What is the difference between homogeneous and homothetic function?

Homogeneous Production Function – If x and x` produce y units of output then 2x and 2x` produce 2y units of output. Homothetic Production Function- If x and x` produce same level of output y then 2x and 2x` produce same level of output, but not necessarily 2y.

What is a homothetic production function?

Homothetic functions are functions whose marginal technical rate of substitution (the slope of the isoquant, a curve drawn through the set of points in say labour-capital space at which the same quantity of output is produced for varying combinations of the inputs) is homogeneous of degree zero.

What does homothetic mean in economics?

(economics) In which the ratio of goods demanded depends only on the ratio of their prices. adjective.

Are all Cobb Douglas functions homothetic?

It can also be shown algebraically that Cobb-Douglas preferences are homothetic because if XαY 1−α > (X )α(Y )1−α then (tX)α(tY )1−α > (tX )α(tY )1−α. (This is ensured mathematically be- cause the Cobb Douglass utility function is homogeneous, meaning that U(tX, tY ) = tN U(X, Y ) where N is the degree of homogeneity.)

What is the meaning of homothetic?

: similar and similarly oriented —used of geometric figures.

Are log functions homothetic?

3 A linear logarithmic utility function is both additive and homothetic; all expendi- ture proportions are constant, and elas- ticities of substitution among all pairs of commodities are constant and equal to unity.

Are all homogeneous functions homothetic?

Any homogeneous utility function is also homothetic. And since homotheticity is an ordinal property, any increasing transformation of a homogeneous utility function is homothetic too. However, not all homothetic preferences have a homogeneous utility representation.

What is meant by homothetic?

Is CES utility function homothetic?

CES utility function approaches one. CES utility functions are a special case of homothetic preferences.

What does Homothetic mean in economics?

Are all homogeneous functions Homothetic?