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Tariffs in Taxi Business:
Surplus Extraction or Moral
Hazard or both?
Souvenirs du Caire / 2007-2010
Peter T. Baltes (MILAK) / Ehab Yassin (GUC)
Cairo by Google Earth
Souvenirs du
For their kind help we thank:
Caire
Walter Furter, Odilo Gwerder, Daniel Lätsch and Maximilian Zangger
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Outline of the Following Analysis
Question:
When taking a taxi, in many countries you must pay a two-part tariff /
nonlinear tariff.
A two-part tariff represents a combination of …
•
a (constant) flat fee up front / initial fare
•
with a variable fee for each kilometer / mile traveled.
Why are two-part tariffs employed in taxi business?
Microeconomics offers two possible explanations.
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Outline of the Following Analysis
First variant of explanation:
This pricing schedule allows the cab driver to increase profits by
extracting additional consumer surplus.
 Traditional Economics
Second variant of explanation:
In a situation of asymmetric information between the driver and the client,
the driver as an agent has a incentive to exploit his superior knowledge by
deviating from the shortest / fastest route available.
The two-part tariff may prevent him from shirking on a less informed
client (principal).
 Glazer / Hassin (Economics of Cheating in the Taxi Market [1982], pp. 25);
Campbell (Incentives [2005], pp. 11)
In contrast, a linear tariff (charging only the distance traveled) would
not be able to overcome this special case of moral hazard.
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Variant 1 – Two-Part Tariff: A Pricing Schedule for Surplus Extraction
Consider the following simplified situation:
One single producer.
•
A bilateral monopoly
One single customer.
•
Supplier sells homogeneous units of a specific good.
•
Supplier has perfect information. In particular, …
o
she does not only know her own cost function
(constant marginal cost & fixed cost of Zero are assumed here),
o
but she also exactly knows the (individual) demand function of her client.
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Variant 1 – Two-Part Tariff: A Pricing Schedule for Surplus Extraction
•
Concerning the distribution of market power between the two parties,
the supplier is strongly favored.
o
As long as she – perhaps due to certain legal restrictions – refrains from
first-degree price differentiation (i.e.: charging a price for each unit equal to the
corresponding maximum willingness-to-pay of the client),
o
the supplier is free to bring forward any “take-it-or-leave-it-offers” to improve her
bargaining position.
o
Credible (!) take-it-or-leave-it-offers are extremely valuable in bargaining.
They imply the following signal to the counterparty:
“Accept the proposed conditions even if that implies only insignificant improvements to
your own welfare / well-being – because there will be no re-negotiation.”
Thus, the “victims” of such offers may end up with a bargaining outcome that leaves
them (nearly) indifferent between “Deal or no deal”.
 In this setting, should the supplier operate with a uniform price to
maximize her profits?
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Variant 1 – Illustrating the Case by Cournot’s Model of Monopoly
In Cournot’s model, the combination of uniform price and quantity sold
that maximizes profits is determined by the following rule…
“Marginal revenue (MR) equals marginal cost (MC).”

