DP2015-30

Revisiting Marshallian versus
Walrasian Stability
in an Experimental Market
Junyi SHEN
Ken-Ichi SHIMOMURA
Takehiko YAMATO
Tokinao O HTAKA
Kiyotaka TAKAHASHI
Revised May 12, 2016

Revisiting Marshallian versus Walrasian Stability in an Experimental
Market*Junyi Shen†, ††, Ken-Ichi Shimomura†, Takehiko Yamato#Tokinao Ohtaka#, and Kiyotaka Takahashi#May, 2016
Abstract
We study dynamics in pit market trading by a laboratory experiment. Our exchange economy
model contains two types of consumers and two kinds of commodities, and three competitive
equilibria exist. The two equilibria with the lowest, and the highest relative prices are beneficial
for one type of the consumers, and the intermediate price gives an equitable allocation. The theoryof Walrasian tatonnement dynamics predicts that relative prices diverge from the intermediate
equilibrium towards the lowest equilibrium or the highest equilibrium depending on initial prices.
On the other hand, Marshallian quantity adjustment process leads the total supplied volume to theintermediate equilibrium only regardless of initial states. In order to examine how robust theequilibrium selection is, we conducted a manual experiment of pit market trading with different
combinations of ethnicities of subjects in Kenya.

Our result shows strong support for theconvergence to the intermediate equilibrium, which is unstable in Walrasian tatonnement dynamics
and is stable in Marshallian quantity adjustment process.
Keywords: Marshallian Stability, Walrasian Stability, Experiments, Pit Market, Kenya
JEL codes: C92, D51* We thank Jean Ensminger, Emiko Fukuda, Hiroyuki Hino, Anjan Mukherji, Charles Plott, Shyam Sunder, and Motoki
Takahashi for their comments and suggestions. We appreciate special supports to conduct this experiment in Kenya by
Mohamud Jama, Michiharu Masui, Joseph Onjala, and Kohei Yoshida. Financial supports from Japan International
Cooperation Agency, the Murata Science Foundation, and the Japanese Ministry of Education, Culture, Sports, Science andTechnology through Grant-in-aid for Scientific Research (B) 26285045, (C) 25380228, and (C) 15K03353 are gratefully
acknowledged.
†

Research Institute for Economics and Business Administration, Kobe University, 2-1 Rokkodai, Nada, Kobe 657-8501,
Japan. shen@rieb.kobe-u.ac.jp (Shen); ken-ichi@rieb.kobe-u.ac.jp (Shimomura)††

School of Economics, Shanghai University, 99 Shangda Road, Baoshan 200444, Shanghai, China.

#
Department of Social Engineering, Graduate School of Decision Science and Technology, Tokyo Institute of Technology,
2-12-1 Ookayama, Meguro-ku, Tokyo 152-8552, Japan. yamato@soc.titech.ac.jp1

1.

Introduction

We investigate dynamics adjustment processes in pit market trading by a laboratory
experiment. We explore two issues in this paper. The first is the fact finding of natures of
disequilibrium and equilibration processes in trading on the floor, or “pit” markets.
Historically, such markets have been widely used in actual trading places. In spite of that,studies on dynamic adjustment process in pit markets have been limited, while mostscholars have investigated this issue in double auction markets. The key difference
between a pit market and a double auction market is whether or not bids and asks as wellas prices are public information. 1
In the experimental economics literature, it has been known that pit market
experiment was first conducted by Chamberlin (1948), who wanted to present that themodel of perfect competition does not predict well. Smith (1962) used the double auction
to show that repeated trades with public information about bids, asks, and trading prices
tend to lead markets to perfectly competitive prices. In our experiment of pit markets (notdouble auction as in Smith, 1962) with repeated trades, different from Chamberlin (1948),
bids and asks were known to the buyer and the seller only in each trade, and what were
publicly revealed to markets are quantities agreed to exchange. We conducted theexperiment repeatedly by setting the initial holdings to be constant in each period of asequence of experiment to observe tendencies of market prices. We had a conjecture thatthe sequence of market prices would converge to a competitive equilibrium because
buyers and sellers can freely trade as many times as they want then information about
exchange rates will become public gradually.
The second issue is the extent to which theoretical models based on adjustment help
with understanding this trading pit process. Almost all dynamic models of perfectcompetition are formulated with the Walrasian tatonnement, which is the only system thatmanipulates a market price by raising a price when the commodity is excessively
demanded and lowering a price when the commodity is excessively supplied. The
dynamic stability of an experimental market is usually analyzed as if the process ofequilibrium price discovery is the Walrasian tatonnement even when it is obviously not.
Existing experimental results from continuous double auctions suggest that data ofmovement in market prices are highly consistent with the Walrasian tatonnement (Smith
1962; Anderson et al., 2004; Crockett et al., 2010). To our best knowledge, there is nosuch evidence with experimental results from trading pit which support any theory ofdynamics in markets. We expected that the Walrasian adjustment process would work1

We would like to give special thanks to Charles Plott for pointing out this issue.

2because a market price goes up whenever the commodity is excessively demanded andthe price falls whenever the commodity is excessively supplied regardless of styles of
trading. We thus actually conducted an experiment of trading pit to investigate what kindof dynamics of market prices appears.
The model to experiment is an exchange economy with two types of consumers andtwo kinds of commodities in which three competitive equilibria exist. One type of
consumers initially own the more of the first good, and the less of the second good, thanthe other type of consumers have. The same type of consumers are all rationed identicalcommodity bundles of endowment. We choose the second good as the numeraire, theprice of which is always fixed to be one, and focus on the behavior of the relative price ofthe first good. In our model, the supply and demand curves intersect at three points,
namely, there are three equilibrium prices. The lowest relative price is beneficial for thetype of consumers having more of the second good, and the highest relative price isadvantageous to the type of consumers having more of the first good. The intermediate
price gives an “equitable” allocation.
According to the Walrasian dynamics, relative prices diverge from the intermediate
equilibrium towards the lowest equilibrium or the highest equilibrium depending on
initial prices. It means that the market mechanism causes an income inequality and the“invisible hand” leads the economy to an efficient but inequitable state. We thus havestrong interest in conducting an experiment of our exchange model with multiple
equilibria. We simply conjectured that trading outcomes would converge to one of theextreme equilibria because they are stable in Walras’ sense. However, our results
obtained in Kenya show strong support for the convergence to the intermediate
equilibrium on average. Thus, our observations tell that pit market trading does not cause
large inequalities of income or welfare. This is the opposite result that the theory ofWalrasian stability predicts.
We therefore investigate our model with another dynamic stability concept of amarket mechanism called the Marshallian adjustment process 2, in which sellers increase
supplies when the supply price is higher than the demand price and decrease them when
the supply price is lower than the demand price. It then turned out that, in our model, thestability of each equilibrium is different in Walras’ and Marshall’s sense. It means thatthe lowest and highest equilibria are stable in Walras’ sense but unstable in Marshall’s
sense, and the intermediate equilibrium is unstable in Walras’ sense but stable in
Marshall’s sense. Our experimental results of trading pit show that the market prices
2

Our first debt is to Shyam Sunder, who suggested us to check Marshallian stability of equilibria
for our model.

3

converged to the intermediate equilibrium, which is unstable in Walras’ sense and stablein Marshall’s sense. Shapley and Shubik (1977) is a pioneering work that presents a
simple exchange economy model with multiple competitive equilibria. Different from thecurrent study, they investigated the Walrasian stability of the three equiribria, but did not
discuss the Marshallian stability.
The paper is organized as follows. In Section 2, we present the model of an exchange
economy with three competitive equilibria which we used to conduct our experiment.
We also discuss the Walrasian stability and the Marshallian stability of each equilibrium.
In Section 3, we explain the design and procedures of our experiment. Namely, we
describe how we transformed the theoretical model into the experiments. In Section 4, weanalyze the results of the experiment to find tendencies of the data and effects of ourscientific controls. Discussions are provided in Section 5. Finally, Section 6 is forconcluding remarks.

2.

An Exchange Economy with Multiple Equilibria

We consider the following exchange economy model with two kinds of commodities
called X and Y and two types of consumers named 1 and 2. The utility functions ofconsumers 1 and 2 are of “Leontief-nested” types in the following forms:

U 1 ( x1 , y1 ) = a1 min[ g1 ( x1 ), y1 ] + b1 andU 2 ( x 2 , y 2 ) = a2 min[ g 2 ( x 2 ), y 2 ] + b2

(2.1)

In the experiment, we set a1 = 52.58 , b1 = 669.96 , a2 = 50 , b2 = 695.07 ,g1 ( x1 ) = x1 / 9.8

if x1 ∈ [0,6.2]=
10 x1 − 6.2(10.5 − 1/ 9.8)

if x1 ∈ [6.2,7.5]=x1 / 9.8 + 1.3(10.5 − 1/ 9.8)

if x1 ∈ [7.5,14.9]=
10.5 x1 − 13.6(10.5 − 1/ 9.8)

otherwise;andif x2 ∈ [0,7.35]

g 2 ( x2 ) = x2 / 9.1=
11.3x2 − 7.35(11.3 − 1/ 9.1)

if x2 ∈ [7.35,8]=x2 / 9.1 + 0.65(11.3 − 1/ 9.1)

if x2 ∈ [8,17.45]=
11.3x2 − 16.8(11.3 − 1/ 9.1)

if x2 ∈ [17.45,18.45]=
x2 / 9.1 + 1.65(11.3 − 1/ 9.1)

otherwise.

