1. Imagine that you would like to know a friend's preference between chocolate (c) and vanilla (v) ice cream scoops. Your friend tells you that her utility function is U(c,v) = c+2*v. (a) An ice cream cone can hold three scoops of ice cream. Calculate your friend's utility for every combination of 3 ice cream scoops she could order: 3 chocolate and 0 vanilla: 2 chocolate and 1 vanilla: 1 chocolate and 2 vanilla: 0 chocolate and 3 vanilla: (b) Given the utilities you calculated in (a), rank these four alternatives from best to worst. (c) Write down another utility function that is also consistent with this ranking of the four alternatives. (d) Suppose your friend instead tells you that her utility function is U(c,v) = c +a*v. Your job is to figure out what a is. Your friend is willing to give you a hint. She tells you that she is indifferent between the following two combinations: 1 chocolate and 3 vanilla Being indifferent between these two options means that she has equal utility for them. Use this information to figure out what her value of a is. AND 2 chocolate and 0 vanilla 3 chocolate and 2 vanilla (e) Suppose that, instead of what she told you in (d), your friend tells you that she has the following two preferences: 0 chocolate and 2 vanilla preferred to 0 chocolate and 4 vanilla preferred to What range of a values would be consistent with these two choices? 1 chocolate and 0 vanilla