Economies of Scale, Natural Monopoly, and Imperfect Competition in an Experimental Market
Author(s): Charles R. Plott, Alexandre Borges Sugiyama and Gilad Elbaz
Source: Southern Economic Journal, Vol. 61, No. 2 (Oct., 1994), pp. 261-287
Published by: Southern Economic Association
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Economies of Scale, Natural Monopoly,
and Imperfect Competition in an
Experimental Market*
CHARLESR. PLOTT
CaliforniaInstituteof Technology
Pasadena, California
ALEXANDRE BORGES SUGIYAMA
Universityof Arizona
Tucson,Arizona
GILAD ELBAZ
IBM Corporation
San Jose, California
I. Introduction
This paperreportson the behaviorof marketsin which all agentshave identicalcosts with economies of scale over the entire range of demand. Each firm, by choosing a larger scale of plant
and a largervolume, can experience lower averagecost. Thus, the marketsare characterizedby
the fundamentaltechnological propertythat has motivateddecades of theorizing about natural
monopoly and imperfect competition. The primaryquestionposed by the researchis whetheror
not a naturalmonopoly emerges and sets prices at monopolylevels, or whetherthe data are more
closely approximatedby some alternativemodel of imperfectcompetition,such as monopolistic
competition, Cournotoligopoly, or contestablemarkettheory.
Some of the principle results of the experimentsreportedhere can, in retrospect,be interpreted as having been anticipatedby the pathbreakingwork of Coursey,Isaac, Luke and Smith
[1, 69-84], and by Coursey, Isaac, and Smith [2, 91-113]. While these previous experiments
involved economic environmentsthat were much less complicatedthanthe one studied here, the
tendencies previouslyobserved are clearly presentin the behaviorsreportedhere. So, in a sense,
the results reportedhere can be interpretedas a majorextension of the previousresults, as well
as replicationand robustnesscheck.
The similaritiesof experimentaldesign with previousexperimentsrest on the facts of falling
average cost and no barriersto entry that existed in all experiments. However,the numberand
*This paperbegan with a projectin an experimentaleconomics class at Caltechin which G. Elbaz and A. Sugiyama
were undergraduatestudents. In addition to the authors, Peter Ying contributedto the project during the initial stages
of research. The comments of William Novshek are also appreciated.The financial supportof the National Science
Foundationand the Caltech Laboratoryfor ExperimentalEconomics and PoliticalScience is gratefullyacknowledged.
261
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262
CharlesR. Plott, AlexandreBorges Sugiyamaand Gilad Elbaz
natureof departuresfrom the previous researchare substantial.The marketsstudied here were
much larger, so parameterstook values in a more continuousmanner.The experimentsstudied
here involved two markets, so entry into the falling averagecost marketwas accompaniedby
the opportunitycost of profits foregone in the alternativemarket.The alternativemarketwas a
computerizeddouble auction which agents generallyenjoy, so entry into the falling averagecost
marketdid not result from an attemptto relieveboredom,which one mighthave suspectedplayed
a role in previousstudies. Agents enteringthe fallingaveragecost marketwere requiredto make a
choice of scale of plant thataffectedcosts. Thus, the theoryof cost minimizationplayed an active
role in developing models. This dimension was completely absent from previous experiments.
Previousexperiments used linear averagecosts that fell with volume until a capacity constraint
was reached (within the range of demand)and then costs became vertical. Averagecosts in the
experimentsreportedhere were nonlinearand fell throughoutthe range of demand. In addition,
the nonlinearities,scale economies, and demandwere configuredto create Cournotequilibriain
the appropriateCournotmodel of the environment.The Cournotequilibriawere separatedfrom
the competitive (price equals averagecost plus opportunitycost) equilibrium.In previousexperiments the Cournot equilibriumwas also the competitive equilibrium.The numberof potential
entrantsused in previous experimentswas small, rangingfrom two to four. In the experiments
reportedhere, there were seven potential competitors.Briefly put, the choice of parametersfor
the experiments reported here was such that the economic environmentwas similar to those
commonly found in the figures in economics textbooks.
II. Experimental Environment, Design and Procedures
A total of three experiments were conducted. Subjects were studentsat the CaliforniaInstitute
of Technology and summer interns at Caltech. Some of the subjects were experienced in the
operationof electronic markets. As it turns out, the empiricaltendenciesthat were observed in
the experiments are so pronouncedthat only three experimentsappearto be needed to answer
the original question posed. Since the experimentsare expensive in terms of time and money, a
decision was made to limit the numberof experimentsto three. Given the behaviorexhibitedby
the twenty-one people studied, the expectationthat anythingwould be learned from additional
replicationsseems too low to justify the cost.
Each experimentconsisted of 7 buyersand 7 sellers. Subjectswith experience were placed
in the more complex role of sellers. Two marketswere created. They will be called marketA
and marketB. The buyers could participatein both. Sellers could participatein either but not in
both. In marketA sellers had identical cost functionsdesigned such that they were guaranteed
a rent from participatingin the market.The parameterswere chosen such that in marketA the
rentsper seller and the marketprice were (theoretically)independentof the numberof sellers that
chose to sell in that market. MarketA was organizedby a (computerized)double auction that
fully occupied the attentionof the sellers that chose to functionin that marketso they would not
be motivatedby boredomto enter marketB.
Market B was different. Sellers that chose to operate in marketB made irrevocabledecisions about scale of plant, the quantitythat they would offer for sale and the price they would
post. Thus, the marketorganizationwas the standardposted price environmentin which commitmentswere privateinformationuntil the marketopened. The only differencewas that a seller
could choose to drop out of the marketonce the decisions of other sellers were public but before
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SCALE, NATURAL MONOPOLY,AND IMPERFECTCOMPETITION
263
1200
Demand in MarketA
1000
P 600
-
400
200
o-
I
I
10
20
40
50
x
50
Figure 1.
the market opened. The decisions to drop out were also private (revealed simultaneously) and
irrevocable. The dropout decision served to limit losses to the opportunity cost of market A profits
foregone, and reduced the probability that subject bankruptcies would disrupt the experiment. In
market B all sellers had the same cost function. The cost function was characterized by economies
of scale.
In summary, the economic environment had the following properties:
1. Participation in market B involved an opportunity cost because reasonably predictable
rents could be gained from participation in market A.
2. Participation in market A was "fun" in the sense that many people enjoy the speed and
activity of the computerized double auction.
3. Participation in market B could be done without exposure to a major out-of-pocket loss.
Sellers could "drop out" if they expected volume to be less than was anticipated at the
time that scale of plant was chosen.
4. All transactions took place in a currency called francs. Each franc was converted to
dollars at a rate of .0075 for buyers and .006 for sellers.
The Market Environment
A continuous approximation of market demands for markets A and B are contained in Figure 1.
The equation for the continuous approximation of the market demand in market B is
P = 1110- 25x.
(1)
Individual parameters for the demanders are in Table I. Each of seven demanders made
money by participating in market A and in market B. Each buyer had the same redemption values
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264
Charles R. Plott, Alexandre Borges Sugiyama and Gilad Elbaz
Table I. IndividualIncentives
Market B
Market A
Costs**
Market Demand***
Unit
Demand*
1
1000
550
1085
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
1000
1000
400
400
400
400
400
400
400
400
400
400
400
400
550
700
700
700
700
700
700
700
700
700
700
700
700
700
1060
1035
1010
985
960
935
910
etc.
-25 each unit
*All buyer agents (00 through06) had the same demandas listed here.
