Present value
In the calculations of the present value of the future consumer surplus from the given product
class, we used the sum of an infinite geometric row starting t periods from now, At.
t=0
1 + r R R
------= R + A, = R +-----+ A7
r 1 1 + r 2
∞ P
A - l.
t=2 1 + r
Transforming F π,r,a,pi,p2
The expected payoff of trying the new brand in the market, F π,r,a,p-x,p2 , is the expected
net value of trying the new brand, π v2-a-p2 + vx-pi Ir + l-π v2+a-p2 1 + r /r,
minus the net value of continuing to purchase the incumbent brand, vi-pl 1 +r Ir.
F π, r, a, pi, p2 can also be expressed as the value of buying a high quality new brand
instead of the incumbent brand, from this period on multiplied by the probability that the new
brand is of high quality 1-π v2+a-p2- v1-∕>1 1 + r /r, minus the value of buying the
incumbent brand instead of the new brand if the new brand is of low
quality vi- pl- v2-a - p2 /(1 + r), multiplied by the probability that the new brand is of
low quality, π.
+ l-π v2+a-p2 1 + r /r- v1 -pλ 1 + r /r
+ l-π v2+a-p2 1 + r Ir- l-π + π vx-px 1 + r /r
.
vx-px Ir + ∖-π v2+a-p2 - vx-px 1 + r /r
∖-π v2+a-p2 - vx-px 1 + r Ir
F ∙ =π
v2-a- p2 +
vi-Pi Ir
(A2)
v2 - a - p2 +
v2 - a - p2 +
v2-a- p2-
V1-Pi /r
1- 1 + r
V1-jP1 +