Multimarket equilibrium, trade, and the law of one price.

• Author: Laury, Susan K.
• Position: Teaching Economics with Classroom Experiments: A Symposium

1. Introduction

   Although the centerpiece of any introductory economics course is the supply and demand model of perfect competition, students frequently have trouble understanding the linkages between individual markets and how differing supply or demand conditions can lead to different price tendencies between markets. Instead of implementing a single-market classroom experiment and asking students why prices converged to, say, $6, it is instructive to set up two markets and let students try to explain why prices in the two markets differ. This two-market approach also illustrates how gains from trade arise when cross-market trading is introduced. Speculators essentially unify the markets and equalize prices as arbitrage opportunities are exploited. Multimarket experiments help bridge the gap in students' knowledge that results when the leap is made from one to many markets, as is done in most microeconomics textbooks.

   We use playing cards to distribute buyers' value information in classroom trading. The dual market setup can be adapted for microeconomics classes at any level, ranging in size from 10 to about 40. Somewhat larger classes can be accommodated by recruiting assistants to help pass out cards or by assigning students to work in groups. The exercise takes about an hour, including discussion. Section 2 outlines the procedures, and section 3 describes how to structure the class discussion to enhance student learning. Section 4 surveys results from (nonclassroom) research experiments in which trading occurs in interrelated markets.

2. Procedures

   The basic setup involves two isolated markets, with identical demand conditions but with different supply conditions. Allowing trade only within each separate market will generate higher prices in the market with tight supply, setting the stage for the subsequent introduction of traders who can buy in one market and sell in the other. We have used two different trading institutions. In the first, we eliminate sellers by conducting auctions in which we sell a fixed number of commodity units to student buyers in each market. This institution is relatively easy to implement, especially for the instructor who has not previously conducted a classroom market exercise. In Appendix 1 we describe a second institution, a pit market, in which buyers and sellers come together in separate trading areas to call out bids and asks and to negotiate trades in a relatively unstructured situation. The pit market is more complex than the auction, but an instructor who has previously conducted a single-market classroom exercise (as described in Holt 1996) might prefer this setup.

   Consider the auction setup with fixed supply and eight buyers assigned to each market. (The numbers of buyers can be increased or decreased as explained below.) Six units are available for sale in the first market, and only two units are available in the second.(1) Buyers submit sealed bids for a single unit in their own market, with the uniform purchase price determined by the highest rejected bid. Thus, if the three highest bids were $9.50, $8, and $7 in the thin (low-supply) market, the buyers with bids of $9.50 and $8 would each receive a single unit but both would pay only $7 for these units. If a tie results for the lowest accepted bid (e.g., if the bids submitted were $9.50, $8, and $8), one of the tied bids is randomly chosen, and all units are sold at the tie price ($8). Buyers are given a motive to bid by providing them with resale values that can be conveniently assigned with playing cards. We use numbered playing cards to determine resale values. The cards are shuffled, and each buyer is given a card, which determines the buyer's resale value in dollars; for example, a 6 of hearts indicates a resale value of $6. A buyer who makes a purchase at a price below the resale value earns a profit that is the difference between the resale value and the purchase price. Bids above resale value are not permitted. Thus, the buyer's value corresponds to a limit price.

   The eight cards used in each market are 10, 9, 8, 7, 6, 5, 4, and 3; these values can be arrayed to form a demand function, as shown in Figure 1. The vertical lines show the perfectly inelastic supply function in each market. The demand function is not shown to students prior to trading, but if buyers bid optimally, the price will be $8 in the thin (low-supply) market and $4 in the thick (high-supply) market.(2) After buyers' resale values and the trading rules are explained by reading the instructions contained in Appendix 2, the cards are dealt, and each buyer submits a bid for a single unit by writing a bid price (identified by the student's name) on a small slip of paper given to them by the instructor. These bids are collected and ordered from high to low in each market, and the market-clearing price is announced. This price is the third-highest bid in the thin market and the seventh-highest bid in the thick market. Buyers then calculate their earnings (equal to zero for those who made no purchase) using the record sheet contained in Appendix 2. These instructions and record sheets can also be downloaded from the Web at http://theweb.badm.sc.edu/laury.

   It might enhance student interest if you collect the cards between rounds, shuffle them (keeping the cards from the two markets separate), and then pass them out again to buyers before bids are made in the next period. Prices should converge to near-equilibrium levels after several periods, at which time trading between markets can be introduced.

   After reading the traders' instructions (also contained in Appendix 2), ask for one volunteer from each market to act as a trader. The lowest-numbered card in each market should be removed before passing out the remaining cards. Because these cards represent extramarginal units, this does not change the equilibrium price in either market. Each trader is given a capital endowment of $20 and is restricted to purchasing a single unit in the thick (low-price) market? Because of the price disparity between markets, this unit can be resold for a profit in the thin (high-price) market. After the introduction of traders, trading in the thick market precedes that in the thin market. Any units bought by traders are automatically added to the available supply in the next (thin) phase of the market.

   With the introduction of traders, the supply in the thin market is increased by the number of units that the traders bring, and the market-clearing price is again determined by the highest rejected bid. The predicted outcome is for two units to be purchased by traders in the thick market and resold in the thin market. The addition of these two units shifts supply out to four in the thin market and lowers the price to $6. Similarly, the additional two units of demand should, in theory, raise the price to $6 in the thick market as the traders leave only four units for buyers in this market.

   To accommodate additional students (i.e., for classes with more than 16 students), you can assign the extra buyers...