Price
20
P(x)
For further details concerning pricing strategies in a monopoly,
please refer to textbooks in Microeconomics like
Snyder / Nicholson (Microeconomic Theory [2008], pp. 491)
15
10
P*(x)
Profit
MC
5
MR(x)
Quantity
10 000
20 000
30 000
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Variant 1 – With Uniform Price, the Supplier Faces a Problem…
However, the supplier can do better: A uniform price exceeding marginal
cost always implies two types of profit reductions…
A share of consumer surplus (generated by units sold for the uniform
price) is evading extraction,
Price
20
Despite the fact that the customer’s willingness to pay remains higher
than marginal cost, the uniform price excludes a number of mutual
beneficial transactions from being realized.
15
10
P*(x)
Profit
P(x)
5
MC
MR(x)
Quantity
10 000
20 000
30 000
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Variant 1 – The Two-Part Tariff Solves this Problem
In this setting, the two-part tariff implies the following two design
components.
Price
20
The customer pays an initial fare upfront
targeting for the full extraction of demand
surplus.
P(x)
15
Supplier’s
10 Profit
A fee per unit is charged to cover total cost.
5
MC(x)
Total Cost
Quantity
10 000
20 000
30 000
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Variant 1 – The Two-Part Tariff Solves this Problem
In comparison to the level of profit realized by this uniform pricing strategy,
the two-part tariff is able to increase profit to first-best optimum.
 Please note that the two-part tariff leaves the customer just indifferent
between agreeing the deal and staying away from it.
Price
20
15
P(x)
 Furthermore, the two-part tariff achieves the same level of
profit generated by first-degree price differentiation.
Profit
 Consequently, no further increase in profits by any
other pricing schedule is possible here.
10
 To sum up, the two-part tariff results in
first-best level of profits. (q.e.d.)
5
MC(x)
Total Cost
Quantity
10 000
20 000
30 000
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Variant 2 – A Two-Part Tariff Prevents Shirking
The Setting
•
You are visiting a foreign country for the first time.
•
You have just arrived at the airport.
•
Now you need a transfer to your final destination.
•
Should you take the bus or a taxi?
•
You decide to take a taxi.
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Variant 2 – The Coordination Problem
The taxi driver knows how to
get to your final destination.
You do not.
He is an
information insider.
You are an
information outsider.
A situation of
asymmetric information
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Variant 2 – The Consequence
A situation of asymmetric information
The cab driver has an incentive to exploit ex post
his information advantage (shirking).
If a linear tariff is employed, he most likely will not get you
to your destination taking the shortest route.
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Variant 2 – The Cab Driver’s Tariff Calculation
The fare must reflect…
The driver’s time spent on the job
Fuel consumption
Idle times (finding new clients)
“Wear and tear” of the taxi
The Tariff must be related
to the distance traveled / time spent by the driver.
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Variant 2 – Implications of a Linear Tariff
A linear tariff: For each mile traveled, the passenger pays
f = 1 Euro (and nothing else).
Revenue From Trip 1:
R1  f  d1
Revenue Lost by Searching
f = 1 Euro
d = Distance in Miles
Distance
Spent
Looking
for Trip
3Trip 3Stops Working
Distance
ofDriver
Distance
of
Distance
Spent
Looking
for
Trip
2Trip
Distance
of to
Trip
1 &
Driver
Starts
Work
Immediately
Finds
a2 Customer
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Variant 2 – A Linear Tariff Regime Results in Shirking
A linear tariff: For each mile traveled, the passenger pays f = 1 Euro (and
nothing else).
By using a linear tariff the cab driver is induced to exploit the asymmetric information by
maximizing the distance of each trip.
Let us assume the customers are completely ignorant.
f
Why does simply
increasing the fee
make no difference?
d
Additional
The Cab Driver
Revenue
Extends
Gained
Tripby
1’ Shirking
Distance
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Variant 2 – The Two-Part Tariff: Central Idea
The linear tariff offers the opportunity to avoid revenue losses resulting from looking for new
costumers.
The cab driver (homo oeconomicus!) will only stop cheating if behaving honestly secures
him at least the same total revenue.
Thus the gains by cheating must be distributed among all the trips the cab driver is able to
serve when behaving honestly (Condition 1).
This additional revenue must be paid independently of the corresponding trip distance
(Condition 2): Hence: An initial fare.
f
d
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Variant 2 – The Two-Part Tariff: Main Effects
Under certain conditions (see below), paying an initial fare induces the
cab driver to behave honestly because he then has the incentive …
to maximize the number of trips
instead of maximizing the distance of single trips.
However, the tariff’s impact on the driver’s behavior comes at a price:
Maximizing the number of trips implies an incentive for the driver to drive in a more
risky way in order to increase income.
Real Life: Number of cab drivers forced to participate in “corrective refresher courses”
to regain their driving license because of being caught driving too fast etc.?
Intermediate Result:
This case of taxi tariffs illustrates a general insight into the Economics of Information:
There is no such thing as a dominating coordination design. Fighting one problem
of asymmetric information by a corresponding contract element triggers another
incentive problem that must be taken care of by another specific contract element.
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Variant 2 –Two-Part Tariff vs. Linear Tariff: A Generalized Model
The Setting
Clients = “Clones”: All customers want to ride the taxi for the same distance
of d “Units of Distance” (UoD)
Fee to cover variable costs of transportation = 1 Euro per UoD.
Fixed cost of transportation = Zero.
Driver faces legal restriction of working time permitted per day = B UoD > 0.
Example:
The driver is allowed to work 12 h per day (no need for breaks assumed).
He can cover one UoD per minute by car.
 He has a maximum “distance budget” of 720 UoD available per day.
To find each new customer, the driver invests “search cost” of v UoD > 0.
Driver’s goal of Profit Maximization implies Maximization of Revenues
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Variant 2 –Two-Part Tariff vs. Linear Tariff: A Generalized Model
The Setting (contd.)
Modeling the situation of asymmetric information between cab driver and clients
• Driver (= Agent): Knows all possible routes to the client’s destination.
• Clients (= Principals): Have only a vague understanding of the localities, but at
least know for sure when they have arrived at their destination.
• Moral hazard: Driver has an incentive to exploit the asymmetry by shirking.
 The consequences from this constellation of moral hazard can be put more precisely
by interpreting the cab services as a specific type of a credence good.
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Variant 2 –Two-Part Tariff vs. Linear Tariff: A Generalized Model
The Setting (contd.)
 Credence goods can be exposed to the risk of an overtreatment by the agent
(Dulleck et al.: On Doctors, Mechanics and Computer Specialists … [2006]).
 The reason why taxi services may be hampered by this threat of an overtreatment can
be motivated by the following line of reasoning:
o
The clients’ level of information (at least after arriving at their destination) most
likely forces the cab driver to deliver them in any case at their correct destination.
o
However, the driver need not do this by the shortest / fastest route available.
 Therefore, in the following model the cab driver chooses his level of treatment
according to an “extension factor” k:
k  1, k  
• A “k
“k=1”
= k+implies
>1” describes
the driver
thechooses
maximum
the deviation
shortest route
fromdthe
– he
shortest
behaves
route d
honestly.
–
without arousing the clients’ suspicion of being cheated.
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Variant 2 – Revenue Components of the Linear Tariff
Determining Total Revenue per day (TR) under a linear tariff regime
Total Revenues = Distance of each single trip “times” Number of trips
Reminder: The analysis makes no difference between money (dimension) and
distance (dimension) because of 1 UoD = 1 Euro.
Actual distance of each single trip depends on the chosen extension factor by the
driver:
kd
Number of trips per day: Distance budget per day available divided by the sum of
actual distance of each single trip plus the search cost per client v:
B
v  k d
Combining the two components results in Total Revenue under a linear tariff regime,
TRLT:
TR LT 
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v  kd
k d
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Variant 2 – Determining Revenue Maximum for a Linear Tariff
Maximizing the driver’s revenues depends solely on k as his parameter of action.
Question: Does Total Revenue rise or fall by a marginal variation of k?
Solution: Answer requires calculating the first derivative of the TRLT function for k.
1
TR LT 


