What is it that you think I'm confused about? Mostly you haven't said anything that wasn't already included in my prior comment.
However:
> instead it makes sense for the company to pay Jim somewhere between $8000/mo and $10000/mo to work from home, because any of those numbers make both of them no worse off than paying Jim $10500/mo to work from the office.
It can never make sense for the company to pay Jim more than $8,000 / month, because that is the amount he wants. As long as he's willing to work for $8,000 / month, the value of his work to the company can't exceed $8,000 / month.
You might notice that the value $15,000 doesn't occur anywhere in your most recent comment. How do you consider this comment related to your earlier claim that "If you split the difference, you both come out $15,000 ahead"? What difference have you identified that could be split this way?
> It can never make sense for the company to pay Jim more than $8,000 / month, because that is the amount he wants. As long as he's willing to work for $8,000 / month, the value of his work to the company can't exceed $8,000 / month.
The company doesn't know the minimum amount he's willing to work for. They have to guess. If they guess too low, he quits. If they guess too high, they pay more than $8000/mo.
The company also doesn't know exactly how much Jim values being able to work from home, so they have to guess that too. They can reasonably guess that it's in the thousands of dollars per month, but they don't know if it's $1000/mo or $4000/mo.
What they do know is that their cost for having him work from home -- arguably a savings to the company, but perhaps worth $500-$1000 in some cases -- appears to be less than this.
If they guess $1250/mo (i.e. $15,000/year) then they've guessed right in the middle between the start of the range and the actual limit, so each party gets half of the surplus. If the company's costs from allowing WFH are zero then they get to save $15,000/year, and Jim gets to save the $30,000 in commuting expenses in exchange for getting paid $15,000 less, which puts him $15,000 ahead too.
Even if the company's costs are non-zero they're still coming out ahead as long as they're not more than $1250/mo, so if they're $500/mo or $1000/mo and their guess of what he'll take is a reduction of $1250/mo then they'll still want to pay him that much less and let him work from home.
They might also make a better guess and get closer to the actual number of $2500/mo, but then they're running the risk that they overplay their hand and he walks away, and then they don't get the savings of thousands of dollars a year. So who actually gets more of the surplus from letting him work from home is down to salary negotiations, but it's in both of their interests to make it happen.
However:
> instead it makes sense for the company to pay Jim somewhere between $8000/mo and $10000/mo to work from home, because any of those numbers make both of them no worse off than paying Jim $10500/mo to work from the office.
It can never make sense for the company to pay Jim more than $8,000 / month, because that is the amount he wants. As long as he's willing to work for $8,000 / month, the value of his work to the company can't exceed $8,000 / month.
You might notice that the value $15,000 doesn't occur anywhere in your most recent comment. How do you consider this comment related to your earlier claim that "If you split the difference, you both come out $15,000 ahead"? What difference have you identified that could be split this way?