Journal on Policy & Complex Systems Volume 1, Number 2, Fall 2014 | Page 134

��������������������������������������������������������������������������������������� j is
Total marketing effect for a platform
MM ! = MM ! !"!#!$% + MM ! !""#$#%!&'() − MM ! !"#$%&&'($ dddd
MM ! !""#$#%!&'() = SS ! σσ
1 yyyyyyyy
MM ! !"#$%&&'($ =
MM ! ττ !"#$%&'() 1 yyyyyyyy where S j is the total marketing spending per platform j in $ MM / year , σ is market effectiveness in 1 /$ MM , and τ marketing is marketing forgetting time in years .
Given all the possible mechanisms of view change listed above , the full equation for the flow changing stock of vehicles
V i , j , v , a is
ff !,!,!,! = ∆ !"#$%"& !,!,!,!,! + ∆ !"# !,!,!,!,! + ∆ !"#$%&'() !"#$%&&'($ !,!,!,!,!
+ ∆ !,!,!,!,!
!
− ∆ !"#$%"& !,!,!,!,! + ∆ !"# !,!,!,!,! + ∆ !"#$%&'() !"#$%&&'($ !,!,!,!,!
+ ∆ !,!,!,!,!
!
Since ∆ i , j , v , a is the outflow , the first term depletes the stock of vehicles having view v to all other potential views , and the second term fills stock of vehicles having view v with the inflow from all other views . Each age group has the outflow of retirement of vehicles ff !"#$!"%"&# !,!,!,! = VV !,!,!,! ρρ ! vvvvhiiiiiiiiii yyyyyyyy ρρ ! = 0.001 , 0.01 , 0.1 , 0.3
1 yyyyyyyy where ρ a is retirement fraction for each age group .
The inflows and outflows to establish the mechanism of aging along the aging chain are given as
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