Question

The accompanying table shows six consumers' willingness to pay (his or her individual marginal benefit) for one MP3 file copy of a Jay-Z album. The marginal cost of making the file accessible to one additional consumer is constant, at zero. \begin{tabular}{l|c} Consumer & Individual marginal benefit \\ Adriana & \(\$ 2\) \\ Bhagesh & 15 \\ Chizuko & 1 \\ Denzel & 10 \\ Emma & 5 \\ Frank & 4 \end{tabular} a. What would be the efficient price to charge for a download of the file? b. All six consumers are able to download the file for free from a file- sharing service, Pantster. Which consumers will download the file? What will be the total consumer surplus to those consumers? c. Pantster is shut down for copyright law infringement. In order to download the file, consumers now have to pay \(\$ 4.99\) at a commercial music site. Which consumers will download the file? What will be the total consumer surplus to those consumers? How much producer surplus accrues to the commercial music site? What is the total surplus? What is the deadweight loss from the new pricing policy?

Short answer

Answer: The deadweight loss from the new pricing policy is $2.97.

Step-by-step solution

Determine the efficient price for the MP3 file

As the marginal cost of making the file accessible to one additional consumer is zero, the efficient price would be to charge $0 for the file.

Analyze the case where the MP3 file is available for free

When Pantster offers the file for free, all six consumers will download the file because their individuals' marginal benefit is greater than the download price. The total consumer surplus can be calculated by summing their individual marginal benefits. Total consumer surplus = \(2 + 15 + 1 + 10 + 5 + 4 = \$37\) As the file is available for free, the producer surplus is $0.

Analyze the case where commercial music site charges \(\$ 4.99\) per download

When the file is available for \(\$ 4.99\), only consumers with a willingness to pay equal to or greater than \(\$ 4.99\) will buy the file. These consumers are Bhagesh, Denzel, Emma, and Frank. Total consumer surplus for these consumers can be calculated as follows: Total consumer surplus = \((15 - 4.99) + (10 - 4.99) + (5 - 4.99) + (4 - 4.99) = \$10.04 + \$5.01 + \$0.01 - \$0.99 = \$14.07\) The producer surplus accrues to the commercial music site, and it is the total revenue generated from the file downloads. Producer surplus = \(4.99 \times 4 = \$19.96\) Total surplus can be calculated as the sum of consumer and producer surpluses. Total surplus = \(14.07 + 19.96 = \$34.03\) Deadweight loss can be calculated as the difference between the total surplus from the free file-sharing scenario and the commercial music site scenario. Deadweight loss = \(37 - 34.03 = \$2.97\) So, in this case, the deadweight loss from the new pricing policy is \(\$ 2.97\).

Key concepts

Marginal Cost

Marginal cost represents the cost of producing one additional unit of a good or service. In the case of digital goods like MP3 files, this cost can often be zero. Since the file is already created, sharing it with more consumers typically incurs no additional cost.
In economic terms, a zero marginal cost means that distributing the MP3 file to one more listener doesn't require more resources. Thus, the efficient price, which equals marginal cost, would be $0.
Understanding this helps to explain why digital goods can be shared widely at very low or zero cost. It also underscores the importance of pricing models in the digital economy as the marginal cost doesn't reflect the value perceived by consumers.

Efficient Price

The efficient price of a good is closely tied to its marginal cost. This is the price point where the cost of making one extra unit of the good equals the value placed on it by consumers.
For the MP3 file example, since the marginal cost of allowing one more person to download the album is zero, the efficient price should also be zero. Charging any higher creates a barrier where some consumers who value the file more than its marginal cost do not make a purchase.
This principle ensures that resources are optimally allocated. It helps avoid scenarios where a higher price excludes consumers who would otherwise benefit, possibly leading to inefficiencies and losses in societal welfare.

Deadweight Loss

Deadweight loss occurs when market inefficiencies lead to a loss of economic welfare that no one receives. It often happens when prices are set above or below the efficient price, preventing some trades that would otherwise increase total surplus.
In our scenario, charging $4.99 for the MP3 file instead of the efficient $0 means fewer consumers purchase it. This results in a deadweight loss of $2.97, as some consumer surplus that existed when the file was free is lost.
To visualize this, think of the lost trades when price is above marginal cost. Consumers like Chizuko, with a marginal benefit less than or equal to $4.99, are pushed out of the market, even though providing them the file costs nothing extra. This disconnect is what creates deadweight loss, showing how setting prices can significantly impact market efficiency.