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.: 146 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 0}" xmlns="http://www.w3.org/1998/Math/MathML"> 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.: 147 In a model where competitive consumers optimize homothetic utility functions subject to a budget constraint, the ratios of goods demanded by consumers will depend only on relative prices, not on income or scale. This translates to a linear expansion path in income: the slope of indifference curves is constant along rays beginning at the origin.: 482 This is to say, the