# Extracting  Data From Classroom Trading Pits

Ted Bergstrom and Eugene Kwok
University of California Santa Barbara

In their introductory economics text, Experiments with Economic Principles, Theodore Bergstrom and John Miller introduce economics to college students by means of classroom market experiments. In these experiments,  students buy and sell hypothetical goods in a trading pit environment.  These experiments have now been conducted in hundreds of classrooms, and for many of these classes the results have been preserved and recorded in convenient form.  We have collected data on transaction prices and quantities  from 32  classrooms at 10 universities for each of three different market experiments.   Although these experiments were designed for instructional purposes, the data collected is likely to provide information of interest for those who want to understand the behavior of people in trading markets as well as for those who are curious about what happens in classroom experiments.

# A Simple Supply and Demand Experiment

Experiment 1 is a simple pit-trading market with the following rules.  Each participant is assigned a role as a supplier or a demander of "apples."   Suppliers can sell at most one unit (a bushel)   and demanders can buy at most one unit.  Each supplier is  assigned one of two possible ``seller costs'' and each demander is  assigned one of  two possible ``buyer values''  for a bushel of apples  Buyers and sellers are asked to roam around the room and try to make make as profitable a deal as possible.   When a seller and a buyer agree on a price, they write  this price on a sales contract, along with their identification numbers and the  seller cost and  buyer value.  The market manager records transaction prices on the blackboard for all to see as the contracts are turned in.    If a seller with seller cost  C sells a unit at price to a buyer with buyer value B, then the seller's profit is  P-C   and the buyer's profit is B-C.

This experiment included two different  sessions with  different distributions of buyer values and seller costs in each session.  Each session consists of two rounds.   In the second round of each session,  the distribution of buyer values and seller costs is the same as in the first round.  In the second round, however, participants  can  use any information they have gained from participating in the first round  and  from observing the list of first-round transaction prices.

## Competitive Demand and Supply in Session 1

The exact  number of persons with each buyer value and seller cost will, of course,  depend on  class size,  but we have arranged the distribution so that the competitive price and the main qualitative features of supply and demand are the same for all class sizes.   For example,  a class of 47  students would have 8 demanders with buyer values of \$40, and 16 demanders with buyer values of \$20.  There would also be 15 suppliers with seller costs of \$10 and 8 suppliers with seller costs of \$30.

Figure 1.1 below shows the competitive supply and demand curve and the competitive equilibrium price and quantity  in Session 1 with a class  47 students.   As we see from the graph, the  competitive equilibrium price is  \$20 and the competitive equilibrium quantity is 15 units sold.

Figure 1.1 ## Prices in Session 1

Participants in the market are not told anything about the distribution of Buyer Values and Seller Costs.  They know only their own values and anything they find out by talking to other participants.   Typically, they participate in this market before they have even studied the theory of supply and demand.  But even if they were familiar with competitive equilibrium theory,  students would not know the demand curve or the supply curve and thus would not know the competitive equilibrium price at the time they make their trades.

Since individuals have very limited knowledge of market conditions when they participate in the first round,  we would not expect  all transactions  to take place at or close to the competitive equilibrium price.  Nevertheless, the data shows that in the first round of Session 1,  the average price observed in most classrooms is strikingly  close to the competitive equilibrium price. This can be seen in  Figure 1.2, which records the distribution of mean prices across the 32 classrooms for which we have data.

#### In the second round,  as traders learned more about the prices at which others bought and sold, the mean prices in classrooms tended to cluster closer to the competitive equilibrium price of \$20, with mean prices remaining slightly higher than the competitive price.  This is shown in Figure 1.3

Figure 1.3 We have also recorded and plotted the distribution of all recorded transactions in all sections.  In Figure 1.4, the purple line shows the distribution of transaction prices in Round 1 and the yellow line shows the distribution in Round 2.  Notice that in round 1, there are large numbers of transactions at the  "focal" prices \$15, \$25, \$30, and \$35.  In Round 2, the number of transactions at these prices dimishes, while there is an increase in  the number of transactions that take place at prices close to the competitive equilibrium price of  \$20.

Figure 1.4 ## Competitive Supply and Demand In Session 2

Session 2 of this experiment has fewer low cost suppliers and more high value demanders than Session 1. As in Session 1,  demand and supply curves vary with class size, but  the competitive price and the main qualitative features of supply and the demand are the same in all classes.  In this session, the competitive equilibrium price is \$30 rather than \$20 as in Session 1. Figure 1.5 shows the competitive supply and demand curve and the competitive equilibrium price and quantity for a class of 47 students.

