This is kind of an interesting problem, but it overlooks another variable, at least in the case of skis - it's not just how many days I'm going to use them this year, but also for the next few years. Yes, there are people who buy new skis regularly, but more commonly the person that makes the buy vs rent decision decides that over the next multiple seasons they intend to ski enough to justify the buy decision. This is especially true if you are buying new skis rather than say, rental skis at the end of the season (think kinda like buying a used car that has been depreciated, you can buy used skis that still have a lot of miles...). So my point is simply that the real world problem is actually even more interesting than this hypothetical.