4

The individual endowment of consumer 1 is given by ( x1 , y1 ) = (25,1) and theindividual endowment of consumer 2 is ( x 2 , y 2 ) = (5,29) .
Figure 1 displays this economy in an Edgeworth box. The solid (resp. dashed)piecewise linear line denotes consumer 1’s (resp. consumer 2’s) “offer curve,” derived byvarying prices and asking the consumer how much she would like to trade to maximize
her utility at each price. Notice that the offer curves are given by y1 = g1 ( x1 ) andy 2 = g 2 ( x 2 ), because the utility maximization points are the loci of the verteces of the
L-shaped indifference curves.

There are three competitive equilibrium allocations

denoted by the points of intersection of the two offer curves: A = (7.00, 9.01), B = (12.01,
14.74), and C = (15.48, 21.13) in terms of agent 1’s consumption bundle. Figure 1 can bealso regarded as demonstrating symmetric equilibrium outcomes in a market with n
traders on each side when all traders of the same type take the same action.

Figure 1. Exchange Economy with Three Competitive Equilibria

Figure 2 represents a diagram of the demand and supply curves for good X which arederived from our two-good economy model. 3 Notice that the supply curve isdownward-sloping. The intuitive reason is as follows. Suppose that the price for X
relative to good Y, Px/ Py, decreases. Then the income of consumer 1 who initially has a
3

We only need to focus on trades of good X because, based on the Walras’ law, the market ofgood X is clear when that of good Y is clear. Notice that Walras’ law holds in our model since theutility functions of all consumers satisfy local nonsatiation.

5

large amount of X becomes smaller. Because consumer 1’s utility function is of a
Leontief type, there is no substitution effect and a large income effect. Therefore,
consumer 1’s demand for X decreases, implying that the supply (endowment minus
demand) of X by consumer 1 increases. Since consumer 1 is the only supplier of X, thesupply for X increases when the relative price for X decreases.

Px Py
Demand4
Supply3

A, C: Walrasian stable and Marshallian unstable equilibrium
B: Walrasian unstable and Marshallian stable equilibrium

(W1)

C

2
(W2)

B

1

A

(W3)
(W4)

5

(M1) (M2)

(M3)

(M4)

10

15

20

25

30

Amount of X

Figure 2. Local Walrasian and Marshallian Stability of Three Competitive
Equilibria in a Demand-Supply Diagram.

Figure 2 shows three equilibria at which the demand and supply curves intersect: A =(xA, pA) = (18.00, 0.44), B = (xB, pB) = (12.99, 1.06), and C = (xC, pC) = (9.52, 2.11). There
are two well-known concepts of local stability of a competitive equilibrium: Walrasianand Marshallian stability. These concepts give opposite answers to the question ofwhether each of the three equilibria is locally stable or unstable. First of all, let us
consider Walrasian dynamics of price adjustment process, which works off equilibrium inthe market. According to this dynamics, if the relative price of X, p = Px/ Py, is lower
than pA (higher than pC), the demand for X is larger (smaller) than the supply for X, sothat p increases (decreases). If p lies between pA and pB (between pB and pC), the demand
for X is smaller (larger) than the supply for X, so that p decreases (increases). Therefore,

6the equilibrium B is locally unstable in Walras’ sense, whereas the other two equilibria A
and C are both locally stable in Walras’ sense.

Next let us examine Marshallian dynamics of quantity adjustment process.
According to this dynamics, if the quantity of X, x, is larger than xA (smaller than xC), thedemand price at x is higher (lower) than the supply price at x, so that x increases(decreases). If x lies between xA and xB (between xB and xC), the demand price at x is
lower (higher) than the supply price at x, so that x decreases (increases). Therefore, theequilibrium B is locally stable in Marshall’s sense, whereas the other two equilibria A and
C are both locally unstable in Marshalls’ sense. 4

A3

Figure 3. Discrete Version of the Exchange Economy

In our experiment, subjects chose integers as trading units, not real numbers as inusual theory. Therefore, it is important to consider a discrete version of the exchange
economy corresponding to the experimental setting to make a rigorous theoreticalprediction. Figure 3 shows this discrete exchange economy in an Edgeworth box. The
locus of circles ( ) (resp.

multiplication signs (´ )) denotes consumer 1’s (resp.

4

See Appendix 1 for the formal definitions of local stability and instability of equilibrium
according to Walrasian price adjustment process and those according to Marshallian quantity
adjustment process.

7

consumer 2’s) offer curve, which is thick, in the discrete economy. The two offer curvesintersect at seven points indicating competitive equilibria. In terms of consumer 1’s
consumption bundles, these equilibria are given by A1 = (7, 8), A2 = (7, 9), A3 = (8, 9),
B1 = (12, 15), B2 = (12, 16), C1 = (16, 20), and C2 = (16, 21) together with thecorresponding equilibrium price ratios PX / PY = 0.39, 0.44, 047, 1.08, 1.15, 2.11, and2.22, respectively.
Moreover, we prohibited subjects from trading commodities at which the price ratio

PX / PY , the trading ratio of Y to X (= (Amount of Y)/(Amount of X)), was lessthan 1/4 = 0.25. For PX / PY < 1/4, there are several competitive equilibria other than theabove seven equilibria. In Figure 3, we omit these equilibria and focus on the sevenequilibria close to the three equilibria in Figure 1 of the usual Edgeworth box.
Table 1 summarizes the equilibrium predictions. The equilibria A1, A2, and A3
with low relative prices of commodity X, PX / PY , are beneficial for type 1 consumer
having more of commodity Y, while the equilibria C1 and C2 with high relative prices ofcommodity X is advantageous to type 2 consumer having more of commodity X. In thissense, these four equilibria are not equitable. From the viewpoint of stability, these four
equilibria are locally stable in Walras’ sense, but locally unstable in Marshall’s sense.

Table 1: Theoretical Predictions about Discrete Equilibria
Allocation

PayoffWalrasianMashallianType 1

Type 2

Stability

Stability

U1

U2

0.39

stableunstable

1091

1745

(23, 21)0.44

stableunstable

1143

1745

(8, 9)(22, 21)0.47

stableunstable

1143

1739

B1

(12, 15)(18, 15)

1.08

unstablestable

1445

1445

B2

(12, 16)(18, 14)

1.15

unstablestable

1445

1395

C1

(16, 20)(14, 10)

2.11

stableunstable

1722

1136

C2

(16, 21)(14, 9)2.22

stableunstable

1669

1136

Type 1

Type 2(x1, y1)(x2, y2)

A1(7, 8)(23, 22)A2(7, 9)A3

Price

On the other hand, the equilibria B1 and B2 with intermediate prices give allocations
that generate the minimal difference between the payoffs to the two types of consumers.

8

We say that the equilibrium and allocation are fair. In particular, each type receives thesame equilibrium payoff at B1. They are locally unstable in Walras’ sense, but locallystable in Marshall’s sense. There are trade-off between local Walrasian stability and“equity” of the competitive equilibria, whereas local Marshallian stability and allocation
equity are compatible.

3.

The Experimental Design and Procedures

The experiment was conducted at the University of Nairobi in Kenya during August
10-12 of 2010. We recruited subjects from three ethnic groups (i.e., Luo, Kikuyu, andKalenjin) to attend the experiment. 5 The subjects were students at major Kenya
universities such as the University of Nairobi, Kenyatta University, Moi University,
Egerton University, Mount Kenya University, Kimathi University College of Technology,
and Jomo Kenyatta University of Agriculture and Technology. No subject had priorexperience in market experiments. The number of subjects from each of the three ethnic
communities was 40 for a total of 120 distinct subjects. For each ethnic group, 20
subjects played the role of type 1 consumer and another 20 subjects did the role of type 2
consumer. Their roles were fixed throughout the experiment.
Each subject participated in two sessions. In the first session they played withsubjects from the same ethnic group and in the second session they played with thosefrom a different ethnic group. In each session, there were 10 subjects who played the roleof type 1 and 10 subjects who played the role of type 2. The subjects who played thesame role in each session were always from the same ethnic group. As a result, a total of
12 sessions was conducted. Table 2 presents the details of these sessions. In the table, The
roles of type 1 and type 2 that subjects played are indicated by the numbers 1 and 2,
respectively, and L, Ki, and Ka refer to Luo, Kikuyu, and Kalenjin subjects, respectively.
For example, L1-L2 and L1*-L2* refer to the sessions in which Luo subjects of type 1
played with Luo subjects of type 2, refer to the session in which Luo subjects of type 1
played with Kikuyu subjects of type 2, etc. In addition, it should be noted that the
subjects participated in the experiment changed every day. For example, the Luo subjects
in L1-l2 session on the first day differed from those in L1*-L2* session on the third day,and the Kikuyu subjects in Ki1-Ki2 session on the first day differed from those in
5

We investigated whether ethnicity affects subjects’ trading behavior in another study (seeShimomura and Yamato (2012)). However, there are several differences in both the experimental
design and procedures between that study and the current one (see detailed discussions in Section
5).

9Ki1*-Ki2* session on the second day, etc.

Table 2. Time schedule of the experimentAMPM

8/10/2010

8/11/2010

8/12/2010

L1-L2: 20 subjects

Ka1-Ka2: 20 subjects

Ka1*-Ka2*: 20 subjects

Ki1-Ki2: 20 subjects

Ki1*-Ki2*: 20 subjects

L1*-L2*: 20 subjects

L1-Ki2: 20 subjects

Ka1-Ki2*: 20 subjects

Ka1*-L2*: 20 subjects

Ki1-L2: 20 subjects

Ki1*-Ka2: 20 subjects

L1*-Ka2*: 20 subjects

Notes: The roles of type 1 and type 2 that subjects played are indicated by the numbers 1 and
2, respectively. L, Ki, and Ka refer to Luo, Kikuyu, and Kalenjin subjects, respectively.

