Economics of Casual Fridays
Casual Friday began in the late 1950s originally as an attempt to raise worker morale in the new white-collar office environment.(Wikipedia also mentions the clothing industry pushing for it to shift clothing demand from formal, European clothes to cheap clothes made in Asia.) Anyway, let's assume that the goal is to increase worker happiness. Let's also assume that there is a (small?) productivity cost to casual dress. If we don't assume this, then employers are just cruel since casual dress makes workers happy. If there's no cost to that, then your boss really is a jerk.
We generally assume that utility is concave (increasing at a decreasing rate, or u'>0, u''<0). To determine why casual Fridays should be on Fridays, we need to assume something about a production function. Let's say that the relevant input affected by all this is effort, or effort-adjusted labor hours (call it L). So the idea is that casual dress reduces the "formality" of the office and everyone goofs off a little more. Would we all agree that the production function would be increasing in effort-adjusted hours, but at a decreasing rate (so that FL>0 and FLL<0)? (A standard production function has that relationship with unadjusted labor hours.)
Now, if we assume that Friday is no different from any other day, then it doesn't matter what day you make casual dress day. But Friday isn't like any other day, is it? It's a day when people tend to goof off a little more, anyway. We daydream about the weekend, sneak out early to head a start on travel, etc. So, it's probably a safe assumption that LFRIDAY is lower than Li, where i is any other work day. Given that (and our assumptions on the concavity of the production function), adding casual dress day to Friday suggests that you are reducing effort-adjusted labor hours on the one day of the week in which it has the largest possible negative marginal impact.
Simultaneously, it's likely that all that Friday day-dreaming, goofing off, and cutting out earlier means that workers already have higher levels of utility on Friday than on other work days. Thus, the boost that workers get from casual dress is "wasted" on a Friday, since marginal utility is lowest on Fridays. That is, it's likely that Friday is the worst possible day for casual dress day. Rather, casual dress day should be on the day of the week that has the highest level of effort (so that that marginal impact of slacking off is minimized) and the lowest level of worker happiness (so that the marginal utility of wearing jeans is maximized). Likely, these two things go hand-in-hand. And, very likely, they are not on Fridays. So maybe we should all have casual Mondays, rather than casual Fridays. (Or casual Wednesdays, or whatever day you think fits the criteria discussed.)
So, why do we have casual Fridays? One easy answer is coordination. Someone started it on Fridays, and so everyone coordinates on that day, even if it's less than optimal. (This is still a bad answer, because it begs the question of why it started on Fridays.) Another possibility is that I'm wrong and that things don't work the way I layed them out. Maybe casual dress enters the production function differently, or maybe there's no relationship between Fridays and slacking off, who knows? Or maybe, and this is what I'd choose if forced to choose something, there is a complementarity between Fridays and casual dress and that it's not the case that the marginal utility of jeans is lower on Fridays. Maybe being able to wear jeans on the day you sneak off early for the weekend is a huge utility boost, much more than you'd get on a Monday or Wednesday. If that's the case, casual Fridays may well be optimal, even if the productivity loss is greater on Fridays than on other days.