Shape of the demand curve

The law of demand; reservation prices; shape of the demand curve

One-half hour activity early in an introductory economics course. Activity should be used before the instructor has shown the supply/demand model.

Prior to class the instructor will obtain one item for auction during the class session. Possible items include: school logo t-shirt; school logo mug (or any other item of likely use for most students in the course and not of such high value that the price will go above a few dollars).

Photocopy, upload for projection or post on the board the following:

• Before conducting the auction, make certain that all students know this is an actual auction for which they will need to produce payment at this time. Also, make certain that no student can curry favor with you by bidding for the item.
• Show the item to the class, indicating that you have only one and that one student in the class will receive it. The question is: who will receive it? (Note alternative activity below in which students suggest allocation mechanisms.)
• Say that today you will use an auction to determine who receives the item. At this point, it is a good idea to discuss the advantages and disadvantages of the auction (it will reveal students' desire for the item at relatively low cost in terms of time and effort; on the other hand, the auction will disadvantage those who do not have financial resources with them at the moment.)
• Students write their bid on a piece of paper along with their name. Collect the papers and re-distribute them at random back to the class.
• Collect data on the prices and post them for students to see the bids, organized in convenient intervals (say $0 -1, $1- 2 etc. up to the highest bid.) At this point, leave data in categories. That is, do not cumulate the numbers, a task that will done later.
• Identify the winner, give her or him the item (better to collect payment after class.)
• Discuss with students the meaning of the bids. Note that 1 cent is a rational bid, indicating a low reservation price and suggest reasons for it. Note that these prices indicate the students' willingness and ability to pay. The data would be better displayed as a line graph and indeed economists do precisely this: explain that quantity demanded will be on the x-axis and price on the y-axis.
• What shape will the graph have? Based on the choices in accompanying file, ask students to choose? (Note choices are upward sloping straight line; downward sloping straight line; convex to origin upward curve; convex to origin downward curve; u-shape up; u-shape down; upward curve with decreasing slope; downward curve with increasingly negative slope.)
• Have students vote individually (use clickers or simply ask students to show with their fingers). If there is significant disagreement, ask students to consult with a a partner, then vote again.
• Then, either graph the results yourself, or ask students to draw a graph, perhaps working in pairs. In either case, it will be necessary to cumulate the data so that they show total demand at each price. Use this as an opportunity to discuss the difference between reservation price and market price: as lower prices are considered, those who would have been willing to pay more will, in fact, pay less, a difference (surplus) that won't be revealed except in this type of auction.
• When the graph is drawn (always in my experience a near hyperbola convex to the origin) ask students which graph is correct. As a follow-up ask students why the graph has this shape.

• Use a Vickrey-style auction below in which the winning bid is the highest, but the price paid is the next highest price. Explain to students the advantages of this type of auction and its use in the real world (see references below).
• (Alternative activity) Before conducting the auction, ask the class to brainstorm methods for distributing the item. Classify these methods using the matrix available below (market mechanisms; command mechanisms; cooperative mechanisms.) Note that all three mechanisms are used: many examples of markets; military uses command; families and other institutions use cooperative mechanisms.) As an whole class discussion, fill in the advantages and disadvantages of each mechanism including: efficiency, cost, and equity.

Matrix for distribution alternatives (Microsoft Word 31kB Jul27 12)

Present students with a set of auction bid reservation prices. Students should be able to draw the resulting demand curve, remembering to cumulate the quantities from highest to lowest bid.

On this auction see: Michael Salemi 'Clickenomics: Using a classroom response system to increase student engagement in a large enrollment principles of economics course', The Journal of Economic Education, 40 (4), 385-404

On the Vickrey auction see Wikipedia