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

express the manufacturer’s price-cost margins vector Γ = w — μ as depending on the function s(p)
by replacing the expression (6) for P_w in (4).

3.2 Two-Part Tariffs and Endogenous Retail Buyer Power

We now consider the case where manufacturers and retailers can sign two-part tariffs contracts.
As in Rey and Vergé (2004) and Bonnet and Dubois (2010), we assume that manufacturers make
take-it-or-leave-it offers to retailers and characterize symmetric subgame perfect Nash equilibria.
Rey and Vergé (2004) have proven the existence of equilibria under some assumptions on this
multiple common agency game. These contracts consist in the specification of franchise fees and
wholesale prices but also on retail prices in the case where manufacturers can use resale price
maintenance. All offers are public⁴ and retailers simultaneously accept or reject. Contrary to Bonnet
and Dubois (2010), where it is assumed that if one offer is rejected then all contracts are refused
and retailers obtain a fixed reservation utility, we allow the possibility that a retailer rejects a
contract while accepting others. Once offers have been accepted, the retailers simultaneously set
their retail prices, demands and contracts are satisfied.

We consider that two-part tariffs contracts are negotiated at the firm level and not by brand,
which implies that manufacturers use bundling offers to retailers. This is likely to increase the
market power of multiproduct manufacturers and reduce the buyer power of retailers which depends
on the brand ownership structure of multiproduct manufacturers and on the presence of store
brands owned by retailers. Retailers can then refuse a manufacturer’s offers and accept those of
other manufacturers but cannot refuse part of the brands offered by a manufacturer while accepting
others owned by this same manufacturer.

The profit function of retailer r now writes :

∏^r = V^ ^ [⁽p_s ^— W ^— c_s)a_s{p) ^— F_s]                         ⁽⁷⁾

where F_s is the franchise fee paid by the retailer r for selling product s ∈ S_r (negative if backward
⁴This is a convenient benchmark case that can be justified in France by the nondiscrimination laws of the 1986
edict of free pricing which prevents the offer of different wholesale prices to purchasers who provide comparable
services.

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