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8. (a) A firm has production function q(k,l) = k/312/3, where k denotes the capital used andl denotes the labour employed. Suppose that each unit of capital costs v dollars and each unit of labour costs w dollars, so that the capital and labour costs are vk + wl. Use the Lagrange multiplier method to determine the values of k and l that minimise the cost of producing Q units of the firm's good. Find the corresponding minimised value, C, of this cost and the value, A*, of the Lagrange multiplier corresponding to the optimising values of k and l. Show that

8. (a) A firm has production function q(k,l) = k/312/3, where k denotes the capital used andl denotes the labour employed. Suppose that each unit of capital costs v dollars and each unit of labour costs w dollars, so that the capital and labour costs are vk + wl. Use the Lagrange multiplier method to determine the values of k and l that minimise the cost of producing Q units of the firm's good. Find the corresponding minimised value, C, of this cost and the value, A*, of the Lagrange multiplier corresponding to the optimising values of k and l. Show that

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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8. (a) A firm has production function q(k,l) = k1/312/3¸ where k denotes the capital used andl denotes the labour employed. Suppose that each unit of capital costs v dollars and each unit of labour costs w dollars, so that the capital and labour costs are vk + wl. Use the Lagrange multiplier method to determine the values of k and l that minimise the cost of producing Q units of the firm's good. Find the corresponding minimised value, C, of this cost and the value, A*, of the Lagrange multiplier corresponding to the optimising values of k and l. Show that aC X* =
Transcribed Image Text:8. (a) A firm has production function q(k,l) = k1/312/3¸ where k denotes the capital used andl denotes the labour employed. Suppose that each unit of capital costs v dollars and each unit of labour costs w dollars, so that the capital and labour costs are vk + wl. Use the Lagrange multiplier method to determine the values of k and l that minimise the cost of producing Q units of the firm's good. Find the corresponding minimised value, C, of this cost and the value, A*, of the Lagrange multiplier corresponding to the optimising values of k and l. Show that aC X* =
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