EDITOR’S PROOF
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partial derivatives, I prove thatqhas a strictly positive effect onT whenever for
πRI∈[π,π].
To study the effect ofπRIwe must note that it has two effects onT: a direct effect,
and an indirect effect through its effect onS. In total, we have thatdπdTRI=∂π∂TRI+
∂T
∂S∂S
∂πRI. It is easy to calculate that∂T
∂πRI=−S[XRE( 1 −πL)−XLπL]
( 1 −πL)(πRI+S)^2 which is strictly
negative. On the other hand I just calculated that∂T∂Sis strictly positive, and we
know from Lemma4 that∂π∂SRIis non-positive. We therefore have thatdπdTRI<0 and
Tis strictly decreasing withπRI.A.10 Proof of Theorem 5
Note from Lemma2 thatS=0 whenπRI∈[π, 1 ). And remember thatT ≡
S[XRE( 1 −πL)−XLπL]
( 1 −πL)(πRI+S). Hence, whenπRI∈[π,^1 )we have thatT=0 for any value
of the other parameters.References
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