilibrium point (cf. Ohta, 1977).
The second definition involves oligopolistic rivalry rather than Chamberlinean
monopolistic competition. Moreover, it also involves a disequilibrium state of cutthroat excesscompetition such as classic Bowley duopoly (cf. Wako-Ohta, 2015).
The classic Bowley duopoly or any other oligopolistic competition models are usually
predicated upon horizontally related industries. A more recent definition of excess competition,by contrast, involves industries that are vertically related. Such a third, ‘vertically related’
industries model is proposed by Wako-Ohta (2015).
Related to this third definition and theory of ‘excess competition under vertical relations’(WO), however, is a departure reference point model of ‘successive monopolies’ a la Greenhutand Ohta (GO, 1976). We therefore present in the next section such a reference point model ofsuccessive monopolies, following GO,Section 2. The Successive-Monopoly Model as a Depar ture Point Analysis
Consider vertically related industries that consist of n = 2 or more markets, but here assumed n= 2 for simplicity. Call them a retail market downstream and a wholesale market upstream,respectively. The retail market demand for a product Q is assumed as a function of price p, i.e.,
Q = f(p), or its inverse function f-1(p), called (a monopolist’s) average revenue AR as follows.
(2-1)

AR: p = f-1(QR) = 1 − QR2

where p is the retail price, or (gross) average revenue accrued to the monopolist who sells at theretail market downstream. Here the monopolist’s AR is defined as a linear function of QR, theproduct carried from the wholesale market upstream.
Consider now the retailer’s net average revenue: pR ≡ p − pW, net of purchase cost pWfrom the market upstream where he behaves as a price taker. This combined with (2-1) above
gives the retailer’s net average revenue ARR as a function of QR.
(2-2)R

net-ARR: pR = (1−pW) −QR.

This net average revenue, net of pW, for the retailer in turn yields his net marginal revenue
net-MRR (net of purchase costs):(2-3)R

net-MRR= (1−pW)−2QR.

Equating this net MRR to MC=0 for maximization of profit (or net revenue) requires
net-MRR=0, which yields his optimal sales quantity QR* to be purchased at the market upstream,in turn, at the final market downstream for sale:(2-4)RQR*=(1−pW)/2.

Note that this (2-4)R reveals to the wholesaler upstream how much quantity he can sell tothe retailer from the market downstream once he decides on his wholesale price. In other words,
any pW he decides on will determine his sales quantity QR* that he should produce. Thus,rewriting (2-3)R yields the upstream wholesaler’s average revenue ARW in terms of Q*(=QW*)
produced for sale QR* at the final retail market.
Inasmuch as the wholesaler upstream is a monopolist, his profit maximizationcondition (FOC: MR=MC) is readily derived from (2-3)W above as (2-4)W below:(2-4)WMRW (Q*) = 1− 4 Q* = MC,

where Q* is the optimal quantity that the wholesaler sells to the retailer. Thus, if thewholesaler’s MC is assumed to be zero, then Q*= (QW*=QR*) =1/4.1
Given this Q* produced, the wholesaler sells it Q*(=QW*) at the wholesale market tothe retailer at pW*=1/2 (via (2-3)W). The retailer who purchases QR*(=QW*) at pW*=1/2, thenresells it at the final retail market at pR*=3/4 (via (2-1)R), which is given by equating theretailer’s MRR to his/her MCR (=pW*). Thus,(2-5)

MRR =1−2QR*= MCR (=pW*)=1/2

which yields the equilibrium solution to the vertically related industry with two independent
1

Note here that even though the wholesaler’s MCW may be assumed zero for simplicity, theretailer’s MCR cannot since pW>0.

3

firms presiding over two markets, upstream and downstream, respectively:(2-6)

Q* (=QR*= QW*) =1/4,(2-7)

pW*=1/2, and(2-8)

pR*(=1−QR*) =3/4.

Each successive monopolist as a seller, either upstream or downstream, is required tobehave as a competitive buyer.2 That is, the same economic agent behaves as a monopolist
seller, but at the same moment behaves as a competitive buyer, at each and every market point
successively related upward and/or downward.
This in a nutshell is a crucial necessary condition for a successive monopoly to bedefined successfully. Despite its seeming success (in theory at least) the ‘successive monopoly’model was challenged by GO (1976). The upshot was a counter-proposal model of verticalmerger of successive monopolists as a Pareto-improving outcome.
But more realistic vertical relations may involve oligopolistic rivalry in downstream
retail markets that are vertically related to and regulated by a more monopolistic wholesaleindustry upstream. This is an alternative postulate proposed by WO (2015) that pertains tobridge the successive monopolies model and its counterpart model of vertically related markets,
in which only a market upstream is monopolized, but the one downstream is not. Section 3reviews it and shows that the Bowley excess competition under vertical relations is equivalent
to the GO vertical merger.
However, no matter how excessive the downstream competition, the monopolist
upstream may deter competitive entry therein by indulging in ‘rent-seeking competition’(Ekelund and Tollison, 1981). This may not only discourage unlimited entry upstream, but also
waste scarce resources until pure monopoly profit evaporates. Efficiency loss and related
welfare loss may accordingly be inescapable anyway.
Thus, despite the efficiency equivalent outcome of either the GO vertical merger orthe Bowley horizontal excess competition under vertical relations, the efficiency loss from puremonopoly remains to be inescapable, such a recent argument as ‘in defense of monopoly’(McKenzie) aside. Even if technological efficiency is attained under vertically related Bowley
duopoly, efficiency loss is unavoidable unless free entry is guaranteed at any and every market
point. But skipping to review the related WO, we next get to Section 4.

