PRICING AND REVENUE MANAGEMENT

Beirut Congestion Charges

Report

Mohamad Kassab

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Executive summary:

The purpose of this report was to explain the approach we used in solving the BCC case

and state all the assumptions used and conclusions found.

We deduced the percentage of motorists (demand) entering the zone during peak periods

and those entering during off-peak periods and from the 2 percentages we formulated two

demand functions.

With an objective to maximize revenues, we tried to find the flat rate which BCC would

charge for motorists entering the new charged zone taking into consideration the data

collected from the survey about the willingness to pay of people and the 2 demand

functions estimated in earlier stage of the report. Then we worked on finding a single

price to charge in peak and off-peak periods of the day with an objective to minimize

CO2 emission while generating a level of revenues which will cover the 500 Million.

And in the final scenario, we solved for 2 different prices (higher for peak time and lower

for off-peak) subject to minimizing CO2 emissions and generating a minimum of 500

million revenues.

And finally, we tackled some broader issues and we wondered how taxi drivers and

public transportation might be affected from such a fee which they have to pay to enter

the charged zone. And we briefly discussed how students might also be affected.

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Optimization:

We will be assuming that each peak hour will be equivalent to 4 off peak hours

since the number of cars that enter during the periods of 7:00 am to 9:00 am and 4:00 pm

to 6:00 pm is numerous due to several factors such as people going to work and students

going to their schools and universities in Beirut in the morning and leaving later in the

afternoon. Since we have 4 peak hours, 4*4 = 16 and we already have 20 off-peak hours

so now we have a total equivalent of 36 off peak hours.

Taking this ratio into consideration, we can estimate the proportion of our total

demand per day that will go at peak hours and at off-peak hours. For our peak hour

demand, we have ((4*4)/36)) = 44.44% and for the off-peak hours we have, (20/36) =

55.56%. Thus our portion of demand allocated is as follows:

Peak hour portion of demand: 192000 * 44% = 84480

Off-Peak hour portion of demand: 192000 * 56% = 107520

Since we have our ratio we can get the portion of demand that will go at peak

hours and the portion of demand that will go at the off peak hour thus estimating 2

demand functions. For a second assumption, we will take the willingness-to-pay as

normally distributed thus having the median equal to the average willingness-to-pay.

Therefore we can take 2 points and estimate the slope; the 2 points are at p=0 where our

demand will be the intercept at y-axis equal to the total portion of demand calculated

earlier, and p=average willingness to pay where demand is half the total portion.

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Average WTP

peak off-peak

Average 8 5

Peak hour demand function: Y = aX + b 2 points (0, 84480)

*b = 84480 (8, 42240)

*│a│ = 84480 – (84480/2)

8 – 0

= 5280

----> Y = 84480 - 5280X where Y is the demand and X is the Price

Off-Peak hour demand function: Y = aX + b 2 points (0,107520)

*b = 107520 (5, 53760)

*│a│ = 107520 – (107520/2)

5 – 0

= 10752

----> Y = 107520 - 10752X where Y is the demand and X is the Price

4

Flat rate-Maximizing revenues:

Formulating these demand functions on excel with our revenue formula of R(p) =

d(p)*p which we want to maximize, and entering our variable cell which is price, we get

our maximum revenue under non-linear formulation.

Thus, a single price of 6,000 LBP will be optimal generating revenues of $574,850.

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Single Price-Minimizing CO2 emissions:

If we change our objective from maximizing revenues to minimizing CO2

emissions while covering at least 500,000,000 LBP in costs we will remodel our

formulation to include CO2 emissions as our objective to minimize in addition to an

operating cost constraint of 500,000,000 LBP to be covered.

Based on the scientific study, CO2 emissions depend on the average speed of the

cars, and it is 30-0.0625*(thousand cars). We will take the demand we have from the first

formulation to estimate the average speed:

Peak Average Speed: 30-0.0625 * (d(p1)/1000)

Off-Peak Average Speed: 30-0.0625 * (d(p2)/1000)

By changing our variable cell which is still the single price for both peak and off-

peak, our demand will thus change and speed average speed will change. If speed

is less than or greater than 25 we have different levels of CO2 emissions. Relying

on the parametric relationship between speed and emission; as speed increases in

km/h, CO2 emissions decrease by g/km.

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If speed < 25: CO2 Emissions = 616.6-16.7*Speed

If speed > 25: CO2 Emissions = 235.7-1.4*Speed

We then sum up the CO2 emissions for both peak and off-peak hours to get the

total CO2 emission per day, and minimize this number by changing the price and

making sure the sum of motorists during peak hours does not exceed 84480, and

the sum of motorists during off-peak hours does not exceed 107520 while

maintaining revenues of at least 500,000,000 LBP.

