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

where,
p^v_k = the “virtual” price of capital.

A big advantage of the duality approach is that is allows a clear comparison between the behaviour
of the CMF and the PMF. In general:

(8)

This expression is referred by Chambers (1988) as the “fundamental duality inequality”. It
implies that profits of the PMF must be at least equal to those generated by the CMF. More
specifically it implies that the profit function of the PMF is in general “more convex” in respect of
output and variable input prices. By implication responses to price changes will be more sluggish
for the CMF compared to the PMF⁸. The intuition for this result can be understood by comparing
the price responses of the PMF and the CMF.

If the cooperative firm behaves as a virtual profit maximiser then:

y^c(p_ypv,k,m (p_y,w,k,p_m)) = y (p_y,w,k,p_m)

Similar results can be established for the all other price responses⁹. It will be noted that a sufficient
condition for the cooperative and profit maximising firms to have identical price responses is if:

(10)

It is important to note that the CMF will not exhibit perverse price responses.

10

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