Consider a market for a popular software DoorsTM . There are 100 support-oriented (type-O) consumers, and 200 support-independent (typeI) consumers, withutility functions given by U O def =  3q − p buys the software q pirates (steals) the software 0 does not use this software, and UI def =  q − p buys the software q pirates (steals) the software 0 does not use this software, where q denotes the number of users of this software (which includes the number of buyers and the number of pirates, if piracy takes place). Suppose that the software is costless to produce and costless to protect. Also, assume that DoorsTM provides support only to those consumers who buy the software.

(a) Suppose that DoorsTM is not protected, so piracy is an option for every consumer. Calculate the software seller’s profit-maximizing price. Prove your answer.

(b) Suppose that DoorsTM is protected, so piracy is impossible. Calculate the software seller’s profit-maximizing price. Prove your answer.

(c) Suppose that the producer of DoorsTM has the option to protect or not to protect the software. Which option yields a higher profit. Prove your answer.