Dynamic Explanation of Industry Structure and Performance
Cotterill
the wholesale and retail price, and a vertical Stackleberg
game where in the second stage of the game a retailer
decides on the profit maximizing price given a wholesale
price and in the first stage of the game a processor
maximizes profit by choosing the wholesale price taking
into account the reaction function of the retailer.
This model assumes that one has retail data for
individual chain supermarkets (IRI key account data). It
also assumes vertical dyadic relationships between
processors and retailers, i.e. each retailer deals with one
exclusive processor. This is clearly not the case, and is a
shortcoming. Other research on vertical structural
models has the same constraint (e.g. Kadiyali et al. 1996,
1998). One can allow for more processor interactions via
vertical competition for customers by disaggregating the
commodity into branded and private label (Cotterill,
Putsis and Dhar, 2000). One could continue such
disaggregation to the brand level. Then the model would
be more disaggregate than the typical firm since a brand
is supplied to more than one retailer. In these
disaggregate models, modeling competition among
processors as a vertical game through retailers rather
than a direct horizontal game among processors at the
wholesale level seems sufficient and reasonable.
Processors compete with each other through retailers in
the retail market for the sale of their products.
Let the demand functions of the retailers be the
following:
π R = (p 1 - w 1 к 1
∏ R =(P 2 - w 2 )q 2.
[3(a)-(b)]
Following Choi (1991), in the Vertical Nash game, a
linear mark-up at retail is conjectured by the processor
on retail price; so, retail price can be written as:
P1 = w1 + r1
P 2 = w 2 + r2
[4(a)-(b)]
where: r1 and r2 are the linear mark-ups at the retail
level.
In the Stackleberg game, each processor develops a
conjecture from the first order condition of the retailer.
The retailer’s first order conditions are:
1
P1 = -w 1 - a0 - a2P2
21 [5(a)-(b)]
P 2 = 2 w 2 - b 0 - b1 P1.
q 1 = a 0 + a 1 p 1 + a 2 p 2
q 2 = b 0 + bl P1 + b 2 P 2.
[1(a)-(b)]
We assume that each manufacturer only knows its
own retailer’s reaction function and that the
manufacturer ignores impacts of its wholesale price
change on the other retail price. The resulting
Stackleberg conjectures are:
Processor level demand is derived from the retail
level demand specifications given retail conduct and
margin. To derive these processor level demand
functions different conjectures are assumed at the
processor level concerning retailer reactions. These
conjectures can be perceived as assumptions by the
processors about retailer pricing behavior given a
wholesale price. For the vertical integration (full
coordination) game we need no vertical conjecture
assumptions because the channel has only one industry-
integrated retailers.
Let the retailer’s cost function be the following:
1 Conjecture
|
— and |
aP 2 |
1 |
|
2 |
aw 2 |
_ = 2 Conjecture |
We simplify the processor level marginal cost function
in the following manner:
wmc 1 = m + m1
wmc 2 = m + m 2
[6(a)-(b)]
TC1 = w1 * q 1
TC 2 = w 2 * q 2
[2(a)-(b)]
where: w1 and w2 are the wholesale prices received by
the processors.
So, the retailers’ profit functions can be written as:
Food Marketing Policy Center Research RePort No. 53
where: m is the industry specific marginal cost
component and m1 and m2 are the processor specific cost
components.
So, the processors profit functions can be written as:
∏P =(w 1 - m - m 1 )q 1
∏ P = (w 2 - m - m 2 )q 2.
[7(a)-(b)]
Using the profit maximizing first order conditions
both at the processing and retail level we derive the cost
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