**All seller agents (07 through 13) had the same costs as listed here.
***Individualagents demandrotatedeach period
in market A each period. That is, in market A both the market demand and the individual redemption values were constant over periods. In market B, the market demand was constant over
periods but the redemption value of each individual changed from period to period. A fixed family
of schedules was rotated among the individual demanders. The rotation schedule is contained
in Plott, Sugiyama, and Elbaz [8]. The rotation convention was used because uncertainty about
which model might be most accurate gave us little confidence in our ability to predict incomes of
buyers. We wanted the income of all subject buyers to be sufficiently high to keep their interests.
The rotation had a useful feature of removing dramatic asymmetries. Each of seven sellers had
identical costs throughout the experiment. The fact that the costs were identical was not known
by any agent in the markets. Each had the option of participating in either market A or in market
B, but not in both. A seller that participated in market A used the cost schedule in Table I. For a
single seller the graph of the (marginal) costs are included in Figure 1. As can be seen, the seller
had two low cost units and then had constant cost afterwards for enough units to satisfy the entire
demand.
Given these individual costs in market A, the market price (according to the competitive
model) will be constant at 700 at all volumes near the demand (at 21 units) regardless of the
number of suppliers in market A. As will be stated more clearly below, the equilibrium price will
be near 700 and rents for all sellers in market A will be about 300 (2 units at 150 = 700 - 550
each) regardless of the number of other sellers in market A, as long as there are at least two.'
The costs of all seven suppliers were the same for market B. Each subject had separate tables
1. Typically,two or three sellers are enough for competitiveequilibriumbehaviorin a double auctionmarket.
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SCALE, NATURAL MONOPOLY,AND IMPERFECTCOMPETITION
265
(in differentcolors) for marginalcost, averagecost, and total cost. The total cost table is shown
as Table II. As can be seen, costs dependedupon both scale of plant and volume of sales.
A continuous approximationto the underlyingdiscrete parametercost function has been
useful in the development of behavioralpredictions, as well as experimentaldesign decisions.
Figure 2 contains a graph of the long-runaveragecost curve in this continuousmodel, and also
the short-runaveragecosts for selected scales of plant. A continuousapproximationof the market
demandcurve is imposed over the averagecost for comparison.
The formula for the competitive model is as follows. The model is restrictedto the values
of parametersin the range of the tables of costs. The model begins with short-runaverage cost
(SRAC)which depends upon output and the scale of plant (x, s). In the discrete values of costs
in the table the scale of plant is indicatedby letters of the alphabet,startingwith the letter A. In
the continuousmodel, if scale is A then s = 11; if scale is B then s = 12, etc., with a change of
one in s as the letters change:
SRAC(x,s)
= 3/4(x - s)2 + 1/4(s - 40)2 + 300.
(2)
The optimum scale of plant given a quantityx is indicatedby s*(x). The formulais
s*x) = 10 + 3/4x.
(3)
Substituting(3) into (2), the long-runaverage cost function,LRAC(x) is obtained.
LRAC(x) = SRAC(x,s*(x)) = 600-
15x + 3/16x2.
(4)
Of course this yields the long-runtotal cost (LRTC)and the long-runmarginalcost (LRMC)
as follows:
LRTC(x) = 600x - 15x2 + 3/16x3
LRMC(x) = dLRTC(x)/dx
= 600 - 30x + 9/16x2.
(5)
(6)
The continuousmodel will be very useful to the interestedreader.The complicatedcalculations for the equilibriaof variousmodels were first done in the context of the continuousmodel.
The location of the equilibriain models based on discreteparameterswas always nearby.
MarketOrganization
MarketA was a computerizeddouble auction.MarketB was a posted price market.Both markets
opened at the same time for trading. Sellers were informedaboutthe marketdemandfunction in
marketB but they knew nothing about the marketdemandfunctionin marketA. Since marketA
followed standardproceduresfor MUDA markets,2only the timing and the details of marketB
need to be reviewed.
Before each period all seller agents were requiredto decide which marketthey would enter.
After deciding they (privately)drew a large X throughthe recordsheet of the marketnot chosen.
Agents choosing marketB would then fill in the blankson theirrecordfor the period committing
2. See Plott and Gray [6, 245-58] for a detailed descriptionof this market,or see Plott [5] for a descriptionof the
computerizedversion.
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Table II. Cumulativeor Total Costs
Production Schedule
__
A
__
Total
Units
Sold
I
2i
3
4
5
6
7
V
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
565
a
587
C
590
1142
1675
2188
2686
3174
3656
4136
4619
5110
5613
6132
6672
7238
7834
8464
1142
1670
2176
2664
3138
3603
4064
4525
4990
5464
5952
6458
6986
7541
8128
1146
1672
2172
2651
3114
3565
4008
4448
M71
Afl0
9414
10122
.10580
.
9018
9676
Q133
9846
10607
.I11420
. .. .
12290
13222
4890
5338
5796
6269
6762
7279
7824
.
.
11692
I
.
.
.
.
.
10380
11135
__
__
__
E
603
F
613
G
H
I
624
638
653
J
671
K
690
L
712
M
735
N
761
0
788
p
818
Q
849
1154
1679
2176
2649
3102
3540
3968
4390
4810
5233
5664
6107
6566
7046
7552
1166
1693
2188
2656
3102
3530
3944
4349
4750
5151
5556
5970
6398
6844
7312
1182
1712
2208
2674
3114
3533
3936
4327
4710
5090
5472
5860
6258
6671
7104
1202
1738
2236
2701
3138
3551
3944
4322
4690
5052
5412
5775
6146
6529
6928
1226
1769
2272
2739
3174
3582
3968
4336
4690
5035
5376
5717
6062
6416
6784
1254
1807
2316
2786
3222
3628
4008
4367
4710
5041
5364
5684
6006
6334
6672
1286
1850
2368
2844
3282
3687
4064
4417
4750
5068
5376
5678
5978
6281
6592
1322
1900
2428
2911
3354
3761
4136
4484
4810
5118
5412
5697
5978
6259
6544
1362
1955
2496
2989
3438
3848
4224
4570
4890
5189
5472
5743
6006
6266
6528
1406
2017
2572
3076
3534
3950
4328
4673
4990
5283
5556
5814
6062
6304
6544
1454
2084
2656
3174
3642
4065
4448
4795
5110
5398
5664
5912
6146
6371
6592
1506
2158
2748
3281
3762
4195
4584
4934
5250
5536
5796
6035
6258
6469
6672
1562
2237
2848
3399
3894
4338
4736
5092
5410
5695
5952
6185
6398
6596
6784
1622
2323
2956
3526
4038
4496
4904
5267
5590
5877
6132
6360
6566
6754
6928
R
883
1686
2414
3072
3664
4194
4667
5088
5461
5790
6080
6336
6562
6762
6941
7104
7807
7561
7348
7170
7025
6915
6838
6706
6787
6813
6872
6966
7093
7255
8334
8897
7794
8270
7576
8013
7398
7795
7254
7614
7146
7472
7074
7367
7038
7301
7038
7272
7074
7282
7146
7329
7254
7415
7398
7538
OADn
60
848
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annf%
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Choice .-......>
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9381
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18176
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15094
16092
17177
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17560
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16643
21UUU
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17700
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SCALE, NATURAL MONOPOLY,AND IMPERFECTCOMPETITION
267
700 -
650 -
600 -
550-
500 -
300-
LAC
250 -
200
I
0
5
10
I
15
I1
20
25
I
30
35
I
I
40
45
Figure 2. Long-RunAverageCost, Selected Short-RunCosts and MarketDemand
themselves to a scale of plant, a quantityto be offered, and a price. The computerizedMUDA
programallows the simultaneousoperationof multiplemarkets.Each of the seven sellers was assigned to a "personalmarket"in which no other seller could participate.The sellers would enter
their (price, quantity)pairs in an orderbox fixed on their individualmarkets.At the appropriate
(public) signal each seller would press the enterkey, therebymakingtheirprivatedecisions public
to all buyersand sellers as they were displayedby the computeras asks (to sell) in their individual
markets.Once sellers had seen the asks of other sellers, they had the opportunityto cancel their
own asks. This was done simultaneouslyon signal. Sellers canceling asks were not permittedto
enter the A market.They did nothing for the remainderof the period. Thus, sellers who entered
marketB and canceled experiencedthe opportunitycost of A profits.