The procedure in each session was exactly the same. At the beginning of a session,
each subject received one experimental instruction, one record sheet, one payoff table andone name tag. 6 The name tag of each subject indicated her team name (A, B, C, …, or T)
and her identification number (1 or 2). Ten subjects (A-J) played the role of type 1, andten subjects (K-T) played the role of type 2. Each subject was given pink cards and/or
white cards in an envelope. One pink card was one unit of commodity X, and one whitecard was one unit of commodity Y. We explicitly noticed to every subject that she was notallowed to reveal any information regarding her payoff table or endowed color cards toany other subject.
Then, the subjects walked around a relatively large laboratory room and found a
subject to trade. We prohibited any subject from trading any amount of commodity X or
Y more than what they held. In addition, as explained in the previous section, the trading
ratio of Y to X should be greater than or equal to 1/4 = 0.25 to exclude undesirable
equilibrium allocations. We told the subjects to trade commodity X for Y or Y for X when
two subjects reached an agreement. After writing the trading results in their record sheets,
the subjects reported them to the experimenter. The following information on the results
was entered into the computer and displayed publicly through a projector: the team namegiving commodity X, the amount of the traded X, the team name giving Y, the amount of
the traded Y, and the trading ratio of the commodities (= Y/X). This was the end of one
trade. The subjects had 10 minutes for each period and they were allowed to trade as
many times as they wanted within the time limit. For the next trading partner, the subjects
could choose any subject as they wanted. That is to say that the next partner might be thesame as or different from one of the subjects they had already traded. After each period, the6The experimental instruction and payoff tables are provided in Appendix 2 and Appendix 3,
respectively..

10

subjects went back to their seats and the experimenter collected all commodity cards. This
was the end of one period.
At the beginning of the next period, the subjects received the same materials as those of
the previous period. In particular, holdings of commodities were reset at the end of theprevious period and each subject held the same endowment as that at the beginning of theprevious period. After a 2-minute break, the next period started. One session had 5 periods,
which means that the above steps were repeated 5 times.
Earnings of each subject or team depended on the final payoff that she or her teamearned in one randomly selected period from the experiment. This period was chosen by arandom device after the experiment. The two sessions in which each subject participatedrequired approximately 3 hours and half to complete in total. The mean payoff per subject was
3026 Ksh (One US dollar approximately exchanged for 80 Ksh in August of 2010).

The

maximum payoff among the 120 subjects was 3865 Ksh, and the minimum payoff was 2068
Ksh.

4.

Experimental Results

In this section, we are going to exhibit whether our experimental results support the
Walrasian adjustment process or the Marshallian adjustment process based on thediscussions on the ratio of the three equilibria, the average distances to the fairequilibrium, price movement, and final holdings of commodity X.
Table 3 provides the ratios of the three equilibria (i.e., A2, B1, and C1) bundles andthe ratios of bundles near these three equilibria in the end-of-period holdings of X and Y.
These ratios are also presented in Figure 4 to help understanding visually. 7 The bundles
near A2, B1, and C1 are defined as being within 1 unit of A2, B1, C1 for each commodity.
For example, the bundles of near B1 for type 1 (i.e., (12,15)) are (11, 14), (11, 15), (11,16), (12, 14), (12, 15), (12, 16), (13, 14), (13, 15), and (13, 16), and the bundles of nearB1 for type 2 (i.e., (18,15)) are (17, 14), (17, 15), (17, 16), (18, 14), (18, 15), (18, 16), (19,14), (19, 15), and (19, 16). There were 120 subjects and each subject who was assigned tobe either type 1 or type 2 participated in 2 experimental sessions in which each session
consisted of 5 periods. Hence, the number of the end-of-period bundles for each typesubjects is 600. Among these bundles, as shown from Table 3 and Figure 4, both ratios of
the fair equilibrium B1 bundle and the ratios of bundles near B1 were respectively much
7

In Figure 4, Panel I is for the ratios of the three equilibria bundles and Panel II is for the ratios ofbundles near these three equilibria.

11

higher than those of A2 (resp. C1) and those near A2 (resp. near C1) for either type 1
subjects or type 2 subjects. This result is strongly supported by the test of proportions. All
the p values are smaller than 0.001 in any cases.
Table 3. Ratios of Three Equilibria Bundles to All Final Holdings
Type 1

Type 2

Both types

A2

0.17% (=1/600)

0.33% (=2/600)

0.25% (=3/1200)

Near A2 (±1)

0.50% (=3/600)

1.00% (=6/600)

0.75% (=9/1200)

B1

7.83% (=47/600)

6.33% (=38/600)

7.08% (=85/1200)

Near B1 (±1)

27.83% (=167/600)

27.33% (=164/600)

27.58% (=331/1200)

C1

1.00% (=6/600)

0.17% (=1/600)

0.58% (=7/1200)

Near C1 (±1)

2.67% (=16/600)

0.67% (=4/600)

1.67% (=20/1200)

Panel I
.08
.04
0

.02

.04
.02
0

.04
.02
0

A2

Both types

.06

.08

Type 2

.06

.06

.08

Type 1B1C1

Panel IInear A2

.1

.2

.3

Both types

0

.1

.2

.3

Type 2

0

0

.1

.2

.3

Type 1near B1

near C1

Figure 4. Ratios of Three Equilibria Bundles to All Final Holdings

12Figure 5 shows the average distances from subjects’ end-of-period holdings to thefair equilibrium B1 consumption bundle. 8 As indicated clearly from the figure, theaverage distances to B1 decreased as the period went by for both types of subjects. A
panel data regression of the variable Distance on the variable Period was run to test
whether this decrease is statistically significant. We found that the coefficient of Period
was negatively significant at 0.1% level in either type-separated case or type-pooled case,which confirms that the decreasing tendency in Figure 5 is significant.

Type 1

1

2

3

4

5

6
2
1

1

1

2

3

3

4

4

5

5

5
4
3
2

Distance

Both types

6

6

Type 2

1

2

3

4

5

1

2

3

4

5

PeriodFigure 5. Average Distances to the Fair Equilibrium B1

Figure 6 shows the price movements of PX / PY by periods. The three equilibria (i.e.,
the low, middle, and high equilibria) are also presented by the green, red, and orange lines,
respectively. To draw these price movements, we first divided the subjects into 4 groups
according to their prices in Period 1 and then trace their movements of the prices in
Periods 2 – 5. The prices were calculated by subjects’ end-of-period holdings of
8

Here the distance of each subject at each period is defined as the Euclidean distance, which canbe written as ( X it − 12) 2 + (Yit − 15) 2 for type 1 subjects and( X it − 18) 2 + (Yit − 15) 2 fortype 2 subjects, where i and t refer to subject and period indices, and X and Y stand for a subject’s
end-of-period holdings of commodities X and Y, respectively.

13

commodities X and Y, and the 4 groups were based on 4 price intervals: (i) price ≤ 0.44
(2.93% of subjects); (ii) 0.44 < price ≤ 1.08 (50.13% of subjects); (iii) 1.08 < price ≤ 2.22
(41.17% of subjects); and (iv) price > 2.22 (5.77% of subjects). As shown in the figure, acertain level of fluctuation in the price can be observed among the subjects whose prices
in Period 1 were either not larger than the price at A2 (see Figure 6 – I) or larger than theprice at C1 (see Figure 6 – IV). For the majority of subjects (91.3% of subjects), when
their prices in Period 1 were between the prices at A2 and B1 (resp. between the prices at
B1 and C1), an upward (resp. a downward) tendency towards the middle equilibrium canbe observed. Although the panel data regression of the variable Price on the variable
Period confirmed the significance of these two tendencies (p < 0.05 in both cases), theresults obtained from a Wilcoxon signed-rank test indicates that it is only in the case of
the initial price being between 1.08 and 2.22 that the price in Period 5 is equal to the
middle equilibrium price (p = 0.3842). 9

II. 0.44<Price<=1.08.2.2.8 1.4.8 1.4

2 2.6 3.2

2 2.6 3.2

I. price<=0.44

Price

1

2

3

4

5

1

2

4

5

4

5

.8 1.4.2.2.8 1.422

2.6 3.2

IV. price>2.22

2.6 3.2

III. 1.08<Price<=2.22

3

1

2

3

4

5

1

2

3

PeriodFigure 6. Price Movement by Periods

9

For other two initial price intervals, the prices in Period 5 are also significantly not equal to the
middle equilibrium price.

14

Figure 7 presents the movements of the type 1 subjects’ final holdings of commodity
X by periods. 10 The three equilibria (i.e., the low, middle, and high equilibria) are again
presented by the green, red, and orange lines, respectively. Similar to the case of the pricemovements, to draw the movements of final holdings of X, we first divided the type 1
subjects into 4 groups according to their final holdings of X in Period 1 and then trace
their movements of the amount of X in Periods 2 – 5. The final holdings of X in Period 1
were based on 4 intervals: (i) X ≤ 7; (ii) 7 < X ≤ 12; (iii) 12 < X ≤ 16; and (iv) X > 16. As
indicated from the figure, it seems that no matter where they started the final holdings ofcommodity X converged to the middle equilibrium with the passing of periods. By
combining the results from the panel data regression and the Wilcoxon signed-rank test
together, we confirmed that the end-of-period holdings of X converged to the middle
equilibrium in Period 5 in three of four intervals that mentioned above. 11 The only
exceptional interval was that the final holdings of X in Period 1 were larger than between
the low equilibrium and the middle equilibrium (i.e., 7 < X ≤ 12). In this interval, we
found that the variable Period did not have significant effect on the final holdings of X,
and the amount of X was statistically equal to 11 in all the 5 periods (see the dark blue

1

2

period3

45line in Figure 7).

