Production Functions with Continuous Factor Substitution

  • Sven Danø


The “classical” type of factor substitution, long predominant in economic theory by virtue of its plausibility and analytical convenience, finds expression in a production function
$$ x=x\left( {{v}_{1}},\text{ }{{v}_{2}}\ldots ,\text{ }{{v}_{m}} \right), $$
assumed to possess continuous first- and second-order partial derivatives in the region of definition v i ≥ 0, x ≥ 0. The underlying process must be technologically defined in such a way as to make the production function single-valued; when the existing technical knowledge leads to a multiplevalued function because a given set of input amounts v i may be organized in different ways, this means that the process is incompletely specified. To obtain uniqueness in such cases it is usually assumed1 that the factors are always organized in a technically optimal fashion so that the production function is defined as giving the maximum amount of output for any factor combination.


Cost Function Marginal Cost Production Function Marginal Productivity Average Cost 
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Copyright information

© Springer-Verlag/Wien 1966

Authors and Affiliations

  • Sven Danø
    • 1
  1. 1.University of CopenhagenCopenhagenDenmark

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