Determine whether each of the production functions below displays constant, increasing, or decreasing returns to scale:...

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Determine whether each of the production functions below displays constant, increasing, or decreasing returns to scale:...

Determine whether each of the production functions below displays constant, increasing, or decreasing returns to scale:
1. Q = K + L + KL
2. Q = 2K² + 3L²
3. Q = KL
4. Q = min(3K, 2L)

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Answer 1

Answer #1

1)Q=K+L+KL

For determining returns to scale, we need to multiply the constant with both the inputs and the output.

If f(xK,xL)> xf(K,L) then it is increasing returns to scale.

If f(xK,xL)< xf(K,L), then decreasing returns to scale

If f(xK,xL)= xf(K,L)., then constant returns to scale

f(xK,xL)= xK+xL+x²KL> x(K+L+KL)=xQ

Hence this would be the case of increasing returns to scale

2) Q=2K²+3L²

f(xK,xL)= 2(xK)²+3(xL)²= x²(f(K,L)>xf(K,L)= xQ

Hence it is also giving increasing returns to scale

3)Q=KL

f(XK,xL)= (xK)(xL)= x²KL> xQ

This also displays increasing returns to scale

4)min(3K,2L)

f(xK,xL)= min(3xK,2xL)= xmin(3K,2L)= Qx

This displays constant returns to scale.

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Answer 2

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