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

The theoretical cross-price elasticity of demand of product j with respect to price of product к is

then

Дуй

_ ∂s_j p_k _ Pk 1 ]_ ∙^-'∙ ∂Pjj∖

∂pk Sj    Sj ∖N ²-^i=ι ∂pk J

_ ^pk (N ∑i=ι (/ ^aibij^t(ai)Likt(a_i)f (a_i)⅛))

which can be simulated using

^sEj^{k _ p}k N ∑*=ι (⅛ ∑<∙=ι ^a^^(аг)цы(^аг))

Similarly, the theoretical own price elasticity is

E∙ ∙

^Ejj

^dsj p±
∂pj ^sj

^pj A ¹ ∖^'' ^dPij ʌ
Sj ∖N ^z-^≈=∣ ∂pj )

_s. Nn ^ ʌ; 1 ʃ ^ai^Lijt{^ai⁾ (1   ^Lijt{^ai⁾'⁾ f (щ^а^^

which is simulated using

^sEjj _ -^pΓ [N ∑Γ ₁ (⅛ Σ^ ₁ a^rLijt(a^r) (1 - L_l3t(^a)))
Sj   IN      ^— ¹∖^-ZL     > —¹                                   J

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