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- The aggregate production function is Y = 5KL. If there are 18 units of capital and 50 units of labor, the capital productivity is ___________.1. The Primary Metals production function in Table 7.4 of the MMH textbook, holding nonproduction workers constant, can be roughly expressed as Q = 100*L.08*K.37. Use this function to answer the following. Suppose a firm wishes to produce 1200 units of Q. Use an Excel Spreadsheet to find the MRTSLK in adding a 10th unit of Labor. Conduct your analysis using an Excel Spreadsheet and changing Labor by 1, 2, 3, etc., that is, use integer values of L only. In absolute value terms, the MRTSLK when we add the 10th unit of L is ______. A. 114.9. B. 18.4. C. 11.6. D. 7.5. E. 3.6. 2. This is a continuation of the previous problem. Suppose a Primary Metals company’s ratio of PL to PK is 1.40. What is the optimal (cost minimizing) combination of L and K that should be employed by the firm to produce Q = 1200? Conduct your analysis using an Excel Spreadsheet and changing Labor by 1, 2, 3, etc., that is, use integer values of L only. Use a Spreadsheet and not Excel Solver. The optimal L = _____…Confirm that the Cobb-Douglas production function satisfies all the three properties: more is better, concavity, and CRS.
- The cumulative average labor hours to assemble the first five units of product A were 15.882 hours. If the learning curve, based on the previous experience with similar products, is 85%, what is the estimated time (labor hours) that will be required to assemble the 20th unit?Consider the following Cobb-Douglas production function for the bus transportation system in a city: Q = Lβ1Fβ2Bβ3 Where L = labour input in worker hours F = fuel input in gallons B = capital input in number of buses Q = output measured in millions of bus miles Suppose that the parameters (α, β1, β2 and β3) of this model were estimated using annual data for the past 25 years. The following results were obtained: β1 = 0.45, β2 = 0.20 and β3 = 0.30 a. Determine the (i) labour, (ii) fuel, and (iii) capital-input production elasticitiesWhat is the input use level for total value product maximization for the following function? y = x1 + 0.1x12 - 0.05x13 + x2 + 0.1x22 - 0.05x23
- S1. A firm's production function is well described by the equation Q21-0112 + 3K -02K2. Input prices are $10 per labor hour and $20 per machine hour, and the firm sells its output at a fixed price of $10 per unit. a. In the short run, the firm has an installed capacity of K = 50 machine hours per day, and this capacity cannot be varied. Create a spreadsheet ( based on the example below) to model this production setting.Consider the following Cobb-Douglas production function for the bus transportation system in a city: Q = Lβ1Fβ2Bβ3Where L = labour input in worker hours F = fuel input in gallons B = capital input in number of buses Q = output measured in millions of bus miles Suppose that the parameters (α, β1, β2 and β3) of this model were estimated using annual data for the past 25 years. The following results were obtained: β1 = 0.45, β2 = 0.20 and β3 = 0.30a. Determine the (i) labour, (ii) fuel, and (iii) capital-input production elasticities .b. Suppose that labour input (worker hours) is increased by 2 percent next year (with the other inputs held constant), determine the approximate percentage change in output. c. Suppose that capital input (number of buses) is decreased by 3 percent next year (which, certain older buses are taken out of service). Assuming that the other inputs are held constant, determine the approximate percentage change in output. d. What type of returns to scale appears…Show that the two-input CES production(attached) has DRS, CRS, or IRS depending on whether B (beta) is smaller than, equal, or greater than 1.
- A second firm's production function is given by the equation Q = 12L.5K.5. Input prices are $36 per labor unit and $16 per capital unit, and P = $10. a. In the short run, the firm has a fixed amount of capital, K = 9. Create a spreadsheet to model this production setting. Determine the firm's profit - maximizing employment of labor. Use the spreadsheet to probe the solution using your spreadsheet's optimizer.The profit function in dollars for a product is given -x^3+76x^2-380x-2800 where x is the number of units produced and sold. If break even occurs when 10 units are produced and sold find a quadratic factor of the profit function and find a number of units other than 10 that gives break even for the product.The Department of the Navy estimates that the learning rate for shipbuilding is 80%. Assuming the 80% rate applies to nuclear submarines, how long should it take to build the 12th vessel, if the first one took 62 months to complete?
