Consider 101 individuals who live in a remote location. Each has an identical endowment for living in this remote place, e = 20. Each individual in the community can use their endowment to contribute to a fund to maintain and improve the local fresh water supply, a village spring well. The more money that is contributed to the well, the better the water supply is, meaning, every individual benefits increasingly from every unit of funding the well receives, but if the total contribution is less than 20, the well will be closed. The well water can be accessed by anyone in the community, there is no possibility of exclusion. Every unit, xi, contributed to the fund for the well by individual i, returns 0.2 xi worth of benefits to all the individuals in the community. Every unit of e; not contributed to the well is kept by the individual, e; - x, for their own use. Write down the payoff function for an individual in this public good proposition. [3 points] i. If 100 individuals contribute their entire endowment and 1 does not contribute anything, what will be the payoff to the individual who contributes 0 to the well fund? What will be the payoff to the individuals who contribute? [7 points] What would be the theoretical outcome in this community, in terms of the fund for the well? Will the well stay open, in theory? [5 points] Discuss, with reference to what you have learned on the course about experiments with public goods, what outcomes may occur in practice. [5 points] Imagine a social media app is launched in the village. Participation is compulsory and each individual's photograph, name and contributions to the well fund are broadcast on it. Discuss how this might change contributions to the public good. ii. iii. iv. V.