Figure 1.5 ## Prices in Session 2

Figures 1.6 and 1.7 show the distribution of mean prices in the 32 sections for Session 2.     In this session, we see that average prices are clustered a bit below the competitive equilibrium price of \$30 in the first round and  move closer to \$30 in the second round.

Figure 1.6 Figure 1.7 Figure 1.8 shows the distributions of prices in individual transactions for each of the two rounds of Session 2. Notice that in Round 1 there are a significant number of transactions at \$20, which was the equilbrium price in Session 1 and that in Session 2,  the number of such transactions decreases sharply,  while there is a corresponding increase in the  number of transactions taking place at prices close to \$30, which is the Session 2 competitive equilibrium price.

Figure 1.8 ## The Profit-Splitting Hypothesis

In both sessions of this experiment,  average transaction prices in most classrooms were fairly close to the competitive equilibrium prices in the first round and got   closer in the second round of trading.   While these results are usually  enough  to convince students that the competitive theory has impressive predictive power, the competitive theory is not the only interesting possible explanation for the data observed.

An alternative theory of the events in these  experiments is the following profit-splitting hypothesis.  Suppliers and demanders are paired at random.   In any pair for which the demander's buyer value exceeds the seller cost of the seller,  the demander and supplier will agree to a price halfway between the demander's buyer value and the seller's seller cost.  If the demander's buyer value is less than the seller's seller cost, so that no mutually profitable deal can be struck, then the buyer and the seller will not transact and will search for another partner with whom they can make a profitable trade.

### Profit-Splitting and the Outcome in Session 1

In Session 1 of this experiment, approximately 1/3 of the demanders have buyer values of \$40 and 2/3 have buyer values of \$20.  Approximately 2/3 of the suppliers have seller costs of \$10 and 1/3 have seller costs of \$30. If encounters are random, then on average, 2/9 of the encounters will be between  demander with buyer value  \$40 and a supplier  with seller cost  \$10.   According to the price-splitting hypothesis, they would trade at a price of \$25.   About 1/9 of the random encounters would be between a demander with buyer value \$40 and a supplier with seller cost \$30.  They would trade at a price of \$35.  About 4/9   the encounters would be between a demander with buyer value \$20 and a  supplier with seller cost \$10.  They would trade at a price of \$15.  Finally, about 2/9 of the encounters would be between a a demander with buyer value of \$20 and a supplier  with seller cost \$30.   These latter individuals would not trade.  We see that in this market, the only individuals who do not make a trade with the first person they meet are demanders with \$20 buyer values and suppliers with \$30 seller costs. Since everyone can make only one trade and since all of the low cost sellers and high value demanders transact with the first person they meet, those who  fail to make a trade  in their first encounter will never find any mutually profitable trading opportunities.

Thus  the profit-splitting hypothesis predicts that 7/9 of the traders will make trades.  Prices paid will vary, depending on the buyer values and costs of the supplier and demander who happen to be matched. Under this hypothesis, approximately  28% (2/7) of all trades will take place at a price of \$25,  14% (1/7)  will take place at a price of \$35, and  4/7  (56%) will take place at a price of \$15.

In contrast, the competitive hypothesis predicts that about 2/3 of all traders will make trades and that all trades would occur at \$20.

We see from Figure 1.4 that there is some support for the profit-splitting hypothesis, especially in the first round of trading.  The graph of transactions in Round 1 has peaks at \$35, \$25, and \$15. Moreover, as predicted by the profit-splitting theory, the most frequent price is \$15.  But there is also some support for competitive behavior.    Contrary to the predictions of profit-splitting,  about 30% of  the  transactions in Round 1 occur at prices in the range \$18-20. In Round 2, the competitive hypothesis appears to gain at the expense of the profit-splitting hypothesis.  In Round 2, the number of transactions at the extreme prices \$35 and \$15 decreases sharply, while the percentage of transactions occuring at prices within \$2 of the competitive price  increases from 30% to more than 40%.

### Profit-Splitting and the Outcome of Session 2

In Session 2,  approximately 2/3 of the demanders have buyer values of \$40 and 1/3 have buyer values of \$20, while 1/3 of the suppliers have seller costs of \$10 and 2/3 have seller costs of \$30. The hypothesis of random encounters with price-splitting  predicts that approximately 28% (2/7) of all transactions would occur at a price of \$25,  56% (4/7)  of all transactions would occur at a price of \$35, and 14% (1/7) would occur at a price of \$15.

