## Case 2: Pit market (hand run)

This case study was written by Bradley Ruffle. A pit market is a suitable experiment for any level of student – sixth form up to postgraduate. It is particularly suitable for microeconomics, industrial organisation and public economics.

The primary benefit is to teach students the relevance and robustness of the competitive-equilibrium solution. Extensions allow for the demonstration of price floors and ceilings and the tax-liability-side equivalence theorem. The pit market is designed to be run by hand. For a computerised experiment that demonstrates the competitive solution, a double-auction market is the nearest equivalent.

### Procedures

Prior to the experiment, prepare two sets of cards; one from which buyers' valuations are drawn and the other from which sellers' costs are drawn. You can use playing cards (see Holt, 1996) or prepare your own with any numbers you like on them. Make sure you choose the cards ahead of time so that the resultant supply and demand curves overlap where all or almost all of the units may be traded at a profit at the competitive price.

When the students arrive, divide them into two groups of buyers and sellers. Ensure that there are at least four sellers and four buyers for convergence to the competitive outcome. The groups of buyers and sellers need not be of equal size. Give each student a record sheet (included along with instructions for participants in the downloadable file (link below)) to track their progress. Distribute randomly one or more cards to each of the buyers and sellers from their respective deck of cards. After everyone has received one or more cards, allow students to enter the pit (a large open space in the classroom) where they freely negotiate with one another. When a buyer and a seller agree upon a price, they report their negotiated price to one of the experimenters and turn in their cards face down. To speed up convergence to the competitive equilibrium, recruit a helper from among the students to write the negotiated price on the board for all to see. Have a timekeeper announce the time remaining at regular intervals. At the end of the round, collect all unused cards, shuffle and redistribute randomly for the next round.

### Discussion of results

In an introductory microeconomics course, the pit-market experiment can be conducted prior to teaching supply and demand and the competitive equilibrium, to motivate the relevance of these topics. I prefer to conduct it immediately following the lecture on these topics. Begin by showing students the results from their experiment in a transactions graph (software downloadable from the link below).

Also, show them the distributions of buyers' valuations and sellers' costs and ask them to explain why prices converged to the particular observed levels (27 to 28 in the example above). Surprisingly, in a principles course, you will rarely, if ever, hear the correct answer. Instead, students will claim that the observed prices ‘are the average of all of the cards,’ or ‘at these prices buyers and sellers earn the same’. Use asymmetric supply and demand curves (like those in the figure below upon which the transaction prices above are based) in order to reject these explanations and focus on the profit maximisation motive and the forces of supply and demand.

Review the textbook assumptions underlying the competitive-equilibrium model and discuss why some of these assumptions are unnecessary for convergence (e.g. full information and the inability to collude or form cartels) and others are imprecise (e.g. ‘large’ numbers of buyers and sellers). Market efficiency, alternative market institutions and the role of displaying transaction prices on the board (or information more generally) are additional topics for class discussion.

### Extensions

Expect prices and quantities to converge to the competitive equilibrium within three or four rounds. If you have additional time, you might want to shift either the demand or supply (this requires a careful change in playing cards used), then it is fun to ask the students to guess what you did (based upon the changes of price and quantity). Also you might try imposing a price floor above the competitive price or a price ceiling below it. More interestingly, announce an n-unit tax on the buyers imposed on each unit traded and listen to them groan. The following period replace the tax on the buyers with an (equivalent) n-unit tax on the sellers. Afterwards, you can display to students the outcomes from these two tax periods; namely, that the net prices paid and received and the quantity traded are equivalent in the two tax treatments and the incidence of the tax depends solely on the relative elasticities of supply and demand. See Ruffle (2005) for a further discussion of experimental tests of tax incidence equivalence and the analogous theorem for subsidies.