09 Jun Question S18 SOCI 111: Social Networks Homework 4
Question
S18 SOCI 111: Social Networks Homework 4
DUE: 6/6/19 81 points total Instructions:
As before, these problems give you an opportunity to use the concepts and techniques we’ve learned in class to analyze interesting social systems. This time I’ve leaned more toward interesting conceptual puzzles rather than brute calculations. I encourage you to work in groups (of no more than 5), but each student should prepare her or his own solutions, along with a note at the top of your assignment crediting other members of the working group. Please make sure you truly understand the solution to a problem, and please: DO NOT COPY SOLUTIONS. This includes copying solutions from earlier years. We will figure it out. Do not go to the testbank at SAC, do not go to Course Hero, and do not get solutions from friends who have taken the course in the past. This will impede your learning, it will not prepare you for the final exam, and I will treat it as academic misconduct.
In general, you should show your work rather than just writing down a number. This makes it easier for us to see that you know what you are doing, and easier for you to see when you’ve made a trivial mistake. On the other hand, don’t just throw everything vaguely relevant at the wall and hope that something sticks. You need to be judicious!
Please turn in a hard copy of your solutions to the TA at the beginning of class. Your submission should be neat and legible: you can type it up or write it out by hand, but we aren’t going to engage in decipherment here. Please follow the breakdown of questions into parts (a, b, c, etc.) to make these easier for your TA to grade.
Q1. Why is it sometimes rational to imitate the behavior of others? Briefly describe two reasons, and give an example of each. (6 points)
Q2. You are in charge of marketing a new smartphone app, SeeFood, that allows users to share pictures of food with each other. Uptake of the app will obey the following dynamical rule:
If the company spends $50,000 on marketing, it can get a fraction z’ of the population to Adopt the app at time 0. This fraction z’ is between B and C—just above B, in fact. If the company spends $300,000 on marketing, it can get a fraction z’’ of the population to Adopt at time 0 (mostly by giving the App away). This fraction z’’ is close to D. You think that the company should spend the $300,000, as it will get you close to total adoption. Your intern argues that you should spend $50,000 on marketing instead. If adoption settles at fraction A, your company will make $0 in revenue; at fraction B, your company will make $100,000 in revenue; at fraction C, your company will make $200,000 in revenue; and at fraction D, your company will make $500,000 in revenue.
a) Explain why you are wrong, by showing that you will actually lose money if you spend the $300,000 to get a fraction z’’ of the population to Adopt. Remember, in all cases, you need to subtract the cost of your campaign from the revenue. (5 points)
b) Show why it is better to follow the intern’s suggestion and spend $50,000 to get a fraction z’ of the population to Adopt. You should demonstrate that this will result in a net profit for your company. (5 points)
c) Explain why fraction C is a stable equilibrium. (2 points)
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