3. A firm's production function has the Cobb-Douglas form Q =100K 0.50.25 (a) Find the marginal products of capital and labour and show that they can be written respectively as aQ ak = 0.5 and aL -0.25- (b) Are the marginal products of capital and labour ever negative? Explain how you reached your answer. Give an economic interpretation to your answer. (c) How are the marginal products of capital and labour related to the respective average products? Explain how you reached your answer. (d) Sketch the graphs of the marginal and average product functions. (e) Show that the four second-order partial derivatives can be written as a2 Q -0.25 Q a2Q 3 . Q 22Q 1Q ; and ak 2 K 2 aL2 16 2 aLak 8 KL aKal | 8 KL (f) Is diminishing marginal productivity a characteristic of this production function? If so, does it operate at some, or all, levels of input and output? Explain how you reached your answer. (g) What is the effect on the marginal product of one input if the other input is increased to a new fixed value? Explain how you reached your