BAA is a private company that operates some of the largest airports in the Unite
ID: 1101975 • Letter: B
Question
BAA is a private company that operates some of the largest airports in the United Kingdom, including Heathrow and Gatwick. Suppose that BAA recently commissioned your consulting team to prepare a report on traffic congestion at Heathrow. Your report indicates that Heathrow is more likely to experience significant congestion between July and September than any other time of the year. Based on your estimates, demand is Q1d = 600 - 0.25P, where Q1d is quantity demanded for runway time slots between July and September. Demand during the remaining nine months of the year is Q2d = 220 - 0.1P, where Q2d is quantity demanded for runway time slots. The additional cost BAA incurs each time one of the 80 different airlines utilizes the runway is
Explanation / Answer
In the summertime:
If you were not constrained....
Q = 600 - 0.25 P
P = 2400 - 4Q
R = Q*P
R =2400 Q - 4 Q^2
marginal revenue
dr = 2400 - 8 Q
equals marginal costs
1100 = 2400 - 8 Q
8Q = 1300
Q = 162.5 -- double current capacity.
Since we can't fly that many planes.... what is the pricing such that Q = 80
P = 2400 - 4*80 = 2080.
Since Heathrow can't service this capacity, the optimal summer time pricing would be at a level such that demand = 80
P = 2400 - 4*80 = 2080.
Off peak pricing
P = 2200 - 10Q
R = 2200Q - 10Q^2
dr = 2200 - 20Q
1100 = 2200 - 20Q
Q = 55
P = 2200 - 550
P = 1650
Should Heathrow consider the runway expansion?
The optimal use is below capacity during non-peak months. So, we look at the profits foregone in the peak months and see how long it will take to recoup the cost.
Daily revenue at maximal pricing for current capacity
80*2080 = 166,400
Daily profit at current capacity
80*(2080 - 1100) = 78,400
Seasonal profit.
78,400 * 91 = 7.1 million
Supposing capacity was doubled to 160 and priced optimally for that load -- 1760
Daily profit at expanded capacity
160*(1760 - 1100) = 105,600
Seasonal profit
9.6 million
change in profitability = 2.5 million
number of years to break even
6 billion / 2.5 million = 2,400 years... probably not worth the investment...
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