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Question - You are one of ten students in a room, and all of you are greedy income-maximizers. Each student has $1 and must choose (without communicating with the others) whether to invest it in a private investment X or a public investment Y. Each dollar invested in the private investment X has a return of $2, which goes entirely to the investor. Each dollar invested publicly has a return of $20 which is divided equally among the ten students (even those who invest privately). So if six students invest publicly, the total public return is $60, divided equally among the ten students; the four students who invested privately get an additional $2 each from their private investment.
(a) What outcome do you predict if all the students must write down their investment decisions at the same time?
(b) Is this outcome Pareto efficient? If not, identify a Pareto improvement.
(c) "The central difficulty here is that the students must decide without knowing what the other students are doing. If you knew what the other students decided, you would behave differently." Do you agree with this argument?
(d) If communication were possible, what sort of mechanism do you suggest for reaching the optimal outcome in this game? Hint: Make sure to think about enforcement!
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