After sellers who had made the decision to enter marketB had the opportunityto cancel, all
marketsopened for trading. MarketA proceeded along the standardlines for the computerized
MUDA. In marketB, sellers who remainedeach had a price posted and a maximumquantity.At
any time duringa period buyerscould toggle to any of these marketsand purchasethe numberof
units desired at the posted price, up to the amountfor sale that the seller had left. Buyers could
only accept the asks in these markets. That is, they could not tenderbids in any marketexcept
marketA.
A comment about the organizationis in order.MarketA was a double auctionand it existed
as a source of income and entertainmentfor those who chose not to enter marketB. MarketB
was a posted price marketbecause it is thoughtto providethe best circumstancesfor monopoly
behavior[10, 83-106]. When the demandfunctionis known, and prices are posted, the seller is
most likely to successfully charge monopoly prices. Double auctions are known to have strong
tendencies to converge to a competitiveequilibriumeven in the presenceof monopoly. If market
B had been a double auction, then any tendencyto converge to a competitiveequilibriumcould
have been attributedto the marketmicrostructurealone, as opposed to the industrialorganization. Thus, the posted price institutionwas thoughtto be a more favorableenvironmentfor the
emergence of monopoly pricing than the double auction.
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268
Charles R. Plott, Alexandre Borges Sugiyama and Gilad Elbaz
The cancellationpropertyis importantas a risk reductionfeaturein this type of market.If a
seller chooses a large scale of plant and succeeds in selling only a few units, large losses can be
experienced. Buyers have the capacity to punishhigh-pricedsellers by purchasingonly a unit or
two. Similarly,well-meaningbuyers who want to sharethe volume by spreadingpurchasesover
sellers can be very costly to a seller who does not otherwiseget the volume. Likewise, accidental
purchasescan be very costly. Cancellationallows those sellers who choose relativelyhigh prices
the opportunityto avoid such risks.
The experimentcontained one other special feature. A marketdemandfunctionfor market
B was privatelydistributedto the sellers on a sheet of paper.All sellers knew what it meant. The
demand function given sellers was actually 10 francs below the actual induced values. Buyers
typically do not tradewithout a small profitmarginfor themselves. We believed that the function
we gave them was a better model of what they would experiencethan would be the actual limit
values.
Procedures
The experiments were conducted in the Laboratoryfor ExperimentalEconomics and Political
Science at Caltech. Subjectsconsistedof undergraduates,graduatestudentsat the CaliforniaInstitute of Technology, plus high school students who were attendinga special summer program.
Most had previous experience in some type of computerizedmarket.All had paged through a
computerizedinstructionroutine that familiarizedthem with key functionsand the mechanics of
makingbids, offers, and acceptances.
In additionto the three experimentsreportedhere, pilot experimentswere conducted. The
pilot experimentswere discardedbecause they typicallyinvolvedchoices of parametersthat were
based on a miscalculationof the theoreticalmodels. The parametersand proceduresof one experiment were exactly like those reportedin this paper but the data are not reportedbecause
one subject evidenced substantialconfusion. The results of these unreportedexperiments appearedqualitativelysimilarto the experimentsthatarereportedhere. Space constraintseffectively
preclude their publication. Should anyone want to study them in detail, the data will be made
availableupon request.
Experimental sessions which lasted on the order of three hours began in the evening at
about 7:00 P.M. The detailed instructionsthat were read to the subjects are contained in Plott,
Sugiyama, and Elbaz [8]. In addition, the materialpresentedon the chalkboardand the step-bystep proceduresfor conductingthe experimentare also included.
The highlightsof these experimentalproceduresare as follows. Subjectswere paid a "show
up" fee of $5.00 if they were extras and were turnedaway from participation.Subjects agreed
to work off any losses incurredduring the experimentat a rate of $10.00 per hour. Of course,
buyerscould make no losses unless they resultedfrom some sort of (foolish) speculationor from
a typo. Contractsinvolving obvious typos thatwould resultin large losses were always voided by
the experimenter(a standardpractice). However,sellers could make a loss. If a seller enteredthe
B marketat a substantialscale of plant and sold only a small numberof units the losses could be
considerable.
Sellers who wanteda sure returncould participatein the A market.The design of this market
was such that a rent of $1.80 per period was almost certainfor participationin marketA and the
seller was exposed to no possibility of a loss. On average, each participantmade approximately
$30 from the experiments.
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SCALE, NATURAL MONOPOLY,AND IMPERFECTCOMPETITION
269
Each seller was provided cost schedules for marketA sales.3For marketB each seller had
color-coded tables that gave marginalcost (pink), averagecost (green), and total cost (yellow),
of combinationsof volume and scale of plant on 11 by 14 sheets of paper. Scale of plant could
take 24 values, labeled A throughY.
Two practiceperiods were conducted.The parameterswere the same as those thatwere used
in the experiment. The mechanicsof the experimentwere very complex and many questionswere
promptedduring these sessions. The answersto all questionswere given publicly in a form that
yielded no informationabout parametersthat was not alreadypublic. After each period, for the
firstfive periods (includingthe two practiceperiods), the accountingof each subjectwas checked
and spot checks were made throughoutthe experiment.
III. Models
Tendifferenttypes of models can be appliedto the economicenvironment.Of coursethese models
share many basic principles but they also differ in many ways. Some give sharppredictionsand
the others remain vague. Where possible the models will be applieddirectlyto the environment
in a technical, mathematicalfashion. Speculationsand theorizingabout which model might be
expected to fit the data best are not consideredto be partof the exercise at this stage of the experimentalinquiry.Table III contains a summaryof the predictionsfor those models for which
predictionscan be computed. The paragraphsbelow will briefly describe each model listed in
the table.
A note on efficiency may be useful, especially for those who are not familiarwith experimental economics. The measure inventedby Plott and Smith [7, 133-53] is a direct adaptation
of consumers' and producers' surpluses. The buyers receive franc redemptionvalues from the
experimenterthat can be modeled as a (derived)demandfunction. The total value of francs redeemed by buyers is like the gross benefits to buyers from the units they acquired. Sellers pay
francsto the experimenterfor units sold. These paymentsarecosts. The allocationthatmaximizes
gross benefits minus costs is the most efficient. It is the one thatmaximizesfrancearningsof subjects (exhaustsall possible gains from exchange). Actualfrancearningsdivided by the maximum
possible is the efficiency with which the system is operating.
Under ordinarymodes of organization, 100 percentefficiency of operationis thoughtto be
unattainablein the downwardsloping averagecost case. If a single price is charged, and if price
is equatedto marginalcost, then sellers would lose money.This degree of inefficiencyis thought
to be structuralin the falling-averagecost case.
