7. Long-run cost Suppose Clancy is opening a new restaurant that will produce pizzas using a combination of workers (L) and ovens (K). Clancy knows from experience that the total number of pizzas he can produce in an hour is given by the function g = 6K 05105, Clancy can rent ovens for an hourly cost of $2 and must pay his employees $8 per hour. Therefore, his total hourly cost function is given by IC =2K +2L v Complete the following table by calculating the total cost of producing 24 pizzas per hour using 1 and 3 workers. Pizzas per Hour Workers Ovens Total Cost (q) (L) (K) (Dollars) 24 1 16 24 2 8 32.00 24 3 5.33 82.60 24 4 4 40.00 The cost-minimizing bundle of labor and capital used to produce 24 pizzas is v 3 workers, 5.33 ovens In this example, the rate of technical substitution of labor for capital, when p Suppose Clancy wants to double the number of pizzas he makes in an hour. 1 worker, 16 ovens The cost-minimizing bundle of labor and capital used to produce 24 pizzas is v . In this example, the rate of technical substitution of labor for capital, when producing optimally, is . Suppose Clancy wants to double the number of pizzas he makes in an hour. Complete the following table by computing the total cost of producing 24 pizzas per hour using 3 a Complete the following table by computing the total cost of producing 24 pizzas per hour using 3 and 4 workers. Pizzas per Hour Workers Ovens Total Cost (q) (L) (K) (Dollars) 48 2 32 48 3 21.33 66.66 48 4 16 48 5 12.8 65.60 At the new level of output, the optimal combination of labor and capital is . The cost-minimizing ratio of labor to capital to produce 48 pizzas is w the cost-minimizing ratio needed to produce 24 pizzas. This is always true of production functions that exhibit W returns to scale. At the new level of output, the optimal combination of labor and capital is W . The cost-minimizing ratio of labor to capital to produce 48 pizzas is w the cost-minimizing ratio nee his is always true of production functions that 3 work 21.33 xR 2 sreturns;to:scale: 2 workers, 32 ovens On the following graph, use the blue line (circle symbol) to show the long-| 5 workers, 12.8 ovens Plotting the minimum total costs associated with producing 24 and 48 pizzas, based on your answers to the previous quest 4 workers, 16 ovens At the new level of output, the optimal combination of labor and capital is . The cost-minimizing ratio of labor to capital to produce 48 pizzas is w the cost-minimizing ratio needed to produce 24 pizzas. This is always true of production functions that exhibit v B, different from On the following graph, (circle symbol) to show the long-run total cost function by plotting the minimum total costs associated with At the new level of output, the optimal combination of labor and capital is W . The cost-minimizing ratio of labor to capital to produce 48 pizzas is w the cost-minimizing ratio needed to produce 24 pizzas. This is always true of production functions that exhibit returns to scale. decreasing h, use the blue line (circle symbol) to show the long-run total cost function by plotting the minimum total costs associated with increasing i 3 . pizzas, based on your answers to the previous questions. constant ) On the following graph, use the blue line (circle symbol) to show the long-run total cost function by plotting the minimum total costs associated with producing 24 and 48 pizzas, based on your answers to the previous guestions. @ 80 O 72 Long-Run Cost 64 56 48 40 32 COST (Dollars) 24 0 6 12 18 24 30 36 42 48 54 60 QUANTITY (Pizzas per hour)