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S1. A firm's production function is well described by the equation 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 uni 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. Determine the firm's profit-maximizing employment of labor. Use the spreadsheet to probe the solution by hand before using your spreadsheet's optimizer. Confirm that MRPL = MCL. A C D 1 2 3 4 5 6 7 8 9 10 11 B Labor MPL Q = 2L - .01L² + 3K - .02K². 20.0 1.600 OPTIMAL INPUTS MRPL 16.0 MCL 10.0 E Capital MPK F 50.0 1.000 MRPK 10.0 MCK 20.0 G H Output Price I Cost Ave Cost 136.0 10.0 MR 10.0 Revenue 1360.0 1200.0 8.8

S1. A firm's production function is well described by the equation 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 uni 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. Determine the firm's profit-maximizing employment of labor. Use the spreadsheet to probe the solution by hand before using your spreadsheet's optimizer. Confirm that MRPL = MCL. A C D 1 2 3 4 5 6 7 8 9 10 11 B Labor MPL Q = 2L - .01L² + 3K - .02K². 20.0 1.600 OPTIMAL INPUTS MRPL 16.0 MCL 10.0 E Capital MPK F 50.0 1.000 MRPK 10.0 MCK 20.0 G H Output Price I Cost Ave Cost 136.0 10.0 MR 10.0 Revenue 1360.0 1200.0 8.8

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)
Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)
14th Edition
ISBN:9781305506381
Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Chapter7: Production Economics
Section: Chapter Questions
Problem 8E
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S1. A firm's production function is well described by the equation 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. Determine the firm's profit-maximizing employment of labor. Use the spreadsheet to probe the solution by hand before using your spreadsheet's optimizer. Confirm that MRPL = MCL. C 1 2 3 4 5 6 7 8 9 10 11 12 13 A B Labor MPL Q = 2L .01L² + 3K-.02K². 20.0 1.600 MRPL 16.0 MCL 10.0 D OPTIMAL INPUTS E F Capital 50.0 MPK 1.000 MRPK 10.0 MCK 20.0 G H Output Price MR Revenue Ave Cost I Profit 136.0 10.0 Cost 1200.0 8.8 10.0 1360.0 160.0 b. In the long run, the firm seeks to produce the output found in part (a) by adjusting its use of both labor and capital. Use your spreadsheet's optimizer to find the least-cost input amounts. (Hint: Be sure to include the appropriate output constraint for cell 13.)
Transcribed Image Text:S1. A firm's production function is well described by the equation 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. Determine the firm's profit-maximizing employment of labor. Use the spreadsheet to probe the solution by hand before using your spreadsheet's optimizer. Confirm that MRPL = MCL. C 1 2 3 4 5 6 7 8 9 10 11 12 13 A B Labor MPL Q = 2L .01L² + 3K-.02K². 20.0 1.600 MRPL 16.0 MCL 10.0 D OPTIMAL INPUTS E F Capital 50.0 MPK 1.000 MRPK 10.0 MCK 20.0 G H Output Price MR Revenue Ave Cost I Profit 136.0 10.0 Cost 1200.0 8.8 10.0 1360.0 160.0 b. In the long run, the firm seeks to produce the output found in part (a) by adjusting its use of both labor and capital. Use your spreadsheet's optimizer to find the least-cost input amounts. (Hint: Be sure to include the appropriate output constraint for cell 13.)
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