Otherpracticalsources of inefficiencyexist. Toughbargainingsometimesresults in failures
to trade. Suppliers might choose the "wrong" scale of plant and therebyimpose more costs on
the system than necessary. Suppliersmight choose to enter the B marketand then cancel. The
efficiency loss would be due to the opportunitycost of the low cost unitsthat such supplierscould
have delivered to the A market. Suppliersmight choose an unnecessarilylimiting quantityof x
offer to the marketB. In the section on models the efficiencyof the equilibriaallocationpredicted
3. Rounding errors caused slight discrepanciesbetween these schedules. For example, total cost at the contested
marketequilibriaof scale W and volume 31 was 9765, if computedfrom the averagecost table, and it was 9773 as listed
on the total cost schedule, a differenceof 4.8 cents.
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TableIII. ModelsandPredictions
MarketB
Model
1. Naturalmonopoly
Per
Per
Number
Agent Number
of
Profit
of
Scale Market Market Agent
Agents Choice Price Volume Volume (Francs) Agents
I
2. Tacit collusion
M
684
17
17
-
-
-
-
609
600
20
20
10
1400
6
7
498
670
20
20
31
31
5
4
31
(31,0)
351
228
302
(302,0)
0
0
2
3
(1)
(2)
G,H
Monopolistic Competition
(Sym. Cournot)
5. Quadopoly*
6. Quintopoly*
7. Perfectlycontested (competitive)
8. Over-contested
4
5
I
5
C,D
C
W
W
9. Unstable ("Bertrand")
10. Market collapse
0
3. Cournot(sym) duopoly
4. Cournot(asym) triopoly*
D,E
E
-
600
600
325
325
-
4841
-
-
in pricedetermination.
a transaction
costwasimposedas a parameter
*Foreaseof computation
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6
-
5
4
3
2
6
2
7
SCALE, NATURAL MONOPOLY, AND IMPERFECT COMPETITION
271
Price
1000 -
800 -
SRMC
600
LRMC
400
-
200 -
Demand
\MR
? ^
0
I
10
I
20
I
30
I
50
I
40
Ouantity
Figure 3. Monopolist in MarketB: A ContinuousApproximation
by each model is listed. The logic of each of these modelsjustifiesthe natureand potentialreasons
for inefficiencies.
NaturalMonopoly(Classical)
The classic model is naturalmonopoly. According to this model, because of the existence of
economies of scale, competition will lead to the existence of a monopoly. All other sellers will
participatein marketA. This monopoly facing the marketdemandcurve will choose the profit
maximizing value of variableswithout regardto the effect that this action might have on the actions of other sellers, such as their proclivity to enter marketB. That is, where P = D(x) is the
marketdemand function and long-runcosts are C(x,s(x)) the monopolist sets the value of the
variablesto
(x)x - C(x, s (x))].
maximize[D
x
For the parametersof the experimentthe solutionis a price of 684, a quantityequal to 17, a scale
of plant of size M and a profit of 4841 in francs. These can be read from the table. Figure 3
demonstratesthe model. For convenience the continuousmodel, which is only an approximation
of the underlyingparameters,is used in the figure. The accuratepredictionsbased on the discrete
environmentare in Table IV.
TacitCollusion
Collusionmodels are very numerousdependinguponthe complexityof the agreementthat can be
enforced. It is assumed here that collusion would lead to choices of variablesthat are good from
the seller's point of view. We presumethat the values would be somethingbetween Cournotand
monopoly and that the volume would be similarlyrestricted.
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272
CharlesR. Plott, AlexandreBorges Sugiyamaand Gilad Elbaz
Table IV. ExperimentalResults:AverageTransactionPrices, Numberof Entrants,Volumes, Efficiencies
061191
A
Period P
062791
A
B
Vol.
P
Vol. N
Eff.
P
071891
B
Vol.
P
A
Vol.
P
697
704
682
693
701
703
696
697
694
696
696
696
639
696
697
695
700
697
697
21
21
21
21
21
21
21
21
20
23
21
21
21
21
21
21
21
23
21
403
351
350
340
324
319
319
318
330
325
320
321
319
330
328
324
403
321
29
30
30
28
31
31
31
31
31
31
31
31
27
31
31
33
19
0
31
21
336
28 2.4 90%
Vol. N Eff. P
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
717
691
696
685
691
703
696
700
698
701
691
698
698
700
702
700
700
700
701
22
21
19
21
21
21
21
21
21
19
21
21
21
21
24
21
21
22
21
325
312
325
324
322
315
323
320
321
400
350
345
330
335
328
327
326
323
30
31
30
31
31
31
31
31
31
28
30
28
31
31
0
32
31
31
31
5 92% 584
3 92% 727
2 92% 696
2 97% 709
3 97% 702
4 95% 701
2 99% 702
2 99% 699
1 100% 696
2 93% 698
3 72% 700
3 90% 701
3 97% 700
2 99% 699
3 32% 700
2 92% 700
2 99% 700
2 97% 700
2 94% 691
25
20
21
21
21
23
21
23
22
21
21
21
21
22
22
21
21
21
19
412
437
402
387
355
339
330
324
330
326
324
335
325
330
326
327
325
437
26
26
30
31
30
32
31
33
0
30
31
33
30
31
31
31
31
31
26
AV.
698
21
331
29 2.5 91% 695
21
356
29 2.6 91% 694
3
5
2
4
2
2
4
2
0
3
3
4
2
3
3
3
2
2
1
83%
88%
89%
94%
96%
95%
95%
95%
40%
96%
97%
95%
98%
95%
95%
97%
99%
97%
93%
B
Vol. N
Eff.
4 78%
5 85%
2 98%
3 93%
3 97%
2 98%
2 99%
3 97%
1 98%
2 96%
3 97%
1 100%
2 85%
1 98%
3 97%
3 97%
3 71%
3 34%
2 99%
Cournot Models
Cournot models are all derived from the same general principles. Each competitor evaluates the
market as if the quantity offered by the other sellers is a constant and the resulting market price
is that determined by the sum of the quantities offered by sellers. For insights about the structure
of these models, especially in the presence of non convexities as in the case with economies of
scale, see Novshek [3, 61-70; 4].
Application of the class of models to any real market, especially the ones created for these
experiments, might be met with three a priori criticisms/qualifications. First, the Cournot solutions to the technical problems are generally not unique. Typically, both symmetric solutions in
which all firms act identically and asymmetric solutions, in which some firms are larger than
others, exist. The symmetric solutions and those asymmetric solutions that have been identified
and seem plausible have been included in Table III. The second qualification is that the principles
that might govern entry into a market are not systematically integrated (unless lack of entry is
treated as part of an asymmetric solution) into the analysis. For this reason, a special treatment
of Cournot models, under a heading called monopolistic competition, is included. The third criticism is derived from the nature of the market structure itself. Agents in these markets post a price
and a quantity. There is every reason to assume that the seller with the lowest price will sell all
units that the seller offers, up to the demand function limits. The hypothesis that the quantity
sold by other sellers remains constant, will almost certainly be violated. Thus, the structure of
the decision problem might appear to resemble that of the Bertrand theory, more than Cournot,
depending upon how the posted quantity is treated in the analysis.
