��������������������������
ff !"#$%& !,!,!,!!
= NN ! VV !"# !,!,! αα + VV !"#$!"%"&# !,!,! 1 − αα , kk = 1
ff !"#$%!& !,!,!,!!!!
, ∀ kk ≠ 1 vvvvhiiiiiiiiii yyyyyyyy
ff !"#$%!& !,!,!,!
=
0 , |
aa = llllllll aaaaaa gggggggggg |
|
VV !,!,!,! ττ
!"#
|
, |
aa = ooooheeeeeeeeeeee |
vvvvhiiiiiiiiii yyyyyyyy
VV !"# !,!,! =
VV !"#$!"%"&# !"# !,!,! − VV !,!,!
!"!#!$% ττ !"#$ !"#$"!%&'( dddd + VV !,!,!
VV !"#$!"%"&# !,!,! =
0 , ∀ ii = jj ∧ ( vv = uuuuuuuuuuuuuuuuuuuuuu ∨ vv = uuuuuuuuuuuuuuuuuuuu )
!"#$!"%"&# ! ff !,!,!,!
!"#$!"%"&# !,! ff !,!,!,!
, ooooheeeeeeeeeeee
VV !"# !,!,! =
Where N i is the vehicle sales of platform i in vehicles per year , VV !,!,! is the ma-
!"#
trix of views of first time vehicle buyers , and
!"#$!"%"&#
is VV !,!,! the matrix of views of existing owners of vehicles , α is fraction of first owners in the vehicle sales , τ view perception is time to change the views of first time buyers based
αα = 0.25
1 |
0 |
0 |
|
|
0 |
1 |
0 |
, |
ii = GGGGGG |
0 |
0 |
1 |
|
|
0 |
1 |
0 |
|
|
1 |
0 |
0 |
, |
ii = HHHHHH |
0 |
0 |
1 |
|
|
0.95 |
0.05 |
0 |
|
|
0.05 |
0.85 |
0.1 |
, |
ii = SSSS GGGGGG |
1 |
0 |
0 |
|
|
VV !"!#!$% !"!#!$% !,!,!,! = II !" VV !,!,!
on the prevailing opinions of retired vehicles owners , and τ age is the aging chain step in years .
In order to ensure the stocks are initialized in equilibrium , the following equations are used to compute the initial values , assuming four age groups
VV !,! = VV !,!,!,! !
ρρ !! ττ !"# 1 + ρρ !! ττ !"# 1 + ρρ !! ττ !"# , aa = aa !
1 + ρρ !! ττ !"# 3 + ττ !"# ρρ !! + 2ρρ !! + ρρ !! ρρ !! ττ !"#
II !" = FF ! ×
|
VV !,!!
1 + ρρ !! ττ !"#
|
, |
aa = aa !
|
|
VV !,!!
1 + ρρ !! ττ !"#
|
, |
aa = aa !
|
VV !,!! ρρ !! ττ !"# , aa = aa
|
|
! |
For other aging steps and number of links in the aging chain , the equations for initial equilibrium conditions become more complicated and are not included in this paper .
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