Personal opinion: the people who voted this in are politicians who need to get reelected and not economists who have actually considered the ramifications of their actions:
Personal opinion aside: A new equilibrium will develop...eventually. When I was in St. Louis, the starting salary for a Kelley day basic (aka, part time, 24 hours a week) was 18.50 in the area for 911. The Medic wage was 25. This was a few years ago so I don't know if it's still about the same, higher, or lower. But if all of a sudden, STL County passed something that said $15 minimum, it wouldn't affect the companies out there at all--initially. They'd still pay their basics and medics 18.50 and 25 an hour. But then as the cost of labor increases, so does the cost of goods and services, and those people who were perfectly content at their 18.50/25 jobs will start looking for work that pays more (or look for a cheaper place to live). In order to recruit and retain new people, they'll have to raise their wages.
Here's what I think will happen in LA, EMS-wise. Companies will evaluate whether or not to move their stations/base of operations outside of the limits of the wage (not sure if it's county limits or city limits). Those that don't have a need to have rapid response times into places that can't be service by a facilitys outside the limits will have the easiest time moving. They'll look at the increased fuel costs (if any) from moving their location and make a decision that way.
Those that move out will continue to operate as they do now. As the cost of living increases, wages will have to change (note, i said change, not match) to adapt. The only difference I see being that the cost of living will increase faster than the general US cost of living.
Those that don't will have a harder time dealing with it. I anticipate that most businesses will just charge more--once again, just like in normal day-to-day life, as costs increase so do prices--only it'll be accelerated in LA. But EMS has a business model where the prices are set by a 3rd party. Their only way to maintain the same profit margin is to cut costs. I can see them increasing their wait times for transports and running their crews harder. I don't know how things work out there exactly, but around here, the private companies that mostly do IFTs will usually try to sit a crew or two during the day so they can respond to emergencies at their contracted facilities. I can see them doing away with these. Here, there are a limited number of private trucks that have 3 man crews. I can see them cutting back to 2. As someone mentioned above, if there is supply, I can see them doing away with basics and hiring only medics.
But in the long run, I see no differences. Prices will go up in LA and the medics who work there will either demand more compensation, or will look for jobs elsewhere. The quality of life for a medic right now at $15 an hour won't give him the same quality of life so the wages will have to increase to keep up with that. Overall, as employers have to pay more, costs will go up and people will adjust--either by having a higher cost of living and wages to go with it (think Manhattan) or by leaving.