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

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x²

x C(1)

---an and the problem of the co-op
2ψ

(37)

s.t.

^ΠC(1)

I_C≥0 =>( p_C

^-wC(1)

- c ) XC (1) - '∖   ≥ 0

2ψ

where MW₍₁₎ is the welfare of the pre-innovation membership in stage 1. The optimality conditions for

the co-op’s optimization problem suggest that the co-op will find it optimal to choose its price such that
the investment constraint binds, i.e., the co-op will price its input so that it raises exactly the amount of
capital needed for its innovation activity in stage 2. The best response function of the co-op is then:

4tψp_C+w_I(1) -t(4cψ+1)

^WC (¹) =           4 tψ +1

The Nash equilibrium prices and quantities at the pre-innovation stage of the mixed oligopsony

are given by:

(38)

_'    t-4t²ψ+(4tψ-3)p_C+4tψp_I

w (¹) =             8tψ - 3

-c

(39)

_'     8t²ψ²+4tψ-3+8tψ²(p_I-p_C)

x¹ (¹) =        ( 4 tψ +1)(8 tψ - 3)

4t-12t²ψ+(32t²ψ²-8tψ-3) p_C+4tψp_I

(40)   wC_fn =--------------------—--------------------

^C(1)               (4tψ+1)(8tψ-3)

(41)

`     ^8tψ[³>tψ ^{-1 +} ψ(PC ^- Pi )]

^XC(¹) =     (4tψ +1)(8tψ - 3)