ECONOMICS 450/550 ? PUBLIC FINANCESPRING 2012Homework 6DUE: April 24, 2013Answer each of the following questions. Your answers should be typed and then saved as a Worddocument file or a PDF file and uploaded to Blackboard before midnight on the listed due date.Assume that we have seven board members deciding among four investment rates {3%, 4%, 5%, and 6%} and thepreferences are as listed below. Use this information to answer the following questions:First 3.0 4.0 4.0 5.0 6.0 5.0 4.0Second 4.0 5.0 5.0 4.0 5.0 6.0 5.0Thrid 5.0 3.0 6.0 6.0 4.0 4.0 3.0Fouth 6.0 6.0 3.0 3.0 3.0 3.0 6.01) (15 Points) Find the winning investment rate for each of the following voting rules:a. Plurality Runoff (first round includes all policies and second round includes only top two vote getters)b. Condorcet Procedure (the policy, if any, that beats all other possible options)c. Borda Count (if there is a tie, remove the policy with the least number of points and vote again).2) (5 Points) Graph these preferences and state whether they are single peaked.3) (5 Points) Identify the median voter(s) and state whether this voter?s optimal choice is in fact a Condorcetwinner.4) (15 Points) Assume that preferences change to those shown below. How does this change your answer, if at all,for each part of question (1)?Tom Julian Jen April Alex Ryn KayceeFirst 3.0 4.0 4.0 5.0 6.0 6.0 6.0Thrid 6.0 3.0 6.0 6.0 4.0 3.0 5.0Fouth 5.0 6.0 3.0 3.0 3.0 4.0 4.05) (10 Points) Again identify the median voter(s) and state whether this voter?s optimal choice is still the Condorcetwinner with the new preferences ordering. If not, explain why.