Problem 5 The short-run production function of a competitive firm is y =L) = 6L? where L is the amount of labor. The cost of a unit of labor is w = 6 and the price of a unit of output is p = 3 (a) Plot a few points on the graph of the production function and sketch the production function in the L y space. (b) Write an equation of the prot function: (c) Write an equation of the isoprofit line: (d) What is the slope of the isoprofit line? (9) On the graph in part (a) use different color to draw isoprofit lines going through points (L.Y)=(0.12), (L.y)=(0.8), and (L,V)=(014)- (f) Does the isoprofit line going through point (L,y)=(0,12) have any inputoutput combinations that are feasible? (9) Label the segment of the isoprofit line going though point (L.y):(0,4) that includes feasible input-output combinations by AB. (h) If MPL = Li how much labor will this profitmaximizing firm hire? L 3 (i) How much output will the firm produce? (j) If the firms has no other costs. what is its profit? (k) Suppose the cost of labor falls to 4 (w' = 4) but the price of output stays the same (p = 3). On the previous graph, use different ink to draw the new isoprofit line that goes through the previously optimal labor-output combination (from parts (h) and (i)). (I) Will the firm increase its output at the new cost of labor and why? Use your diagram to explain