Honestly, the price increase on both platforms recently has pushed my household (Wife + Me) back to Muni/Driving. Previously, if one of us used ride sharing it was ~$5-8 each way. Now for the same ride we regularly hit $12-20. It was so bad the last week of my wife using them that she paid ~$18-20 each way, when I reminder her that that was $200 for the week just to get to work, she was shocked. At 4 weeks in the month thats a decent Mercedes payment, getting close to insurance+gas locally.
Now we only use it for the occasional night out where we just factor in the expense as entertainment. These services only have a marginal value that is approximately 2-3x public transit. In SF that is Muni at $2.50-$3, so $5-9 one way. Once you cross the $10 and creep into $15-20, you have a problem and the business crashes and burns.
In my twenties I remember working at a bar near chinatown. I would get off and my feet would be killing me. It was only maybe 6-8 blocks up Sutter to get to my old place, but every once in a while I would waste money on a Taxi. I remember it killing me that they started the meter at $3.50 and it would end like $8-10. Always felt like if they just flat rated it at $5 for my 6-8 blocks, I would take it everyday to and from (Uber sort of did just that and I rode it like crazy for a while), but at $10 it was a special treat and the rest of the time I schlepped up Sutter, feet be damned.
If Uber pays drivers more than Lyft to a point where drivers stop driving for Lyft, riders won't be able to get a ride on Lyft, so they'll pay Uber's higher prices. Not everyone will; some will opt for a regular taxi, driving themselves, or transit. But I suspect that there is actually some combination of higher ride prices and higher driver salaries that will keep Uber alive and growing, though probably not at the same rate.
I believe that you have the power dynamic reversed. I.e. The drivers will go where the customers are more than the customers will go where the drivers are.
A driver only gets paid if a passenger rides. If Uber increases the costs of their rides over a competitor, the the customers will opt to the competition.
If they raise prices then quantity of rides will go down. If quantity of rides goes down, it becomes harder to earn a living as a driver. If it is harder to earn a living as a driver, there are fewer drivers. If there are fewer drivers, then the cost of drivers goes up.
Not to mention the fact that if uber becomes 10% more expensive a large chunk of those customers will just go to lyft.