13) Joe owns a coffee house and produces coffee drinks under the production function q=K

^{2}L

^{3}, where q is the number of cups generated per hour, K is the number of coffee machines (capital), and L is the number of employees hired per hour (labor). Consider the following statements to answer this question:

I β Average product of labor is AP_{L}=K^{2}L^{2}

II βMarginal product of labor is MP_{L}=3K^{2}L^{2}

III β Marginal rate of technical substitution is MRTS_{L,K}= 2K/3L

A) I is true, II and III are false

B) II is true, I and III are false

C) I and II are true, III is false

D) II and III are true, I is false

E) I, II and III are true