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Define a production function F:R X X 12 F(x, x2 ) = { x₁ + x2 1 2 + if x +x >0 1 2 0 if x +x¸ = 0 1 2 > R by → + where x and x, are the amounts of two 1 2 inputs used to produce a single out - put. Given input prices w ω, > 0, > 0 and W 2 consider the problem of finding the cost minimizing input combination of producing at least an output level of one unit: mina x 1 1 (xx) ≥0 1 2 + 2x2 subject to F(x,,x) ≥ 1 and 2 Find the cost - minimizing input demand. Use second order condition and Hessian Matrix

Define a production function F:R X X 12 F(x, x2 ) = { x₁ + x2 1 2 + if x +x >0 1 2 0 if x +x¸ = 0 1 2 > R by → + where x and x, are the amounts of two 1 2 inputs used to produce a single out - put. Given input prices w ω, > 0, > 0 and W 2 consider the problem of finding the cost minimizing input combination of producing at least an output level of one unit: mina x 1 1 (xx) ≥0 1 2 + 2x2 subject to F(x,,x) ≥ 1 and 2 Find the cost - minimizing input demand. Use second order condition and Hessian Matrix

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Define a production function F:R X X 12 F(x, x2 ) = { x₁ + x2 1 2 + if x +x >0 1 2 0 if x +x¸ = 0 1 2 > R by → + where x and x, are the amounts of two 1 2 inputs used to produce a single out - put. Given input prices w ω, > 0, > 0 and W 2 consider the problem of finding the cost minimizing input combination of producing at least an output level of one unit: mina x 1 1 (xx) ≥0 1 2 + 2x2 subject to F(x,,x) ≥ 1 and 2 Find the cost - minimizing input demand. Use second order condition and Hessian Matrix
Transcribed Image Text:Define a production function F:R X X 12 F(x, x2 ) = { x₁ + x2 1 2 + if x +x >0 1 2 0 if x +x¸ = 0 1 2 > R by → + where x and x, are the amounts of two 1 2 inputs used to produce a single out - put. Given input prices w ω, > 0, > 0 and W 2 consider the problem of finding the cost minimizing input combination of producing at least an output level of one unit: mina x 1 1 (xx) ≥0 1 2 + 2x2 subject to F(x,,x) ≥ 1 and 2 Find the cost - minimizing input demand. Use second order condition and Hessian Matrix
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