5

6

7

8

9

10

11 12 13 14
final holdings of X

15

16

17

18

19

Figure 7. Final Holdings of X

10

By Walras’ law, we only need to focus on market of commodity X. In addition, by feasibility it
is sufficient to consider the movements in final holdings of subjects of type 1 only.
11
The panel data regression was run by regressing the variable Final holdings of X on the variable
Period, and the Wilcoxon signed-rank test was conducted to test whether the end-of-period
holdings of X was equal to 12. These results are available upon request.

15

Summing up the above descriptions, while existing experimental evidences
supporting Marshallian dynamics are mostly provided in a double auction market (e.g.,
Plott and George, 1992; Plott and Smith, 1999; Plott et al., 2013), our results exhibit thatMarshallian path is even supported in a pit market.

5.

Discussions

Shimomura and Yamato (2012) studied how different compositions of ethnicities (i.e.
Kikuyu, Luo, and Kalenjin) in Kenya trade in the similar market environment as in thecurrent study. They found that ethnic diversity plays an important role in the evolution ofmarkets. In sessions with Luo and/or Kikuyu subjects only, there was no convergence ofallocations. However, in the sessions with Kalenjin subjects, allocations converged to theintermediate allocation, especially in later periods. Moreover, convergence to theintermediate equilibrium occurs considerably faster with Kalenjin subjects and thefrequency of transactions with Kalenjin subjects is significantly lower than that with Luo
and/or Kikuyu subjects only. They concluded that less frequent transactions resulted in
the more efficient outcomes of the experimental market. In the current study, we also
perform a robustness check to investigate whether our findings of Marshallian path in apit market are similarly driven by the Kalenjin subjects. The comparison results for thedata with and without Kalenjin subjects show that Marshallian dynamics is supported inboth the sessions with and without Kalenjin subjects, and it is more obvious in thesessions where Kalenjin subjects participated than those with Luo and/or Kikuyu subjects
only. 12In our view, the evidence that there is no convergence to the intermediate
equilibrium in sessions with Luo and/or Kikuyu subjects only in Shimomura and Yamato(2012) might be due to the differences in experimental design between their study andours. These differences are threefold. First, the parameterization of subjects’ utility
functions is different. In Shimomura and Yamato (2012), the parameterization led thepayoff of the intermediate equilibrium for both types of subjects to be 2000 tokens, whilein the current study we avoid this happening because the number of 2000 might be too
conspicuous to attract subjects’ notice. Second, different from that each trader in thecurrent study is individual, each trading group in Shimomura and Yamato (2012)
contained two subjects from the same ethnicity, which allows them being able to discusswith each other within each group. Third, each subject in Shimomura and Yamato (2012)
participated in three experimental sessions, while that number in the current study is two.
12

These results are not reported here, but are available upon request.

16

Given that the above-mentioned differences might lead to different experimental behavior,
more research in future is needed to verify our findings.

6.

Concluding remarks

Our laboratory experiment is designed to study dynamics in pit market trading. In our
exchange economy model, three competitive equilibria exist. The two equilibria with thelowest, and the highest relative prices are beneficial for one type of the consumers, andthe intermediate price gives an equitable allocation. Our result shows strong support forthe convergence to the intermediate equilibrium, which is unstable in Walrasiantatonnement dynamics and is stable in Marshallian quantity adjustment process. In our
experiments, Marshallian path predicts that consumers in the market finally reach at an“equitable” allocation where payoffs for both types of consumers are identically thesame. 13 This naturally raises the question of whether our experimental results were due
to subjects’ fairness preferences on payoffs. However, our experimental design rules out
this possibility, because each type of subjects can only know their own payoffs.
Plott (2000) reports that in a double auction market the Marshallian model works
well when supply curves are forward-falling, in contrast, in the backward-bending casestability is captured by the Walrasian model and the Marshallian model of dynamics isrejected. Given that said, under what conditions Marshallian dynamics work in a pit
market remains still unknown to us. In a recent study on investigating the change in theprice in call market experiments, Plott and Pogorelskiy (2015) demonstrate that the
Newton-Jaws model based on the Newton method provides a better description of how
the markets operate than the Walrasian model. The Newton method (see details in
Bossaert and Plott (2008)) might be a useful tool for examining this question. We leavethis issue open and welcome any efforts to explore it.

13

In our data, both two-tailed t test and Wilcoxon rank sum test cannot reject that mean andmedian payoffs are the same in Period 5, respectively (t test: p = 0.6294; Wilcoxon rank sum test:
p = 0.7022).

17

References
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Granat (2004): “Global Instability in Experimental General Equilibrium: the Scarf
Example,” Journal of Economic Theory 115, 209-249.
Bergstrom, Theodore C., Ken-Ichi Shimomura, and Takehiko Yamato (2009):“Simple Economies with Multiple Equilibria,” The B.E. Journal of Theoretical
Economics 9: Article 43.
Bossaerts, Peter and Charles R. Plott (2008): “From Market Jaws to the Newton
Method: The Geometry of How a Market Can Solve Systems of Equations,” In: Charles
R. Plott and Vernon L. Smith (eds) Handbook of Experimental Economics Results, Vol. 1,
Elsevier B. V.
Cason, Timothy, Tatsuyoshi Saijo, and Takehiko Yamato (2002): "Voluntary
Participation and Spite in Public Good Provision Experiments: An International
Comparison," Experimental Economics 5, 133-153
Chamberlin, Edward H. (1948): "An Experimental Imperfect Market," Journal of
Political Economy, 56, 95-108.
Chipman, John S. (2010): “Multiple Equilibrium under CES Preferences,” Economic
Theory 45, 129-145.
Crockett, Sean, Ryan Oprea, and Charles R. Plott (2010): “Extreme WalrasianDynamics: The Gale Example,” American Economic Review 101, 3196-3220.
Gale, David (1963): “A Note on Global Instability of Competitive Equilibrium," Naval
Research Logistics Quarterly 10, 81-87.
Holt, Charles A. (1996): “Classroom Games: Trading in a Pit Market,” Journal of
Economic Perspectives, 10, 1996, 193-203
Huber, Juergen, Martin Shubik, and Syham Sunder (2009): “Default Penalty as
Disciplinary and Selection Mechanism in Presence of Multiple Equiliria,” Cowles
Foundation Discussion Paper No. 1730, Yale University.

18

Plott, Charles R. (2000): “Market Stability: Backward-bending Supply in a Laboratory
Experimental Market,” Economic Inquiry 38, 1-18.
Plott, Charles R. and Glen George (1992): “Marshallian Vs. Walrasian Stability in an
Experimental Market,” Economic Journal 102, 437-460.
Plott, Charles R. and Jared Smith (1999): “Instability of Equilibria in Experimental
Markets: Upward-Sloping Demands, Externalities, and Fad-Like Incentives,” Southern
Economic Journal 65, 405-426.
Plott, Charles R., Nilanjan Roy, and Baojia Tong (2013): “Marshall and Warlas,disequilibrium trades and the dynamics of equilibration in the continuous double auction
market,” Journal of Economic Behavior and Organization 94, 190-205.
Plott, Charles R. and Kirill Pogorelskiy (2015): “Call Market Experiments: Efficiency
and Price Discovery through Multiple Calls and Emergent Newton Adjustments,” Social
Science Working Paper 1404, Division of the Humanities and Social Sciences, California
Institute of Technology.
Roth, Alvin E., Vesna Prasnikar, Masahiro Okuno-Fujiwara, and Shmuel Zamir(1991): "Bargaining and Market Behavior in Jerusalem, Ljubljana, Pittsburgh, andTokyo: An Experimental Study," American Economic Review 81, 1068-1095.
Scarf, Herbert (1960): “Some Examples of Global Instability of the Competitive
Equilibrium,” International Economic Review 1, 157-171.
Shapley, Lloyd. S. and Martin Shubik (1977): “An Example of a Trading Economy
with Three Competitive Equilibria,” Journal of Political Economy 85, 873-875.
Shimomura, Ken-Ichi and Takehiko Yamato (2012): “Impact of Ethnicities on Market
Outcome: Results of Market Experiments in Kenya.” in Hino, H., J. Lonsdale, G. Ranis,
and F. Stewart (eds.) Ethnic Diversity and Economic Stability in Africa, Cambridge
University Press, pp. 286-313..
Smith, Vernon L. (1962): “An Experimental Study of Competitive Market Behavior,”
Journal of Political Economy 70, 111-137.

