A Duality Approach to Testing the Economic Behaviour of Dairy-Marketing Co-operatives: The Case of Ireland

Now,

_k = ^c_k = о, iff

_k(p_y,w,k)- ^c_km(p_y,w,rn,k) + p_mrn = O

(6)

If condition (6) holds then the cooperative firm is behaving “as if’ it were maximising πk. The price
it pays for its raw material p_m is chosen consistent with maximising the returns to the given
quantity of raw materials and the capital stock. Hence this price is sometimes referred to as the
“virtual” price (Neary and Roberts (1980)) denoted here for convenience as p^v_m. In other words, if
(6) holds then the amount of raw material processed is exactly equivalent to what a profit-
maximising firm would have freely processed when faced with a given price p_m. Thus from an
economic perspective if p_m= p,,,^en equations (3) - (4) are identical to (1) - (2). We could thus
characterise such a cooperative as a virtual profit-maximising firm (VPMF for short).

Of course this conceptual framework can be extended further to the case where capital is assumed
to be variable even in the short run. The conditions for the cooperative firm to be a “virtual” profit
maximiser in these circumstances are given in (7):

∖ m J

( ^{c λ}i
k,m

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