Aaron Betty

Aaron, Betty, and Charlie are neighbors. Their neighborhood has a localized problem with polluted runoff that affects the three of them (and no one else). Aaron would be willing to pay up to $12,000 to x the problem. Betty would be willing to pay up to $3,000. Charlie would be willing to pay nothing. Aaron proposes that they x the problem and divide up the cost equally. Suppose the three of them vote on Aaron's proposal, and each person votes to x the problem if (and only if) the cost to him/her is less than or equal to his/her willingness to pay. What is the most that it could cost to x the problem where Aaron's proposal would get a majority of votes? What is the most that it could cost to x the problem where Aaron's proposal would produce a Pareto improvement? What's the lowest amount that it could cost to fix the problem where Aaron's proposal would not produce a Kaldor-Hicks improvement