Always wanted to post this but never had the time to plot the graph.
pax.png 4.1KB 1 downloads
Red dots represent passenger preferences. An airline choose to position itself at Y and C. Passengers will purchase tickets where price is lower and service quality is better than their personal expectations. Hence all passengers in area y goes to Y seats and c goes to C seats. e will be split according to the ratio of the distance between E-Y and E-C. Passengers in white area are untapped market.
Given passenger distribution function f(n) (in this graph I use 96/(4*x*x+5*y*y-8*x*y-512*x+384*y+20481) anyone has a better equation?), volume of y can be obtained by integration for f(n) over p to r and 0 to q; c by integrating f(n) over r to ∞ and q to s.
This is not just for distribution of passengers over different classes within the same flight, but can also be used to model competition between airlines.