3) 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 $3,000, the value to Homeowner 2 is $5,000, and the value to Homeowner 3 is $8,000. 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 homeowners 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: Costs are allocated equally among the three homeowners if the road is provided. 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. Furthermore, each homeowner also has to pay an additional tax as calculated by the VCG mechanism (as specified in your lecture notes). (a) Suppose that C=$13,500, so that each homeowner has to pay $4,500 as his share of the cost. i) Will the road be fixed? ii) What will be the additional tax paid by each homeowner? iii) How does each homeowner's welfare change as a result of the VCG mechanism? How does total welfare change? 3) 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 $3,000, the value to Homeowner 2 is $5,000, and the value to Homeowner 3 is $8,000. 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 homeowners 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: Costs are allocated equally among the three homeowners if the road is provided. 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. Furthermore, each homeowner also has to pay an additional tax as calculated by the VCG mechanism (as specified in your lecture notes). (a) Suppose that C=$13,500, so that each homeowner has to pay $4,500 as his share of the cost. i) Will the road be fixed? ii) What will be the additional tax paid by each homeowner? iii) How does each homeowner's welfare change as a result of the VCG mechanism? How does total welfare change