Question

Consider the production function: Y=f(K,L)=120K¹/³ L ²/⁵

A. Prove that the production function follows a homogenous function. Do you think that this satisfies the constant returns to scale? Explain your answer.

Answer 1

The production function is a homogenous function of degree one and satisfies constant returns to scale.

Step-by-step explanation:

The production function Y = f(K, L) = 120K1/3 L2/5 is a homogenous function of degree one. A function is homogenous if it satisfies the property f(tK, tL) = t^r * f(K, L), where r is the degree of homogeneity. In this case, the degree of homogeneity is 1, so the production function satisfies this property.

Now, let's check if the production function satisfies constant returns to scale (CRS). CRS means that if we scale all inputs by a factor t, the output will be scaled by the same factor t. To check if the production function satisfies CRS, we substitute tK and tL into the production function and observe if the output is scaled proportionally.

Y = f(tK, tL) = 120(tK)1/3(tL)2/5 = t(120K1/3L2/5) = tY