Re:Twice as happy customers means half the marketing spend
by eterm on Friday June 23, 2017 @05:16AM
(#14617907)
That's a good point. I guess with a background in maths it's "obvious" that a system with constant in-flow and an out-flow proportional to the volume would approach equilibrium, but that perhaps isn't as obvious to others.
I guess it's perhaps also worth pointing out then that the same equilibrium is reach from either side. If you start with a much higher volume of subscribers you'll reach the same equilibrium through attrition down to that number also.
Re:Twice as happy customers means half the marketing spend
by infinite8s on Friday June 23, 2017 @07:18AM
(#14618338)
That's only obvious if you remember differential calculus.
One could assume that "well if I keep on going my customer count will keep on going up... right?" This is showing that it won't.
Bonus pedantry: your proof just showed that _if_ there's a steady state, then that's the steady state. Turns out that you'll always get the steady state because of "maths" but if you replace 50% with 0% there's no fixed point.