Abstract
This last chapter provides an example of how to integrate the production economic theory presented in the first ten chapters of this book and the Linear Programming approach presented in the last three chapters. The example shows how is it possible to use Linear Programming to numerically generate the output supply function of the firm. This approach has shown to be a suitable modelling unit in a sector modelling context, in which the supplies from the individual firms are aggregated into the total industry supply.
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- 1.
For further details on the context in which this modeling approach can be used, see Rasmussen (2007).
- 2.
Output other than the main product y.
- 3.
Marginal cost is the shadow price of the restriction y j = f j (x 1,…, x N , z 1, …, z K ) ≥ Y j in (21.8), which is provided as output from most mathematical programming software.
- 4.
Or rather, expected marginal revenue.
- 5.
For convenience the index for farms j is dropped.
- 6.
In the present example, r(y) = {(x 1, z 1) , …, (x S, z S)}.
- 7.
As defined here, there is only one production process for each netput x n . As with the output y, one could include the possibility of having additional scale specific production plans for production of each netput. To keep things simple this has not been done here. (If needed, the extension is straight forward).
References
Georgescu-Roegen, N. (1972). Process analysis and the neoclassical theory of the production function. American Journal of Agricultural Economics, 54, 279–294.
Jacobsen, B., Petersen, B. M., Berntsen, J., Boye, C., Sørensen, C. G., Søgaard, H. T., & Hansen, J. P. (1998). An integrated economic and environmental farm simulation model (FASSET). Copenhagen: Statens Jordbrugs- og Fiskeriøkonomiske Institut.
Rasmussen, S. (2007). Agricultural sector modelling. A micro-based approach based on mathematical programming. FOI Working Paper nr. 10, Institute of Food and Resource Economics, University of Copenhagen, Copenhagen.
Rosenthal, R. E. (2012). GAMS – a user’s guide. Washington, DC, USA: GAMS Development Corporation.
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Rasmussen, S. (2013). Modelling Supply Functions Using Linear Programming. In: Production Economics. Springer Texts in Business and Economics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30200-8_21
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DOI: https://doi.org/10.1007/978-3-642-30200-8_21
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