19

Appendix 1: Local Stability Conditions of Price and Quantity Adjustment Processes
in Two-Consumer Two-Good Exchange Economies
First of all, we give formal definitions of “two-good exchange economy,” and“competitive equilibrium”:

DEFINITION A1. A two-good exchange economy is a list ( I ,U , ω ) such that I is anonempty finite set, U = (U i )i∈I is a profile of real-valued functions from R 2+ , and ω= (ωi )i∈I , where ωi = ( xi , y i ) , is a profile of points of R 2+ . Then an element of I iscalled a consumer. For each i ∈ I , U i and ωi are called the utility function, and theindividual endowment, of consumer i , respectively. The profile of non-negative vectors
is called an allocation of ( I ,U , ω ) if

( xi , yi ) i∈I∑ y =∑ y .
i∈I

i∈I

i

∑ x =∑ x
i∈I

i

i∈I

i

and

i

DEFINITION A2. Let ( I ,U , ω ) be a two-good exchange economy. Then the vector( ( xi *, yi *)i∈I , ( p X *, pY *) ) ∈ (R 2+ ) I × R 2 is a competitive equilibrium, or simply
equilibrium, for ( I ,U , ω ) if

p X * xi * + pY * yi * ≤ p X * xi + pY * yi , and(1) for each i ∈ I ,

U i ( xi *, yi *) ≥ U i ( xi , yi ) for each ( xi , yi ) ∈ R 2+ such that p X * xi + pY * yi ≤p X * xi + pY * yi ;(2)

∑ x * =∑ x and ∑ y * =∑ y .
i∈I

i

i∈I

i

i∈I

i

i∈I

i

The profile of non-negative vectors ( xi *, yi *)i∈I , and the vector ( p X *, pY *) are calledan equilibrium allocation, and an equilibrium price vector, for ( I ,U , ω ), respectively.

We next investigate local dynamics of price adjustment process, which work inneighborhoods of equilibria.

Simply speaking, the price adjustment process, or“Walrasian” adjustment process, means that the relative price of X goes up when X
is excessively demanded, and the relative price of X goes down when X is20

excessively supplied. We first give the definitions of market excess demand function,and the local stability and instability of Walrasian adjustment process.

DEFINITION A3. Let ( I ,U , ω ) be a two-good exchange economy, and d iX be thedemand function forof consumer i ∈ I . Define the set of the demanders

X

ID(P) for X and the set of the suppliers IS (P) of X by
ID(P) = { i ∈ I | d iX ( P,1) − x i ≥ 0 }; andIS (P) = { i ∈ I | d iX ( P,1) − x i < 0 }.
Then the market demand function, simply demand function for X

for each P > 0 .
is defined by()

D X (P) = ∑i∈ID ( P ) d iX ( P,1) − x i ,the market supply function, simply supply function of X is defined by()

S X (P) = ∑i∈IS ( P ) x i − d iX ( P,1) ,and the market excess demand function, simply excess demand function for X is
defined by(

E X (P) = D X ( P) − S X ( P) = ∑i∈I d iX ( P,1) − x i)for each P > 0 .

DEFINITION A4. Let ( I ,U , ω ) be a two-good exchange economy. Suppose that

D X (P*) = S X (P*) = x * .

Then Walrasian adjustment process with the excess

demand function E X is the ordinary differential equation: P = W ( E X ( P )) , where

W is a real-valued function from R such that W (0) = 0 and W ′( z ) > 0 for each z ∈R.

We say that ( x*, P*) is locally Walras-stable (resp. locally Walras-unstable) if

E X ' ( P*) <0(resp.

( ( xi *, yi *)i∈I , ( p X *, pY *) )E X ' ( P*)
for

>

0).

( I ,U , ω )Thecompetitive

equilibrium

is called a locally Walras-stableequilibrium (resp. locally Walras-unstable equilibrium) if ( D( p X * / pY *), p X * / pY *)21

is locally Walras-stable (resp. locally Walras-unstable) .

The local Walrasian stability and instability of a competitive equilibrium for a
two-consumer economy is characterized in an Edgeworth box in the following way: Let( ( x1*, y1*) , ( x2 *, y2 *) , (P*,1) ) be a competitive equilibrium, then E X (P*) = 0.
Suppose that ( ( x1*, y1*) , ( x2 *, y2 *) , (P*,1) )is a locally Walras-stable equilibriumsuch that x1 − x1 * > 0. Then E ' ( P*) < 0. Draw the budget line passing through
X

(

)(

the competitive allocation and the initial allocation. Note that x1 − x1 * / x2 * − x2
1 because x1 * + x2 * − x1 − x2 = 0.

)=

Consider a relative price slightly higher thanP * , draw the new budget line, and find the intersections with the offer curves of the
Denote by ( x1 , y1 ) , and ( x2 , y2 ) the intersections of the budget line with

consumers.

the offer curves of consumers 1 and 2, respectively. Recall E X ' ( P*) < 0, then theP * becomes negative when the relative price is marginallyzero excess demand at
higher thanThus, x1 + x2 − x1 − x 2 < 0, namelyP*.

(x − x )/ (x − x ) > 1.
1

1

2

2

Then X is excessively supplied, so that the relative price decreases and converges toP * . Similarly, by considering a relative price slightly lower than P * , we can havex1 + x2 − x1 − x 2 > 0, namely(x − x )/ (x − x ) < 1. Then X is excessively
1

2

1

2

P * . The points

demanded, and thereby the relative price increases and converges to

A and C in Figure A1 therefore represent locally Walras-stable equilibria.
On the other hand, suppose that ( ( x1*, y1*) , ( x2 *, y2 *) , (P*,1) )is alocally Walras-unstable equilibrium such that x1 − x1 * > 0. Then E ' ( P*) > 0, andX(x − x )/ (x − x ) = 1. Consider a relative price slightly higher than
1

1

2

2

P * , andchoose ( x1′ , y1′ ) , and ( x2′ , y2′ ) in the same way as a locally Walras-stable equilibrium isP*considered. Then we can see that the zero excess demand at
when the relative price marginally goes up.

becomes positiveThus, x1′ + x2′ − x1 − x 2 > 0.

Hence,(x − x′ )/ (x′ − x ) < 1. Similarly, by considering a relative price slightly lower thanP * , we can have x′ + x′ − x − x < 0, namely (x − x′ ) / (x′ − x ) > 1. The point
1

1

2

2

1

2

1

2

1

1

2

2

B in Figure A1 therefore describes a locally Walras-unstable equilibrium.

22

x2
30

25

(W1)

(W2)
C

15

(W3)

y2

y1

20

B
A

10

5

(W4)
( x, y )

0
0

5

10

20

15

25

30

x1

Figure A1. Local Walrasian Stability of Three Competitive Equilibria

We next discuss dynamics of quantity adjustment process. We give thedefinitions of local stability and instability of “Marshallian” adjustment process. To
formulate them, we define the “demand price function” and the “supply price function” ofan exchange economy, which are respectively “local inverse functions” of the demandand supply functions.
Let D X and S X be the demand function, and the supply function, for X ,respectively. Let D X (P*) = S X (P*) = x * , and assume D X ' ( P*) ≠ 0 .

Then, byR ++such thatthe inverse function theorem, there exists an open interval

x* ∈ Vand a function ∆Xfrom VtoVin

P* = ∆X ( x*) ,R + + such thatx = D X (∆X ( x)) and ∆X ' ( x) = 1 D X ' (∆X ( x)) for each x ∈ V .
∆X

is a local inverse function of D . Similarly, by assuming S ' ( P*) ≠ 0 , we

W

in

to

R ++

can show that there exists an open interval

R ++such that x* ∈ Wdifferentiable functionΣx = S (Σ ( x)) andΣ ' ( x) = 1 S ' (Σ ( x)) for each x ∈ W .

X

Σ

X

The function
X

X

X

X

from W

X

X

X

X

is a local inverse function of S . Notice that23such thatand a

P* = Σ ( x*) ,X

The function

G = V ∩ W is an open interval

in

R ++

x* ∈ G . Hence, suppose thatsuch thatthe neighborhood 14

G = V = W . By consideringx * , we may define the following concepts:

G of

DEFINITION A5. Suppose that D X (P*) = S X (P*) = x * , D X ' ( P*) ≠ 0 and

S X ' ( P*) ≠ 0 . Let
on G

X

G

x * . The demand price function for

be a neighborhood of

is defined by{}∆X (x) = P > 0 | x = D X ( P )for each x ∈ G .

The supply price function of X

{

on G

is defined by}

Σ X (x) = P > 0 | x = S X ( P) ,for each x ∈ G . The excess demand price function for X

on G

is defined by

Φ X (x) = ∆X ( x) − Σ X ( x)for each x ∈ G .

Notice that

Φ X (x*) = ∆X ( x*) − Σ X ( x*) = P * − P * = 0.

DEFINITION A6. Suppose that D X (P*) = S X (P*) = x * , D X ' ( P*) ≠ 0 and

S X ' ( P*) ≠ 0 . Let G be a neighborhood of

x * , and Φ X be the excess demand

price function for X on G . Then Marshallian adjustment process with the excess
demand price function Φ X

on G is the ordinary differential equation: x =M (Φ ( x)) , where M is a real-valued function from R such that M (0) = 0 andX

M ′( z ) > 0 for each z ∈ R. We say that ( x*, P*) is locally Marshall-stable (resp.
locally Marshall-unstable) if Φ X ' ( x*) < 0 (resp. Φ X ' ( x*) > 0). The competitive
equilibrium ( ( xi *, yi *)i∈I , ( p X *, pY *) ) for ( I , U , ω ) is called a locally Marshall-stableequilibrium
X(resp.

locally( D ( p X * / pY *), p X * / pY *)14

isMarshall-unstablelocally

We call an open interval containing the real number

24

equilibrium)

Marshall-stablex * a neighborhood of x * .

(resp.

iflocallyMarshall-unstable).

The local Marshallian stability and instability of a competitive equilibrium for a
two-consumer economy is characterized in an Edgeworth box in the following way:
Suppose that ( ( x1*, y1*) , ( x2 *, y2 *) , (P*,1) )is a locally Marshall-stablecompetitive equilibrium such that x1 − x1 * > 0.

