State whether the following production functions exhibit dec

State whether the following production functions exhibit decreasing returns to scale, increasing returns to scale, or constant returns to scale, briefly explain: Q = K/(L)^2. Q = 4K + 2L. Q = AK^aL^b(a + b=l). dQ = A K^aL^b (a + b

Solution

(a) Q = K/(L)²

This function exhibits decreasing returns to scale. Because when the inputs are doubled, output will double.

Let, L = 2 & K = 2

Q = 2/2² = 0.5

Now, let the inputs are doubled.

Q = 4/4² = 0.25

(b) Q = 4K + 2L

This function exhibits constant returns to scale. Because when the inputs are doubled, output will double.

Let, L = 2 & K = 2

q = 4(2) + 2(2) = 12

Now, let the inputs are doubled.

Then, Q = 4(4) + 2(4) = 24

(c) Q = AK^aL^b (a+b=1)

This function exhibits increasing returns to scale. Because when the inputs are doubled, output will more than double.

Let, L = 2 & K = 2;    q = 0.6 & b = 0.4     and A = 5

Q = 5(2)^0.6(2)^0.4 = 9.306

Now, let the inputs are doubled.

Q = 5(4)^0.6(4)^0.4 = 20.01

(d) AK^aL^b (a+b<1)

This function exhibits decreasing returns to scale. Because when the inputs are doubled, output will more than double.

Let, L = 2 & K = 2;    q = 0.5 & b = 0.3     and A = 5

Q = 5(2)^0.5(2)^0.3 = 8.67

Now, let the inputs are doubled.

Q = 5(4)^0.5(4)^0.3 = 15.2