Yes, but your economic analysis needs to be correct.
It doesn't take much math to see the value.
In 2014, Michigan's official attendance numbers dipped down to around 100K with capacity close to 110K. So that's a minimum of 10K seats not being sold during Hoke's last year. Tickets tend to go for a minimum of $70 - $80. However, this is all being very conservative. Michigan's actual attendance during 2014 dipped down to around 65K - 70K for many games. Michigan was also selling tickets at deeply discounted prices as low as $5 - $10 to fill seats.
There's no way to know the precise numbers since they aren't public, but even going by the conservative number, that's $700K in lost revenue per game. Once you start factoring in the discounted pricing, it's likely that this number swells to about $2 million per home game.
We're not even counting concessions or merchandise sales yet. If we assume the average attendee brings in $5 worth of profit for concessions, then the stadium only having 70K people instead of 110K ends up costing another $200K.
I have no great way to estimate the losses to merchandise sales, but it's pretty obvious that winning teams sell more merchandise than losing teams. If we assume lost merchandise sales end up accounting for $800K, then we're already at about $3 million per game.
There are certainly miscellaneous other factors here (e.g. sponsorship deals), as well, that would be almost impossible for us to estimate, but even with what we can estimate, we can surmise that Harbaugh's hiring has added about $20 - $25 million per year in profits.
This is why, contrary to popular belief, the best college coaches are actually underpaid from an economic perspective.
Oh, and do you think Ohio State or Bama have seen sales rise by that much or more since their latest coaches arrived? So why aren't they paid $9M or even $10M, $12M a year?
The salaries are slowly pushing up in that direction. The reason why it's taken so long, however, is largely due to public perception. The general public considers it "immoral" that college football coaches make such high salaries, while educators make a small fraction of that.
Fact is, it's not about paying the coach as much as he makes for you. It's about paying him enough to land him as your coach (supply and demand), and then getting results (wins building to championships) in return.
It's really not about this at all. Nick Saban could demand $15 million tomorrow and Alabama would almost certainly have to meet the demand.
I think there are mitigating factors, though. Most college coaches understand that public perception is important and they are reluctant to make big demands to extract their full value.
Most coaches also care about the universities and don't see much benefit in "bleeding out every last penny of value". Is there really much difference in the quality of your life making $6 million than there is making $14 million? Probably not.
The best coaches also care more about their legacy than the money. They want the opportunity to compete for championships. That's more important to them than a few million bucks (when they are already multi-millionaires).
Until then, he's being paid more than the best college coaches in America and delivering (so far) significantly less.
I'm not sure how you conclude that from one season. Nick Saban didn't win a national title at Bama till his 3rd season. Harbaugh has only been at Michigan for 1.5 seasons. He turned a 5-7 team into a 10-3 team in one season and now has the #2 team in America, which has had dominating performances almost every single week.
And he turned a Stanford program that was one of the worst of all P5 programs into an absolute powerhouse than won the Orange Bowl within 4 years.
I think you'd have to be blind to conclude that Harbaugh isn't a well-proven coach. He might not have won a championship yet, but he had Stanford close to one within 4 years and already has Michigan in the hunt for one in Year #2.