Then, S X (P*) = x1 − x1 * =x2 * − x2 = D X (P*) . This means that consumer 1 is the supplier, and consumer 2 isthe demander, forx1 − x1 * , thenallocation.

Xat the relative price P * .

Definex * = S X (P*) =Φ X ' ( x*) < 0. Draw the vertical line passing through the competitive

Note that(x − x *)/ (x * − x ) = (y * − y )/ (y − y *) = 1 because
1

1

2

1

2

x1 * + x2 * − x1 − x2 = y1 * + y2 * − y1 − y2 = 0.
x1 − x1 *consumer 1 slightly more than

1

2

2

Consider a supply of X

byunder the feasibility constraint of X ,x1 * + x2 * − x1 − x2 = 0. Draw the vertical line at the new supply level of X , andfind the intersections with the offer curves of the consumers. Denote by ( x1 , y1 ) , and( x2 , y2 ) the intersections of the vertical line with the offer curves of consumers 1 and 2,
respectively.

P1 and P2

In addition, let

be the associated supply price of consumer

1 and demand price of consumer 2, respectively. Recall Φ X ' ( x*) < 0, then the zero
excess demand price atgreater than x * .

becomes negative when the supply of X is marginallyx*

Thus, P2 − P1 < 0, namely P2 < P1 .

Then consumer 2, thex * , sodemander, appreciates X less than consumer 1, the supplier, does at the levelthat the supply of X decreases and converges tox * . Similarly, by considering a

supply level slightly less than x1 − x1 * , we can show P2 > P1 . Then the demander 2appreciates X more than the supplier 1 does, so that the supply of X increases andconverges to x * .

The point B in Figure A2 therefore represents locally Marshall-stableequilibria.
On the other hand, suppose that ( ( x1*, y1*) , ( x2 *, y2 *) , (P*,1) )locally Marshall-unstable equilibrium such that x1 − x1 * > 0.

x1 − x1 * = x2 * − x2 = D (P*) .
X

is a

X

Then, S (P*) =x * = S (P*) = x1 − x1 * , thenX

DefineΦ ' ( x*) > 0. Draw the vertical line passing through the competitive allocation.
X

Note

that

(x − x *)/ (x * − x )
1

1

2

2

(y * − y )/ (y − y *)

=

1

25

1

2

2

=

1

becausex1 * + x2 * − x1 − x2 = y1 * + y2 * − y1 − y2 = 0.
consumer 1 slightly more thanx1 − x1 *Consider a supply of X

byunder the feasibility constraint of X ,x1 * + x2 * − x1 − x2 = 0. Draw the vertical line at the new supply level of X , andfind the intersections with the offer curves of the consumers. Denote by ( x1 , y1 ) , and( x2 , y2 ) the intersections of the vertical line with the offer curves of consumers 1 and 2,
respectively.

P1 and P2

In addition, let

be the associated supply price of consumer

1 and demand price of consumer 2, respectively.
excess demand price atgreater than x * .

x*Recall Φ X ' ( x*) > 0, then the zero

becomes positive when the supply of X is marginallyThus, P2 − P1 > 0, namely P2 > P1 .

Then consumer 2, thedemander, appreciates X more than consumer 1, the supplier, does at the level x * , sothat the supply of X increases and diverges fromx * . The points A and C in Figure

A2 therefore describe locally Marshall-unstable equilibria.
x2
30

25

C
y2

y1

20

15

B
10

A
(M4) (M3) (M2) (M1)5( x, y )
0
0

5

10

15

20

25

30

x1

Figure A2. Local Marshallian Stability of Three Competitive Equilibria

26

Appendix 2: Experimental Instruction
This is an experiment about decision making and economics. The instructions are simple.
If you follow them carefully and make good decisions, you might earn a considerable
amount of money that will be paid to you. In this experiment, you will make decisions to
trade or hold two kinds of commodities, called X and Y in a sequence of trading periods.

I.

Introduction

1.

There are ( 20

) traders in total. Please make sure that you have the following

items:

2.

a)“Payoff Table” (one)b)“Record Sheet” (three)c)

Name tag (one)Please check whether your trader name (A, B, C…) in your “Record Sheet” is thesame as the first letter in your name tag.
3.

Your “Payoff Table” is your own SECRET information. You are NOT allowed toreveal the information regarding your “Payoff Table” to any other person. We will show
you how to read the “Payoff Table” later.
4.

At the beginning of each period of the experiment, you will be given some amountsof Commodity X and/or Y. These amounts are shown in the first row of your “Record
Sheet”. This endowment is also your own SECRET information, so you are NOT allowed
to reveal the information regarding your endowment to any other person.

II. Trading Rules
The trading rules are as follows:1.

First of all, please put on your name tag so that the other traders can see your trader

name.
2.

Each trader will be given pink cards and/or white cards in an envelope. One pinkcard is one unit of commodity X, and one white card is one unit of commodity Y. The
number of pink cards (resp., white cards) equals to the amount of Commodity X (resp.,
Commodity Y) in the first row of your “Record Sheet.” You can take pink and white cards(Commodities X and Y) out of the envelope only when you check the number of cards or27

trade them.
3.

Walk around this room and find a person to trade. Be careful NOT to reveal to any

other person your “Payoff Table” and “Record Sheet”. The same notice applies to thefollowing steps 4, 5, and 6.
4.

Start a negotiation when you find a person that wants to trade with you. You

CANNOT give Commodity X or Y more than you hold. Moreover, the trading ratio of Y
to X (= (Amount of Y)/(Amount of X)) should be greater than or equal to (0.25). Remember that the trading ratio of Y to X cannot be less than (= 0.25
5.

1/4 =
1/4

).

If you reach an agreement, then report the agreement to an experimenter. In front of

the experimenter, trade Commodity X with Commodity Y according to the agreement.
After that, write the trading result in your “Record Sheet.” This is the end of one trade.
6.

Repeat the above steps 3-5 after one trade is completed. You have (12)

minutes for each period. You can trade as many times as you want within the time limit.
For the next person to trade with, you can choose any person: she/he may be the same asor different from one of the persons you have already traded. We accept only agreementsthat have reached within the time limit.
7.

Please go back to your seat after each period. Please make sure that all commodity

cards you traded are in your envelope. This is the end of the first period.
8.

At the beginning of the second period, you will receive the same materials as thoseof the first period. That is, the amounts of Commodities X and Y you initially have at
Period 2 are the same as those at the beginning of Period 1. We will distribute pink cards
and /or white cards in an envelope. Those amounts are shown in your “Record Sheet”. We
will also collect the commodity cards and the envelope used in Period 1. After a 2-minutebreak, Period 2 starts. This experiment has (repeated ( 55) periods. The above steps are) times.

III. An Example
We will give you an example to explain how to read the “Payoff Table” and how to fillout the “Record Sheet” by way of an example. In the following explanations, we will use

28the “Pilot Payoff Table” which has nothing to do with the “Payoff Table,” but the “Pilot
Payoff Table” should help you read the “Payoff Table” in the experiment.
1.

Suppose that your trader name is “A”.

2.

Take a look at Table 1-(a). Your endowment is shown in the second row of the“Record Sheet.” In this example, you are given endowment of 9 units of Commodity X
and 8 units of Commodity Y.

Record Sheet
Date (day/month/year):
Trader Name:

Time:

A

Your Name Tag ID:

xxxxx

Your Name

xxxxx

~

xxxxx

Period 1

Trade
Amount of Amount of Person You Amount of Amount of
Number Change in X Change in Y Trade with
X
Y

9

0

8

Payoff4905

1

Table 1-(a)Next please see Table 2. This table represents a part of the “Pilot Payoff Table.” In thistable, the horizontally aligned numbers denote the amounts of Commodity X and thevertically aligned numbers denotes the amounts of Commodity Y. You are endowed with
9 units of Commodity X and 8 units of Commodity Y, so your initial payoff is the numberin the cell of column 9 - row 8, that is, 4905. This number is the value shown in the“Payoff” of “Trade Number 0” in the “Record Sheet”.

29Amount of Y

Pilot Payoff Table
25 ・・・・
24 ・・・・
23 ・・・・
22 ・・・・
21 ・・・・
20 ・・・・
19 ・・・・
18 ・・・・
17 ・・・・
16 ・・・・
15 ・・・・
14 ・・・・
13 ・・・・
12 ・・・・
11 ・・・・
10 ・・・・
9 ・・・・
8 ・・・・
7 ・・・・
6 ・・・・
5 ・・・・
4 ・・・・
3 ・・・・
2 ・・・・
1 ・・・・
0 ・・・・
・・・・

7209
7145
7073
6994
6907
6810
6703
6585
6455
6311
6152
5976
5781
5566
5328
5066
4776
4455
4101
3709
3276
2798
2269
1685
1039
325
3

7284
7220
7148
7069
6982
6885
6778
6660
6530
6386
6227
6051
5856
5641
5403
5141
4851
4530
4176
3784
3351
2873
2344
1760
1114
400
4

7359
7295
7223
7144
7057
6960
6853
6735
6605
6461
6302
6126
5931
5716
5478
5216
4926
4605
4251
3859
3426
2948
2419
1835
1189
475
5

7434
7370
7298
7219
7132
7035
6928
6810
6680
6536
6377
6201
6006
5791
5553
5291
5001
4680
4326
3934
3501
3023
2494
1910
1264
550
6

7509
7445
7373
7294
7207
7110
7003
6885
6755
6611
6452
6276
6081
5866
5628
5366
5076
4755
4401
4009
3576
3098
2569
1985
1339
625
7

7584
7520
7448
7369
7282
7185
7078
6960
6830
6686
6527
6351
6156
5941
5703
5441
5151
4830
4476
4084
3651
3173
2644
2060
1414
700
8

7659
7595
7523
7444
7357
7260
7153
7035
6905
6761
6602
6426
6231
6016
5778
5516
5226
4905
4551
4159
3726
3248
2719
2135
1489
775
9

7734 ・・・・
7670 ・・・・
7598 ・・・・
7519 ・・・・
7432 ・・・・
7335 ・・・・
7228 ・・・・
7110 ・・・・
6980 ・・・・
6836 ・・・・
6677 ・・・・
6501 ・・・・
6306 ・・・・
6091 ・・・・
5853 ・・・・
5591 ・・・・
5301 ・・・・
4980 ・・・・
4626 ・・・・
4234 ・・・・
3801 ・・・・
3323 ・・・・
2794 ・・・・
2210 ・・・・
1564 ・・・・
850 ・・・・
10 ・・・・

Amount of X

Table 2
Let us begin the first trading.
3.

