A market-clearing classroom experiment. (Targeting Teaching).

1. Introduction

One of the most delicate tasks in teaching undergraduate micro- and macroeconomic courses is the transition from partial equilibrium models to the general equilibrium framework. At the same time, the price mechanism and the clearing of markets is crucial for students' understanding of modern economic theory. The experiment described here provides participants with an opportunity to see these economic principles in action.

The experiment is very simple: Students receive random endowments of two goods and a simple utility function that they may maximize by trading goods with each other. The only information available to each student concerns his or her own endowment, the existence of the two goods, the utility function, and the possibility of trading with other students. Each student knows neither the total supply of the goods nor the endowments of other students. Since the individual endowments are different, utility-improving trades lead to an equilibrium, with a market-clearing price proportional to the ratio of the total endowments of both goods.

The spontaneous behavior of students corresponds to the invisible hand of the price mechanism, which induces a truly endogenous equilibrium defined only by the total endowments and the form of the utility function. In contrast to the case for similar experiments, trading is not restricted by reservation prices or a willingness to trade being imposed on the participants. Thus, the students can personally experience the role of prices in the market-clearing process. The experiment also illustrates important economic concepts (e.g., that there is no trading in equilibrium, that the excess supply or excess demand for goods is zero, the principle of Pareto optimality). Students deepen their understanding of the classroom economy analytically through a problem set.

The experiment provides a way of using the classroom as an artificial closed economy with many agents. It makes economic theory more approachable for students not majoring in economics or for those students who prefer collaborative learning and concrete experiences to abstract conceptualization (see the discussion in Bartlett 1996). Its positive impact on students' learning and classroom participation reflects recent evidence on learning types (Becker and Watts 1995, 1996; Lage, Platt, and Treglia 2000).

The next section contains a description of the experiment. Section 3 summarizes experience with the experiment so far. The fourth section provides conclusions. Detailed instructions, a record sheet, and an example of a problem set can be found in the appendices.

2. The Experiment

The market-clearing experiment is intended for intermediate micro- or macroeconomic classes with at least 20 students. Giving instructions and distributing endowments takes approximately 15 minutes (see the detailed instructions in Appendix A). The "classroom economy" clears in about 10 or 20 minutes, depending on the number of participants, the motivation of the participants, and the trading intensity. Material requirements are minimal and are enumerated in Table 1.

Before the experiment begins, the instructor prepares endowments of two goods, such as red and green pieces of paper. The endowments are distributed by the instructor or drawn by the students from a hat. It is important that the total endowment of one color be different from that of the other and that students' individual endowments be sufficiently variable to ensure mutually beneficial trades. Table 2 displays the endowment distribution in one of the experiments run in an intermediate macroeconomic class at the University of Chicago. While students could generally observe the endowments of some of the other students, the total number of goods should not be revealed.

After distributing the endowments, the instructor writes the following utility function on the blackboard:

U(r, g) = rg,

where r and g are the numbers of red and green goods, respectively, held by each student. The students write down their initial endowments and utility on distributed record sheets (see Appendix B at http://home.cerge-ei.cz/Radim/experiment/index.html for an example). A prize (e.g., $10 or $20) is promised to the student who has attained the highest utility level by the end of the class. (1) No other information or instruction is given to the students.

The monetary reward serves as an incentive to maximize the utility function. At least some students quickly figure out that an exchange of goods with other students increases their utility level. Moving around the classroom, individual students exploit the differences in prices (exchange rates) between different traders in the classroom market. If some students do not participate in the game, the actively trading students will seek the passive students out and trade with them. Initially, most students try to maximize the symmetric utility function by seeking a portfolio composed of equal amounts of each good. Thus, the initial exchange rate is usually one red good for one green good. Over time, the scarcity of one good induces the exchange rate to converge to the equilibrium value proportional to the ratio of the aggregate endowments. Trading stops when no mutually beneficial (Pareto improving) trades are possible.

Once the market has cleared, the instructor writes the market-clearing price (exchange rate) on the blackboard and the students record their final allocations on their record sheets. The instructor rewards the student with the highest utility. A problem set may be distributed immediately or during the next class (see Appendix C at http://home.cerge-ei.cz/Radim/experiment/index.html). Topics for a classroom discussion can be found in the problem set; students can discuss their trading strategies. There is a classic interpretation of the price mechanism and the role of information in Hayek (1945).

There are many possible variations on the basic setup described above. The instructor may increase the curiosity of the students by announcing at the beginning of class that he or she knows the price that will prevail at the end of the experiment. To prove the claim, the instructor should write the exchange rate on a sheet of paper, put it in an envelope, and open it at the end of the experiment.

The experiment can be also conducted with three (or more) goods. For example, with the addition of a blue good, the students can maximize a utility function U(r, g, b) = rg + b, or even U(r, g, b) = rg - b, in which the blue good is a bad. In all cases, the utility function ought to be easily computable.

