A firm produces a single output (Q) using labor (L) and capital (K). In the short run, capital is fixed at K units of capital. a. Suppose the firm's technology is described by the Cobb-Douglas production function Q=10KVI. Does this technology exhibit a diminishing marginal product of labor? A diminishing average product of labor? (Show your calculations.) What therefore can you say about the shape of this firm's short-run marginal cost curve (e.g. positively sloped, negatively sloped, flat or U-shaped)? What can you say about the shaped of its short-run average variable cost curve? Explain in each case. b. Now suppose that the firm's short-run (total) cost function is given by C(Q=Q2+Q+100 for all output Q20. What does the cost function imply about the shape of the firm's average product of labor curve (e.g. is it positively sloped, negatively sloped, constant or "inverted-U"- shaped)? What does it imply about the shape of its marginal product of labor curve? Explain