ECON2080/ECON8180 Economic Analysis of the Digital Economy

(ANU, S1 2021)

Week 4 – Tutorial Questions (ASSESSABLE) – Assessment A1.1

Your highest grade on A1.1 and A1.2 will count for 10% of the final grade of the course

Submit via Wattle by 5pm Friday 19 th March.

This is not a group assessment: you must work on this on your own.

Word limit: ECON2080 – 550 words; ECON8180 – 700 words.

Question 1: Power law distribution, or not? (3 marks)

Imagine you have been hired at a company that runs a web forum for technology enthusiasts. In this web forum, registered users are able to ask questions (relating to technology) and answer questions asked by other users. The forum has a voting system whereby users can give "upvotes" to helpful or useful answers written by other users.

You have been given a dataset to analyse (see spreadsheet “A1_1_Q1_data.xlsx”) containing data on two variables: (1) the total number of upvotes the user has received (an aggregation of the upvotes for each answer the user has written on the forum) in the last year; (2) the total number of answers the user has written on the forum in the last year.

However, unfortunately in the dataset the variables are labelled only “Variable 1” and “Variable 2”, and so you don't know which variable is number of upvotes received by the user and which is number of answers written by the user!

Using the plotting technique shown in Section 7.4 of Web Social Science (on Wattle), provide an assessment whether the variable is distributed according to a power law or not. As part of your answer you should insert an image (e.g. png or jpeg) of relevant plots, and explain (either in words or using mathematical notation, but with explanation) how you made the plot. You should also give an intuitive explanation of what a power law distribution is. Note that this graphing or (“eyeballing”) approach is not a formal statistical test of a power law distribution.

Finally, is Variable 1 the total number of upvotes received (and Variable 2 is total number of answers written) or the other way around? Explain your answer.

Question 2: Measuring the importance of the Long Tail (3 marks)

Assume you are working as an analyst on a project which aims to assess how the Internet has impacted on the book industries in Australia and New Zealand. Your data shows (note: these data are fictional, obviously...):

• New Zealand: In 1998 there were 500 book titles sold, and the bottom 80% of titles accounted for 18% of sales. In 2018 there were 500 titles sold, and the bottom 80% of titles accounted for 22% of sales.

• Australia: In 1998 there were 500 book titles sold, and the bottom 80% of titles accounted for 23% of sales. In 2015 there were 800 titles sold, and the bottom 80% of titles accounted for 17% of sales.

(i) Briefly explain Anderson’s (2004, 2006) Long Tail Hypothesis or Proposition regarding the potential impact of the Internet on sales of goods such as books. What is the relevance of long tail statistical distributions to the Long Tail Hypothesis?

(ii) Provide a brief definition of the Relative Long Tail (RLT) measure. Explain what the RLT measure leads you to conclude about the changing importance of the long tail in these two markets.

(iii) Provide a brief definition of the Absolute Long Tail (ALT) measure. Assuming that the cutoff for computing the ALT is 500 titles sold, what does the ALT tell us about the changing importance of the long tail in these two markets?

Question 3: Estimating network effects (4 marks)

Imagine you are working as an consultant providing economic advice to an online dating company. For the purposes of this question, assume the online dating site is for heterosexuals only. The dating site makes its money from website users (there is no online advertising), who purchase different levels or tiers of access plus access to certain features (e.g. ability to send messages to other users). The online dating company has provided you with a time series dataset with the following variables (recorded weekly):

• Women (Men) – number of women (men) registered on the site

• RevPerWoman (RevPerMan) – average revenue per woman (man)

You conduct correlation analysis and find the following correlation coefficients (note: all correlations are statistically significant at p < 0.01):

• Women and RevPerWoman: -0.004

• Men and RevPerMan: -0.008

• Women and RevPerMan: 0.006

• Men and RevPerWoman: 0.002

(i) Describe the online dating site using the terminology of platform-intermediated markets. What insights do the correlation coefficients provide on nature of the network effects?

(ii) On the basis of the estimated network effects, can you provide any advice to the online dating site (in terms of revenue maximisation) in relation to the proportion of males and females it should aim to attract to the site?

(iii) [ECON8180 only] Assume that you are attempting to estimate network effects using time series data on number of users and number of titles on a videogame console. Given the price of consoles has decreased over time (as computer components become cheaper), how might this affect your ability to accurately estimate network effects?