A government can be introduced to regulate trades and prices or to tax the endowments and the gains from trade. For instance, the government can set a price ceiling on one of the goods. (2) The resulting equilibrium can then be compared with that reached in the unregulated economy in terms of allocations and the welfare of individual students as well as that of the whole economy.

Also, an open or growing economy can be simulated by distributing additional goods of one color into the economy after the market has cleared. This setup can provide students with intuition on how the relative scarcity of one good affects the price and the allocations. Students will experience a transition process from one steady state to another. Market failures can be simulated by a low or random enforceability of trades with stress on the role of traders' reputations. Students can also be heterogeneous in their utility functions: for example, one group of students may prefer green goods, and a second group may prefer red goods.

In my opinion, however, the cost of such variations might outweigh the benefits associated with the transparency of the basic setup. In the context of the literature, the main strengths of this experiment are its simplicity, its true endogeneity, and the uniqueness of the resulting equilibrium. For instance, a related experiment proposed by Schotter and Corns (1997) has been used by a colleague as a complementary experiment. The Schotter-Corns In-Class Experiment 2: Exchange lets two participants bargain over two goods that are very unequally distributed. Since the core is large, numerous outcomes are possible, depending on bargaining or computational mistakes. Such an outcome cannot arise in this market-clearing experiment.

3. Experience with the Experiment

In the four experiments conducted so far, the trader with the highest final utility always started from a very low endowment and gained, by exploiting price differences around the classroom. In one experiment, some students sold their goods to other students who wanted to win the monetary prize for the highest utility at the end of the experiment. In two experiments, a few students pooled their resources and traded as a group.

Although such spontaneous behavior might lead to unexpected situations during the experiment, the market-clearing process is not affected. I decided not to prevent such situations or to prepare students for them. Not only do these situations provide for stimulating questions in the problem set (see question 10 in Appendix C), but, more importantly, it is worthwhile to preserve the informational and procedural purity of the experiment. In contrast to many experiments in Delemeester and Brauer (2000), this experiment has no induced values imposed on individual students (willingness to trade or number of goods to exchange) to control the result. Except for the randomly drawn endowments, all students have the same (lack of) information, the same objective function, and an equal opportunity to increase their utility level by trading.

The result of the experiment is determined by students' optimal decisions, subject only to the resource constraints and the form of the utility function.

The instructor may wish to ask the students to record their individual trades on their record sheets. However, the students trade very actively (indeed, they resemble stock market brokers) and might not have enough patience and time to record each trade they make. On the other hand, such a detailed trade record would provide useful feedback for the problem set or the classroom discussion.

4. Conclusions

In their valuable survey, Delemeester and Brauer (2001) classify only 11 of 113 surveyed classroom experiments as being relevant to macroeconomics. Modern macroeconomic theory is based on two principles: the optimal behavior of utility-maximizing rational agents (the micro-foundations of macroeconomics), and the equilibrium in the economy (the clearing of markets). This experiment focuses exactly on these two principles. Given the price, all agents behave optimally (in this sense, the price determines agents' behavior). On the other hand, given the decision rules of the agents, the market-clearing condition determines the price (in this sense, agents' behavior determines the price). The assumption of rational expectation closes the system: The market-clearing price implied by the agents' behavior is assumed to be the same as the price on which agents' decisions are based.

Students' understanding of this equilibrium system is one of the most important aspects of teaching macroeconomics at any level of abstraction and difficulty. This experiment provides a first-hand and very intuitive experience of the price mechanism and the clearing of markets. It has become a reference point in teaching more advanced concepts of monetary theory (the role of money), the macroeconomics of open economies (gains from trade), labor economics (the equilibrium search process), social security policy (generations of trading agents), rationality, and the role of information.

Appendix A: Instructions

This appendix offers a full script for the experiment. Instructions to students are in italics, and comments and suggestions for the instructor are in brackets. It is assumed that the intermediate macroeconomics class in which the experiment is to take place contains 20 students. The instructor prepares packages for all students from 300 red and 100 green goods as shown in Table 2. An example of a record sheet is shown in Appendix B (http://home.cerge-ei.cz/Radim/experiment/index.html).

Today we are going to conduct an experiment in which our classroon becomes a closed endowment economy with many agents. The experiment will demonstrate how an equilibrium in such an economy emerges. First, each of you will receive a record sheet for our experiment and draw an endowment of red and green pieces of paper that represent the goods available in the economy. [The instructor distributes the record sheets and goes around the class and lets students draw random endowments from a hat. The instructor then writes the utility function on the blackboard.]

Each of you values the goods in the economy as follows: U(r, g) = rg. where r is the number of red goods and g is the number green goods you hold. Goods are indivisible. Please record your endowment and your current utility level on the record sheet. At the end of the class, the student with the highest utility level will receive a prize in the amount of $10. [Alternative schemes of student motivation and monetary rewards, as discussed in the paper, can be used.] During the experiment, you may leave your seat and trade goods with other agents in the economy.