Bk d 2
 v  k d 2
B
v  k d


 k d  B v  k d   k d

 :h  x 

:y
x




 ? 1  B   v  k  d 
TR LT
k
 vB kdd  
Bkd2
 v  kd 2

Bd v  kd 
 v  kd 
2
2

:g  x 
d k  d  v Bkd d
 Bk d 2  Bdv  Bk d 2
 v  k d 2

Bdv
 v  kd 2
0
Result: Under a linear tariff regime, the driver maximizes his revenue by always choosing
the highest possible level of shirking– k+.
Pr oduct Rule : f  x   g  x   h  x   f '  x   g '  x   h  x   g  x   h '  x 


Chain Rule : u  y  x   '  u '  x   y '  x   g '  x 
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Variant 2 – Components of a Two-Part Tariff
As in the case of the linear tariff before, Total Revenue under a two-part tariff (TR2PT) is
determined by a product: Number of trips times Revenue per trip.
Furthermore, the fraction describing the number of trips remains the same.
However, in addition to the linear fee the driver receives the initial fare F.
Consequently, TR2PT represents a combination of the following two components:
TR 2PT 
B
v  k d
Number
of trips
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Initial
fare
kd )
Variable fee
(represents the
real dist an ce)
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Variant 2 – Revenue Maximum Under a Two-Part Tariff Regime
TR 2PT 
B
v  k d
Number
of trips
( F  kd )
Initial
Fare
Paying for
the Actual
Dis tan ce
Analogous to the calculations for the linear tariff, the first derivative of TR2PT for k can be
identified as:
TR 2 PT
k

dB F dk 
 v  kd 2
 ddkB v 
dB v  F 
 v  kd 2 
0
This result has the following implications for the driver’s decision to shirk:

The first derivative becomes Zero for v = F. This implies that the driver is indifferent to all
feasible k – i.e., between behaving honestly and any possibility to shirk.

