2. 1
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.
3. 2
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.
4. 3
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
5. 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.
6. 5
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.
7. 6
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
8. 7
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
9. 8
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.
10. 9
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
11. 10
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
12. 11
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.
