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2011 | OriginalPaper | Buchkapitel

10. Optimisation of Production Under Restrictions

verfasst von : Svend Rasmussen

Erschienen in: Production Economics

Verlag: Springer Berlin Heidelberg

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Abstract

The general criteria for the adjustment of production when product and factor prices change were described in Chap. 3–5. The general results are derived under the general assumption that the producers wish to maximise profit. The general criterion for profit maximisation is that the addition of input should be continued as long as the increase in total revenue (i.e. marginal revenue) is greater than the increase in costs (i.e. marginal costs). This general criterion includes the following two criteria as special cases: (1) The value of the marginal product for all (variable) inputs must be equal to the price of the corresponding input (VMP i  = w i ), and (2) The marginal costs must be equal to the price of output (MC = p y ).

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Fußnoten
1
The Lagrange function is a well known mathematical tool used in economics. For further explanation see any advanced mathematical textbook or mathematical economics textbook such as Chiang (1984).
 
2
Repeat the homothetic production function in Sect. 4.​3.
 
3
The example is naturally somewhat simplified. Hence, the possibility of the available land being used to grow other crops is not considered here. Also, please note that the model in Fig. 10.2 and 10.3 used for land in fact presupposes: (1) the existence of fixed input (e.g. labour) in addition to x 1 and x 2, or (2) that the quality of land declines with the increasing amount of acreage. Otherwise, there would be no profit maximum at A!
 
4
For the sake of simplification, the meat production that is normally part of milk production is disregarded. Please refer to the original article which includes meat production.
 
5
The reason why this is optimal is because a possible further reduction in production will not be motivated by the quota restriction but by a desire to achieve profit maximisation.
 
Literatur
Zurück zum Zitat Chiang, A. C. (1984). Fundamental methods of mathematical economics (3rd ed.). Singapore: McGraw-Hill Book Company. Chiang, A. C. (1984). Fundamental methods of mathematical economics (3rd ed.). Singapore: McGraw-Hill Book Company.
Zurück zum Zitat Rasmussen, S., & Hjortshøj Nielsen, A. (1985). The impact of quotas on the optimal adjustment of milk production at the farm level. European Review of Agricultural Economics, 12, 351–364. Rasmussen, S., & Hjortshøj Nielsen, A. (1985). The impact of quotas on the optimal adjustment of milk production at the farm level. European Review of Agricultural Economics, 12, 351–364.
Metadaten
Titel
Optimisation of Production Under Restrictions
verfasst von
Svend Rasmussen
Copyright-Jahr
2011
Verlag
Springer Berlin Heidelberg
DOI
https://doi.org/10.1007/978-3-642-14610-7_10