Mathematical methods for economic theory | 合法醫療器材資訊網
2.5 Homogeneous functions
Definition
Multivariate functions that are “homogeneous” of some degree
are often used in economic theory. For a given number k, a
function is homogeneous of degree k if, when each of its
arguments is multiplied by any number t > 0, the
value of the function is multiplied by
tk. For example, a function is
homogeneous of degree 1 if, when all its arguments are multiplied
by any number t > 0, the value of the function is
multiplied by the same number t.
Here is a precise definition. Because the definition involves the relation between the value of the function at (x1, ..., xn) and its values at points of the form (tx1, ..., txn) where t is any positive number, it is restricted to functions for which (tx1, ..., txn) is in the domain whenever t > 0 and (x1, ..., xn) is in the domain. (Some domains th...
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Homogeneous function | 合法醫療器材資訊網
Positive homogeneous | 合法醫療器材資訊網
positively homogeneous function | 合法醫療器材資訊網
HOMOGENEOUS EXTENSIONS OF POSITIVE | 合法醫療器材資訊網
HOMOGENEOUS FUNCTIONS | 合法醫療器材資訊網
Mathematical methods for economic theory | 合法醫療器材資訊網
Positively Homogeneous Functions Revisited | 合法醫療器材資訊網
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Homogeneous functions | 合法醫療器材資訊網
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