I've always found this incentive structure perverse. Take Peter Norvig and place him in LA vs Louisville. In either case he's a remote employee working from a home office. <very profitable company> will want to pay him differently depending on where he lives and depending on where their HQ is. And yet his output is the same. Let's say he prefers less dense cities, maybe then his output is even higher in Louisville, as the lower cost of living affords him a better home setup and a social circle that all can afford to live nearby each other.

Society seems to want to cram people into as small a space as possible near work places, optimizing for business progress. Seems to me to make sense in the short term and fail in the long term. Here's to hoping a silver lining of the pandemic is better utilization of space towards human happiness and the health of the global ecology. :)

I don't think you'll get an LA salary in Louisville. But you can get a high salary for Louisville from an LA company.

In the long run I imagine this affects the cost of living in an area for people that work for companies in that area. Ex. what happens to smalltown Iowa when people get remote jobs and drives up prices for housing and food?

If they are remote employees, why would the employee's city matter to the employer in either of the cases you mentioned (beyond any tax or employment law implications)? If the company is sure enough that the remote candidate from Louisville is talented enough for the job, it makes no financial sense for the company to lose that candidate over salary if they would have paid the same amount to a candidate in a different, more expensive city.

One exception I can see is if the company would pay a premium for remote employees living in a city where they have an office, so that they can be asked to come in if there is an emergency.

"Satellite office" may have been a better term.