3. Red, Brooks, and Heywood enjoy the occasional song played over the public address (P.A.) system at their prison. Andy is happy to sneak into the warden's office to play these songs, but for his troubles (and risk of solitary confinement), he requires a flat fee of 21 cigarettes per song (cigarettes being the currency in prison, you see). When answering honestly, the three prisoners give these demand functions: Red: Q = 12 - 2P Brooks: Q = 18 - P Heywood: Q = 8 - P/3 where Q represents the number of songs played over the P.A., and P represents the number of cigarettes paid for the privilege. a. In what ways can songs played over the P.A. be considered a pure public good at this prison? In what ways might songs played over the P.A. not be considered a pure public good (hint: it's a prison)? b. Show each of these three demand curves graphically, and find the complete market demand curve for this public good. C. How many songs will Andy play in equilibrium if each of the three prisoners contributes what they would be willing to pay? (Assume Andy is not acting as a monopoly.)