Question

# The KM Corporation builds widgets in Washington. It combines capital (K) and labour (L) in the...

The KM Corporation builds widgets in Washington. It combines capital (K) and labour (L) in the production function in the following way:

Q(K,L) = K1/3L1/3 Labour cost: w = \$8 Capital rental cost: v = \$8

What do we call this form of production function?

This type of production function is called as the cobb-dauglas typeof production function. But, we can see that the capital share is 1/3 and the labour share is 1/3, and the sum of them is less than 1 (i.e. 2/3). So, this is strictly not a cobb-dauglas production function. This is production function exhibits a decreasing returns to scale. Which means that is we increase the labour (L) and Capital (K) by n times, the Output will increase by lessthan the n times. It can be shown as follows:

Thus, the production function is decreasing returns to scale.

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