Ratio of Demand (%)

44% 84480

56% 107520

Price 8.15

Using the demand from

previous calculations and

adding the cost constraint:

Demand Revenue

d1p 41454.51564 337803.15

d2op 19904.46821 162196.85

Total 61358.98385 500000.00

Operating Cost

500000

Average speed Peak Average Speed Off-Peak

27.40909277 28.75597074

CO2 emission(<25) 158.87 136.38

CO2 emission(>25) 197.33 195.44

CO2 Emission 197.3272701 195.441641

Total Emission 392.7689111

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We can minimize our CO2 emissions to 392.76 g/km for both peak and off-peak

summed up at a price of 8,150 LBP while maintaining our breakeven profit.

Variable Prices-Minimizing CO2 emissions

Under a price constraint of 8,000 LBP for off-peak hours while having to charge

higher for peak hours as well as maintaining our operating cost 500,000,000 LBP, we can

remodel for price of peak hours where our objective remains minimizing CO2 emissions

but subject to:

Price of Peak hours ≥ 8,000

Revenues ≥ 500,000,000

Demand of Peak ≤ Portion of 84480

Demand of Off-Peak ≤ Portion of 107520

Price of Peak hours ≥ 0

We know the demand for off-peak here because we have the price at 8,000 LBP and it is:

107520 – 10752*8 = 21504 but we don’t have price for peak so we can formulate:

Ratio of Demand

(%)

44.00% 84480

56.00% 107520

peak 0 84480

8 42240

Price Peak 9.37

slope 5280

Price Off-Peak 8

Demand Revenue

off peak 0 107520

D1(p) 34991.09939 327968.00

5 53760

D2(op) 21504 172032.00

slope 10752

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Total 56495.09939 500000.00

Operating Cost 500000

Average speed Peak Average Speed Off-Peak

27.81305629 28.656

CO2 emission(<25) 152.12 138.04

CO2 emission(>25) 196.76 195.58

CO2 Emission 196.7617212 195.5816

Total Emission 392.3433212

We minimize CO2 emissions at a price for peak hours of 9,370 LBP while

keeping price of off-peak at 8,000 LBP and breaking even. Using this variable pricing

approach, our profit is 0, since we broke even at 500,000,000 LBP cost = 500,000,000

LBP revenue since our objective wasn’t to maximize our revenue but to minimize our

CO2 emissions.

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Beyond question discussions:

Having read the case and solved it over the past week, we as a group had a lot to say

about many topics that surround the idea of congestion charges. These topics would

sometimes advocate the essence of the case and at other times they might conflict with

the essence of the case; thus these topics should be tackled in order to provide a better

picture.

Monopoly and Elasticity!

In this case, the government is acting a monopoly since government regulations is the

most obvious case of monopoly and the only case that can stand in reality. Given the fact

that the market is a monopoly, then the economy is perfectly inelastic, which means that

the changes in price leads to a decrease in demand but an increase in total profit because

the proportion of decrease in demand is less than the proportion of increase in price.

Having this as a starting point and assuming that the government should not be seeking

only profits regardless of the situation of the citizens we tackle the following points:

a) Taxi cabs.

Given the situation we are put through, and the fact that whenever a car enters the

congestion are the driver is charged with a certain fee, it is important to tackle the

problem of taxi cabs since they enter to these areas multiple times a day and thus it is not

ethical to charge them for every entrance.

The situation in Lebanon provides the following conclusion: Cab drivers are among the

poorest people in Lebanon. So starting from here it is really not in the advantage of them

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to charge them for every entrance to the congestion area and thus some regulation should

be enforced at this point to ensure that cab drivers don’t make any move against the

government and thus cause the whole country problems, by doing strikes for example.

One solution to this problem is having cab drivers to pay a fee at the beginning of each

year and thus would ensure that they pay for their entrance but once and at a rate which is

really much lower than the official daily rate. By doing this we will solve the problem of

the cab drivers and the government. For more insight about the problem, the government

should install cameras that can detect color and thus won’t charge cars with a red plate.

b) Public transportation.

By implementing this plan, the city of Beirut would be urging people to use

public transportation which has huge advantages on different aspects of the economy and

lifestyle. By urging people to use public transportation the city would be benefiting

different ministries in Lebanon, including the transportation ministry and the ministry of

environment because it would no doubly decrease the emission of CO2.

c) Students.

How can we solve the problem of students? Students come to Hamra, included in

the congestion area, every day to attend universities such as AUB and LAU. So the

question that arises here is the following: Should we charge students given that they are

not included yet in the working force?

As a group we believe that students should be exempted from paying the fees of

congestion because they are still not considered in the workforce and thus don’t have a

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source of income other than the pocket money they take from their parents. But how can

we implement this? Student would be required to pick up a serial number from the

ministry of transportation which enables them to cancel the fees they are charged for on

the internet. So basically they need to log in to the internet and instead of paying the fees

they enter their serial code and the fees would be cancelled. Yet to ensure that no one can

do it other than students, every 4 months the serial number expires and the students have

to go to the ministry again and get a new serial number while proving that they are still

enrolled in the university or school.