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

(5)

maxΠ ₍₃₎
w (3)

⁼(p ^-c ^-w (3))x (3)

where ∈{C, I} , p is the price of Firm ’s final product, and c is the post-innovation marginal

processing cost of Firm . All other variables are as previously defined.

Solving the problem of the two IOFs gives their best response functions as:

wo) = 2 ( w₁ (3)⁺ Pi-^{t -} cû

where j∈{C, I} and ≠j. Solving these best response functions simultaneously and substituting

w_C^* ₍₃₎ and w_I^*₍₃₎ into equations (3) and (4) gives the Nash equilibrium prices and quantities as:

(6)

(7)

^w⅛) = 3 (² Pi ⁺ Pj

-2c_i-c_j-3t)

*     ^{31 - c}i^{+ c}j ⁺ P₁ - Pj

^x3 ^_           61

The equilibrium profits of each IOF are then given by:

(3t-c+c+P-P)²

(8)    ∏*(3) =■(-------i ^j )

i(3)                  18t

and are a function of the degree of producer heterogeneity, the prices of the products produced by the two
IOFs, and their post-innovation processing costs. Ceteris Paribus, the lower the post-innovation
processing cost of a firm, the greater its profits at the 3^rd stage of the game.

¹ The assumption of Nash conjectures is maintained throughout the analysis.