Question

A firm has production function y = f(K,L), where y is output, K is capital, and L is labour. We have:

a. f(K,L) = K^0.4 + L^0.4

b. f(K,L) = (K^0.4)(L^0.4)

What are the firm's production function degree of homogeneity?

I know the answer is 0.4 for A and for B it is 0.8.

But I don't know how to get those answers. I know m = degree of homogeneity. I'm guessing they found A from m = 0.4. For B, i'm not quite sure why the answer is 0.8.

Answer 1

If Production function is given as

f(K,L) and new function is f(@K,@L) then f(@K,@L)=@^b*f(K,L) is called homogeneous function and degree of homogeneity is "b"

Ans A)

f(K,L)=K^0.4+L^0.4

Degree of homogeneity means if inputs such as K,L are increased by scalar quantity @ where @>1

then new production function will become

f(@K,@L)=(@K)^0.4+(@L)^0.4=@^0.4(K^0.4+L^0.4)=@^0.4*f(K,L)

Hence the degree of freedom is equal to the power of scalar multiplier @

therefore degree of homogeneity for a) is 0.4

Ans B)

f(K,L)=(K^0.4)*(L^0.4)

again increasing inputs by scalar @ then we get new function

f(@K,@L)=(@K^0.4)*(@L^0.4)=@^0.8*(K^0.4*L^0.4)=@^0.8*f(K,L)

Hence degree of homogeneity for part b) is 0.8