The plan of the paper is as follows. Section 2 sets out a theoretical framework designed to provide
guidelines for the empirical application. We draw on the traditional and seminal analysis of
Helmberger and colleagues (1962, 1964, 1966) and recast it in a duality framework which proves
highly convenient for the empirical analysis. Section 3 outlines how the theoretical framework
could be applied to achieve the objectives established for the paper. Section 4 sets out the data
used in the empirical application and reports the econometric results. Finally in Section 5 we draw
some conclusions.
2. Theoretical framework
Suppose a dairy-marketing cooperative were classed as a profit-maximising firm (PMF) facing
given prices for all variable inputs, including its principal raw material, and its processed output.
Also let’s suppose that the capital input is short-run quasi fixed. The profit function for such a firm
is given by equation (1):
к = k(Py, w, K) (1)
where,
π k = short-run maximum restricted profits, given k.
py= price of processed output.
w = vector of input prices.
к = short-run quasi-fixed capital stock.
Equation (1) can be thought of as giving the maximum returns to the quasi-fixed input k.
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