14
Substituting the equilibrium pre-innovation membership of the co-op (equation (41)) in equations
(31)-(33) gives the subgame perfect equilibrium innovation levels in the mixed duopsony. Substituting
the new expressions of rI and rC into equations (20)-(26) gives the subgame perfect equilibrium
conditions in the post-innovation stage of the game.
Table 2 summarizes the subgame perfect equilibrium in the mixed oligopsony. It can be seen that,
similar to the pure oligopsony case, the equilibrium is asymmetric with the differences in equilibrium
conditions being determined by the relative quality of the firms’ final products, the degree of producer
heterogeneity, and the size of innovation costs. When the co-op is the high quality firm (i.e., when
pC > pI ), it will offer higher prices to the farmers, will enjoy higher market shares in the pre- and post-
innovation stages, and will undertake higher innovation effort than the low quality IOF.
Interestingly, because of its objective to maximize member welfare, even when the co-op is the
low quality firm (i.e., when pC < pI ) it can still price the farm product above the high quality IOF, enjoy
higher market shares, and innovate more than its rival. For the high quality IOF to offer higher prices to
producers and innovate more than the low quality co-op, it should enjoy a significant quality advantage
relative to the co-op.
When the difference in the prices of the products produced by the two firms is p1 - pc ≥tψ-—-,
ψ
the low quality co-op is driven out of the market and the high quality IOF becomes a monopsonist at the
post-innovation stage of the game (i.e., xC(3) = 0 and xI(3)= 1). Since the co-op exits the market in stage 3,
it will not invest in cost-reducing innovation in stage 2 and will seek to maximize the welfare of its pre-
innovation membership in stage 1. Table 3 presents the subgame perfect equilibrium for the case where the
market structure is altered at the post-innovation stage due to the exit of the low quality marketing co-op.
t (8tψ - 5)
Finally, when pc - pI ≥----------it is the co-op that becomes the sole buyer of the farm
8tψ + 3
product at the post-innovation stage of the game. Since the IOF exits the market in stage 3, it will not
invest in cost-reducing innovation in stage 2, and will seek to maximize its pre-innovation profits in stage