page_title: Cardinal utility
hierarchical_section_title: Cardinal utility
context_page_description: In economics, a cardinal utility function or scale is a utility index that preserves preference orderings uniquely up to positive affine transformations. Two utility indices are related by an affine transformation if for the value of one index u, occurring at any quantity of the goods bundle being evaluated, the corresponding value of the other index v satisfies a relationship of the form
  ,
  for fixed constants a and b. Thus the utility functions themselves are related by
  The two indices differ only with respect to scale and origin. Thus if one is concave, so is the other, in which case there is often said to be diminishing marginal utility.
  Thus the use of cardinal utility imposes the assumption that levels of absolute satisfaction exist, so that the magnitudes of increments to satisfaction can be compared across different situations.
  In consumer choice theory, ordinal utility with its weaker assumptions is preferred because results that are just as strong can be derived.
context_section_description: In economics, a cardinal utility function or scale is a utility index that preserves preference orderings uniquely up to positive affine transformations. Two utility indices are related by an affine transformation if for the value  of one index u, occurring at any quantity  of the goods bundle being evaluated, the corresponding value  of the other index v satisfies a relationship of the form
  ,
  for fixed constants a and b. Thus the utility functions themselves are related by
  The two indices differ only with respect to scale and origin. Thus if one is concave, so is the other, in which case there is often said to be diminishing marginal utility.
  Thus the use of cardinal utility imposes the assumption that levels of absolute satisfaction exist, so that the magnitudes of increments to satisfaction can be compared across different situations.
  In consumer choice theory, ordinal utility with its weaker assumptions is preferred because results that are just as strong can be derived.
caption: A simple example of two cardinal utility functions u (first column) and v (second column) whose values in all circumstances are related by v=2u+3