Question

Let us suppose that the market size is 90,000 for a product with innovation rate 0.018 and imitation rate of 0.25, determine the total number of users during time period 0.?

Pls show me how to calculate by step

Answer 1

Total number of potential buyers is say m which is given here as 90000

Innovation rate, p = 0.018

Imitation rate, q = 0.25

The total number of users at any given time t is given by N(t) = m x (1- e^(-(p+q)*t)) /(1+(q/p)*e^(-(p+q)*t)

e^(-(p+q)*t) = e^(-(0.018+0.25)*t) = e^(-0.268*t)

q/p = 0.25/0.018 = 13.889

Therefore, N(t) = 90000 x (1-e^(-0.268*t))/(1+13.889*e^(-0.268*t))

Now suppose we want to estimate the total number of users at say t = 0.5

Then N(t) = 90000 *(1-e^(-0.138)) / (1+13.889*e^(-0.138))

i.e. N(t) = 90000 *(1-0.871)/( 1+13.889*0.871) = 90000* 0.129/ (1+ 12.098) = 11610/ 13.098 = ~886 users at t= 0.5