Non Linear Contracting and Endogenous Buyer Power between Manufacturers and Retailers: Empirical Evidence on Food Retailing in France

Then, the firm f profits are

^π = ∑ ⁽^ws ^- μ^³^s(p)⁺ Σ2 ^f

s∈Gf sEG_f

= Σ2 (^w≡^- ^s)ʤ(p)⁺ 52 ⁽pj - w - ^ci)¾(p)^- Σ2 ^Fj - 22 ^π

s∈G_f j=l,..,J j⅛G_f r=l,.,R

Since, producers fix the fixed fees given the ones of other producers, we have that under resale
price maintenance :

max ∏
{^ⁱ₁Pⁱli∈Gf

^ ^m^max Σ2 ⁽^ws ^- μ_s)^ss(p) ⁺ 52 ⁽Pj ^-^wj ^-^cj⁾Sj⁽p)
^^p'ⁱⁱ∈Gf sEG_f j=l,..,J

^ max 5 (Ps - μs)βs(p) + 5J (Ps - Ws - Cs')βs(p')
P^pⁱ^ⁱ∈Gf sQGf s?Gf

and with no resale price maintenance

max ∏

{^pi,^wi}i∈G_f

& ^m^max 52 ⁽w ^-^ps⁾^ss⁽P^{) +} 52 ⁽Pj ^- w ^-^cj⁾^sj⁽P⁾( Wi к ∙_cr, ‘ ‘ *

^w^{i G}f _sQGf j=l,..,J

^maχ V ⁽p_s ^- μ_s)s_s(p) ⁺ V ⁽p_s ^- W ^-^c_s')s_s{p)

^W«G, sCGf syGf

Then the first order conditions of the different two part tariffs models can be derived very simply.

7.3 First stage estimation

Table 7 : First stage regression OLS regression of prices

7.4 Additional formula for the demand model (not for publication)

Remind that the average choice probability of buying j at period t is :

^sjt

1 ⅝ ⅝N

N 2^_l=ι ^P'^jt

1 v^ʌ' [

N 5 √ ■ ι I ^Fijt⁽^ai⁾^f {,a_i)da_i

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