I was wondering if buying "upgrade rank" makes things go faster or produce more? I see no change when I buy this.
Every time you upgrade rank (if that store is at rank n, it takes n + 2 bux to upgrade it one level) the amount of stock at all three tiers increases by 10% of the original level 1 level. You'll notice when you do it that the bars representing how much stock you have shift slightly to the left, because the proportion of stock you have to the max has just dropped a little. Time to reorder does not change.
For instance, Dewback Ribs starts out with the cheapest item making 40 units every time I reorder it (not counting dream job doubling). Now at level 7, mine makes 64 units (not counting dream jobs doubling), so I don't have to reorder as often, and my store makes a lot more money overnight, because I have 60% more stock at all levels.
Rank upgrades are useful on the dinky levels, like Mos Espa Cafe, and Workout Center, if you want longer breaks before the level 1 stock runs out and has to be reordered. Also, it is useful to pick whatever level has the most stock (once you have every level, that's the Imperial Court) and upgrade that at a lot, in order to get the maxiumum amount of money from Big Spenders. Use bux for the first few levels, then once it costs too many bux, and you'll want to use Upgraders instead.