Parking Fees , Congestion , And Consumer Welfare

Congestion can be caused by through-traffic and by traffic destined for the area where consumers park. It may appear that congestion should be reduced by increasing the price of parking. This paper shows that if road usage is suboptimally priced, then a lump-sum parking fee can increase welfare, but a parking fee per unit time does not. Indeed, an increase in the price of parking induces each person to park for a shorter time, allows more persons to use parking spaces each day, and can thereby increase traffic. For the same reason, consumers may prefer that parking not be flee. Amihai Glazer Department of Economics University of California, Irvine Irvine, California 92717 USA Esko Niskanen Department of Economics University of Tampere P.O. Box 607, SF-33101 Tampere Finland February 4, 1991 Glazer acknowledges the support of the Institute for Transportation Studies at the University of California, of the University of Tampere and of the Yrj6 Jahnsson Foundation. Niskanen acknowledges the support of the Henry Ford Foundation. We thank Robin Lindsey and Kenneth Small for their comments. Parking Fees, Congestion, and Consumer Welfare Parking has some characteristics of a private good--only one person can use a particular space at a time, and the benefit to a person who parks is not affected by the number of others who attempt to park. But it is closely tied to road usage, and therefore to congestion. This congestion cannot be easily corrected by a parking fee. For a fee that decreases the length of time each person parks can allow more persons to park and thus increase traffic. The model of Section 1 incorporates these features of parking and road congestion. We assume that all parking spaces are identical, and that demand is uniform over time. We thus do not address the role of parking fees in allocating more and less desirable parking spaces to users. For a classic treatment of this location problem see Vickrey (1954). A modern analysis is given by Arnott, Palma, and Lindsey (1989), who consider both the timing of trips and the location of parking; they show that the parking fees charged by competitive firms are inefficient, and indeed can reduce welfare. Section 2 examines the second-best solution: the optimal parking fees if the road-usage fee is too low. The effect of a parking fee on consumer welfare and on the number of parkers is discussed in Section 3. The analysis here can explain why many cities charge for parking on the sides of a road, but allow moving traffic (even if at a snail’s pace) to use the same road for free. 2 This difference cannot be explained solely by technological factors--we should expect innovations as clever as the parking meter were governments seriously interested in congestion fees. Instead, we show that parking fees, unlike road tolls, can increase aggregate consumer welfare, even if consumers are identical and the revenue collected is not returned to them.3 Section 4 uses a queuing model to show that a parking fee can increase consumer welfare and congestion. 1. Parking and through-traffic Consider consumers who can either park downtown, or alternatively drive through downtown on their way elsewhere.4 Heterogeneous would-be parkers are indexed by i. The inverse demand function of person i is p(i,q), with pq < 0. This function also represents his marginal valuation of the qth unit of parking time. This function represents the value to the consumer of shopping, dining, working, and so on while he parks. The continuum of consumers is arrayed in order of their decreasing willingness to pay for parking, so that we can define the partial derivative of the function p(i,q) with respect to i as p~ ___ 0. Heterogeneous through-traffic drivers are also arrayed in decreasing order of their valuations. The ida driver’s valuation of a trip is v(i) with v’ _< 0. Denote by E the number of persons who make a trip with the intention of parking. D is the number of persons who drive through the area. (To recall the notation, think of persons Driving through downtown, and of persons Ending their trip downtown.) We assume away any uncertainty and imperfect information. Trips are perfectly synchronized so that traffic flow and the demand for parking is the same throughout the day. In equilibrium a consumer can immediately find a parking space. This assumption is relaxed in Section 4. Both parkers and through-drivers incur a fixed cost F per trip, which can include the cost of driving, the expected accident costs involved in the act of driving, and so on. This cost is independent of the length of parking time, but can depend on the level of congestion, represented by the total number of drivers; that is, F = F(D+E), where F’ > 0 in the relevant range. Each parker and driver also incurs a road-usage fee, r. Parking fees consist of two parts: a fixed lump-sum fee of l, and a charge of m per unit time. Consumer i’s surplus from parking for q units of time is S(i,q) = I p(i,x)dx mq l r (1) Consumer i maximizes utility by choosing q to satisfy the first-order condition dS(i,q) _ p(i,q) m = 0. (2) dq This determines qa,m), the length of time person i will park as a function of the fee m. This section describes the socially optimal parking fees, road-usage fee, and number of parking spaces. The cost F is a social cost. The parking fees (m and/) and the road-usage fee (r) are income transfers. The cost of supplying N units of parking hours per day (the number of parking spaces times the length of the day) is c(N), with c’ > 0. To restrict attention to the interesting case, we assume that both types of trips are made in equilibrium. Social welfare is the sum of utilities of the E persons who park each day and of the D persons who drive through, minus the costs of providing the parking spaces: