Problem 12 In 2018 pop star Drake was downl... [FREE SOLUTION]

Chapter 9: Problem 12

In 2018 pop star Drake was downloaded twice as often as Cardi B. She, in tum, was downloaded twice as often as Bruno Mars. Yet, downloads for these artists all sold for the same price in Apple's iTunes store. Does this suggest that Apple is failing to maximize profits? (Hint: Make the reasonable assumption that the marginal cost of supplying a download is a constant $\$ 0.25 .$ Then try to construct a graphical example in which very different demand curves produce the same price.)

Short Answer

Expert verified

No, it suggests Apple is not maximizing profits by not differentiating prices according to demand.

Step by step solution

Define the Variables

Let $ D $ represent the number of downloads for Drake, $ C $ for Cardi B, and $ B $ for Bruno Mars. According to the problem statement, Drake's downloads $ D = 2C $ and Cardi B's downloads $ C = 2B $. Therefore, we can conclude that $ D = 2(2B) = 4B $.

Calculate Total Revenue for Each Artist

Assuming the price per download is $ p $, the revenue for each artist is as follows: Drake鈥檚 revenue is $ 4Bp $, Cardi B鈥檚 revenue is $ 2Bp $, and Bruno Mars鈥� revenue is $ Bp $. The total revenue for all downloads is $ 4Bp + 2Bp + Bp = 7Bp $.

Calculate Total Cost for Each Artist

Since the marginal cost is $ \$0.25 $ per download, the total cost for Drake is $ 4B \times 0.25 $, for Cardi B is $ 2B \times 0.25 $, and for Bruno Mars is $ B \times 0.25 $. The total costs for all artists is $ (4B + 2B + B)\times 0.25 = 7B \times 0.25 = 1.75B $.

Determine Total Profit

The profit for each artist is their respective revenue minus their cost. Therefore, the total profit is $ 7Bp - 1.75B $. This simplifies the total profit across all artists to $ B(7p - 1.75) $.

Interpretation of Results

For Apple to maximize profits, the price $ p $ should be set such that $ 7p - 1.75 > 0 $, meaning $ p > 0.25 $. Since the demand for Drake is the highest, and is set at the same price as the others, Apple is likely not optimizing profits from differentiating prices based on demand differences.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Demand Curves

A demand curve is a graphical representation showing the relationship between the price of a good and the quantity demanded by consumers. In this scenario, each artist鈥擠rake, Cardi B, and Bruno Mars鈥攃an be thought of as having their own demand curve for their music downloads.

Each curve reflects the quantity of music downloads people are willing to purchase at various price points. For instance, Drake's downloads are four times that of Bruno Mars and double that of Cardi B, indicating a steep demand curve鈥攁 small price change might cause a substantial difference in the number of downloads due to his popularity.

Conversely, a less popular artist may have a flatter demand curve, with larger changes in price having less effect on the quantity downloaded. Understanding these curves helps businesses like Apple decide on optimal pricing strategies based on individual artist demand rather than a one-size-fits-all approach.

Marginal Cost

Marginal cost is the additional expense incurred to produce one more unit of a product鈥攊n this case, one extra music download. In the example from the exercise, the marginal cost of a single music download is constant at $0.25.

Even though this cost remains the same regardless of which artist's music is being downloaded, it's an essential component of profit calculations. Businesses need to cover these marginal costs with the price they charge customers to be profitable.

A constant marginal cost implies that it doesn鈥檛 get more expensive or cheaper per unit produced after reaching certain production levels. As a result, Apple can effectively predict the expenses they'll incur to supply music downloads across the board.

Revenue Calculation

Revenue calculation is a straightforward process where you multiply the price charged per unit by the total number of units sold. In the case of the music downloads for Drake, Cardi B, and Bruno Mars:

Drake's revenue is calculated as the number of downloads multiplied by the price (i.e., $4Bp$).
Cardi B's revenue is based on her number of downloads multiplied by the price (i.e., $2Bp$).
Bruno Mars' revenue follows the same pattern (i.e., $Bp$).

Total revenue turns out to be the sum of all their revenues, which is $7Bp$. This measurement gives Apple insight into the financial benefits of their pricing and demand conditions.

Market Pricing Strategy

Market pricing strategy involves setting prices based on market demand, competition, and cost structures to maximize profits. This concept is crucial for companies like Apple when determining how to price music downloads for different artists.

Currently, all artists' music is priced the same, regardless of demand differences. This suggests Apple may not be leveraging different demand curves to optimize profits fully. By analyzing individual demand curves, such as charging more for highly demanded downloads like Drake's, businesses can better align their pricing strategies with consumer demand and maximize profits.

Adapting prices to reflect demand differences, while considering constant marginal costs, ensures a balance between customer satisfaction and revenue generation.

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