(10 points} A small residential community is considering purchasing a smokeless grill for the public area. There are six residents living in this community. Each resident has an identical utility function: \"5,350 = (1 + % If: where G is the number of grills in the community, and x,- is the amount of money each resident i has to spend on their private goods. Suppose that there is only enough space in the community for one grill, so 6 is either 0 or 1. Suppose that the price ofgrills is $480 each. The wealth of each resident is shown in the following table. Resident Ll mi 1Victoria Willian Xander Yana lain Wealth (5) 6.900 1300 1500 1,900 8,900 [2.000 {a} Is it Pareto efcient for the community to purchase the smokeless grill? Explain. (b) Yana proposes that the community purchase the smokeless grill and all residents split the total cost equally. Assume that it takes a simple majority (more than half of residents} to pass any proposal, and all residents must vote. 1Will the proposal pass? Explain. {c} Victoria proposes that the community purchase the smokeless grill and each resident's contribution to the total cost should depend on their wealth. All residents whose wealth is below $8,500 will contribute 0.8% of their wealth, and all residents whose wealth is higher than or equal to $8,500 will contribute 1.2% of their wealth. Assume that it takes a simple majority to pass any proposal, and all residents must vote. Will the proposal pass? Explain