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2. A firm uses capital, K, and labor, L, to produce output P according to P = KaL, a, 3 are positive constants. 1) What is the equation of the level curve corresponding to a level of output equal to one? 2) What is the equation of the tangent plane to the production surface at K = L = 1? 3) What is the equation of the tangent 'plane' to the level curve corresponding to P = 1 at K = L = 1? 4) If it were possible to increase K and L slightly in any proportion so that |(K; L)| = k, where k is a small positive number, what change in K and I would lead to the greatest increase in output?

2. A firm uses capital, K, and labor, L, to produce output P according to P = KaL, a, 3 are positive constants. 1) What is the equation of the level curve corresponding to a level of output equal to one? 2) What is the equation of the tangent plane to the production surface at K = L = 1? 3) What is the equation of the tangent 'plane' to the level curve corresponding to P = 1 at K = L = 1? 4) If it were possible to increase K and L slightly in any proportion so that |(K; L)| = k, where k is a small positive number, what change in K and I would lead to the greatest increase in output?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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2. A firm uses capital, K, and labor, L, to produce output P according to P = KaL³, a, 3 are positive constants. 1) What is the equation of the level curve corresponding to a level of output equal to one? 2) What is the equation of the tangent plane to the production surface at K = L = 1? 3) What is the equation of the tangent 'plane' to the level curve corresponding to P = 1 at K = L = 1? 4) If it were possible to increase K and L slightly in any proportion so that |(K; L)| = k, where k is a small positive number, what change in K and I would lead to the greatest increase in output?
Transcribed Image Text:2. A firm uses capital, K, and labor, L, to produce output P according to P = KaL³, a, 3 are positive constants. 1) What is the equation of the level curve corresponding to a level of output equal to one? 2) What is the equation of the tangent plane to the production surface at K = L = 1? 3) What is the equation of the tangent 'plane' to the level curve corresponding to P = 1 at K = L = 1? 4) If it were possible to increase K and L slightly in any proportion so that |(K; L)| = k, where k is a small positive number, what change in K and I would lead to the greatest increase in output?
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