Answer to Question #143886 in Finance for Mr. Dinesh Pal Singh

Question #143886
61. Given the production function
Q = 30 K0.7 L0.5
and input prices r = 20 and w = 30, determine the expansion path.
1
Expert's answer
2020-11-17T07:28:16-0500

"Q=30K^\\frac{7}{10}L^\\frac{1}{2}"

obtain the partial derivative of Q wrt to K and L to find Marginal product of labour and marginal product of Capital (K)

"\\frac{dQ}{dK}=30\u2022\\frac{7}{10}\u2022K^\\frac{-3}{10}L^\\frac{1}{2}"

"=" "21K^\\frac{-3}{10}L^\\frac{1}{2}"


"\\frac{dQ}{dL}=30\u2022\\frac{1}{2}\u2022K^\\frac{7}{10}L^\\frac{-1}{2}"

"=15K^\\frac{7}{10}L^\\frac{-1}{2}"


"C=MpL\\times w+MpK\\times r"

"C=15K^\\frac{7}{10}L^\\frac{-1}{2}\\times30+" "21K^\\frac{-3}{10}L^\\frac{1}{2} \\times20"


Therefore the Expansion Path (C)

"C=450K^\\frac{7}{10}L^\\frac{-1}{2} +" "420K^\\frac{-3}{10}L^\\frac{1}{2}"


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