It turns out there is a rather shocking mathematical error in the 2011 AP Microeconomics exam. You can view the exam at the College Board site here. There is a nice video of the solution here, but the teacher is totally oblivious to the error. See if you can find it. I will describe it below the fold.
I assigned this problem to my students, and one of my better students, who usually breezes through problems, took the whole period and still seemed troubled by his answer. When he showed me that the monopolist’s profits increased when the price ceiling was imposed, I knew that something was wrong with the problem. You can see it in the table below, which is derived from some of the data shown in the diagram for the problem. The last column is not shown on the diagram, but I calculated it by multiplying average total cost times quantity.
|Quantity||Price||Marginal Revenue||Marginal Cost||Average Cost||Total Cost|
*I arrived at 6 by using total revenue = 192 for 8 units and 198 for 9 units. This is not the issue.
The marginal cost curve shows a marginal cost of the 9th unit as 16, when the total cost of producing 9 units is the same as that of producing 8 units, which means that the marginal cost of the 9th unit is zero. This means that the profit-maximizing quantity is not 8 units (at a price of $24), where you would expect it to be if you trusted the marginal cost curve.
If instead you had the silly idea that the profit-maximizing quantity was where you maximized profits, you would have noticed that at 9 units (at a price of $22) you get a profit of $6 per unit, for $54 in profit, compared to $6 per unit at 8 units, or $48 in profit. You would have picked 9 as your answer, which is correct, but it clearly is not the preferred answer.
The rule of setting marginal revenue equal to marginal cost works if you are given correct information. In this case, however, there is an arithmetic inconsistency between marginal and average cost as shown in the diagram.
I tried doing a Google search for “error in 2011 AP microeconomics exam” and I did not find any results, so my student may be the first person to spot it. On the other hand, the scoring guidelines say that a price of $22 is “also acceptable” as the answer for the profit-maximizing price, and that may be their discreet way of deciding that you should not be marked wrong for giving the correct answer.