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. Education Responses to Climate Change and Quality: Two Parts of the Same Agenda?
2. Workforce or Workfare?
3. Federal Tax-Transfer Policy and Intergovernmental Pre-Commitment
4. Globalization, Divergence and Stagnation
5. Do Decision Makers' Debt-risk Attitudes Affect the Agency Costs of Debt?
6. Multi-Agent System Interaction in Integrated SCM
7. CROSS-COMMODITY PERSPECTIVE ON CONTRACTING: EVIDENCE FROM MISSISSIPPI
8. The Impact of Individual Investment Behavior for Retirement Welfare: Evidence from the United States and Germany
9. If our brains were simple, we would be too simple to understand them.
10. Correlation Analysis of Financial Contagion: What One Should Know Before Running a Test