For v > F the first derivative becomes positive. In consequence, the driver maximizes his
revenue by choosing the maximum level of shirking k+.

In the case of v < F, the first derivative is negative. In this situation, the driver behaves
honestly by choosing k = 1.
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 Cab driver‘s distance budget per working day: 720 UoD
Numerical Example
 Distance spent on looking for the next client: v = 5 UoD
 Factor of distance exaggeration available to driver: k  [1,3]
 (Variable) Charge per UoD: 1 Euro
SE, GE
800
Amount paid as initial fee F is sufficient
to induce honest behavior because of F ≥ v.
F=6>v=5
750
F=v=5
TR 2PT

B
v  k d
Number
of trips
( F  kd )
Initial
Fare
Paying for
the Actual
Dis tan ce
TR 2 PT
k

dB v  F  
 v  k d  2 
700
F=4<v=5
F=3<v=5
650
600
F=0<v=5
0
550
Amount paid as initial fee F is not sufficient to
induce honest behavior because of F < v.
500
1.0
1.5
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Conclusions
Setting up a two-part tariff may change the incentive structure for the taxi
driver: He can be induced to behave honestly even in view of an
information disadvantage for the client.
But overcoming constellations of asymmetric information comes with a
price: The information insider has to receive an information rent.
Reason: He has an information advantage, so he must be given an
incentive to voluntarily abandon his options to shirk by exploiting this
advantage (efficiency loss).
The paradigm of asymmetric information provides new insights into why
certain coordination mechanisms are employed in reality.
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Two-Part Tariffs in Reality: A First Test
Observation:
Today in Europe, the use of two-part tariffs by taxis is standard. In contrast,
why do nearly all Egyptian taxis operate under linear tariff regime?
•
Possible explanation No 1:

In Europe the supply side of the market for taxis is heavily regulated.

In Egypt the market can be described as highly competitive (with the exception of
certain “hotspots”).

Thus, establishing mechanisms of surplus extraction is easier in the more cartelized
European environment than under Egyptian conditions.
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Two-Part Tariffs in Reality: A First Test
Observation:
Today in Europe, the use of two-part tariffs by taxis is standard. In contrast,
why do nearly all Egyptian taxis operate under linear tariff regime?
•
Possible explanation No 2:

In Egypt regular taxis have a smaller chance to transport foreigners.

Furthermore, the population explosion during the last few decades has left its mark in
fast changing urban patterns.

Consequently, the agent-principal relationship between driver and client is often
reversed: The client has to tell the driver how to get to the destination.

A need for a two-part tariff to overcome problems of moral hazard is therefore
factually non-existent.
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Two-Part Tariffs in Reality: A First Test
Observation:
Today, the use of two-part tariffs by taxis is the rule in Europe.
In contrast, why do nearly all Egyptian taxis operate with linear tariffs?
•
Whether the existence of two-part tariffs in taxi business is better explained by a
coordination problem of asymmetric information or by the motive of surplus extraction,
cannot be decided here in a conclusive manner.
•
Therefore, further research has to be carried out in order to reach a convincing
answer.
•
To complicate matters further, it can be suspected that actually a mixture of both lines
of explanations is found to be the most convincing argumentation.
•
When the first client of a taxi was asked to pay a two-part tariff, perhaps the
explanation offered to them may have looked like this:
“No, I am not asking for some extra money (indeed I am). It is only to cover my
expenses for the time I had to wait for you / for the deviation from my regular trip
pattern. And besides, it keeps me from getting any wrong ideas about how to make up
/ compensate for these expenses.”
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Feedback
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Flaws?
Hints or Critique?
Contact: peter.baltes.bp “ad” vtg.admin.ch
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