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

Figure 1 shows the decisions and welfare of producers. The downward sloping curve shows the
net returns when the farm product is supplied to Firm I, while the upward sloping curve shows the net
returns when the product is supplied to Firm C for different values of the differentiating attribute α (i.e.,
for different producers). The intersection of the two net returns curves determines the level of the
differentiating attribute that corresponds to the indifferent producer. The producer with differentiating
characteristic α_I(k) given by:
(2) α_I(k): Π_I^f_(k)=Π_C^f_(k)=>w_I(k)-c^f-tα=w_C(k)-c^f-t(1 -α) =>

^{t + w}I (k ) - ^wC ( k )
21

is indifferent between selling to Firm I or to Firm C as the net returns from selling to the two firms are the
same. Farmers located to the left of α_I(k) (i.e., farmers with α∈ [0,α_I(k))) sell to Firm I while farmers
withα∈ (α_I(k),1] sell to Firm C. Aggregate producer welfare is given by the area underneath the effective
net returns curve shown as the (bold dashed) kinked curve in Figure 1.

When farmers are uniformly distributed with respect to their differentiating attribute α, α_I(k)
determines the share of producers delivering their product to Firm I. The share of producers supplying
Firm C is given by 1 -α_I(k). By normalizing the mass of producers at unity, these shares give the input
supplies faced by Firm I, x_I(k), and Firm C, x_C(k), at the kth stage of the game, respectively. Formally,

x_I(k) and x_C(k) can be written as:

After determining the supplies faced by the two firms at the pre- and post-innovation stages, we will now
proceed to deriving the subgame perfect equilibria in the pure and mixed oligopsonies.

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