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

Innovation Competition (2^nd Stage of the Game)

In stage 2, the two IOFs seek to determine their optimal cost-reducing, process innovation effort. The
relationship between the amount of innovation, r, and the post-innovation marginal costs of processing
the farm input is given by:

(9)    c_i(3) = c_i(1) -β_ir_i

where c_i(1) is Firm i's(strictly positive) marginal cost of processing the farm input at the pre-innovation
stage of the game, and r_i ≥ 0 . The parameter β_i represents the effectiveness of innovation effort, i.e., the
degree to which innovation effort is translated into cost reductions for the two rivals. We assume that the
two firms have the same pre-innovation processing costs (i.e., c_I(1) = c_C(1) = c) and β_i =1. In addition to
simplifying our exposition, imposing symmetry on the two firms’ pre-innovation costs and effectiveness
of innovation effort allows us to focus on the effect of the different objective function of the co-op in the
mixed duopsony on the equilibrium innovation and pricing decisions.

While, as indicated by equation (8), innovation effort has the potential to increase the post-
innovation profits of a firm, cost-reducing innovation requires resources. Without loss of generality,
innovation costs are assumed to be an increasing function of the innovation effort (Shy), i.e.,
12

(10) Λ= - ψr∙

where ψ is strictly positive scalar reflecting the size of innovation costs.

Thus, at the innovation stage of the game each IOF seeks to determine the innovation effort that
maximizes its post-innovation profits minus the cost of innovation effort, i.e.,

(3t+r-r+p-p)_1
*ij i j 1₂

⁽¹¹⁾ max ^π _l (2,3) =^π _l (3) ^- I₁ =---------—--^ψψT_l

^ri                                       18t               2

From the first order conditions for each IOF’s problem we obtain their best response function as:

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