The CES- production function or CES- utility function is a
production function for which the substitution elasticity always assumes
the same value. Here, CES stands for c onstant e BeginExpansion
EndExpansion XXX lasticity of substitution. This property is advantageous
in many economic applications. The symmetrical XXX form is:
, where the elasticity
of substitution is .
By variation of
the type of utility function can be changed from Leontief to Cobb-Douglas
to perfect substitution (linear utility function). h indicates the degree
of homogeneity. If h = 1, the function is linearly homogeneous, i.e.,
if all input factors are doubled, the output is also doubled. For
of scale apply, for
XXX negative economies of scale apply.
u represents the production- or utility- level, a the technology factor, and the relative weights of the two input factors x and y.
In the above graph, for n=2 a graph of the CES function is
Since this representation is overparameterized, the parameter was set
so that the relative weight of the two goods is represented only by
A selection of graphical illustrations can be found hier.