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Consider the Cobb-Douglas function f (x1,x2,..,Xn) = x"x i=1 where x; > 0, and a; > 0 for all i=1,2,...,n. Find the condition on a1,ɑ2, ..., An such that ƒ is:

Consider the Cobb-Douglas function f (x1,x2,..,Xn) = x"x i=1 where x; > 0, and a; > 0 for all i=1,2,...,n. Find the condition on a1,ɑ2, ..., An such that ƒ is:

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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Consider the Cobb-Douglas function f (x1,x2,.,Xn) = x i=1 where x; > 0, and a; > 0 for all i = 1,2,...,n. Find the condition on ɑ, ɑ2, ..., Cn such that f is: (c) Suppose that n= 2 so that f (x1,x2) = x“1x?. Is ƒ strictly concave when a1 + a2 = 1? Is f strictly concave when a1+02 < 1?
Transcribed Image Text:Consider the Cobb-Douglas function f (x1,x2,.,Xn) = x i=1 where x; > 0, and a; > 0 for all i = 1,2,...,n. Find the condition on ɑ, ɑ2, ..., Cn such that f is: (c) Suppose that n= 2 so that f (x1,x2) = x“1x?. Is ƒ strictly concave when a1 + a2 = 1? Is f strictly concave when a1+02 < 1?
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