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



We present the estimation results of several models that seem worth of consideration with
some variants on the behavior of manufacturers or retailers. Table 4 then shows the averages of
the estimates of product level price-cost margins under the different models considered7. Price-
cost margins are lower for mineral water than for spring water in percentage of retail price but
are larger in absolute value. Model 1 concerns the case of linear pricing. In order to save space,
variants of linear pricing models with different interaction between manufacturers and retailers are
not presented although they have been estimated. As in Sudhir (2001), we estimated variants of
the linear pricing model by assuming collusion between manufacturers and/or retailers or assuming
that retailers act as pass-through agents of marginal cost of production. All these models are finally
strongly rejected (as in Bonnet and Dubois, 2010, for older data) and thus not shown. We also
consider several non linear contracting models with exogenous or endogenous buyer power. Models
2, 3, 4 and 5 correspond to two part tariffs contracts with resale price maintenance. Remind that,
in this case, whether the retailers can use competing offers to increase their buyer power when
dealing with manufacturers does not change the pricing equilibrium but only the unobserved and
unidentified fixed fees which determine the sharing of the rent in the vertical structure. Thus,
these estimation results are consistent with a model where either the buyer power is endogenous
or exogenous in the vertical relationship. Model 2 is the general case (14) where the equilibrium
wholesale margins are estimated using an additional restriction (22) on total margins across pro-
ducts and markets as described in 4.2. Model 3 corresponds to the case where no wholesale price
discrimination is imposed. In this model, manufacturers are prevented to sell a given product to
different retailers at different prices which implies that the wholesale price of any product
j depends
only on its brand
δ(j) and not on the retailers identity r(j). These restrictions are incorporated
in the estimation of margins using the same method as in (23) where the vector of unknowns Γ
is constrained to uniform wholesale pricing. The results of the estimation of models 2 and 3 show
7Note that the average price-cost margin at the retailer level plus the average price-cost margin at the manufac-
turer level do not sum to the total price cost margin because of the private labels products for which no price cost
margin at the manufacturer level is computed, the retailer price cost margin being then equal to the total price cost
margin.

29



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