## Failure to Brainwash...

My last iClicker question from today's Econ 1: Principles of Economics lecture:

Suppose PDC—Production and Distribution Coordination—decided that we were going to offer four yoga classes at a price of $20/lesson for each student and$200/lesson for each teacher. As before, each class has a capacity of ten students. PDC finds that there are only 25 students and 4 teachers. What should PDC do?

A. Split up the students among the four teachers and announce that the teachers will only be paid $120/lesson. B. Split up the students among the four teachers and announce that the students will each have to pay$32/lesson

C. Pick one of the teachers by lot and send him or her home, and then go draft 5 passers-by and force them to take the class, charging each student $20/lesson and paying each teacher$200/lesson

D. Draft 15 passers-by and force them to take the class, charging each student $20/lesson and paying each teacher$200/lesson

E. Lower the price charged to $19/lesson and the price paid to$190/lesson, and see if any more students are willing to pay that price and if any of the teachers say they would rather go do something else.

The answer I am looking for, of course, is that PDC should mimic the market by choosing option (E). It should use the price system because that way it can balance capacity and attendance by drawing those 5 potential students whose values of yoga classes are between $19/lesson taken and$20/lesson taken into the activity and excluding the one instructor whose reservation price is $200/lesson taught from the activity, and so be sure that (a) everyone taking yoga values it at more than$19/lesson and (b) everyone teaching yoga has a disutility of less than $190/lesson. And so social surplus is maximized. (With distributional impacts to be cleaned up later on by other societal mechanisms.) By contrast, all of the alternatives--down to and including the Stalinoid draft-fifteen-innocent-passersby-at-gunpoint-and-force-them-to-unwillingly-do-the-downward-facing-dog--involve (i) teaching the wrong number of classes and/or (ii) having the classes taught and taken by the wrong people who really would rather be doing something else. Yet those alternatives attract 24% of responses, even after a full fifty-minute brainwashing session in Wheeler Auditorium. I am clearly going to have to slow down, and try to brainwash them once again. Next Monday I am going to have to hit them with the entire argument again, and add to it: Properties of competitive market equilibrium: • It is where the supply and demand curves cross • Nobody who wants to pay or work is rationed out of the market (poor people may be rationed out because they have low money-metric willingness to pay even though they have high desire) • It is stable • It produces the maximum dollar-value social surplus • Other arrangements have • Some of the wrong people teaching the classes • Some of the wrong people taking the classes • Too few classes being offered • Too many classes being offered Other allocations leave open side-deals on the table: • Some of them have some of the wrong people teaching the classes • Suppose Greg320--with his reservation price of$200/lesson taught--is assigned to teach one of the three classes.
• Suppose Greg305--with his reservation price of $50/lesson taught--is not. • Then: "Psst. Will you teach my class?” • There’s$150 of surplus for them to split
• Some of the wrong people taking the classes
• Suppose yogastudent#10 is not assigned to take a class
• Suppose yogastudent#30 is
• Then—“Psst. Will you take my place?”
• There is $4 of surplus for them to split • If too few classes are offered, there are side deals • Suppose only two classes are being offered • Then yogastudent#21 through yogastudent#30 meet Greg315 outside • They set up a class • There is$100 of surplus for them to split
• If too many classes are offered, there are side deals
• Suppose four classes are offered
• Yogastudent#31 through yogastudent#40 meet Greg320 for their class
• They look at each other
• They say: “Let’s just pretend we did this and go home”
• And they split \$20 of surplus
• Allocations that do not mimic the market allocation leave money on the table
• Allocations that do mimic the market do not leave any money on the table
• You may not like where the money goes, but it is not on the table.

David Romer: Ed Glaeser had some nice stuff about this--where he did random assignment in markets with excess demand and showed the Posner rectangles of welfare loss as well as the Harberger triangles. I think it had some very nice graphs...