Question

Difference between homogeneous and homothetic function

Answer 1

Answer:

Step-by-step eThe function f of two variables x and y defined in a domain D is said to be homogeneous of degree k if, for all (x,y) in D  

f(tx, ty) = t^k f(x,y)

Multiplication of both variables by a positive factor t will thus multiply the value of the function by the factor t^k.

When k = 1 the production function exhibits constant returns to scale.

When k < 1 the production function exhibits decreasing returns to scale.

When k > 1 the production function exhibits increasing returns to scale.

f is a homothetic function provided that  

for all (x,y) in D,  

[f(x) = f(y), t > 0] implies f(tx) = f(ty)

A homogeneous function f of any degree k is homothetic. But not all homothetic functions are homogeneous.xplanation: