Suppose the production function for good q is given by q = K L where K and L are

Question

Suppose the production function for good q is given by q = K L where K and L are capital and labor inputs. Consider three statements about this function:

I. The function exhibits constant returns to scale

II. The function exhibits diminishing marginal productivities to all inputs

III. The function has a constant marginal rate of technical substitution

Which of these statements are true?

A) All of them

B) None of them

C) I and II but not III

D) I and III but not II

E) II and III but not I

If you can answer within next 48 hours that would be great

Explanation / Answer

q= K.L

Now, to see whether this production function exhibits constant returns to scale. Double the inputs K and L.

By doubling the input we get,

(2K).(2L)

= 22(K.L)

= 4q >2q [So, this production function exhibits increasing returns to scale]

Now, next to see whether this production function exhibits diminishing marginal prductivities to all inputs. Find the marginal product of labor and marginal product of capital.

MPL = K and MPK = L

Now, do the second-order partial derivatives of the production function, we get.

d MPL/dL =0 and dMPK/dK =0.

This implies that production function exhibits constant marginal productivities to all inputs.

Now, to check whether the production function has a constant marginal rate of technical substitution. Now, calculate the marginal rate of technical substitution.

Marginal rate of technical substitution (MRTS) = MPL/MPK = K/L

Now, when we do the derviative of MRTS w.r.t L then, we get the negative value. So, this implies that the production function has a diminishing marginal rate of technical substitution.

Hence, None of them are correct. Option(B) is correct.

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