Classroom Companion: Business

16.4 
 Conclusions
One of the most important characteristics of digital businesses is that the marginal 
costs of the products are zero; that is, there is no cost associated with production, 
storing, and distributing the good. For companies selling digital goods, it is, there-
fore, no practical limits to how many products they have in store. This has created 
a new type of business that is not practical for products requiring physical space for 
16.4 · Conclusions

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manufacturing, storing, and delivery. This is the long tail of products that are low 
in demand but collectively create considerable revenues. Amazon has successfully 
applied this strategy, and it is claimed that about one-third of their revenues stems 
from the long tail consisting of books not available in ordinary bookstores. There 
are several examples of businesses in the digital economy exploiting the same 
strategy.
Statistically the long tail distribution is related to other statistical distributions 
such as discrete power-law distributions, the discrete zeta distribution, the Zipfian 
distribution, and general discrete heavy tail distributions. For example, the long tail 
distribution of Amazon can be modeled using the Zipfian distribution. Using the 
distribution fitting the empirical data best, the expected sales from the long tail can 
be estimated for a variety of digital businesses so that the concept can also be used 
in strategic business planning.
The distribution of the size of routers on the Internet and connectivity of web-
pages of the World Wide Web have also long tails. This has important consequences 
both for the robustness and the vulnerabilities of these structures.
 
?
Questions
1. How is Airbnb exploiting the long tail of demand and the long tail of supply 
in its business operations?
2. What are the characteristics of the long tail generated by Uber in the personal 
transport industry?
3. What is the probability that that the Internet contains a router with 1000 con-
nections if the size distribution of Internet routers follows a general power law 
with α = 2? To simplify calculations, you can use the fact that Riemann’s zeta 
function with argument 2 is 


2
6
2
 

. If there are ten million routers on the 
Internet, how many are expected to have 1000 connections? How many routers 
have exactly one connection?