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20. Homogeneous and Homothetic Functions

20. Homogeneous and HomotheticFunctionsHomogeneous and Homothetic Functions are closely related, but areused in different ways in economics. We focus on four main areas,starting with a look at Homogeneity and returns to scale page Homogeneity of derivatives, MRS constant along rays, Euler s the-orem, Wicksteed s Theorem page Ordinal Functions and their equivalence via monotonic transforma-tions, which preserves maxima and minima page Homotheticity and its relation to homogeneity page Homogeneous FunctionsHomogeneity is related to the idea of returns to scale.

Of course, the calculation for the marginal rate of technical substitution is essentially the same. Consequences of this include that facts that income expansion paths and scale ex-pansion paths are rays through the origin whenever the original production or utility function is homogeneous. x y

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