Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Q1(2)

(2) Assume that we have a Cobb-Douglas production function for a certain industry:
Q = CL°K®,
where c is a constant, and L and K represent labor input and capital input, respectively.
Assume that the production is fixed at Q
Qo, and at this fixed level of production, K is a
function of L defined by
Qo = CL°K®.
Use the implicit differentiation rule to find the "rate of substitution of capital for labor",
which is measured by aK/ƏL when the production is fixed at Q = Qo (show the necessary
steps).
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Transcribed Image Text:(2) Assume that we have a Cobb-Douglas production function for a certain industry: Q = CL°K®, where c is a constant, and L and K represent labor input and capital input, respectively. Assume that the production is fixed at Q Qo, and at this fixed level of production, K is a function of L defined by Qo = CL°K®. Use the implicit differentiation rule to find the "rate of substitution of capital for labor", which is measured by aK/ƏL when the production is fixed at Q = Qo (show the necessary steps).
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