Question 1 - Abracadabra Magic Wands (40 points)

All wizards need a magic wand. You are the owner of Abracadabra, a company that produces equipment for wizards. You have spent millions of dollars developing a new magic wand that is actually magical. You are the only one that can produce these magic wands because you received a worldwide patent.

Your internal economics team has estimated the following curves for your magic wands:

Q = 320 - 0.2P MC = 100 TC = 100Q

(10 points) If you can't price discriminate, what is the profit maximizing level of output and price?

(25 points) Assume that you know that you have six different segments of customers - expert,

advanced, intermediate, middling, beginner, and amateur wizards. However, you cannot differentiate between them. You have a wizard friend, Gandalf, who states that he CAN identify expert and amateur wizards (although sadly he can't differentiate between the other four segments). He's going to charge you $374 to test each person and reveal to you that the shopper is expert, amateur, or other. Also, the act of Gandalf's testing changes the buying behaviour of your customers (a variation of the Hawthorne Effect where individuals modify an aspect of their behavior in response to their awareness of being observed). The post-testing demand curves for the Amateur and Expert customers are:

Amateur: PA = 900 - 3QA Expert: PE = 1600 - 4QE

Should you hire Gandalf to classify buyers? Explain.