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SCALE, NATURAL MONOPOLY,AND IMPERFECTCOMPETITION
273
Price
800-
/
/
RMC*
/SRAC*
600
400-
LRMC
\\
LRAC
200
\
\
\Demand
\MR
0
10
20
30
40
50
Quantity
Figure 4. Quadopolistin MarketB: A ContinuousApproximation
All of the criticisms/qualificationsare derived in partfrom the fact that the Courot model
is incomplete as a theory. It is silent aboutthe natureof the price determinationprocess. If sellers
(or buyers) are supposed to be involved in price determination,then some sort of explicit coordinationdevice must exist that guides sellers to settle on the same price, and guides buyers so that
sellers share marketvolume in a Cournotfashion. Insteadof dealing with all of this complexity,
the Cournotmodel relies only on axioms typical of game theoreticrepresentationsof marketsthat
assertthat only one price exists, and furtherassertsthatthe one price is determinedby the law of
supply and demand once sellers' quantitychoices are given. Nevertheless,Courot models have
broadexperimentalsupportand must be takenseriouslyin any environmentuntilthe data suggest
otherwise.
The Courot solutions for duopoly and for triopolyare also in TableIII. Notice thatthe price
predictedis 609 and then becomes 600, regardlessof the numberof firms. Of course, firm size
must decrease as the number of firms increases. This means that the scale of plant chosen by
firms must be smaller undertriopoly than underduopoly.
MonopolisticCompetition
The classical model of monopolistic competitionis interpretedas a four firm Cournotmarket.
Scale of plants are small in the equilibriumand the opportunitycost of 300 francs ($1.80) is
barelycovered by the 351 profit. Entryof anotherfirmwould force the profitsto levels below the
opportunitycosts. In the table the Courot equilibriumprofitsfor quintopoly,a fifth firm, are less
than the 300 francs opportunitycost for enteringthe B market.Again, notice from the table that
the price predictionsare the same, regardlessof the numberof firms.
In Figure 4 is shown a representativefirm in the four firm equilibrium.The background
shows the marketdemand function. The costs graphsare from the continuousapproximationof
costs given by equation (4).
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274
CharlesR. Plott, AlexandreBorges Sugiyamaand Gilad Elbaz
ContestedMarkets
The contestable market literaturehas motivated researchersto look for two differenttypes of
phenomenain experimentaldata. The possible phenomenonare called "models" here, but they
operate more like statementsthat characterizethe extremes of what one might expect in data.
Of course, those extremes and the relative tendencies toward them contain potentially useful
information.
Perfectly ContestedMarket (Competitive)Equilibrium.This is the case in which only one
seller exists in the market. The seller produces at a price and output that leaves price equal to
average cost, including opportunitycost. The profits in marketA and marketB would be the
same (therebyjustifying the use of the term "competitive").As indicatedin the table, the price
of the single entrantwould be 325; volume would be 31; scale of plantwould be W, and the other
six sellers would be in marketA. The relationshipsare in Figure3.
Without side payments, such as a subsidyto compensatea firmfor losses, and a completely
different institutionalarrangement,such as marginalcost pricing, or the incentive compatible
equivalent, averagecost pricing might be the best that can be expected from a consumer'spoint
of view. It is used as a measurefor 100 percentefficiency.
Over-ContestedMarketEquilibrium.This model postulatesthatthe price and quantitiessold
would be the same as the perfectly contestedoutcome above. The only differenceis the number
of firms that have decided to enter. Previousexperimentshave definedthis model to predictthat
all of the potentialfirmsenter. Obviously,the plausibilityof such phenomenawould a prioriseem
low but this model is included as a benchmarkerfor completeness.The number,5, is takento be
the maximumthat could leave marketA and still have it behavecompetitively.
Unstable("Bertrand")
We do not know the equilibriumof the Bertrandmodel of these experimentalmarkets.Presumably
it involves some sort of mixed strategy.In the data this would appearas a type of variabilityin
prices. At this point the model is includedfor completenessandto drawattentionto the possibility
that the data might not exhibit any type of monotone convergenceproperty.It is also included
to draw attentionto the fact that the literaturecontains suggestions about how such variability
phenomenamight be modeled should it be observed.
MarketCollapse (Type 1)
Entry into the contested marketwill involve a cost. The possibility of out-of-pocket losses also
exists. Since there are no mechanismsfor coordinatingentry, sellers might all decide to operate
only in the A market. Under such a circumstancethe supply in B would be zero. The market
would have collapsed. Type 1 collapse is the case when no firmentersthe B market.
MarketCollapse (Type2)
The second type of collapse can occur when more than one firm decides to enter but all cancel
leaving no one to supply the market. This is a type of coordinationfailure which can occur
because the decisions to cancel marketB offers are made simultaneously.
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SCALE, NATURAL MONOPOLY,AND IMPERFECTCOMPETITION
275
IV. Results
The centralresults are easy to state. The contestablemarketsmodel is the most accurateof those
considered. After a brief review of the data, the discussionturnsto makingclear the strengthof
this centralproposition. Following the main results, the remainderof this section is devoted to a
discussionof a series of five observationsaboutboth individualand systems behavior.
A typical price time series for both marketsare shown in Figures 5 and 6. Figure 5 contains the time series for marketA, and Figure 6 contains the time series for marketB. Vertical
lines separateperiods. The measure of time differs in the two figures. In marketA the measure
is seconds. In marketB the measure is the numberof events (e.g., asks, contracts)because the
high speed with which events occur in clock time make them indistinguishable,given the units
(seconds) in which clocktime is measured.
The horizontallines in the figuresshow the price predictorsfor variousmodels. The top line
is the monopoly price. The second line is the price predictedby all Cournotand monopolistic
competition models. The bottom line is the "competitive"price predictedby the contestablemarketmodel. Contractsare indicated by circles in both the A marketand the B market;and
in marketB the prices posted by sellers are displayedby small triangles. Cancellationsin the B
marketsare not shown, but in most cases all sellers in the B marketcanceled, except the seller
with the lowest posted price.
Figure 7 contains the price and volume data pooled across all experiments.Each dot represents a period in one of the three experiments.The marketdemandfunctionand the predictions
of selected models are also shown in the figure.
The visual impressions are that prices convergedto the competitiveequilibriumin market
A and that prices converged to the one predicted by the contestable-marketmodel in market
B. These visual impressionsare essentiallycorrect. The firstresultsreportedin this section make
the natureof the data that supportthese impressionsprecise.
The first result is a traditionalstatementintendedto preventany misconceptionsabout what
is being reported. Sometimes experimentaldata are predictedby models in an accuratestatistical
sense. However,in most cases none of the models are statisticallyaccurate.The firstresult makes
clear that these models contain unanticipatedand unexplainederrorsand, thereby,sets the stage
for all subsequentanalysis.
RESULT1. All models can be rejectedas a statisticallyaccuraterepresentationof the data.
Support.All models are staticequilibriummodels. However,the datafor the B markets,such
as the one contained in Figure 6, exhibits an obvious type of convergencepatternwhich is not
capturedby any of the models, even if a randomerrortermis added. In the absence of additional
theory appendedto the models to take care of the dynamics, the models are rejected. I
The second result is perhaps the central result of the paper. It states that the contestable
markettheory is the one best supportedby the data.
RESULT
2. Afterthefirst six periods, all relevanteconomicvariables(prices, volumes,profits,
scale of plant choices, and efficiencies)are closer to the predictionsof the two contestablemarket
modelsthan to the predictionsof any other model.
