Third Problem The short-run production function of a competitive firm is given by f(L) = 6L 2/3 , where L is the amount of labor it uses. The cost per unit of labor is w = 6 and the price per unit of output is p = 3. 1. Plot a few points on the graph of this firm’s production function and sketch the graph of the production function, using blue ink. Use black ink to draw the isoprofit line that passes through the point (0, 12), the isoprofit line that passes through (0, 8), and the isoprofit line that passes through the point (0, 4). 2. What is the slope of each of the isoprofit lines? 3. How many points on the isoprofit line through (0, 12) consist of inputoutput points that are actually possible? 4. Make a squiggly line over the part of the isoprofit line through (0, 4) that consists of outputs that are actually possible. 5. How many units of labor will the firm hire? How much output will it produce? If the firm has no other costs, how much will its total profits be? 6. Suppose that the wage of labor falls to 4, and the price of output remains the same. Will the firm increase its output?