Question

Christine and Paul are deciding how to split their time between writing music and lyrics for their new album. Their PPFs for 72 h of work are shown. Christine and Paul have to write music for 8 songs and lyrics for 12 songs (4 songs already have music). When they are done, they can go to a private island and relax from all their hard work. It is possible that they will use more than 72 h.

Once they start writing lyrics and music, assuming their hired help packs for them and their plane is waiting outside their door, in how many hours can they board the plane to their relaxing island getaway?

Answer 1

Each of them is going to work for 96 hours or 4 days.

• Paul will write the music for 8 songs.
• Christine will write the lyrics for 12 songs.

Step-by-step explanation:

PPFs (72 hours) Music (M) Lyrics (L)

Christine 8 9

Paul 6 4

Christine can write the music the one song in 9 hours and the lyrics in 8 hours.

Paul can write the music the one song in 12 hours and the lyrics in 18 hours.

Paul's opportunity cost of music per lyrics = 12/18 = 2/3, and the opportunity cost of lyrics per music = 6/4 = 3/2

Christine's opportunity cost of lyrics per music = 8/9, and the opportunity cost of music per lyrics = 9/8

Paul should specialize in writing music because his opportunity cost is lower, it will take him 12 x 8 = 96 hours to write down the music for 8 songs.

Christine should be in charge of writing lyrics (lower opportunity cost), it will take her 8 x 12 = 96 hours.

Each of them is going to work for 96 hours or 4 days.

• Paul will write the music for 8 songs.
• Christine will write the lyrics for 12 songs.