"When there's no medallion over head you can charge less and that applies to a hypothetical dispatch co-op too."
This is wrong for two reasons:
1) In general, overheads don't directly affect how much you choose charge for something. By definition, overheads are fixed (i.e. don't change with the output), so don't affect your marginal decision about whether to drive or not.
2) In the specific case of taxis, prices are set via a combination of lobbying and regulation. Taxi tariffs are not set by the market in response to the market value of medallions.
In summary, you have it backwards. Taxis tariffs aren't high due to the cost of medallions. Medallions are worth a lot because taxi tariffs are high.
Overheads absolutely affect marginal decisions. For a Uber driver, their income is revenue - car payment - fuel - other expenses. To remain solvent, that formula needs to be > 0.
For a cab it's similar, except you have labor cost and medallion cost as well. With rates fixed by regulation, the only way to increase profit is to drive more.
"With rates fixed by regulation, the only way to increase profit is to drive more."
That's the reason right there. The rates are totally set by regulation. The number of medallions is similarly set. If medallion rental cost were to go up or down by 20% this wouldn't affect whether the marginal ride would be worthwhile for the driver.
Sure it would. The market of people looking for a ride in price sensitive. If the medallion cost goes down, you need to drive less to breakeven and hit your target profit. If it goes up, you need to drive more to attract more rides.
Likewise, there are mental and affordability factors that influence passengers. When I was still going out to downtown clubs, I lived in a close suburb of my mid-sized city. Cabs were regulated by the city, but unregulated outside. That meant that predatory cab companies would charge as much as $50 for a 5 mile ride, and something like $10 for a 4.8 mile ride within the city.
In NYC, historically this has meant that many cabs are kept in motion 24x7, and are concentrated in specific areas in Manhattan to maximize the number of fares.
This is wrong for two reasons:
1) In general, overheads don't directly affect how much you choose charge for something. By definition, overheads are fixed (i.e. don't change with the output), so don't affect your marginal decision about whether to drive or not.
2) In the specific case of taxis, prices are set via a combination of lobbying and regulation. Taxi tariffs are not set by the market in response to the market value of medallions.
In summary, you have it backwards. Taxis tariffs aren't high due to the cost of medallions. Medallions are worth a lot because taxi tariffs are high.