Question

5. Decide whether the following production functions belong to increasing, constant, or decreasing returns to scale?...

5. Decide whether the following production functions belong to increasing, constant, or decreasing returns to scale?

  1. Q = L^0.3·K60.5

  2. Q = L·K^0.5

  3. Q = L·lnK

  4. Q = L+K^0.8

  5. Q = L+395K

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Homework Answers

Answer #1

1) Q = L^0.3·K60.5

(tL,Kt) = (tL)^0.3 . (tK)^0.5

= t^0.3+0.5 (tL)^0.3 . (tK)^0.5

Power of t = 0.8, so it is decreasing returns to scale.

2 ) Q = L·K^0.5

(tL,Kt) = (tL) . (tK)^0.5

MP of K is falling , it is decreasing returns returns to scale.

3)

Q = L·lnK

(tL,Kt) = (tL) . (IntK)

= t (tL) . (IntK)

Power of t = 1, so it is constant returns to scale.

4)

Q = L+K^0.8

(tL,Kt) = (tL) + . (tK)^0.8

MP of K is diminishing so, it is decreasing returns to scale.

5)

Q = L+395K

(tL,Kt) = (tL)+ . 395(tK)

= t (tL)+ 395(tK)

Power of t = 1, so it is CONSTANT returns to scale.

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