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Parking: An Exercise in Matching

From a network perspective, parking is a classic matching problem. If we consider the set of all available parking spaces in a geographic area to be the “sellers”, and the set of all drivers with their cars searching for a parking spot to be “buyers”, then the parking market can be represented as a bipartite graph consisting of parking spaces and cars. The socially optimal goal, therefore, is to create a matching in that bipartite graph so that each car finds a space where it can be parked. The “price” of the parking space in this case is the overall attractiveness of the spot to the driver of the car, which is a function not only of the monetary price of the spot (if it is metered) but also its geographic location (how far it is from the destination, how far it is from the car’s current position, etc.).

If the socially optimal goal is to create a matching where every car is matched to an open parking spot (it will not be a perfect matching, because there are vastly more spots than cars on the road), then we are not doing a very good job of reaching it. A study on a 15-block radius in Los Angeles conducted by Donald Shoup, a professor of urban planning at UCLA, found that the average time spent searching for parking spots was 3.3 minutes, which added up to 950,000 miles of travel, 47,000 gallons of gas used and 730 tons of carbon dioxide released over the course of a year – all from that 15-block district. This is not for lack of parking spaces, at least in the absolute sense; estimates are that there are at least three parking spaces for every car in the United States. Rather, the problem arises because many people want the same small set of spaces that are most attractive, a classic case of a constricted set where the number of buyers – drivers and their cars exceed the number of sellers – available, attractive parking spaces.

From an economist’s point of view, the remedy is to raise the price of parking enough so that the number of people seeking the most attractive spaces falls to a number equal to the number of spaces there actually are; in other words, selectively raise the price of certain parking spaces until the market clears. Because most parking spaces in the city are either free or offered at a low fixed rate (the meter rate), that is not the case currently. San Francisco, however, has adopted a system called SF Park that implements dynamic pricing on parking spots. The system raises the price of parking spots to reflect demand, leading to higher prices on the most heavily trafficked and sought after spots and lower prices on the less popular spaces. This is precisely the solution predicted by theory on matching markets and market-clearing prices.

While research still needs to be done on the effectiveness of SF Park, a surprising result has been that overall, prices of street parking have fallen. That is because of the finding that many of the less popular spaces were actually overpriced. The theory of market-clearing prices predicts that overall social welfare should increase even with high prices, and this finding proves that to be the case; lower overall prices means that even consumer welfare – just a subset of the total social welfare – has risen. Evidence to date has thus shown that the theory of matching markets and market-clearing prices can be effectively applied to parking.



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September 2014