Percentages are correct or not.

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Chapter 11, Problem 35P

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Percentages are correct or not.

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2. Question The 'Democratic Family' consists of three members {mother m, father f, daughter d}, that have different preferences with respect to how much money X € [0,8] they think should be invested in the new family car. These preferences can be represented by the following utility functions: - Mother m: um(X) = 2X - X² Father f: uf(X) = 10X - X² - Daughter d: ud(X) = 4X - X² Calculate for each family member (f, m, d) the preferred amount of money to invest in the new car denoted by X; for i = {m, f,d}. Assume that (Xf, Xm, Xd) are the three alternatives on which the family must decide. Show that each family member has rational preferences over this domain. Preferences on the family level are determined by pairwise majority voting (all family members vote on two alternatives). Derive the family preference and check whether it is rational. Assume that the final family decision is made by conducting sequential pair- wise majority voting, where the loosing alternative is eliminated. Does…