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

Zero wholesale margins : Fixing the vector of wholesale margins Γ_t to zero is sufficient to get
identification of total margins and thus also retail and wholesale margins which are zero in this
case. This

This corresponds to the particular equilibrium where wholesale prices are such that w*_st = μ_st
for all s, t that is Γ_t = 0, Vt. Simplifying (14), it implies that

Уt = - (∑_r ¹r^s'pISpIr + ∑_f S'_pIf Sp ) (∑_r I_rS'_p£ + ∑_f S'_pIf ) _β(pt)      (19)

Remark that in the absence of private label products, this expression would simplify to the case
where the total profits of the integrated industry are maximized, that is

7t = ^-sP ^ls(Pt^{)                                       (20)}

because then ɪ)f If = I and I_r = 0.

This shows that two part tariffs contracts with RPM allow to maximize the full profits of the
integrated industry if retailers have no private label products, the buyer power of retailers shifting
simply the rent between parties. Rey and Vergé (2004) showed that, among the continuum of
possible equilibria, the case where wholesale prices are equal to the marginal costs of production
is the equilibrium that would be selected if retailers can provide a retailing effort that increases
demand. In this case, if the manufacturer allows the retailer to be the residual claimant of his
retailing effort, it leads to select wholesale prices equal to marginal costs of production.

Zero retail margins : When wholesale prices are such that the retailer’s price-cost margins are
zero (p_st(w_st) — w*_st — c_st = 0 that is y_ft = 0 for all f), then the first order conditions give the
simplified expression of wholesale margins as

^rft = ⁽Pt^- μt ^{- c}t) = ^—(IfSp^Ify^fs⁽_Pt^{)                      (21)}

for all f = 1, ..,F. For private label products, denoting yp!_t + Γ)( the vector of total price-cost
margins of private labels of retailer r, we have

₇pt + rpt = -(Ir Sp Ir )-¹Irs(pt)

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