Question

Given the following production function; Y=AX^(3/4) X^(1/4)

Required:
Calculate the degree of homogeneity of the above function and comment
on the returns to scale.

Answer 1

Solution:

We are going to Calculate the degree of homogeneity of a function Y = $A \space X^{(\frac {3} {4})} X^{(\frac {1} {4})}$

We know, If the bases are equal in the multiplication, we can add the powers

So, the given equation can be written as $Y =A \space X^{(\frac {3} {4})+ (\frac {1} {4})}$ = $A \space X^{(\frac {4} {4})} = A X$

Let f (X) = Y = A X

f(kX) = A (k X) = $k^{1}$ (A X) = $k^{1} f(X)$

Yes, it is a homogeneous function of degree = 1

Measure of returns to scale is 1

Answer: The given function is homogeneous function of order 1