You live in a community house of ten people. This problem is about how clean the house should or will be kept. Six of your colleagues are low demanders for cleanliness and each has a private marginal benefit from a unit of cleanliness which is approximated by: PMB = 0.9 - 0.04 Z ($ per unit of cleanliness) where Z is the units of cleanliness. Four of your colleagues (including you) are high demanders for cleanliness and each has a private marginal benefit from a unit of cleanliness which is approximated by: PMB = 1.75 - 0.02 Z ($ per unit of cleanliness). Cleanliness can only be obtained by having a cleaner. A cleaner produces 2 (units of cleanliness per hour) and charges 12 ($ per hour). a) Is house cleanliness a public or private good? b) What would you mean if you said that your private marginal benefit was 1 ($ per unit of cleanliness)? c) From an efficiency viewpoint, how many hours should the cleaner be hired?d) If cleaning is provided at the efficient level and the cost is shared by the Benefit Principle, how much does the high demander pay and how much does the low demander pay? It may be helpful to graph this. e) If cleaning is provided at the efficient level and the cost is shared by the Benefit Principle, how much better off is each person? That is, the high and low demander. It may be helpful to graph this.f) If cleaning is provided at the efficient level and the cost is shared equally, how much better off is each person? That is, the high and low demander. It may be helpful to graph this. Hint: There is no reason for PMB=PMC at the efficient level of cleaning. g) You have a ever-so-slightly higher PMB than your colleagues. A house meeting is held which decides that the cleaner must be hired privately. How clean will the house be kept and how many hours will the cleaner work? h) You call another house meeting which decides that, since everybody gets the benefit of having the cleaner, everybody should contribute according to their PMB. Unfortunately, 3 of the low demanders free-ride. For how many hours is the cleaner hired