Support. Each of the variables will be discussed in order. All models predict competitive
behavior in the A markets. The competitive price is 700 and the volume is 21. In 51 of the 57
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C/NATMONOP/061191E.STA
1000 h
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Figure 5. MarketA, Price Time Series, Experiment061191
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_
3214
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709
AL
827
945
I
CharlesR. Plott, AlexandreBorges Sugiyamaand Gilad Elbaz
278
N
1000-
\
\
\
Monopoly
Monop-CompDuopoly
+
600
P
+
\
-^
'
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I
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15
20
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I
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35
40
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50
x
Figure 7. Period Prices and Quantities, All Periods, All Experiments
periodsof all experimentsthe averageprice of the periodwas within 10 francs(6 cents for sellers
and .75 of a cent for buyers) of the competitiveequilibrium.In 56 of these periods the volume
was within 3 units of the 21 predictedand in 41 periods the volume was exactly 21 units. The
relevantdata are in Table IV. Since the price and volume in the A marketsbehaved substantially
as predictedby all models, the relevantcomparisonsare all in the B markets.
In the B marketsprices and volumes tended to be closer to the contestablemarketmodels
thanany of the others. In 41 of the 57 periods, prices were within 10 francsof the price predicted
by the contestable-marketmodels (325). In no period was the price within 10 francs of the price
predictedby the naturalmonopoly model (684), and in no period was the price within 10 francs
of the price predictedby any Coumot model (609). The count comes directly from the data in
Table IV and the predictions in Table III. Similarly,the volume was within three units of the
contestablemarketprediction(31) in 49 of the 57 periods. It was neverthatclose to the prediction
of the naturalmonopoly model (17), and it was never within threeunits of the predictionsof the
Courot models (20). Price and marketvolume figuressupportthe contestable-market
model over
the others.
Volume of individualfirmsfurthersupportthe contestabilitymodel over the Courot models
and the monopolistic competitionmodels which, because of symmetryassumptions,predictthat
all B marketentrantswill have the same volume. In 53 of the 57 periods no more than one firm
had positive sales in the B market.Thus, in 53 of 57 periods the data supportcontestabilityover
monopolistic competition. In none of these three periods in which more than one firm made B
market sales, was the distributionvolumes near equality as predictedby the symmetric game
models. As will be implicit in the discussionsbelow, sellers thatchose to enter the B marketdid
not limit their quantitiesas requiredby the Coumot model and as they could have done underthe
procedures.
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SCALE. NATURAL MONOPOLY. AND IMPERFECT COMPETITION
279
In marketB profit levels predictedby competing models are in Table III. Profits should be
at, or above 300, which is the (nearly) certain profit that can be obtained for participationin
marketA. Actual profits are in Table V,A. The listing of actual profits of sellers in market B
are in Table V,B. The "active" firms referencedin the table are those that did not cancel their
posted offer after they had seen the offers of other sellers. Shown also is the numberof sellers
thatenteredthe B marketat the beginning of the period.
Consider only the last four periods of the experimentsafter some level of equilibrationhas
been achieved. The averageprofit of the firms that sell units over all three experimentsis 451.6
francsper period. The averageprofitof all entrantsis 184.0 francsper period. Thus, the average
profit of sellers who entered marketB is closer to the 302 predictedby the perfectly contested
model than to the predictionof any other model, except quintopoly,which can be rejected since
the numberof sellers was always less than five. Considerationof more periods does not change
this conclusion. In fact, the conclusion is only reinforced.The averageprofitearned per period
by all entrantsin marketB, consideringperiod 3 and later, for the three experimentswas 29.4
francs, 279.0 francs, and 74.2 francs, respectively,far below thatpredictedby any model except
quintopoly.
The frequency of scale of plant choices is containedin TableVI. Only three choices are at
scale levels (D, E, G, and M) predictedby any of the alternativemodels to the contested market
model. The contested marketmodel predictsscale W, which is the mode of choices of sellers (41
choices out of 146 total). Over 40 percentof all choices are within one level of that predictedby
the contestable-marketmodel. The small mode at scale K is interestingbecause scale K was the
example used in the instructionsto illustratethe natureof costs.
Efficiency levels are reportedin Table IV. The averageefficiency level for the three experiments is .91, .91, and .90, which is much closer to the .94 predictedby the over-contestedmarket
model than it is the efficiency predictedby naturalmonopoly (80%), duopoly (76%), triopoly
(70%), monopolistic competition (67%), or marketcollapse (41%). On average, the perfectly
contested model is a better predictorof efficiencythan any of the noncontestedmodels.
In all dimensionsthe two contestablemarkettheoriesarebetterpredictorsthanthe alternative
models. If one is forced to choose between the perfectly-contestedmodel and the over-contested
model the choice will be the former. The averagenumberof entrantsper period is 2.56, which
is closer to the one predicted by the perfectly contested model than the five predicted by the
over-contestedmodel. I
The next five observationsfocus on aspectsof strategicbehaviorandon system behavior.The
first four of the observationsare relatedto individualbehaviorand the strategiesthat individuals
employ. The fifth observationis a summarypropertyof the system as a whole.
Observation1 suggests that people bias their choices of prices in favorof those divisible by
5 and that individual strategies exhibit a degree of modificationto take advantageof the underlying bias. For example, knowing about this bias, perhapseven in their own behavior, people
sometimes reduce their own price by a unit. That is, ratherthan quote a price of 325 an individual might quote 324; or a 330 quotationwould be modifieddownwardto 329 ratherthan, say,
increasedto 331.
OBSERVATION1. Price choices are asymmetrically distributed downward around numbers that
end in 0 or 5.
