Homothetic preferences
In consumer theory, a consumer's preferences are called homothetic if they can be represented by a utility function which is homogeneous of degree 1. For example, in an economy with two goods x , y {\displaystyle x,y} , homothetic preferences can be represented by a utility function u {\displaystyle u} that has the following property: for every a > 0 {\displaystyle a>0} : u ( a ⋅ x , a ⋅ y ) = a ⋅ u ( x , y ) {\displaystyle u(a\cdot x,a\cdot y)=a\cdot u(x,y)} In mathematics, a homothetic function is a monotonic transformation of a function which is homogeneous; however, since ordinal utility functions are only defined up to an increasing monotonic transformation, there is a small distinction between the two concepts in consumer theory.