A firm's production function is: Q=K0.6L0.5 where K is capital input measured in machine-hours and L...

 

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"A firm's production function is: Q=K0.6L0.5 where K is capital input measured in machine-hours and L is labour input measured in worker-hours. The firm is perfectly competitive and hires its machines at a constant rental rate (r) of £4 per hour and its workers at a constant wage rate (w) of £12 per hour." a. "Using the Lagrange multiplier method, find the minimum cost of producing 100 units of output." (11 marks) b. "In the same way, find the minimum cost of producing 200 units of output." (2 marks) c. "Comparing your answers to (a) and (b), does increasing output by 100% increase costs by more or less than 100% in this example?" (2 marks) d. "Show that, whatever level of output the firm produces, for minimum cost it will always employ capital and labour in the proportion:" K = = 180 L 5 (1 mark) e. "Show how this proportion is related to the input prices (that is, the prices of capital and labour) and the parameters of the production function (that is, the powers of capital and labour)." (3 marks) "A firm's production function is: Q=K0.6L0.5 where K is capital input measured in machine-hours and L is labour input measured in worker-hours. The firm is perfectly competitive and hires its machines at a constant rental rate (r) of £4 per hour and its workers at a constant wage rate (w) of £12 per hour." a. "Using the Lagrange multiplier method, find the minimum cost of producing 100 units of output." (11 marks) b. "In the same way, find the minimum cost of producing 200 units of output." (2 marks) c. "Comparing your answers to (a) and (b), does increasing output by 100% increase costs by more or less than 100% in this example?" (2 marks) d. "Show that, whatever level of output the firm produces, for minimum cost it will always employ capital and labour in the proportion:" K = = 180 L 5 (1 mark) e. "Show how this proportion is related to the input prices (that is, the prices of capital and labour) and the parameters of the production function (that is, the powers of capital and labour)." (3 marks)

Answer rating: 100% (QA)

a Using the Lagrange multiplier method find the minimum cost of producing 100 units of output The Lagrangian function for this problem is given by LKL ... View the full answer