Suppose that you negotiate with Trader B, and you and B reach the agreement that

“4 units of Commodity X that you have are traded for 7 units of Commodity Y that Trader
B has.”
4.

Report the agreement to the experimenter. The experimenter will fill out thefollowing table on the blackboard for you.

30

Deal
Trader that Amount Trader that Amount
Ratio(=Y/X)
gave Xof X
gave Y
of Y
A

4

B

7

1.75

Table 3-(a)In this case, as shown in Table 3-(a), the experimenter writes “A” in the blank of “Traderthat gave X”, “4” in “Amount of X”, “B” in “Trader that gave Y” and “7” in “Amount ofY.” Remember that the trading ratio of Y to X (=Y/X) should be greater than or equal to(5.

1/4 = 0.25).

Following the experimenter’s guidance, trade Commodity X for Y according to theagreement. You give 4 pink cards (Commodity X) to Trader B and instead receives 7
white cards (Commodity Y) from Trader B.
6.

Next please fill out your “Record Sheet.” See Table 1-(b). Write “-4” in the blank of“Amount of Change in X”, “7” in “Amount of Change in Y”, and “B” in “Person You
Trade with” in the second row of “Trade Number 1” of the “Record Sheet”.
As a result of this trade, you now hold 5 units of Commodity X and 15 units ofCommodity Y. According to the “Pilot Payoff Table” (Table 2), you will find that yourpayoff is “6302.”
Write “5” in the blank of “Amount of X,” “15” in “Amount of Y,” and “6302” in“Payoff”.

31

Record Sheet
Date (day/month/year):

Time:

A

Trader Name:Your Name Tag ID:

xxxxx

Your Name

xxxxx

~

xxxxx

Period 1

Trade
Amount of Amount of Person You Amount of Amount of
Number Change in X Change in Y Trade with
X
Y

9
5

0
1

-4

7

B

8
15

Payoff

4905
6302

2

Table 1-(b)Then, the first trading is completed. Now, let us move on to the second trading.
7.

Suppose that you negotiate with Trader K and agree “to trade your 2 units ofcommodity Y for Trader K’s 3 units of commodity X.”
8.

Report the agreement to the experimenter. The experimenter will fill out thefollowing table on the blackboard for you.

Deal
Trader that Amount Trader that Amount
Ratio(=Y/X)
gave Xof Y
of X
gave Y
A

4

B

7

1.75

G

5

H

4

0.8

L

12

F

14

1.17

K

3

A

2

0.67

Table 3-(b)32As shown in Table 3-(b), the experimenter writes “K” in the blank of “Trader that gave
X”, “3” in “Amount of X,” “A” in “Trader that gave Y” and “2” in “Amount of Y.”
9.

Following the experimenter’s guidance, trade commodities according to theagreement. You will give 2 white cards (commodity Y) to Trader K, and in turn take 3
pink cards (commodity X).
10. Then, fill out your “Record Sheet” as follows. Look at the row of Trade 2 of Table
1-(c). Write “3” in the blank of “Amount of Change in X,” “-2” in “Amount of Change inY” and “K” in “Person You Trade with.”
As a result of this trading, you own 8 units of X and 13 units of Y. According to the “Pilot
Payoff Table,” your payoff is found to be 6156. So write “8” in the blank of “Amount of
X,” “13” in “Amount of Y” and “6156” in “Payoff.”

Record Sheet
Date (day/month/year):
Trader Name:

Time:

A

Your Name Tag ID:

xxxxx

Your Name

xxxxx

~

xxxxx

Period 1

Trade
Amount of Amount of Person You Amount of Amount of
Number Change in X Change in Y Trade with
X
Y

9
5
8

0
1
2

-4
3

7
-2

B
K

8
15
13

Payoff

4905
6302
6156

Table 1-(c)Then, the second trading is completed.
Arrows in the “Pilot Payoff Table” indicate the changes in your payoff. In our experiment,
you can make as many trades as you want within (12) minutes.

Now we will explain about your earnings. Your earnings depend on the final payoff that33

you earn in one randomly selected period from the experiment. This period is chosen by arandom device after the experiment, so nobody can tell during the experiment. Yourearnings are computed in the following way:Your earnings =(your final payoff at one period randomly chosen) × (

1.14

) Ksh

For example, suppose that (i) Period 1 is randomly selected after the experiment, and (ii)
your final payoff at the end of Period 1 is (6156

earnings are (

7018

(

). We round off the decimal places.

7018) Ksh because () as in Table 1-(c). Then your
6156

) × (

1.14

) =

That’s all. If you have any questions, please raise your hand.
Now, let us start the experiment. First, look at your “Payoff Table.” We will give you 5
minutes so that you can look over the table and understand it very well. During thisperiod, please make sure that you completely understand all the rules.
If you have any questions, please let us know quietly. Our staff will come to help you.
Please remember that you are NOT allowed to communicate with any other person until
the experiment starts.
Meantime, our staff will distribute pink and/or white cards in an envelope. Notice that thetrading period number is printed in each card. You can only use cards with the same
number as the numbers of the period going on. For example, in Period 3, you can only
use cards with “3”.
Remember that you are NOT allowed to reveal the information regarding your “Payoff
Table” or the information regarding your “Record Sheet” to any other person. If thishappens, the experiment will be stopped at that point.