Support. Actual prices ending in 0 or 5 accountedfor a large percentageof choices (71 out
of 146). Of the two, prices ending in 0 were the most common, occurring50 times. Prices in a
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TableV,A. MarketA Profitby Experiment,
Period,Individual
Individl
Period
07
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
250
298
249
Experiment062791
Experiment061191
08
09
10
305 660
-
200
250
210
215
335
290
320
300
300
299
300
350
300
300
-
300
300
300
302
302
301
300
301
-
11
12
13
--
07
08
-
-2700
275
0
296
198
344
196 311
270 301
258 304 265
309
298 300 290
300
300 300 300 298 304
260 293
265
299 300 310 305 300
280
310 325 100 283
301
300
300
300
305
300
-
258
-
-
302
290
300
308
303
302
301
267
267
220
290
260
260
300
298
303
301
298
306
300
300
300
350
345
300
300
320
300
300
300
305
300
0
201
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09
10
325 300
310
11
-
870
300
400
300
12
13
290
07
0
-
.-
320 200 301
336
350
300
-
3
4
300 310 309
330
290 300 299
297 275 297 300
300300
293
300
290
280
280
444
300
298
298
300
3
3
3
3
3
300 300301 301
300300300 300
300 300
302
-
3
0
300
-
304
303 325 300 3
307 300 297-90
304 281 300 2
300
303
-
3
302
302
295
294 260 290 300
302
303
300
281
301
299
288
298
2
3
3
3
SCALE, NATURAL MONOPOLY, AND IMPERFECT COMPETITION
281
TableV,B. MarketB VolumeandProfit,by Individual,
by Period
Experiment061191
Indi12
09
10
13
11
07
08
vidual
Period Vol. Profit Vol. Profit Vol. Profit Vol. Profit Vol. Profit Vol. Profit Vol. Profit
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
0
0
31
31
0
0
-101
240
0
120
30
31 -194
22 -1166
0
0
31
457
31
612
0
0
0
0
31
364
0
0
0
0
8 -2936
28
504
0
0
0
0
28
0
0
0
0
0
0
0
0
31
31
0
0
0
0
271
209
0
32
480
2016
0
0
0
0
0
0
0
30
0
0
0
0
31
31
0
0
0
180
0
0
0
0
147
178
0
0
0
0
0
0
0
31 333
31 -612
Experiment062791
IndiIndl07
09
11
08
10
12
13
vidual
Period Vol. Profit Vol. Profit Vol. Profit Vol. Profit Vol. Profit Vol. Profit Vol. Profit
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
26
26
1
31
0
32
0
0
1950
2600
-456
2069
0
736
0
0
0
0
0
0
0
0
0
0
31
26
0
0
0
0
0
0
0
0
256
2600
0
0
0
0
0
0
0
0
0
0
0
0
33
0
0
388
31
31
31
31
0
209
364
333
364
0
0
0
0
0
29 2023
0
0
30 900
0
0
31
33
364
239
30
31
0
30
0
0
0
330
240
0
480
0
0
0
0
0
0
0
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0
0
0
0
282
CharlesR. Plott, AlexandreBorges Sugiyamaand Gilad Elbaz
TableV,B. Continued
Experiment071891
IndiIndividual
07
08
09
10
11
12
13
Period Vol. Profit Vol. Profit Vol. Profit Vol. Profit Vol. Profit Vol. Profit Vol. Profit
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
26
988
3 -1048
28
0
0
0
0
0
0
0
3 -1798
0
0
112
0
0
0
0
0
31
31
31
0
178
23
116
31
31
302
132
31
0
395
0
0
0
0
0
19
185
-952
0
33
0
0
0
0
0
0
0
27
0
0
487
0
0
0
27
30
0
0
0
0
31
31
0
0
31
0
31
0
0
0
0
31
263
870
0
0
0
0
85
302
0
0
178
0
302
0
0
0
0
178
neighborhood, +1, around 0 and 5, were also asymmetrically distributed, with the two numbers
9 and 4 being preferred to the two numbers 1 and 6 by a margin of 22 to 14. A hypothesis of
equal probability can be rejected at .01 level of confidence. I
The second observation suggests that behavior does not reflect the belief that the behavior
of others is independently random with probabilities represented by the relative frequencies of
choices. Table VII shows the relative frequencies with which price choices were made, together
with the expected profit that would result from various pricing decisions, given that the choices
of others are drawn with probabilities equal to the frequencies in the table. If the system was at a
Nash equilibrium, then the expected profit would be the same for all price choices.
OBSERVATION
2. Pricing strategies are not Nash responses given the relative frequency of
that
was
observed.
prices
Support. Consider the potential ask prices in Table VII. The high prices in the neighborhood
of 360 and 385 would yield a profit of 150 percent or greater of the lower prices. I
The third observation is that scale choices of agents are optimal given actual volumes sold by
sellers. This is particularly interesting because the scale choices are not optimal given the quantities offered for sale by sellers. Recall that sellers entering market B chose a scale, a price, and a
quantity offered. The observation is that the scale choice suggests that sellers (correctly) expected
to sell the market demand quantity but they offered a little more than that expectation in hope that
the volume would be (possibly accidentally) higher.
OBSERVATION
3. The scale chosen by agents tends to be optimum given the actual quantity
sold. Actual quantity sold tends to equal induced market demand given the quote of price. Quantity
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283
SCALE, NATURAL MONOPOLY,AND IMPERFECTCOMPETITION
Table VI. Frequencyof Scale of Plant Choice in All Three Experiments,All Periods
Scale
Number of Choices
3
A
B
C
D
0
3
E
F
G
1
0
0
Courot triopolyand more
1
Cournot duopoly
0
1
1
9
0
1
0
H
I
J
K
L
M
N
Monopoly
3
0
P
Q
1
0
R
2
S
8
T
U
V
w
X
7
25
21
41
3
Y
15
Contestedmarket
Table VII. Relative Frequencyof Price Choices in Periodsbeyondthe Sixth and Expected Profitsof Price Strategy
Price Range
318
325
330
335
p < 324
p c 329
<p ? 334
p < 339
340
Relative Frequency of
Posted Price
Profit if
Prob.* of
Low Price Choices
Strategy
Low Price
Low Price
Profit
325
330
335
302
457
612
0.79
0.54
0.43
238
256
257
Expected
19/90
22/90
10/90
5/90
0.21
0.24
0.11
0.07
p c 344
4/90
0.04
340
630
0.39
220
345 cp c 360
360 p
6/90
24/90
0.07
0.27
345
360
385
780
1230
1980
0.33
0.27
0.27
250
307
528
neglectingties.
*Computed
offered for sale is greater than actual sales and the scale of plant chosen is too small given the
quoted quantity.
Support. Figure 8 shows deviations of actual scale chosen from the theoretical optimum scale
given the price quoted by the agent. If the seller has the lowest price then the demand function
can be used to determine the quantity that will be sold. The quantity to be sold can be used
to determine the optimal scale for that quantity. The figure shows deviations from this optimum
where 0 indicates the optimum and + 1 indicates one letter deviations from the optimum. As can
be seen in the figure, the mode of choice is the optimum given the price.
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284
CharlesR. Plott, AlexandreBorges Sugiyamaand Gilad Elbaz
Frequency
70 -
1
60-
50-
40-
30-
20-
10 -
-17
-16
-15
-14
-13
-12
-11
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
2
3
4
5
6
Deviations from Optimum:Actual Scale ChosenMinusOptimalScale (given Price Posted)
Figure 8. Deviations from Optimum:Actual Scale Chosen MinusOptimalScale (Given Price Posted)
The same calculationcan be made using the quantitiesofferedfor sale. Figure 9 shows deviation of scale choice from the optimumgiven the quantityoffered. As can be seen, the scale
choices tend to be smallerthan this calculationof optimum. I
The next observationis that agents specialize in markets.Some agents are always in market
A while others have a propensityto enter marketB. Table VIII contains for each individualof
each experiment, the total numberof times duringthe nineteen periods of the experiment, the
numberof times the individualenteredthe B market.For example, the person with identification
number7 in experiment061191 enteredthe B market14 times out of the nineteenperiods, while
person 8 of that experimentnever entered.
4. Thefrequencywith whichmarketB is enteredis not the same across sellers.
OBSERVATION
Support.Test the hypothesisthatthe decisions made by the two individualswith the lowest
propensity to enter, were independentlydrawn from the same distributionas the decisions of
the two people with the highest propensity.The hypothesis is rejected at the .001 level of
significance. I
The final Observation5 concerns the behaviorof the whole marketsystem. As was noted
in Result 2, efficiencies are not at 100% as they should be if both the competitive model and
the perfectlycontested marketwere workingperfectlyto predictbehavior.On average, excluding
the first periods, the system of both marketsis operatingat an efficiency level of about 91.3%.
While this is much better than the 80% predictedby the naturalmonopoly model, or the 41%
predictedby the marketcollapse model, these two models suggest sourcesof inefficiencythatcan
be interpretedas the social cost of regulation.If more thanone firmhappensto enter the market
there is an opportunitycost of profitsforegone in marketA. On the otherhand, if there is under
entry (no firm enters and sells) an efficiency loss will exist due to the loss of consumer surplus
in marketB. The observationis that the efficiency loss from these two sources amountsto about
67% of the 8.7% averageloss in system efficiency (not includingthe firstperiods).
