What is homogeneous and homothetic functions?

A function is homogenous of order k if f(tx,ty)=tkf(x,y). A function is homothetic if it is a monotonic transformation of a homogenous function (note that this second function does not need to be homogenous itself).

What do you mean by 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.

Are all homothetic functions homogeneous?

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 the difference between homogeneous and homothetic production function?

If the production function is homogeneous (of any degree), the firm’s isoclines including long-run expansion path would be straight lines from the origin. The homothetic production function has the same isoquants as those of its underlying homogeneous function, although, generally, with different quantity indexes.

What homothetic means?

: similar and similarly oriented —used of geometric figures.

What is meant by 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 is homogeneous production function?

Definition: The Linear Homogeneous Production Function implies that with the proportionate change in all the factors of production, the output also increases in the same proportion. Such as, if the input factors are doubled the output also gets doubled. This is also known as constant returns to a scale.

What are 5 examples of homogeneous?

Here are ten examples of homogeneous mixtures:

  • Sea water.
  • Wine.
  • Vinegar.
  • Steel.
  • Brass.
  • Air.
  • Natural gas.
  • Blood.