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

Γ of wholesale prices :

7 + Γ = - (∑_r I_rS'_pI_rSpI_r + ∑._f S'_pι_is_p} ^-

(∑_r IrSPIr [Φ) - SpIrΓ] + ∑_f spIf [_s(p) - Sp(I - If )Γ])       (14)

With RPM, there is a continuum of equilibria depending on the vector of wholesale prices w. We
will see in section 4.2 that further assumptions or restrictions can help characterize and identify
some of these equilibria from observed data.

3.2.2 Without Resale Price Maintenance

We now present the case where where manufacturers cannot apply RPM. Then, whether retai-
lers have endogenous buyer power or not makes a difference on the equilibrium retail prices.

In absence of RPM, the retailers prices p^fr (w) are out of equilibrium prices different from the
retail prices in equilibrium. The first order conditions of the maximization of the profit of f (11)

with respect to wholesale prices w_i, j ∈ Gf, are then :

In matrix notation, the previous first order conditions give

0 = If P_wSpIf Γf + If P_ws(p) - If F>l_s(p^f ) + If P_wSp7 - If P_wSp7^f

and P^,W is the matrix of first order derivatives of retail prices pp^r(j>(w) (for j = 1,.., J) with respect
to wholesale prices w.

Thus the wholesale margins of products of manufacturer f are

Γf = - [IfPwSpIf ' (l_fPws(p) - IfPWstf) + IfPwSp7 - IfPwSp7^f)        (15)

16

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