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


  • G. E. Boyle

    (Economics, National University of Ireland, Maynooth)


The main objectives of this paper are: (i) to establish whether Irish dairy marketing cooperatives behaved "as if" they were profit maximisers over the period 1961 to 1987 and (ii) to determine the response of the sector to the imposition of the milk production quota in 1984. The theory of the cooperative managed firm (CMF) is first recast in a duality framework. The CMF differs from the profit maximising firm (PMF) in (a) having as its objective the aximisation of the price paid to its members for the raw material they supply and (b) being obliged to process all the raw material supplied by its members. A formal test as to whether the Irish dairy-processing sector could be characterised as "virtual" profit maximisers was implemented and could not be rejected. This finding was reinforced by our finding that the elasticity of milk price with respect to the volume of milk processed was zero. Milk price was found to be driven mainly by exogenous changes in the price of processed output. The impact of the quota was to obviously reduce the level of processed output but not proportionately. Our results suggest that every 10% fall in the amount of milk processed reduces processed output of the sector by 6%. We also found a negative relationship between the amount of the milk raw material processed and the demand for labour implying that the introduction of the quota would not of itself have adversely affect employment in the sector.

Suggested Citation

  • G. E. Boyle, 1998. "A Duality Approach to Testing the Economic Behaviour of Dairy-Marketing Co-operatives: The Case of Ireland," Economics, Finance and Accounting Department Working Paper Series n800798, Department of Economics, Finance and Accounting, National University of Ireland - Maynooth.
  • Handle: RePEc:may:mayecw:n800798

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    References listed on IDEAS

    1. Kahana, Nava, 1989. "The Duality Approach in the Case of Labour-Managed Firms," Oxford Economic Papers, Oxford University Press, vol. 41(3), pages 567-572, July.
    2. Conrad, Klaus & Unger, Ralph, 1987. "Ex post tests for short-and long-run optimization," Journal of Econometrics, Elsevier, vol. 36(3), pages 339-358, November.
    3. Neary, J. P. & Roberts, K. W. S., 1980. "The theory of household behaviour under rationing," European Economic Review, Elsevier, vol. 13(1), pages 25-42, January.
    4. Kahana, Nava & Nitzan, Shmuel, 1989. "More on alternative objectives of labor-managed firms," Journal of Comparative Economics, Elsevier, vol. 13(4), pages 527-538, December.
    5. Kulatilaka, Nalin, 1985. "Tests on the validity of static equilibrium models," Journal of Econometrics, Elsevier, vol. 28(2), pages 253-268, May.
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    Cited by:

    1. Senhaji, Arvid, 2008. "Duality theorems summarising some unambiguous qualitative comparative static results for processing cooperatives - The restricted profit function applied," 2008 International Congress, August 26-29, 2008, Ghent, Belgium 44374, European Association of Agricultural Economists.

    More about this item


    co-operative; duality theory; initial profit maximisation; production quotas;

    JEL classification:

    • C39 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Other
    • D21 - Microeconomics - - Production and Organizations - - - Firm Behavior: Theory
    • Q13 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Agriculture - - - Agricultural Markets and Marketing; Cooperatives; Agribusiness
    • R3 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - Real Estate Markets, Spatial Production Analysis, and Firm Location

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