Consider an international airline that has separate check-in counters for business class and economy customers. There is one business class counter that gets 30 customers per hour on average while there are 2 economy class counters that together get 95 customers per hour on average. All economy class customers form one queue in front of the 2 economy class counters.
The consumer's willingness to pay a particular ticket price depends on the average waiting time at the check in counter. Usually, this average waiting time is known to them through information posted by the airline and hence they can factor this in their purchase decisions. For simplicity, we will assume that the airline does not lie about these waiting times (although that can be an issue in the real world). Customers evaluate purchase decisions based on many other attributes of airline service, which we will assume to be unchanged during the course of this problem. Restricting attention to just the impact of waiting time at check in counters, the willingness to pay for different types of customers can be calculated. We are only looking at one particular route from Washington DC to Paris. This is a one way trip.
For the business class customers (in $):
Price = 10000 - 100*T
For the economy class customers (in $):
Price = 2000 - 20*T
Where T = waiting time in minutes at check-in in Washington DC.
All inter arrival times and processing times are exponentially distributed. Any check in counter can process 50 customers per hour on average.
A proposal is underway to combine the business class and economy class counters, primarily as a way to assuage economy class customers about discriminatory treatment.
Question:
Would you support this proposal purely based on revenue considerations? Show all calculations to get full credit.