. There is a community of people in an online community. The people on this website can pursue one of two strategies: either they can Lead and try to come up with new ideas and convince others of these ideas, or Follow and just observe/consume the ideas coming from the leaders. Leading is rewarding, but it becomes more difficult when there are more leaders. Following becomes more rewarding the more people are also following. Let [0, 1] be the fraction of the population who is Leading and let [0, 1] be the fraction who Follow. (Note: since all people Lead or Follow, + = 1.) Then here are the payoffs:

P OL() = 10 8

P OF () = 5 + 2

(a) (10 points) Draw the utility diagram of this problem. Find all equilibria of this problem. Evaluate the stability of all equilibria using phase diagrams. Explain!

(b) (20 points) Find the socially optimal level of Leading. In this case does "the market" produce too much, too little, or the right amount of Leading, or is it hard to say/it depends? Does your analysis line up with your intuition? Why or why not? And, if you could make Lending or Following more costly, would you do so, and which one? Why?