Let’s make some assumptions about the utility of bathroom visits while shopping. First, let’s assume that you’re better off when you and your (opposite gendered) shopping partner can go to the bathroom quickly, without having to wait in line due to a limited number of toilets available. In other words, the more toilets each bathroom has, the shorter the wait.
Second, let’s assume that women take twice as long in the bathroom as men (men claim this is because women are spending too much time touching up make up and gossiping, women claim this is because men are dirty and don’t spend enough time washing their hands; we are going to remain agnostic as to why this might be).
If the number of toilets in the men’s room is represented by m and the number of toilets in the women’s room is represented by w, which of the following utility functions best describes one’s utility from mall bathrooms if the number of men and women attending the mall is equal?