Kusho Industries produces and sells computer chips. Its (hourly) production function is Q=4K 0.4L 0.6 while its (hourly) cost function is C=20L+80K. Furthermore, Kusho must produce q0=400 computer chips per hour. a. Which levels of L and K satisfy the first-order conditions for the constrained minimisation of Kusho’s cost? Use the Lagrange Multiplier (LM) method. Also, find and interpret the value of the Lagrangemultiplier b. Show that MRTS=w at the constrained cost minimising levels of L and K obtained above
Kusho Industries produces and sells computer chips. Its (hourly) production function is Q=4K 0.4L 0.6 while its (hourly) cost function is C=20L+80K. Furthermore, Kusho must produce q0=400 computer chips per hour. a. Which levels of L and K satisfy the first-order conditions for the constrained minimisation of Kusho’s cost? Use the Lagrange Multiplier (LM) method. Also, find and interpret the value of the Lagrangemultiplier b. Show that MRTS=w at the constrained cost minimising levels of L and K obtained above
Chapter10: Cost Functions
Section: Chapter Questions
Problem 10.5P
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Kusho Industries produces and sells computer chips. Its (hourly) production function is Q=4K 0.4L 0.6 while its (hourly) cost function is C=20L+80K. Furthermore, Kusho must produce q0=400 computer chips per hour.
a. Which levels of L and K satisfy the first-order conditions for the constrained minimisation of Kusho’s cost? Use the Lagrange Multiplier (LM) method. Also, find and interpret the value of the Lagrangemultiplier
b. Show that MRTS=w at the constrained cost minimising levels of L and K obtained above
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