Capital Labor 4 Figure 7.10 11.Suppose that airm'production function The cost ofa uit of labor is $20 and the cost of a unit of capital is $80. Graphically illustrate this situation on a graph using isoquants and isocost lines. The isoquant is convex.The optimal quantities of labor and capital are given by the point where the isocost line is tangent to the isoquant.The isocost line has a slope of l/4.given labor is on the horizontal axis.The total cost is TC=2+5=800.so the isocost line has the equation $800=20L+80K. On the graph,the optimal point is point A b.The firm now wants to increase output to 140 units.If capital is fixed in the short run,how uch labor will the firm require?Illustrate this point on your graph and find the new cost. The new level of labor is 39.2.To find this,use the production function =10 and eapital. The new cost is T9.+5=$1184.The new isoquant for an output of 140 is above and to the right of the old oquant for an output of 100. Since capital is fixed in the short run.the firm will move out horizontally to the new isoquant and new Capital Labor 4 4 isocost lines isoquant Figure 7.10 11. Suppose that a firm’s production function is  q =10L 1 2K 1 2 . The cost of a unit of labor is $20 and the cost of a unit of capital is $80. a. The firm is currently producing 100 units of output, and has determined that the cost-minimizing quantities of labor and capital are 20 and 5 respectively. Graphically illustrate this situation on a graph using isoquants and isocost lines. The isoquant is convex. The optimal quantities of labor and capital are given by the point where the isocost line is tangent to the isoquant. The isocost line has a slope of 1/4, given labor is on the horizontal axis. The total cost is TC=$20*20+$80*5=$800, so the isocost line has the equation $800=20L+80K. On the graph, the optimal point is point A. capit al labor isoquant point A b. The firm now wants to increase output to 140 units. If capital is fixed in the short run, how much labor will the firm require? Illustrate this point on your graph and find the new cost. The new level of labor is 39.2. To find this, use the production function  q =10L 1 2K 1 2 and substitute 140 in for output and 5 in for capital. The new cost is TC=$20*39.2+$80*5=$1184. The new isoquant for an output of 140 is above and to the right of the old isoquant for an output of 100. Since capital is fixed in the short run, the firm will move out horizontally to the new isoquant and new