The name is absent

With regard to incoming calls there is a positive effect on the mark-up of termination
rates over per-unit costs as termination rates increase due to i’s investments while ter-
mination costs remain unaffected by i’s investments. Nevertheless, total calling minutes
are reduced as competitors’ off-net prices increase in j’s termination rates. Taking a
look at the terms in large brackets it is unclear whether the individual demand term
exceeds the average or not. With c_-j = c we find for b_-j small, i.e. for calls from smaller
providers terminating on network j , that the expression in brackets is positive. To sum
up, the effect of i’s cost-reducing investment on profits from incoming calls from other
providers to a provider j is ambiguous. While the wholesale price effect is positive due
to the demand increase from network i, the total demand effect from the other networks
is negative. Thus, without further assumptions on the demand functions no distinct
proposition concerning the indirect investment effect could be derived.

A.2 Calculation of the investment effect on own and
competitors’ termination rates

In contrast to the linear pricing situation we fix per-unit prices at per-unit costs, pj,i =
cj + ti, and get for i’s profit from incoming calls:

π_jⁱ_,i = si _jsj(ti - ci)(a - bjpj,i)

= si^P_jsj(ti - ci)(a - bj(cj + ti))

Deriving (22) with respect to t_i yields:

_ ∑j (^{a - b}jcj)   ci

ⁱ =  2 Pj sj bj  +2

Deriving ti with respect to investments yields:

∂ti _ ci(ki)

∂ki =  2

Similarly, we get for the competitors’ termination rates change due to i’s investments:

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