Do the following production functions exhibit constant returnsto scale, increasing returns to scale, or decreasing returns to scale? For full credit, show why.
1)Q= 10L^ 0.5K^0.3
2)Q= 10L^0.5K^0.5
3)Q= 10L^0.5K^0.7
4)Q= min{K, L}
To check increasing / decreasing / constant returns to scale, we need to put L, K as aL and aK respectively. If the constant which we take common have power more than 1, it is increasing funcion. If the power equal 1, function is contant otherwise decreasing.
1) Q = 10L^0.5 * K^0.3
Q = 10(aL)^0.5 * (aK)^0.3
q = 10 a^0.8 L^0.5 * K^0.3
As power to a is less than 1, it is decreasing function.
2) Q = 10L^0.5 * K^0.5
Q = 10 (aL)^0.5 * (aK)^0.5
Q = 10a L^0.5 * K^0.5
As power of a is equal to 1, function gives constant returns to scale.
3) Q = 10L^0.5 * K^0.7
Q = 10 (aL)^0.5 * (aK)^0.7
Q = 10a^1.2 L^0.5 * K^0.7
As power of a is more than 1, it gives increasing returns.
4) Q = min (K, L)
Q = min (aK, aL)
Q = a * min (K, L)
This gives constant returns to scale.
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