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

This case occurs where the processors are perfectly competitive sellers in their product market.
One would have a strong prior that such a structure would characterise the dairy processing
sectors in most countries. In this situation the price of milk is a given (demand for the raw material
is perfectly elastic) and the quantity of the raw material processed is determined solely by the
supply behaviour of farmers (see Helmberger (1964) and Figure 1).

Figure 1: Equilibrium for a processor who is a perfectly competitive seller in his product
market

This result has important implications for empirical analysis that can be illustrated by assuming a
simple Cobb-Douglas profit function:
log( ) = log(p_mzw) = a₀ + a_y ∖o⅛p_y ')+a_w log(w) + a_k log(ŋ + a_m log(m) (11)

⁹The result that ( y^c∕ m)=( y/ p_m)∕( m/ p_m) is derived in Deaton and Muellbauer (1980).

11

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