Question

Suppose Warner Music and Universal Music 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. [LO 15.7\(]\) a. Fill in the revenue payoffs for each scenario in Figure \(15 \mathrm{P}-6 .\) b. If this game is played once, how many artists will each producer sign, and what will be the price of a song? c. If this game is played every year, how many artists will each producer sign, and what will be the price of a song?

Short answer

Each producer will sign 20 artists, both prices settle at $0.30 per song if played once, and may remain at 10 artists with $1.25 per song if repeated annually.

Step-by-step solution

Identify Revenue Parameters for 10 Artists each

When both Warner and Universal sign 10 artists, each artist sells 2 million songs at $1.25 per song. Therefore, the revenue per artist is \(2,000,000 \times 1.25 = 2,500,000\). With 10 artists, each label earns \(10 \times 2,500,000 = 25,000,000\).

Calculate Revenue when One Label Signs 20 Artists

If one label signs 20 artists and the other stays at 10, the price drops to $0.75 per song, and each artist sells 3 million songs. The label signing 20 artists earns \(20 \times 3,000,000 \times 0.75 = 45,000,000\). The label with 10 artists earns \(10 \times 3,000,000 \times 0.75 = 22,500,000\).

Calculate Revenue when Both Labels Sign 20 Artists

If both labels sign 20 artists, the price drops to $0.30 per song. Each artist sells 4 million songs, leading to a revenue of \(4,000,000 \times 0.30 = 1,200,000\) per artist. Therefore, each label earns \(20 \times 1,200,000 = 24,000,000\).

Fill in Revenue Payoffs in Figure 15P-6

The payoff matrix based on previous steps: - If Warner and Universal both sign 10 artists: (25,000,000; 25,000,000). - If Warner signs 20 and Universal 10: (45,000,000; 22,500,000). - If Warner signs 10 and Universal 20: (22,500,000; 45,000,000). - If both sign 20 artists: (24,000,000; 24,000,000).

Determine Strategy if Game Played Once

If played once, both labels will aim to maximize their payoff. Increasing to 20 artists while the other stays at 10 gives a better individual reward. However, both will realize the risk of the rival doing the same, leading to a lower payoff when both increase. Thus, a dominant strategy equilibrium occurs at both switching to 20 artists.

Determine Long-term Strategy if Repeated Annually

In a repeated game, cooperation may occur. If both maintain 10 artists, they both earn the higher payoff of 25,000,000 consistently, against the temptation of a short-term gain by unilaterally increasing artists, which may trigger retaliation in subsequent years.

Key concepts

Pricing Strategy

In a duopoly, the pricing strategy plays a critical role in determining how firms compete against each other. For Warner Music and Universal Music, the strategy involves deciding the number of artists to sign and how this decision impacts the price and sales of songs. Each label has the option to sign either 10 or 20 new artists.

When each label signs only 10 artists, the market is less saturated, allowing each song to sell at a higher price (\\(1.25). This results in higher revenue per artist due to the limited supply, aligning with the basic economic principle of supply and demand.

If one label decides to increase the number of signed artists to 20 while the other does not, the increased supply of songs decreases the price to \\)0.75 per song, affecting revenue. The benefit for the label signing more artists is a possible increase in market share, but at the risk of reduced prices if both labels choose the same strategy.

• Limited Artists (10 each): Higher price, stable revenue.
• Increased Artists (if one label, 20 artists): Lower price, potential market share gain.
• Both labels sign more artists: Even lower prices, diminished returns.

Understanding the dynamics of pricing in a duopoly is crucial for strategic decision-making, as it directly influences profitability and competitiveness.

Game Theory

Game theory provides a framework for understanding strategic interactions between players, in this case, Warner Music and Universal Music. By considering the potential decisions of both firms, game theory allows us to predict likely outcomes of their competitive behaviors.

In the scenario outlined, both labels face choices that resemble the classic 'Prisoner's Dilemma', a situation in strategic games where individual players acting in self-interest lead to a worse outcome than if they had cooperated. Here, if both Warner and Universal choose to sign 20 artists instead of 10, they end up with lower revenues than if they had both maintained 10 artists.

The dominant strategy is for each label to sign 20 artists, as this decision provides a chance to gain the highest possible revenue if the other firm sticks with 10 artists. However, if both adopt this strategy, they face reduced profits. Game theory highlights:

• Dominant strategy: Each signing 20 artists, due to fear of missing out on higher revenue.
• Pareto-efficient outcome: Both signing 10 artists, maximizing collective revenue.

This teaching in game theory helps firms understand the balance of competitive and cooperative strategies.

Revenue Calculation

Revenue calculation is key for firms in determining the profitability of their strategic decisions. It involves multiplying the price per unit by the quantity sold. In this duopoly scenario, understanding revenue changes based on artist contracts is pivotal.

When both Warner and Universal sign 10 artists each, revenue calculation is straightforward: each artist sells 2 million songs at \\(1.25, resulting in \(2,000,000 \times 1.25 = \\)2,500,000\) in revenue per artist. With 10 artists, this amounts to \\(25,000,000 per label.

If one label increases to 20 artists, the price drops to \\)0.75, with each artist selling 3 million songs. Revenue here changes significantly: \(20 \times 3,000,000 \times 0.75 = \\(45,000,000\). However, the unchanged label experiences a revenue decrease to \\)22,500,000 due to the lower price and increased competition.

For both labels signing 20 artists, price further drops to \\(0.30, each artist sells 4 million songs, which results in \(20 \times 1,200,000 = \\)24,000,000\) per label.

Key Points:

• Maintaining 10 artists optimizes revenue due to higher prices.
• Increasing to 20 invites higher initial revenue but risks triggering competitor matching, reducing overall profitability.
• Both moving to 20 leads to diminishing returns from oversupply and price wars.

These revenue calculations show the explicit impact of strategic decisions in a competitive market.