1. Suppose the short run production function for a firm (i.e. given that capital is fixed at K) is given by the following expression: q = f(L, K) = 12 - 30 13 a. From the above short-run production function, solve for the marginal product of labor. b. For what values of L is the MPL non-negative? c. From the above short-run production function, solve for the average product of labor. d. For what values of L is the APL non-negative? e. What level of L maximizes the APL? f. At what (non-zero) level of L does APL=MPL? How does this value compare to your answer from (e)? g. For values of L lower than the level that equates APL and MPL (solved for in part (f) above), is the MPL greater than or less than the APL? For values of L lower than the level that equates APL and MPL, is the APL upward sloping or downward sloping? h. Finally, using your answers to all of the above questions, plot on a graph (with the level of labor on the horizontal axis) the APL and MPL functions. 2. For the short-run production function given by: q = f(L, K) = 5L + 612 - 13 a. Solve for the levels of L where the following occur: MPL reaches its maximum ii. APL reaches its maximum ii MPL = APL b. Draw the short-run production function (q as a function of L) on graph and the MPL and APL functions on a separate graph. Clearly label on your graphs points (i) through (iii) of part (a). 3. For each of the short-run cost functions listed in (a) and (b) below: i. Solve for the AFC, AVC, AC, and MC for any level of output (q) ii. Graph AVC, AC, and MC in the same figure