The production function $q = \sqrt { K L }$
A)exhibits constant returns to scale and constant marginal productivities for K and L.
B)exhibits diminishing returns to scale and diminishing marginal productivities for K and L.
C)exhibits constant returns to scale and diminishing marginal productivities for K and L.
D)exhibits diminishing returns to scale and constant marginal productivities for K and L..

Question

Quizplus · Accepted Answer

The production function exhibits constant returns to scale because if we double the inputs, the output will also double (i.e., 2q = 2√(KL) = √(4KL) = √(K2L2) = q). However, the marginal productivities of K and L are diminishing because the partial derivatives of q with respect to K and L are ∂q/∂K = 1/2√(KL) and ∂q/∂L = 1/2√(KL), respectively. As K and L increase, the marginal productivities decrease, indicating diminishing returns to each input individually.

The Production Function q=KLq = \sqrt { K L }q=KL​ A)exhibits Constant Returns to Scale and Constant Marginal Productivities for A)exhibits

The Production Function $q = \sqrt { K L }$ A)exhibits Constant Returns to Scale and Constant Marginal Productivities for A)exhibits