Q4. Homeowners 1, 2, and 3 live at the end of a badly deteriorated road. Fixing the road would cost $C. The value to Homeowner 1 of fixing the road is $4,000, the value to Homeowner 2 is $5,000, and the value to Homeowner 3 is $10,000. Each homeowner claims that fixing the road is not worth much to him, because each wants the others to pay the cost. The local government suspects that the total value to these homeown- ers of fixing the road is greater than $C and has decided to require the three homeowners to use the VCG mechanism to determine whether to fix the road. Since the government had no idea of the individual values for fixing the road, it decided to allocate the costs equally among the three homeowners. Each homeowner is asked to report his value for fixing the road. If the sum of the reported values is greater than C, the road will be fixed and each homeowner will have to pay $C/3 and also will have to pay an additional tax as calculated by the VCG mechanism (GC tax scheme we studied). (a) Suppose that C = $13,500, so that each homeowner has to pay $4,500 as his share of the cost. Explain what is going to happen. Report all calcuations. (b) Suppose that C = $18,000 and so each homeowner will have to pay a $6,000 share of the cost. Explain what is going to happen. Report all calcuations. (c) Suppose that instead of 3 homeowners at the end of the road, there were 30 homeowners, 10 of type 1 who valued repairing the road at $4,000, 10 of type 2 who valued repairing the road at $5,000 and 10 of type 3 who valued repairing the road at $10,000. Suppose that the cost of repairing the road is C = $180,000. Explain what is going to happen. Report all calcuations