RDP 2012-03: ATM Fees, Pricing and Consumer Behaviour: An Analysis of ATM Network Reform in Australia
Equation (C2)
∂
L
i
∂
σ
i
=
N
ρ
j
i
(
F
i
+
(
f
i
−
τ
)
ρ
i
i
−
c
ρ
i
i
−
m
)
−
N
(
ρ
j
i
)
2
(
σ
i
+
τ
−
c
)
+
N
j
(
ρ
j
i
−
σ
i
+
τ
−
c
2
l
)
−
λ
j
ρ
j
i
=
0
MathType@MTEF@5@5@+=feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=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@85EB@
Equation (C3)
∂
L
i
∂
F
i
=
N
i
−
N
(
F
i
+
(
f
i
−
τ
)
ρ
i
j
−
c
ρ
i
i
−
m
)
+
N
ρ
j
i
(
σ
i
+
τ
−
c
)
−
λ
i
=
0.
MathType@MTEF@5@5@+=feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=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@6C19@