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8. Consider the production function Q = (-1/2 + K1/2)2/3, where L denotes labor and K denotes capital. How many of the follow

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Answer #1

Returns to scale can be found out by seeing if the output increases by the same/greater/lesser scale with an increase in the inputs in the same proportion.

Q = (JT +5€) 43 OCAL, AK) = (hil + fe) / ( ( + JG) % yetem (Jet salles sy (JE + Sta) 93

For a lambda increase in inputs, the output increases by less than lambda amd hence we have decreasing returns to scale not increasing.

Therefore this is false.

MRTS shows the rate at which for a given level of output , and for an additional increase in labour , the amount of capital that is needed to be given up.

Q: (se + ja) 43 dan (5t+ sa) *** (41%) (+ sa). 13 (4 x V) dl dk MRTS - MRTS 2

Now, dMRTS/dL is negative i.e.dMRTS/dL = -(0.5)√(KL) <0

This means for an additional increase in labour, the amount of capital that is needed to be given up is decreasing , to maintain a given level of output.

Hence this statement is true.

When L = 2 and K = 8, MRTS = 2 , hence third statement is also true.

So, 2 out of the three statements are true.

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