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

identified, whether there is endogenous buyer power or not.

4.2.3 Two-Part Tariffs contracts with RPM

In the case of two part tariffs contracts with RPM, multiple equilibria prevent the full identifica-
tion of price-cost margins without further restriction. Actually, given that we have J products and
T markets, we have potentially JT marginal costs of distribution and JT marginal costs of pro-
duction, or equivalently JT retailer margins and JT manufacturer margins, to identify. Identifying
the JT retailer level and JT manufacturer level price-cost margins implies that 2 JT parameters
have to be identified while our structural model generally gives a system of JT equations. These
equations can be written as equations linking the vector of total margins (Γ_t + 7_t), for market
(period) t, as a function of the vector of wholesale margins (Γ_t) of the form

(Γ_t + 7₁)= H (Γ_t)

where H(.) is the known function (14) depending on the demand shape and the structure of the
industry in terms of products ownership at the retailing and manufacturing levels.

As retail prices and the correspondence H(.) are known, there exists a one to one correspondence
between the vector of unknown JT parameters Γj_t and the vector of unknown JT total marginal
costs denoted Cj_t because

Cjt = Jjt + ^cjt = Pjt - (Γjt + 7jt) = Pjt - Hj(Γt) for all j = 1,.., J and t = 1, ..,T

where Hj denotes the j'^h row of H.

The degree of underidentification is thus at most equal to the dimension of the vectors of
wholesale prices (or wholesale margins Γ_t), that is JT. Then, identification cannot be obtained
unless additional restrictions are imposed.

We consider several possible restrictions, from very strong ones (the ones considered in Bonnet
and Dubois, 2010) imposing zero wholesale or retail margins to a general case with a less restrictive
one.

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