Simple: the number of cabs at which taxi driving is no longer profitable is far, far more than the optimal number of cabs.
The optimal number of cabs balances cab availability with traffic such that the time taken to go from point A to point B is minimal. This takes into account the time it takes to hail the cab (waiting around if there is none) and the time it takes for the cab to fight though traffic to point B. An additional constraint is that the number of cabs shouldn't prevent miserable gridlock for other drivers.
The number of cabs required before cab driving becomes unprofitable is a function of the number of people willing to work for meager wages, often less than minimum wage (in a big city, this number can be considered unlimited, especially if the job is part-time), the cost of gas, car, and insurance, and the market fare. Assuming the amortized cost of a car is fifty cents a mile, there is enough profit in cab driving for less privileged workers, even if the cab is idle most of the time.
Most importantly, traffic congestion in a big city is non-linear: it only takes a few extra cars on the road to create major gridlock.
> Simple: the number of cabs at which taxi driving is no longer profitable is far, far more than the optimal number of cabs.
Do you have any evidence of this claim? As with anything, there isn't some magical shut-off point where everyone is selling something and then no one is after the price increases another dollar.
Your analysis strikes me as too simplistic. It ignores opportunity costs and the possibility that it might decrease personal car ownership outright if a viable taxi system were to exist.
At any rate, even if it's taken as fact it doesn't justify a fixed number of medallions revised once every few decades. A price set on them, adjusted regularly, would achieve the same cause and be less limiting and more responsive to growth (something cities tend to do a lot of between the issuance of new medallions).
Creating artificial scarcity does nothing but enable some people to profit with little risk.
The market fare is also affected by the number of cabs - if the number of cabs available significantly exceeds the demand for cabs, the market fare will fall. This means that each additional cab on the road is a double-whammy against the profitability of all cabs - it reduces the market fare and it increases the average idle time.
The optimal number of cabs balances cab availability with traffic such that the time taken to go from point A to point B is minimal. This takes into account the time it takes to hail the cab (waiting around if there is none) and the time it takes for the cab to fight though traffic to point B. An additional constraint is that the number of cabs shouldn't prevent miserable gridlock for other drivers.
The number of cabs required before cab driving becomes unprofitable is a function of the number of people willing to work for meager wages, often less than minimum wage (in a big city, this number can be considered unlimited, especially if the job is part-time), the cost of gas, car, and insurance, and the market fare. Assuming the amortized cost of a car is fifty cents a mile, there is enough profit in cab driving for less privileged workers, even if the cab is idle most of the time.
Most importantly, traffic congestion in a big city is non-linear: it only takes a few extra cars on the road to create major gridlock.