[If the instructor wants to put any restriction on students' behavior (coalitions), he or she should inform them of these restrictions at this moment. The instructor should not directly tell the students to maximize the utility function or exactly how the experiment will end. After questions have been answered, the instructor attaches a $10 bill to the blackboard.] Here is the reward. The experiment has begun. [Students will soon realize that an exchange of goods may increase their utility. There is no need to encourage passive students: The actively trading students will seek these students out and trade with them. Over time, the initial exchange rate (usually one red good for one green good) will converge to the equilibrium exchange rate. If the time allotted for the experiment is short, the instructor may want to announce the local exchange rates to the whole class in order to speed up the convergence to the market-clearing exchange rate. When the market-clearing exchange rate is attained, the trading inte nsity will slow down and eventually stop.]

What is the exchange rate? Is anyone interested in trading at this rate? [If no trade is made for about one minute, the instructor writes the last exchange rate, [p.sup.*.sub.g] = 3, [p.sup.*.sub.r] = 1, on the blackboard.] This is the exchange rate or which trading has stopped. It is called the market-clearing price and we express it as the number of red goods you have to give away in order to obtain one green good. Please record now your final holdings of both goods and compute your final utility level. [The instructor rewards the student(s) and may distribute the problem set. A problem set pertaining to actual situations that occurred during the experiment would have to be distributed in the next class session. Altematively, a classroom discussion based on the questions in the problem set in Appendix C (http://home.cergeei.cz/Radim/experiment/index.html) may begin.] This problem set asks you to analyze the experiment more formally. Please use the data from your record sheet: the initial and final holdings of goods and utility levels. Your grade on the problem set will not be related to these data or your actual performance in the experiment.

Table 1

Summary of the Market-Clearing Classroom Experiment

Course         Microeconomics, macroeconomics
Level          Intermediate
Subject        General equilibrium, market
               clearing, price mechanism
Material       Endowments of two goods, such as
 requirements   red and green paper; for a class
                with n students, use 15n red goods
                and 5n green goods. The n
                individual endowment packages are
                prepared before the experiment and
                put into a hat. Most of the
                individual endowment packages
                should be very different from the
                average endowment.
Class size     20 or more students
Time           One class period (30-45 minutes)
Variations     Different utility functions, more
                than two goods, price regulation
Table 2

Data from an Experiment Conducted in Intermediate Macroeconomics 202 at
the University of Chicago in 1999

Number of students           20
Aggregate endowments         300 red and 100 green goods
Individual endowments (red/  15/5, 10/4, 5/12, 20/3, 25/2,
  green goods)                12/3, 16/3, 15/5, 11/2, 20/2,
                              17/4, 12/3, 19/8, 8/13, 15/5,
                              22/5, 15/2, 15/10, 10/6, 18/3
Equilibrium price            Three green goods for one red
                              good
Time (minutes)               35 total: 15 for introduction,
                              20 for convergence

(1.) Instead of thc highest-utility-level criterion, the instructor may opt for the largest difference in (or ratio of) the final and initial utility levels. Although the latter criterion seems fairer, it would require that the initial endowments be recorded by the instructor, which may inhibit students' spontaneous participation in the experiment (with recorded endowments, they might worry about their performance). Of course, the instructor can reward the best two or three traders. Alternatively, the instructor may randomly choose one student at the end of the experiment and pay that person some fraction of his or her utility. This would motivate students to maximize absolute rather than relative utility. I thank the anonymous referee for suggesting this incentive scheme.

(2.) The maximal allowed price must be smaller than the market-clearing price of that good. Interestingly, a black market might arise in the classroom. Monitoring, enforceability, and related issues can be discussed in the class and in the problem set.

References

Bartlett, Robin L. 1996. Discovering diversity in introductory economics. Journal of Economic Perspectives 10(2):141-53.

Becker, William E., and Michael Watts. 1995. Teaching tools: Teaching methods in undergraduate economics, Economic Inquiry 32:692-700.

Becker, William E., and Michael Watts. 1996. Chalk and talk: A national survey on teaching undergraduate economics. American Economic Review 86:448-53.

Delemeester, Greg, and Jurgen Brauer. 2001. Games economists play: Non-computerized classroom-games for college economics. Journal of Economic Surveys 15:221-36.

Hayek, Friedrich A. 1945. The use of knowledge in society. American Economic Review 35:519-30.

Lage, Maureen J., Glenn J. Platt, and Michael Treglia. 2000. Inverting the classroom: A gateway to creating an inclusive learning environment. Journal of Economic Education 30:30-43.

Schotter, Andrew K., and Adam Corns. 1997. Instructor's manual with in-class experiments to accompany microeconomics: A modern approach. 2nd edition. Boston: Addison-Wesley Press.

Radim Bohacek *

* CERGE-EI, Politickych veznu 7, 111 21 Prague, Czech Republic; E-mail [e-mail].

I am grateful to Carlos Perez-Verdia, Jose Ignacio Sanchez-Macias, Grace Tsiang, and especially Andreas Ortmann and an anonymous referee for helpful suggestions and to the students in Economics 202 and 203 at the University of Chicago for their participation in the experiments.