We see from Table 1.8 that  the profit-splitting hypothesis does not perform very well in explaining the results of either round of trading.  Transactions at prices of \$15 and of \$35 are much less common than the profit-splitting hypothesis would predict.

In Round 1, about 35% and in Round 2 about 50% of the transactions were at prices within \$2 of the competitive equilibrium price of \$30.  It is interesting to notice that in Round 1, about 15% of the transactions took place at prices that were approximately \$20, the  equilibrium price for Session 1 transactions.  Since prices in Round 2 of session 1 were typically clustered around \$20,  this price appears to have been focal for many traders in the first round of Session 2.  In Round 2,  market pressures seem to have erased most of this effect.   The proportion  of transactions at prices close to \$20 fell to less than 5%.

## Quantities in Both Sessions

In almost every section the number of units sold was within one or two units of the competitive equilibrium quantity. As we see from Figure 1.9, it was much more common for the experimental quantity to be larger than rather than smaller than the competitive equilibrium quantity. This result accords with  observations reported by Edward Chamberlin  who pioneered the use of classroom markets. (Journal of Political Economy, 1948 )

### Figure 1.9 In a unique competitive equilibrium,  every transaction is profitable for  at least one of the two traders and neither makes a loss. Competitive equilibrium is not the only outcome with this property.  For example, assignment generated by random matching with profit splitting also has this property.  As we demonstrated previously, random matching with profit splitting results in  the expected number of transactions being about 7/9 of the number of traders, while competitie equilibrium results in a number of trades equal to just 2/3 of the number of traders.

Consider now an outcome in  matchmaker arranges  matchings so as to maximize the total number of supplier-demander pairs in which the  demander's buyer value exceeds the seller's seller cost and requires these pairs to trade at some price profitable to both.  For the distributions of buyer values and seller costs in this experiment, it is always possible to do this in such a way that  every person in the market makes a trade at a profit.

Thus we have two examples of  outcomes in which everyone makes a profit and the number of trades exceeds the number of trades in competitive equilibrium.  These examples illustrate the following general theorem.

Theorem  If there is a unique competitive equilibrium quantity,  then if the number of trades is smaller than the competitive equilibrium quantity, there must remain at least one demander-supplier pair who have not traded, but could make a mutually profitable trade.

Proof:  In a competitive equilibrium, every demander has a buyer value at least as high as the competitive equilbrium price and every seller has a seller cost no higher than the competitive equilibrium price.  It follows that the buyer value of every demander who trades in competitive equilibrium is at least as high as the seller cost of every supplier who trades.   Indeed if the competitive equilibrium  quantity is unique, it must be that the buyer value of every demander who trades is higher than the seller cost of every supplier who trades.

Consider an allocation with fewer trades than the number of trades in competitive equilibrium.  It must be that in this allocation, at least one of the suppliers who sells in competitive equilibrium does not trade and at least one of the demanders who buys in competitive equilibrium does not trade.  From the result of the previous paragraph, we see that the buyer value of this demander is higher than the seller cost of at least one supplier who does not trade in equilibrium.  These two individuals could make a mutually profitable trade.
QED

From this theorem, we see that if traders understand their buyer values and seller costs and sufficiently aggressive to find mutually profitable trade possibilities so long as such exist, then the number of trades will be at least as large as the competitive equilibrium quantity.  We see from  Figure 1.9 that there were a few classes in which the number of trades fell short of the competitive equilibrium quantity.  In these classes it must be that at the end of trading there remained at least one demander and at least one supplier who did not trade but could make  a mutually profitable trade with each other.  On the other hand, as our examples illustrate, it is possible that trading leads to outcomes in which everyone who trades makes a profit and where the number of trades exceeds the competitive equilibrium number.

## Related Results

We have collected and done some similar analysis with  the  results of two other experiments from Experiments with Economic Principles.  These results  can be accessed by clicking on their  experiment numbers.

Experiment 2  (shifting supply) is  an experiment in which a fixed quantity is produced at zero marginal cost, but the quantity shifts from one session to the next.

Experiment 3 (sales tax) is run first with no sales tax, then with a sales tax collected from sellers and finally with a sales tax collected from buyers.