Bugs / [Not a bug] Market share model
« on: March 25, 2008, 10:54:56 am »The number of passengers is a constant. Let's represent it by the letter c.
Also, let's represent the number of available seats in all companies before you increased the frequency by a and the number of available seats in all companies after you increased the frequency by A.
Now, we have A>a, which is obvious. Therefore, 1/a>1/A (a and A are positive numbers). Let's multiply it by c and we have c/a>c/A. c/a and c/A are the number of passengers per available seat before and after the change, respectively.
Obviously, they are proportionate with the interest in each available seat (let's use letters i and I). Therefore, i>I. Since the optimal price (let's use p and P) is proportionate to the interest in each available seat, p>P is also valid. Hence, the optimal price before you increased the frequency was bigger than after you increased the frequency. Hence, you needed to lower your price.
Hope this helps!