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cluster coefficient

You can see the notes that are attached. Please solve the following problems based on the notes.

1. Assume that the disutility of travel for consumers arrayed uniformly along a "Hotelling" line is not t as discussed in class, but t2, (i.e. the utility of a consumer for the product is:
Utility(Product i) = 3 - (ideal point - actual location product i)^2

There are two firms, A and B. The firms' locations are fixed and customers are uniformly distributed between the firms and the distance between the two firms is D. Each firm chooses a single price, PA and PB. Assume costs are zero.
A. What is the equation for the consumer at point X who is indifferent between the two firms?
B. What proportion of customers will buy from A and what proportion will buy from B?
C. What is firm A's profit function (as a function of prices and distance)?

2. You want to calculate the cluster coefficient for your own email contact list. That is, the set of names in your email address book is the relevant social network for your calculation.

A. Compose an email that you could send to each of these individuals asking for the data you would need to complete the calculation of the cluster coefficient.
Assume that:
Your friends have no idea what you are talking about, but they trust you and will provide you the data you ask for if you are clear about what you want.
You are not worried about maintaining the privacy of your email contact list or theirs.
You want to ask for the least amount of information as possible.

B. (Not necessarily in the email). Describe why if your friends comply this is enough data to compute the cluster coefficient.

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Solution Summary

Help is given to compute the cluster coefficient.