Question

Suppose Warner Music and UMG are in a duopoly and currently limit themselves to 10 new artists per year. One artist sells 2 million songs at $1.25 per song. However, each label is capable of signing 20 artists per year. If one label increases the number of artists to 20 and the other stays the same, the price per song drops to $0.75, and each artist sells 3 million songs. If both labels increase the number of artists to 20, the price per song drops to $0.30. and each artist sells 4 million songs. Fill in the revenue payoffs for each scenario in the table above. If this game is played once, each producer will sign artists, and the price of a song will be $ If this game is played every year, each producer will sign artists, and the price of a song will be $

Answer 1

The revenue payoffs for each scenario in the Warner Music and UMG duopoly are $2.5 million, $4.5 million, and $4.8 million per label.

Step-by-step explanation:

In a duopoly between Warner Music and UMG, the number of new artists they sign and the price of songs affects their revenue payoffs.

If both labels limit themselves to 10 artists, one artist sells 2 million songs at $1.25 per song, resulting in a revenue payoff of $2.5 million.

If one label increases the number of artists to 20 while the other stays the same, the price per song drops to $0.75, and each artist sells 3 million songs, resulting in a revenue payoff of $4.5 million per label.

If both labels increase the number of artists to 20, the price per song drops to $0.30, and each artist sells 4 million songs, resulting in a revenue payoff of $4.8 million per label.

Answer 2

In this business scenario, duopoly dynamics and game theory predict that Warner Music and UMG will base their decisions on how many artists to sign on strategic considerations, with different outcomes depending on whether the game is played once or repeatedly.

Step-by-step explanation:

The scenario described represents a duopoly situation involving Warner Music and UMG, where they need to decide how many new artists to sign each year. The revenue payoff for each scenario depends on their individual and collective decisions regarding the number of artists they sign and the subsequent market price per song that results from those decisions.

Scenario 1: If one label signs 20 artists and the other sticks with 10, the first label's earnings would be 20 artists × 3 million songs/artist × $0.75/song = $45 million, while the second label would make 10 artists × 2 million songs/artist × $1.25/song = $25 million.

Scenario 2: If both labels sign 20 artists, they would both earn 20 artists × 4 million songs/artist × $0.30/song = $24 million each.

In a single play scenario, both firms might opt for a higher number of artists to avoid being undercut. If this game is played once, each producer will likely sign 20 artists, and the price of a song will be $0.75. However, if played annually, they might strategize differently to maintain prices and consumer surplus, potentially settling for a higher price and fewer artists to avoid a race to the bottom. This reflects strategic behavior similar to game theory principles.