# Intro to Econ: Sixth Lecture – A supply and demand classroom experiment

My students have played a short supply and demand experiment in class this year. The experimental design goes back to the work of Chamberlin (1948, JPE) and Vernon Smith (1962, JPE). I have used the beautiful online design developed by Heinrich Nax, Diego Gabriel Nunez Duran, and Bary Pradelski at the ETH Zürich. I ran three sessions and had 60 students participating in each. I am afraid I did not pay any money, so if you are interested in the experiment you may want to go back to the original Vernon Smith (1962) experiments and the literature that followed, in which subjects are almost always given (some) monetary incentives. The results I got with my students were not that different, however, to what researchers found with monetarily incentivized students.

So how does it work? The program randomly declares 30 of the 60 students “buyers” and the other 30 “sellers” of some indivisible good. So the idea is that the 30 sellers each own some identical object (say all the same book, in the same condition) and the 30 buyers would possible be interested in buying this book. Each of the 30 sellers is randomly given a “value” of how much the object is worth to them. They can ever only sell their object at a price higher than their value. I, the experimenter, can choose the different values the sellers get. Each of the 30 buyers is also randomly given a “value” of how much such an object would be worth to them. Again, I, the epxerimenter, choose the range of values buyers could get. As all objects (that the sellers own) are identical it does not matter who the buyer buys the object from. Buyers can only buy an object at a price lower than their value.

Once the sellers and buyers are chosen and their values distributed, they can all make offers and can accept or reject offers made by others. While none of the buyers and sellers are informed about the distribution of values that others have, they do see some information on their screens. They see what offers are being made and they see the latest deals that were struck.

For the first two sessions I chose a value distribution that gives rise to a linear demand and a linear supply function. How does this work? I chose buyer values 10,11,…,39 and seller values 20,21,…,49. How do we get the demand and supply function from this? Give me a price, say 37. Then what is the demand at price 37? It is the number of buyers (as one person can only buy one object) who have a value above and possibly including 37. How many are there? There are three, those buyers with value 37, 38 and 39. What about the supply at this price? It is the number of sellers with a value of 37 or below. These are sellers with values from 20 to 37. So these are 18 people. At a price of 37 the supply far outweighs the demand. The software that Heinrich Nax and his colleagues have provided delivers the following picture of the demand and supply functions.

Note that in the experiment people can trade at any price. Here is the figure with all the deals that were made (over time).

Note that while the prices of deals vary a fair amount they fluctuate around a price of 30. What is so special about the price of 30? It is the market price. It is the price at which supply equals demand. There is one more thing you may want to note. How many deals have been made? The first session had two rounds and the supply demand diagram suggests that there should be 10 deals in each round. How many deals did we get? We got 21 in two rounds, one more than we “should have” according to the theory.

Here is the figure of deals over time in the second session with the same supply and demand functions.

Students played two rounds in the second session. Note again how the price fluctuates around a price of 30. In fact it looks like that the price fluctuates a bit less than before. This could be due to the growing experience students had with this problem. This time we got only 17 deals. This is now three short of what we “should have” according to the theory.

For the third session (with again two rounds) I changed the supply function. I left the demand function the same. I told the students that I am changing things, but I did not tell them how. Here is the supply and demand figure:

Note that the market price in this new setting, that is the price where demand and supply intersect, is now 35. Here is the figure with deals in this new setting:

Interestingly the first deal had a price of even less than 30, but then quickly after that the price fluctuates (not even all that much – except for two deals) around 35. How many deals “should” there be and how many were there? Well, we saw 30 deals this time, when the theory says that we “should have”, in fact, 30 deals.

A caveat: This is probably working almost too well. In many ways this is a pretty simple market, just one good and all potential traders are coming together in one central (here online) market. Financial markets, in fact, work very much like this and approximately so do many markets for basic agricultural products such as coffee beans and wheat, but not all markets do. Some markets are much less centrally organized – the market for holiday apartments for instance. Also often traders have to be active in several markets at the same time and if the price of one good is too high they would rather buy another good at another market (because the two goods are close substitutes). The theoretical literature in fact shows that, in principle, there could well be a collection of markets such that a dynamic trading process will not lead to the “market equilibrium”. See for instance the survey article by Franklin M. Fisher “The stability of general equilibrium—what do we know and why is it important?”, Chapter 5 of the book ”General Equilibrium Analysis”, edited by Pascal Bridel, Routledge, 2013.