Tariffs in Taxi Business: Surplus Extraction or Moral Hazard or both?

1. Tariffs in Taxi Business: Surplus Extraction or Moral Hazard or both? Souvenirs du Caire / 2007-2010 Peter T. Baltes (MILAK) / Ehab Yassin (GUC)

2. For their kind help we thank:Walter Furter, Odilo Gwerder, Daniel Lätsch and Maximilian Zangger Cairo by Google Earth Birmensdorf / Cairo 2007-2010

3. 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 employedin taxi business? Microeconomics offers two possible explanations.

4. Outline of the Following Analysis First variant of explanation:This pricing scheduleallows 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.

5. 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, … • she does not only know her own cost function(constant marginal cost & fixed cost of Zero are assumed here), • but she also exactly knows the (individual) demand function of her client.

6. 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. • As long as she – perhaps due to certain legal restrictions – refrains fromfirst-degree price differentiation (i.e.: charging a price for each unit equal to the corresponding maximum willingness-to-pay of the client), • the supplier is free to bring forward any “take-it-or-leave-it-offers” to improve her bargaining position. • 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?

7. 20 15 10 5 10 000 20 000 30 000 40 000 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).”  For further details concerning pricing strategies in a monopoly, please refer to textbooks in Microeconomics likeSnyder / Nicholson (Microeconomic Theory [2008], pp. 491) Price P(x) P*(x) Profit MC MR(x) Quantity

8. 20 15 10 5 10 000 20 000 30 000 40 000 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 evadingextraction, Price 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. P*(x) Profit P(x) MC MR(x) Quantity

9. 20 15 10 5 10 000 20 000 30 000 40 000 Variant 1 – The Two-Part Tariff Solves this Problem In this setting, the two-part tariff implies the following two design components. Price The customer pays an initial fare upfront targeting for the full extraction of demand surplus. P(x) Supplier’sProfit A feeper unit is charged to cover total cost. MC(x) Total Cost Quantity

10. 20 15 10 5 10 000 20 000 30 000 40 000 Variant 1 – The Two-Part Tariff Solves this Problem In comparison tothe 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 agreeingthe deal and staying away from it. Price 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. Profit byFirst-Degree Price Differentiation =Profit by Nonlinear Tariff • To sum up, the two-part tariff results in first-best level of profits. (q.e.d.) MC(x) Total Cost Quantity

11. 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.

12. Variant 2 – The Coordination Problem • You do not. The taxi driver knows how to get to your final destination. He is aninformation insider. You are aninformation outsider. A situation ofasymmetric information

13. Variant 2 – The Consequence A situation of asymmetric information The cab driver has an incentive to exploit ex posthis information advantage (shirking). If a linear tariff is employed, he most likely will not get youto your destination taking the shortest route.

14. 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 relatedto the distance traveled / time spent by the driver.

15. Distance of Trip 1 Distance Spent Looking for Trip 2 Distance of Trip 2 Distance Spent Looking for Trip 3 Distance of Trip 3 Variant 2 – Implications of a Linear Tariff A linear tariff: For each mile traveled, the passenger paysf = 1 Euro (and nothing else). Revenue From Trip 1: Revenue Lost by Searching f = 1 Euro d = Distance in Miles Driver Starts to Work & Immediately Finds a Customer Driver Stops Working

16. 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 Revenue Gained by Shirking The Cab Driver Extends Trip 1’ Distance

17. 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

18. 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.

19. 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 distanceof 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 availableper 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

20. 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.

21. 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 whytaxi services may be hampered by this threat of an overtreatment can be motivated by the following line of reasoning: • 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. • However, the driver need not dothis 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: • A “k=1” implies the driver chooses the shortest routed – he behaves honestly. • A “k = k+ >1” describes the maximumdeviation from the shortest routed – without arousing the clients’ suspicion of being cheated.

22. 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: 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: Combining the two components results in Total Revenue under a linear tariff regime, TRLT:

23. 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. Result: Under a linear tariff regime, the driver maximizes his revenue by always choosing the highest possible level of shirking– k+.

24. 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:

25. Variant 2 – Revenue Maximum Under a Two-Part Tariff Regime Analogous to the calculations for the linear tariff, the first derivative of TR2PT for k can be identified as: 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.

26. 800 750 700 650 600 550 500 1.0 1.5 2.0 2.5 3.0 • Cab driver‘s distance budget per working day: 720 UoD • 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 Numerical Example SE, GE Amount paid as initial fee F is sufficientto induce honest behavior because of F ≥ v. F = 6 > v = 5 F = v = 5 F = 4 < v = 5 F = 3 < v = 5 F = 0 < v = 5 Amount paid as initial fee F is not sufficient to induce honest behavior because of F < v. k

27. Conclusions Setting up a two-part tariff may change the incentive structure for the taxidriver: 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 insightsinto why certain coordination mechanisms are employed in reality.

28. 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.

29. 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 explosionduring 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.

30. 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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