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



with respect to all retail prices, i.e.

/

Sp


∂sγ
dpi


∂sj
dpi


.

dsi
∂p J


.

ds j
dp j


In vector notation, the first order condition (1) implies that the vector 7 of retailer r’s margins
(rows corresponding to products not sold by
r are set to zero), i.e. the retail price p minus the

wholesale price w minus the marginal cost of distribution c, is1

7 p w c = (IrSpIr) 1 Irs(p)

(2)


Remark that for private labels, this price-cost margin is in fact the total price-cost margin p μ c
which amounts to replace the wholesale price w by the marginal cost of production μ in this
formula.

Concerning the manufacturers’ behavior, we assume they maximize profit choosing the whole-
sale prices
Wj of their own products and given the retailers’ response (1). The profit of manufacturer
f is given by

f = j (wj μj )sj (p(w))

where μj∙ is the manufacturer’s (constant) marginal cost of production of product j. Assuming the
existence of a pure-strategy Bertrand-Nash equilibrium in wholesale prices between manufacturers,
the first order conditions are

sj+ Σ Σ (ws μs)jsS^p. = 0’  foranjeGf               (3)

s<EGf 1=1,..,J               pι     j

We denote If the ownership matrix of manufacturer f that is diagonal and whose jth element is

equal to one if j is produced by the manufacturer f and zero otherwise.

We introduce Pw the matrix (J x J) of retail prices responses to wholesale prices, containing

1Abusing notations, we consider the generalized inverse when noting the inverse of non invertible matrices, which
means that for example

2  0    ’_ Γ 1/2  0

Iool I 0    0 .




More intriguing information

1. Estimation of marginal abatement costs for undesirable outputs in India's power generation sector: An output distance function approach.
2. Short- and long-term experience in pulmonary vein segmental ostial ablation for paroxysmal atrial fibrillation*
3. The name is absent
4. Feeling Good about Giving: The Benefits (and Costs) of Self-Interested Charitable Behavior
5. The name is absent
6. The name is absent
7. The name is absent
8. The name is absent
9. Implementation of the Ordinal Shapley Value for a three-agent economy
10. Fiscal Reform and Monetary Union in West Africa