Robin derives utility from consuming popcorn (x1) and buying new movies (x2).

a) Suggest a utility function for the following scenarios. Assume that no matter how much she has, increasing consumption of both goods together will provide some utility.

i) Robin's utility from consuming popcorn is does not depend on the number of movies she buys.

ii) Robin wants exactly one bag of popcorn per movie, and does not want movies without popcorn or popcorn without movies.

iii) Robin always values movies twice as much as popcorn.

iv) Each additional bag of popcorn brings less and less happiness to Robin, but new movies always provide the same level of happiness.

v) If offered a choice between two bundles of popcorn and movies, where one bundle has more movies but less popcorn than the other, Robin always prefers a third bundle made of half of each of the other bundles.

b) Are any of your answers to (a) unique?