3. Do each of the following production functions exhibit decreasing, constant or increasing returns to scale?...

3. Do each of the following production functions exhibit decreasing, constant or increasing returns to scale? Prove your answers. • Q = .5L^.34 + K^.34 • Q = [min (K, 2L)]^2 • Q = (0.3L^.5 + 0.7K^.5)^2 • Q = 4KLM where K, L, M are inputs

Expert Solution

To check the returns to scale, when we multiply each of the factors by t and check the resulting output. If the resulting output is t times the original output, then it is constant returns to scale. If the resulting output is more than t times the original output then it is increasing returns to scale while decreasing returns to scale when the resulting output is less than t times the original output.

1. Q=0.5L^.34+K^.34

Now multiplying K and L by t will give us: 0.5(tL)^.34+(tK)^.34 =t^(.34+.34) (0.5L^.34+K^.34) =t^.68(0.5L^.34+K^.34) which is less than tQ and hence it exhibits the decreasing returns to scale.

2. Q=[min(K,2L)]^2

Now multiplying K and L by t will give us: [min(tK,t2L)]^2 =t^2 [min(K,2L)]^2 which is more than tQ and hence it exhibits the increasing returns to scale.

3. Q=(0.3L^.5+0.7K^.5)^2

Now multiplying K and L by t will give us: (0.3(tL)^.5+0.7(tK)^.5)^2 = t^(.5+.5)*2 (0.3L^.5+0.7K^.5)^2 = t^2 (0.3L^.5+0.7K^.5)^2 which is more than tQ and hence it exhibits the increasing returns to scale.

4. Q=4KLM

Now multiplying K, L and M by t will give us: 4(tKtLtM) = t^3 4(KLM) which is more than tQ and hence it exhibits the increasing returns to scale.

Rahul Sunny answered 2 years ago

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