34

Appendix 3: Payoff Tables

A mo u n t o f Y

A. Payoff table for the type 1 subjects
30 670 675 681 686 691 697 702 1145 1424 1429 1434 1440 1445 1450 1456 1516 2068 2247 2247 2247 2247 2247 2247 2247 2247 2247 2247 2247 2247 2247
29 670 675 681 686 691 697 702 1145 1424 1429 1434 1440 1445 1450 1456 1516 2068 2195 2195 2195 2195 2195 2195 2195 2195 2195 2195 2195 2195 2195
28 670 675 681 686 691 697 702 1145 1424 1429 1434 1440 1445 1450 1456 1516 2068 2142 2142 2142 2142 2142 2142 2142 2142 2142 2142 2142 2142 2142
27 670 675 681 686 691 697 702 1145 1424 1429 1434 1440 1445 1450 1456 1516 2068 2090 2090 2090 2090 2090 2090 2090 2090 2090 2090 2090 2090 2090
26 670 675 681 686 691 697 702 1145 1424 1429 1434 1440 1445 1450 1456 1516 2037 2037 2037 2037 2037 2037 2037 2037 2037 2037 2037 2037 2037 2037
25 670 675 681 686 691 697 702 1145 1424 1429 1434 1440 1445 1450 1456 1516 1984 1984 1984 1984 1984 1984 1984 1984 1984 1984 1984 1984 1984 1984
24 670 675 681 686 691 697 702 1145 1424 1429 1434 1440 1445 1450 1456 1516 1932 1932 1932 1932 1932 1932 1932 1932 1932 1932 1932 1932 1932 1932
23 670 675 681 686 691 697 702 1145 1424 1429 1434 1440 1445 1450 1456 1516 1879 1879 1879 1879 1879 1879 1879 1879 1879 1879 1879 1879 1879 1879
22 670 675 681 686 691 697 702 1145 1424 1429 1434 1440 1445 1450 1456 1516 1827 1827 1827 1827 1827 1827 1827 1827 1827 1827 1827 1827 1827 1827
21 670 675 681 686 691 697 702 1145 1424 1429 1434 1440 1445 1450 1456 1516 1774 1774 1774 1774 1774 1774 1774 1774 1774 1774 1774 1774 1774 1774
20 670 675 681 686 691 697 702 1145 1424 1429 1434 1440 1445 1450 1456 1516 1722 1722 1722 1722 1722 1722 1722 1722 1722 1722 1722 1722 1722 1722
19 670 675 681 686 691 697 702 1145 1424 1429 1434 1440 1445 1450 1456 1516 1669 1669 1669 1669 1669 1669 1669 1669 1669 1669 1669 1669 1669 1669
18 670 675 681 686 691 697 702 1145 1424 1429 1434 1440 1445 1450 1456 1516 1616 1616 1616 1616 1616 1616 1616 1616 1616 1616 1616 1616 1616 1616
17 670 675 681 686 691 697 702 1145 1424 1429 1434 1440 1445 1450 1456 1516 1564 1564 1564 1564 1564 1564 1564 1564 1564 1564 1564 1564 1564 1564
16 670 675 681 686 691 697 702 1145 1424 1429 1434 1440 1445 1450 1456 1511 1511 1511 1511 1511 1511 1511 1511 1511 1511 1511 1511 1511 1511 1511
15 670 675 681 686 691 697 702 1145 1424 1429 1434 1440 1445 1450 1456 1459 1459 1459 1459 1459 1459 1459 1459 1459 1459 1459 1459 1459 1459 1459
14 670 675 681 686 691 697 702 1145 1406 1406 1406 1406 1406 1406 1406 1406 1406 1406 1406 1406 1406 1406 1406 1406 1406 1406 1406 1406 1406 1406
13 670 675 681 686 691 697 702 1145 1354 1354 1354 1354 1354 1354 1354 1354 1354 1354 1354 1354 1354 1354 1354 1354 1354 1354 1354 1354 1354 1354
12 670 675 681 686 691 697 702 1145 1301 1301 1301 1301 1301 1301 1301 1301 1301 1301 1301 1301 1301 1301 1301 1301 1301 1301 1301 1301 1301 1301
11 670 675 681 686 691 697 702 1145 1248 1248 1248 1248 1248 1248 1248 1248 1248 1248 1248 1248 1248 1248 1248 1248 1248 1248 1248 1248 1248 1248
10 670 675 681 686 691 697 702 1145 1196 1196 1196 1196 1196 1196 1196 1196 1196 1196 1196 1196 1196 1196 1196 1196 1196 1196 1196 1196 1196 1196
9 670 675 681 686 691 697 702 1143 1143 1143 1143 1143 1143 1143 1143 1143 1143 1143 1143 1143 1143 1143 1143 1143 1143 1143 1143 1143 1143 1143
8 670 675 681 686 691 697 702 1091 1091 1091 1091 1091 1091 1091 1091 1091 1091 1091 1091 1091 1091 1091 1091 1091 1091 1091 1091 1091 1091 1091
7 670 675 681 686 691 697 702 1038 1038 1038 1038 1038 1038 1038 1038 1038 1038 1038 1038 1038 1038 1038 1038 1038 1038 1038 1038 1038 1038 1038
6 670 675 681 686 691 697 702 985 985 985 985 985 985 985 985 985 985 985 985 985 985 985 985 985 985 985 985 985 985 985
5 670 675 681 686 691 697 702 933 933 933 933 933 933 933 933 933 933 933 933 933 933 933 933 933 933 933 933 933 933 933
4 670 675 681 686 691 697 702 880 880 880 880 880 880 880 880 880 880 880 880 880 880 880 880 880 880 880 880 880 880 880
3 670 675 681 686 691 697 702 828 828 828 828 828 828 828 828 828 828 828 828 828 828 828 828 828 828 828 828 828 828 828
2 670 675 681 686 691 697 702 775 775 775 775 775 775 775 775 775 775 775 775 775 775 775 775 775 775 775 775 775 775 775
1 670 675 681 686 691 697 702 723 723 723 723 723 723 723 723 723 723 723 723 723 723 723 723 723 723 723 723 723 723 723
0 670 670 670 670 670 670 670 670 670 670 670 670 670 670 670 670 670 670 670 670 670 670 670 670 670 670 670 670 670 670
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29
Amount of X

A mo u n t o f Y

B. Payoff table for the type 2 subjects
30 695 701 706 712 717 723 728 734 1103 1108 1114 1119 1125 1130 1136 1141 1147 1152 1465 1723 1728 1734 1739 1745 1750 1756 1761 1767 1772 1778 1783
29 695 701 706 712 717 723 728 734 1103 1108 1114 1119 1125 1130 1136 1141 1147 1152 1465 1723 1728 1734 1739 1745 1750 1756 1761 1767 1772 1778 1783
28 695 701 706 712 717 723 728 734 1103 1108 1114 1119 1125 1130 1136 1141 1147 1152 1465 1723 1728 1734 1739 1745 1750 1756 1761 1767 1772 1778 1783
27 695 701 706 712 717 723 728 734 1103 1108 1114 1119 1125 1130 1136 1141 1147 1152 1465 1723 1728 1734 1739 1745 1750 1756 1761 1767 1772 1778 1783
26 695 701 706 712 717 723 728 734 1103 1108 1114 1119 1125 1130 1136 1141 1147 1152 1465 1723 1728 1734 1739 1745 1750 1756 1761 1767 1772 1778 1783
25 695 701 706 712 717 723 728 734 1103 1108 1114 1119 1125 1130 1136 1141 1147 1152 1465 1723 1728 1734 1739 1745 1750 1756 1761 1767 1772 1778 1783
24 695 701 706 712 717 723 728 734 1103 1108 1114 1119 1125 1130 1136 1141 1147 1152 1465 1723 1728 1734 1739 1745 1750 1756 1761 1767 1772 1778 1783
23 695 701 706 712 717 723 728 734 1103 1108 1114 1119 1125 1130 1136 1141 1147 1152 1465 1723 1728 1734 1739 1745 1750 1756 1761 1767 1772 1778 1783
22 695 701 706 712 717 723 728 734 1103 1108 1114 1119 1125 1130 1136 1141 1147 1152 1465 1723 1728 1734 1739 1745 1750 1756 1761 1767 1772 1778 1783
21 695 701 706 712 717 723 728 734 1103 1108 1114 1119 1125 1130 1136 1141 1147 1152 1465 1723 1728 1734 1739 1745 1745 1745 1745 1745 1745 1745 1745
20 695 701 706 712 717 723 728 734 1103 1108 1114 1119 1125 1130 1136 1141 1147 1152 1465 1695 1695 1695 1695 1695 1695 1695 1695 1695 1695 1695 1695
19 695 701 706 712 717 723 728 734 1103 1108 1114 1119 1125 1130 1136 1141 1147 1152 1465 1645 1645 1645 1645 1645 1645 1645 1645 1645 1645 1645 1645
18 695 701 706 712 717 723 728 734 1103 1108 1114 1119 1125 1130 1136 1141 1147 1152 1465 1595 1595 1595 1595 1595 1595 1595 1595 1595 1595 1595 1595
17 695 701 706 712 717 723 728 734 1103 1108 1114 1119 1125 1130 1136 1141 1147 1152 1465 1545 1545 1545 1545 1545 1545 1545 1545 1545 1545 1545 1545
16 695 701 706 712 717 723 728 734 1103 1108 1114 1119 1125 1130 1136 1141 1147 1152 1465 1495 1495 1495 1495 1495 1495 1495 1495 1495 1495 1495 1495
15 695 701 706 712 717 723 728 734 1103 1108 1114 1119 1125 1130 1136 1141 1147 1152 1445 1445 1445 1445 1445 1445 1445 1445 1445 1445 1445 1445 1445
14 695 701 706 712 717 723 728 734 1103 1108 1114 1119 1125 1130 1136 1141 1147 1152 1395 1395 1395 1395 1395 1395 1395 1395 1395 1395 1395 1395 1395
13 695 701 706 712 717 723 728 734 1103 1108 1114 1119 1125 1130 1136 1141 1147 1152 1345 1345 1345 1345 1345 1345 1345 1345 1345 1345 1345 1345 1345
12 695 701 706 712 717 723 728 734 1103 1108 1114 1119 1125 1130 1136 1141 1147 1152 1295 1295 1295 1295 1295 1295 1295 1295 1295 1295 1295 1295 1295
11 695 701 706 712 717 723 728 734 1103 1108 1114 1119 1125 1130 1136 1141 1147 1152 1245 1245 1245 1245 1245 1245 1245 1245 1245 1245 1245 1245 1245
10 695 701 706 712 717 723 728 734 1103 1108 1114 1119 1125 1130 1136 1141 1147 1152 1195 1195 1195 1195 1195 1195 1195 1195 1195 1195 1195 1195 1195
9 695 701 706 712 717 723 728 734 1103 1108 1114 1119 1125 1130 1136 1141 1145 1145 1145 1145 1145 1145 1145 1145 1145 1145 1145 1145 1145 1145 1145
8 695 701 706 712 717 723 728 734 1095 1095 1095 1095 1095 1095 1095 1095 1095 1095 1095 1095 1095 1095 1095 1095 1095 1095 1095 1095 1095 1095 1095
7 695 701 706 712 717 723 728 734 1045 1045 1045 1045 1045 1045 1045 1045 1045 1045 1045 1045 1045 1045 1045 1045 1045 1045 1045 1045 1045 1045 1045
6 695 701 706 712 717 723 728 734 995 995 995 995 995 995 995 995 995 995 995 995 995 995 995 995 995 995 995 995 995 995 995
5 695 701 706 712 717 723 728 734 945 945 945 945 945 945 945 945 945 945 945 945 945 945 945 945 945 945 945 945 945 945 945
4 695 701 706 712 717 723 728 734 895 895 895 895 895 895 895 895 895 895 895 895 895 895 895 895 895 895 895 895 895 895 895
3 695 701 706 712 717 723 728 734 845 845 845 845 845 845 845 845 845 845 845 845 845 845 845 845 845 845 845 845 845 845 845
2 695 701 706 712 717 723 728 734 795 795 795 795 795 795 795 795 795 795 795 795 795 795 795 795 795 795 795 795 795 795 795
1 695 701 706 712 717 723 728 734 745 745 745 745 745 745 745 745 745 745 745 745 745 745 745 745 745 745 745 745 745 745 745
0 695 695 695 695 695 695 695 695 695 695 695 695 695 695 695 695 695 695 695 695 695 695 695 695 695 695 695 695 695 695 695
0 1 2 3 4 5 6 7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Amount of X

35