Classroom Companion: Business

 
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Questions
1. Assume that Network A in 
.
Fig. 
9.1
grows to Network B and finally to 
Network C. Assume that each link has a value equal to 1. Applying the defini-
tion of network effects, how does the value per user increase as this network 
evolves?
2. Snapchat is a social media service available for smartphones.
(a) Identify network effects in Snapchat (positive, negative, direct, indirect, 
cross-side, and same-side network effects).
(b) How are network effects in Snapchat different from network effects in 
Facebook?
3. Does Sarnoff’s law give an accurate valuation of Instagram?
4. Draw two graphs—one linear and one logarithmic—that show the network 
effect as a function of the number of users using (1) Sarnoff’s law, (2) Metcalfe’s 
law, and (3) Odlyzko-Tilly’s law. How would you interpret the graphs? (The net-
work effect is defined in 
7
Sect. 
9.6.1
.)
 
Chapter 9 · Network Effects

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145
9
5. Assume two competing social media companies, A and B, with N
A
= 10 million 
users and N
B
= 20 million users. Assume that these two companies plan to merge, 
making a new company, C, with N
C
= N
A
+ N
B
= 30 million users. Assume fur-
ther that the valuation of the companies depends on the number of users only. 
What is the total gain (in percentage) from such a merger when estimating the 
company’s value using:
(a) Sarnoff’s law?
(b) Metcalfe’s law?
(c) Odlyzko-Tilly’s law?
6. Consider a social media network that you are a part of (e.g., Facebook, Twitter, 
or Snapchat).
(a) How many users are there in total in the chosen social media network?
(b) How many users do you link to in the chosen social media network?
(c) How will you rank and quantify the importance of your links?
(d) Does Metcalfe’s law or Odlyzko-Tilly’s law best describe the value that the 
social media network offers to you?
7. Facebook has, by 2018, approximately 2.2 billion monthly active users.
(a) Based on this number, calculate the total value of Facebook. You can use 
the formula V(n) = 5.7 × 10
−9
× n
2.
(b) What does this value represent?
(c) How many users does Facebook need to have for a total value of 1?
8. Which of the three laws (Sarnoff, Metcalfe, and Reed) are valid for the valua-
tion of the following digital services: Google Search, Gmail, World of Warcraft, 
Wikipedia, Netflix, Twitter, YouTube, eBay, and Facebook?