Using Demand Elasticities to“Balance” Transit Fares and

Service Levels

Ian SavageNorthwestern University

My basic thesis . . .

“Acceptance of inflation-indexing of fares is dependent on convincing people that fares have been set in accordance with the same level of professional determination as service frequency, rather than being set at an arbitrary level based on some historical or political precedent”

Travel demand models . . . • Concept of “generalized cost” of travel = fare +

valuation of time + valuation of other attributes (positive and negative)

• Traveler compares generalized cost of competing modes (“mode choice”)

• Time taken comprises access/egress time, wait time, in-vehicle time, interchange time

• Transit access/egress time and wait time inversely related to density of routes and frequency of service

• Time taken is inversely related to service levels

Transit demand . . . • Demand (Q) = f (P,VM-1,X,Y)

P = fare

VM = vehicle-miles (service level)

X = other demand variables outside control of transit agency (“exogenous”)

Y = other demand variables under control of transit agency (“endogenous”)

• Considerable empirical evidence on elasticities

Data on elasticities . . .

• Richard Balcombe (editor), The Demand for Public Transport: A Practical Guide, Report TRL593, Crowthorne, UK: TRL Limited, 2004

• Transit Cooperative Research Program, Traveler Response to Transportation System Changes, chapters 9 (service level), 10 (service coverage), 12 (fares), Transportation Research Board, 2004

Definition of price elasticity . . .

• eq,p = % change in demand divided by % change in price

• Usually negative• All evidence is 0 > eq,p > -1 or “inelastic”• Fare increase leads to increased farebox

revenue• Fare decrease leads to decreased farebox

revenue

Fare elasticities vary by mode and time...

Short-run (1-2 yrs) Peak Off-Peak

Bus -0.3 -0.5

Mass transit rail -0.2 -0.4

Commuter rail -0.35 -0.8

• Longer-run elasticities in range -0.6 to -1.0

Suggests time-of-day pricing . . .

• Price increases in the peak produce largest increases in revenue with loss of the least amount of riders

• Off-peak fare discounts are the most effective at increasing ridership

• Reverse of most transit pricing?

• “Ramsey pricing” can increase ridership while generating same amount of revenue

Overall service elasticity . . .

• eq,vm = % change in demand divided by % change in vehicle-miles

• Bus short-run elasticity of +0.4, long-run elasticity of +0.7

• More sensitive in evenings and Sundays

Revenues and costs . . .

• Total Farebox revenue = P*f(P,VM-1,X,Y)

• Total Cost = c(VM)

• With subsidy of $B, budget constraint is:

P*f(P,VM-1,X,Y) + B = c(VM)

• Multiple combinations of fare and service level satisfy this budget constraint

Fare

Vehicle Miles

Budget Constraint = B

Fare

Vehicle Miles

Budget Constraint = B

More Subsidy

Fare

Vehicle Miles

Budget Constraint = B

Less Subsidy

Objectives of the transit agency . . .

• Objectives are constrained by amount of subsidy available ($B)

• Credible objective is maximizing social benefit

• A proxy for total social benefit is ridership (passenger-miles, passenger trips)

• Should some trips be weighted more than others?

Fare

Vehicle Miles

More Riders

Less Riders

Fare

Vehicle Miles

More Riders

Less Riders

Budget Constraint = B

Fare

Vehicle Miles

More Riders

Less Riders

Budget Constraint = B

P*

VM*

Balance point . . .

• The combination of P* and VM* is called the “balance point”

• Maximizing Q = f (P,VM-1,X,Y) subject to constraint P*f(P,VM-1,X,Y) + B = c(VM)

• P and VM are the agency’s choice variables

• Knowledge of price elasticities crucial to empirically finding the balance point

Balance point . . .

• The balance point maximizes user benefits / ridership.

• Once you are at the balance point, logical to suggest that the real value of P* should be maintained by indexing

Getting to the balance point . . .

• Values of P* and VM* may vary by mode and time of day

• The current combination of fare and frequency may be more out of line at some times of day and on some modes compared with other times and modes

Fare

Vehicle Miles

More Riders

Less Riders

Budget Constraint = B

P*

VM*

Benefits per $1 of subsidy . . .

Weekday Weekend

Peak Off-Peak Saturday Sunday

CTA Bus - 1994

Fares 1.39 1.77 1.77 1.80

Service 0.21 1.11 1.24 1.16

CTA Rail - 1994

Fares 1.26 1.18 1.18 1.18

Service 0.34 0.97 0.77 0.54

Getting to the balance point . . .

• Discounted fare in off-peak, especially on the bus system

• Too much peak-period capacity in both modes

• Somewhat excessive weekend rail capacity

What about costs? . . .

• Cost reduction will improve benefit-cost ratio of providing extra service

• But will not affect benefit-cost of changing fares

If unit costs fell by 20% . . .

Weekday Weekend

Peak Off-Peak Saturday Sunday

CTA Bus - 1994

Fares 1.39 1.77 1.77 1.80

Service 0.27 1.61 1.82 1.68

CTA Rail - 1994

Fares 1.26 1.18 1.18 1.18

Service 0.43 1.26 1.00 0.69

Cost reduction . . .

• In this case has restored more of a balance between fares and service levels

• Bus passengers have been at a disadvantage compared with rail passengers

• Still advantageous to provide a price discount and extra service in the bus mode in the off-peak by reducing capacity in the peak

In summary . . . • Fare and service elasticities vary by mode and time

of day• Consequently, ridership-maximizing combination of

fare / service level varies by mode and time of day• A fare schedule that is based on a strategy that

maximizes ridership (user benefits) is more defensible if the agency wishes to index it against inflation

• Casual empiricism from Chicago is that fares held constant for lengthy periods trigger a fiscal crisis (1957-65, 1970-79, 1992-2003)

Contact Information:

• ipsavage@northwestern.edu

• (847) 491-8241

• www.econ.northwestern.eduLook under “faculty” tab to link to my personal web site