THE EFFECT OF MARKETING COOPERATIVES ON COST-REDUCING PROCESS INNOVATION ACTIVITY

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4. Innovation and Pricing Decisions in a Mixed Oligopsony

In this case, Firm C is a co-op instead of an IOF. The market structure is, thus, a mixed duopsony
consisting of an IOF (Firm I) and a co-op (Firm C).

Price Competition at the Post-Innovation Stage in the Mixed Oligopsony

Similar to the pure oligopsony case, at the 3^rd stage the IOF seeks to determine the input price that
maximizes its profits. Thus, both its objective function and its best response function are identical to those
in the post-innovation stage of the pure duopsony.

Unlike Firm C in the pure oligopsony, the co-op seeks to identify the input price that maximizes
the welfare of its members (i.e., farmers that patronize its activities) subject to not incurring economic
losses. Member welfare is given by the shadowed area MW_(k) in Figure 1 where k=3 and the
cooperative’s problem can be expressed as:

(¹⁹)   max MW(3) =(^wC(3) ^- c^f ) ^xC(3) ^{- 1 tχ}C(3)

wC(3)                                     2

s.t. Π_C(3) ≥0 =>p_C-w_C(3) -c_C≥0

Solving the optimality conditions of the co-op’s problem, shows that the co-op will find it
optimal to not exercise its oligopsonistic power when procuring the farm product at the post-innovation
stage (i.e., w_C(3) =p_C-c_C).² The Nash equilibrium prices and quantities at the post-innovation stage of
the mixed oligopsony are:

⁽²⁰⁾   w_f(3) = ɪ(Pc ⁺ Pi ^{- c}C ^{- c}I ^{- t})

4t

² It should be noted that this will be the optimal pricing strategy of the co-op at the post-innovation stage no matter if
it seeks to maximize the welfare of all farmers that deliver their product to the co-op at this stage or the welfare of
only a subset of its post-innovation membership. The obvious reason is that the welfare of any producer group is
positively related to the farm product prices.

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