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@