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

Hotelling’s Lemma (Varian (1978)) gives us the processed output supply and variable input
demand equations for the cooperative firm as equations (4)(a) and (4)(b):

~ = y^c =y^c(p_yyym,k) (a)

∖,P_y J

r -. -. -                                           ¹⁴¹

- = -χ^c = χ^c(p W,m,k) (Z>)

<P_y J

where,
χ^c= profit-maximising quantities of variable inputs demanded by the cooperative firm such that
χ^c < X.

On the face of it equations (3) - (4) appear quite different from the system in (1) - (2). However,
under certain additional assumptions the derivative relationships may be shown to be identical.
This is of course an implication of the well-known Le Chatelier-Samuelson principle or the
Envelope Theorem (Varian (1978)).

To see the correspondence between the system (1) - (2) and (3) - (4), consider the implied returns
to capital for the cooperative firm which are defined in equation (5) as:

k= kΛPy^^w^^k)-Prn^m

where,
p_m = price of milk paid to cooperative members.

<<   6   7   8   9   10   11   12   >>

More intriguing information