(a) A firm has production function q(k,l) = k'/³12/3, where k denotes the capital used and I 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 %3D are vk + wl. Use the Lagrange multiplier method to determine the values of k and I 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 A* = be

(a) A firm has production function q(k,l) = k'/³12/3, where k denotes the capital used and I 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 %3D are vk + wl. Use the Lagrange multiplier method to determine the values of k and I 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 A = be

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

.(a) A firm has production function q(k,l) = k'/³1²/3, where k
denotes the capital used and I 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 I 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, X*, of the Lagrange multiplier corresponding to the
optimising values of k and l. Show that
d* =

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