Revenue Maximizing Parking Tickets

The economics of parking tickets have been on the mind recently as I received one a couple of weeks ago. Let's assume cities want to maximize the revenue gained from parking. This comes in two forms-- 1) metered/garage parking, where individuals pay up-front for the parking, and 2) issuing tickets for violations.

Of the garages that I've frequented, there's not too much of a story here. You either pay for a pass which allows you access or pay by the trip, which happens before or immediately after the parking is done. I don't see much non-compliance here-- it's not terribly difficult to enforce the arrangement. Revenue comes in from drivers, expenditures go out to workers, ticket machines, upkeep on the garage, etc. End of story.

Things get interesting with the meters, however. Revenue at the meters is a function of a number of things-- garage availability and price, price to park at the meter, price of the ticket for not paying the meter, and the probability of receiving a ticket for not paying the meter. In turn, the probability of receiving a ticket is a function of the number of people working to catch violators. Costs of such an arrangement are upkeep on meters, hiring people to collect the money, a court system to enforce the tickets and hear appeals, and, again, hiring individuals to enforce the arrangement and catch violators. The number of people hired to catch violators comes in on both revenue and costs-- this leads me to believe that there's an optimal number of people to hire.

Appeals are costly and are a function of the price of the ticket. I got uncountable $5 parking tickets in Morgantown; why appeal? If those were $5000 parking tickets, every single ticket would likely be appealed. Naturally, the city make more money by increasing ticket prices, but only to a point.

I'm curious about the optimal mix of parking meters and garages. It should also be noted that most (all?) private parking arrangements are done without meters; I think this is important to consider and makes me think that a best case scenario does not involve meters. Then again, cities don't have the full spectrum of options at their disposal-- they can't have unlimited garages due to space constraints, and along similar lines, there isn't infinite space for parking meters.

So the questions, then: What is the optimal ticket price? What is the optimal meter price? What is the optimal garage price? What is the optimal mix of garages and meters? What is the optimal number of people searching for meter violators? Is there an optimal number of appeals?

All are a function of local conditions and all matter in determining the others.