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

When retailers have no endogenous buyer power :

If retailers have no endogenous buyer power, we can suppress the constraints (10) and take
only into account the constraints (9). Then, as shown in appendix 7.2, the manufacturers profit
maximization is equivalent to set wholesale prices in the following program

The first order conditions are : for all i ∈ Gf

which gives in matrix notation

If P_ws(p) + I_f P_wS_pIf (P - μ - c) + If P_wS_p (I - I_f )(p - w - c) = 0

This implies that the total price-cost margin is such that for all f = !,..,F,

7f ⁺ Γf = ^(If ^pw^spⁱp⁾ l^-If ^Pw^{s(p) - 1}f^Pw^Sp ^{(I - 1}f^{) (p - w - c)}] .          ⁽¹⁷⁾

Using (2) to replace (p - w - c) and (6) for P_w, this allows us to estimate the price-cost margins

with demand parameters. Remark again that the formula (2) provides directly the total price-cost
margin obtained by each retailer on its private label.

4 Identification and Econometric Method

4.1 A Random Coefficients Logit Demand Model

The estimation of price-cost margins under the different models previously considered requires
the observation of the market structure and of the demand shape. As in Villas-Boas (2007) or
Bonnet and Dubois (2010), we use the demand and structural equation to infer margins. A careful
demand estimation is thus important. The market demand is derived using a standard discrete
choice model of consumer behavior that follows the work of Berry (1994), Berry, Levinsohn and
Pakes (1995) and estimated on individual choices as in Revelt and Train (1998). We use a random-
coefficients logit model which is a very flexible general model (McFadden and Train, 2000). Contrary

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