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SCALE, NATURAL MONOPOLY, AND IMPERFECT COMPETITION
285
Frequency
70-
50 -
40-
30-
20-
10 -
?0 I I
-17 -1,
-5
-, :n,:
I:I,i,
-9 -6 -7
-4
-14 -13 -12 -11 -10
, -5
-4
-3
-2
-1
0
1
2
3
4
, 5 ,!,6
Deviations from Optimum:Actual Scale ChosenMinusOptimalScale (given Ouantity Offered)
Figure 9. Deviations from Optimum:Actual Scale Chosen Minus OptimalScale (Given QuantityOffered)
Table VIII. Numberof Decisions to Enterthe B Marketin All Nineteen Periods:By Individual,by Experiment
Individual Identification Number
Experiment
061191
062791
071891
7
8
9
10
11
12
13
14
18
6
0
1
3
4
12
8
11
1
0
7
14
11
10
2
2
2
2
18
5. Excluding first periods, efficiency loss due to over entry is about 2.19% and
efficiency loss due to under entry is about 3.32%.
OBSERVATION
Support. If exactly one firm leaves market A and enters market B the system can operate
at 100% efficiency. This maximum possible efficiency expressed as a function of the number of
entrants, n is: maximum possible efficiency = 100 - (.01475)(n - 1) if n > 0. However, the
maximum possible efficiency is .41 if n = 0. Thus, (.01475)(n - 1) is the efficiency loss due to
over entry and .59 is the efficiency loss due to no entry (or under entry). Of course, both over
entry and under entry can occur at the same time if several firms enter and all cancel their asks
and thus sell nothing.
The number of firms that left market A with an intent to enter market B each period of each
experiment is contained in Table IV. Application of the formula to the numbers in the table produces for all experiments and for all periods (except the first periods), an average loss of .0219
due to over entry. The table also shows three periods, one in each experiment, in which no units
were sold in market B due to no entry either by virtue of leaving market A and canceling (two
periods) or by not leaving market A (one period). The efficiency loss averaged over all periods
except the first periods, is 0.0332. I
If the efficiency losses identified in Observation 5 are interpreted as the cost of market
regulation then the overall average efficiency loss of 8.7% can be decomposed into an implicit
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286
CharlesR. Plott, AlexandreBorges Sugiyamaand Gilad Elbaz
regulatorycost of 5.5% and "other inefficiencies" of 3.2%. Of course, whether or not this is
the least expensive regulationpossible is not addressedhere. The majorpoint is to identify the
inefficiencyand demonstratethat it can be measured.
Once the "regulatorycost" or "uncoordinatedentry cost" is removed, the remaining3.2%
efficiencyloss is of interest.This percentagerepresentsthe combinedeffects of typos, wrongscale
choices, inefficiencies due to strategic maneuvering,inefficiencies due to posted prices above
averagecost, etc. The fact thatthe combinedeffect of all sourcesof inefficiencyis small, strongly
suggests that, with the exception of uncoordinatedentry,the perfectlycontestedmarkettheory is
predictingalmost perfectly.That is, the cost expendedon this form of regulationhas been almost
perfect in achieving its desired effect.
V. Conclusions
This paperposed a series of questions. First, will increasingreturnsresultin a single seller? Will
the single seller charge a monopoly price? If a monopoly price is not charged, do models exist
that accuratelypredict what the price will be?
The answer to the first question is "yes." For the most part, all sales tend to be made by
a single agent. This is a particularlyinterestingresult since neithermonopolisticallycompetitive
or oligopolistic structurestended to evolve, even thoughthey could have. In particular,the data
provideno supportat all for Cournotmodels of industrialstructureand pricing.
The answerto the second questionis "no." Eventhoughsales were almostalwaysby a single
seller, monopolisticpricingdid not emerge. Instead,the single seller sold at prices nearthose that
would prevail if units were supplied at the lowest averagecost that covered the opportunitycost
of the supplying firm. The supplyingfirm chose to operateat a scale of plant and at prices such
that consumers paid the lowest possible price subject to the constraintthat the supplierdid not
make a loss. Briefly put, the system behaviorwas closer to that describedby contestablemarket
theorythan any of the other models considered.
In some respects, the data here providestrongsupportfor the conclusionsdrawnfrom other
studiesthatexperimentallyexaminedthe possibilityof contestabilitytheory.One could have been
concernedthat the results of other studies might have been due to subjectboredom, the linearity
of costs, the lack of latitude for monopolisticallycompetitiveorganizations,etc. The results of
this paperdemonstratethat such concernaboutpreviousresultsare not well-founded.The fundamental tendencies reportedby others were observed after all of the potential explanationswere
controlled.
To the extent that contestablemarkettheory fell shortof accuratepredictions,the natureof
the failureof contestabilitytheory is interesting.The tendencyto enterthe "monopolized"market
is too great and there is a chance that no one will enter. Firmstendedto enter the industryin the
hope that the incumbent would try to raise prices to near monopoly levels. Given the behavior
of the incumbent, these firms would have been better off participatingin alternativeeconomic
activity. In a sense, the policing activity was the cost of regulatingthe incumbent.Aside from
this monitoringcost, the system workedsubstantiallyas predictedby contestabilitytheory.
Obviously there exist many alternativeways to conduct experimentsand check the robustness of the results reportedhere. Existingtheory,especially game theory,is rich with suggestions
for furtherexperiments,Shapiro[9, 330-414]. Theoretically,the timingof decisionscould switch
marketbehaviorbetween Bertrandand Cournot.Theoriesof signaling,repeatedgames, and other
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SCALE, NATURAL MONOPOLY,AND IMPERFECTCOMPETITION
287
facets of dynamic rivalry,suggest variablesand circumstancesthatmighthave dramaticeffects on
behavior.The message, at this point, seems to be that futureresearchand experimentaldesigns
to explore these many possibilities should proceed on the presumptionthat contestabilitytheory
will have considerableexploratorypower.
References
1. Coursey,Don, R. MarkIsaac, M. Luke, and VernonL. Smith, "MarketContestabilityin the Presenceof Sunk
(Entry)Cost." RandJournal of Economics, Spring 1984, 69-84.
2. Coursey, Don, R. Mark Isaac, and VernonL. Smith, "NaturalMonopoly and ContestedMarkets:Some ExperimentalResults." Journalof Law and Economics, April 1984, 91-113.
3. Novshek, William, "FindingAll n-FirmCournotEquilibria."InternationalEconomicReview, February1984,
61-70.
4.
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Unit Double Auction." Social Science WorkingPaper no. 783, Pasadena:CaliforniaInstituteof Technology, November 1991.
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and PeterGray, "The MultipleUnit Double Auction."Journalof EconomicBehaviorand Organization,
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and VernonL. Smith, "An ExperimentalExaminationof Two ExchangeInstitutions."Review of EconomicStudies, February1978, 133-53.
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, Alexandre B. Sugiyama, and Gilad Elbaz. "Economies of Scale, Natural Monopoly and Imperfect Competitionin an ExperimentalMarket."Social Science WorkingPaperno. 773, Pasadena:CaliforniaInstituteof
Technology,revised February1994.
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R. Schmalensee and R. D. Willig. Amsterdam:Elsevier Science PublishersB.V., 1989, pp. 330-414.
10. Smith, Vernon L. "An Empirical Study of DecentralizedInstitutionsof Monopoly Restraint,"in Essays in
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Quirk. West Lafayette, Indiana:PurdueUniversityPress, 1981, pp. 83-106.
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