2Thus, for a final downstream seller to behave as a monopolist at the same moment that anupstream seller also behaves as a monopolist against the buyer from the downstream market thathe/she monopolizes, the monopolistic seller downstream must also behave as a competitive buyer
upstream.

4Section 4. Super-Excess Competition Model: MO Revisited
Assumptions and Notation
We begin by assuming that a portion of the domestic market is insulated from certain foreign
goods. Despite the insulation, domestic producers, we assume, to have evolved to a point ofeffectively competing foreign producers. Domestic demand for this good, Q, is fully met fromhome production. This home supply is provided under Cournot oligopoly among homeproducers. The number of firms is endogenous; market entry by home producers eliminatesoligopoly profits. Thus the time frame of our comparative static analysis must be of suchduration as to allow adjustment in the number of firms, or price quantity pressures fromincipient adjustments in numbers to take effect.
If domestic firms are globally competitive, they can market their product at a profit
abroad as well. Based on this intuition we will postulate that the neo-mercantilist state’s
producers have achieved various degrees of cost parity with foreign competitors. The rest of theworld market is competitive and price-taking, so domestic mercantilist producers do not
influence world prices. Thus, the home country produces a commodity Q, and sells there at aconstant world price, pW. High distribution costs at home completely exclude foreign supplies ofQ. Although we assume asymmetry between home and foreign suppliers, oligopoly within theneo-mercantile sector, by contrast, is symmetric. There are n domestic firms each producing q(= Q/n) under symmetric oligopoly. Each firm sells qH at home at the one price pH and qE abroad(qE ≥ 0) at price pW while producing q = qH + qE. Throughout this paper we use specificfunctional forms of costs and demand to derive/illustrate these effects. Home demand (pH),revenue (TR), cost (TC, AC, MC), production (q), and profit (π) conditions are given byequations (4-1), (4-2), (4-3), (4-4), and (4-5). The parameter A is market reservation price, and b(> 0) is a parameter reflecting the size of the market.
(4-1)

pH = A- bnqH,(4-2)

TR(qH, qE; A, b, n, pW) = pWqE + pHqH

(4-3)

TC(q; F, α) = F +αq2,(4-4)

q = q H + q E,

(4-5)

π (qH, qE; A, b, n, F, α, pW) = TR(qH, qE; A, b, n, pW) - TC(q; F, α)

AC = F/q +αq,

MC = 2αq,

Mercantile Equilibrium Conditions
In our asymmetric oligopoly equilibrium with pW assumed given, each firm maximizes
profit, setting pW, MC, and MR all equal to yield:5(4-6)∂p/∂qE = 0: pW = 2αq,(4-7)∂p/∂qH = 0: A − bnqH − bqH = pH− bqH = 2αq.

The system of 7 equations above includes eight unknown (endogenous) variables: pH, qH,qE, q, π, TR, TC, and n. Thus, if n is given (and small enough to make π >0), all the otherendogenous variables will be determined. However, free entry n increases until π diminishes
and approaches zero:
(4-8)

π =0.

This is when what we call super-excess competitive equilibrium is reached and the rest ofendogenous variables above are also solved, with their selected relations illustrated
diagrammatically below.

pSW1

DW
pC

SW0

MCAC

pW1
n1qE1

MR1

AR0

pW0
MR0QworldqH 0qE1qH, qE

Cournot Off-Tangency Equilibrium with Export vs. Tangency Equilibrium with No
Export: Matured Stage of Endogenous Mercantilism (MO, RIE, 2005)

Super-excess entry beyond Cournot tangency equilibrium can thus restore productive
efficiency inasmuch as aggregate output for both export and domestic supply, but individual
firm’s increased output will be almost entirely allocated to export and the rest still remaining todomestic supply.

REFERENCES
Robert E. Ekelund and Robert D. Tollison, Rent-Seeking Society, College Station, TX: Texas
A&M University Press, 1981.
Wilfred J. Ethier, “Dumping,” Journal of Political Economy, 90 (30) 1982.
Melvin L. Greenhut and Hiroshi Ohta, “Related Market Conditions and Inter-Industrial

6Mergers,” American Economic Review, 1976.
Fritz Machlup and Martha Tabor, “Bilateral Monopoly, Successive Monopoly, and Vertical
Integration ,” Economica, 1960.
Martin McGuire and Hiroshi Ohta, "Implicit Mercantilism, Oligopoly, and Trade," Review ofInternational Economics, 13(1) 2005.
Hiroshi Ohta, "A Successive-Monopolies Model of the Tragedy of Mercantilism," in M. Hosoeand E. Rasmusen (eds.), Public Policy and Economic Theory, Kyushu University Press,
1997.
Hiroshi Ohta, "On the Excess Capacity Controversy," Economic Inquiry, April 1977.
Tohru Wako and Hiroshi Ohta, “Bowley Duopoly under Vertical Relations,” Pacific Economic
Review,” forthcoming, 2015.

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