Consider the minimization problem M(p, y) = min x -U(x) s.t. p1 · x1 + ... + pn · xn < y where U:Rn → Ris continuous. Prove that the function M(p, y) : Rn + x R+ → R is quasi-concave. [Hint: the subscript + means that all elements of a vector are nonnegative and at least one is strictly larger than zero.]
Consider the minimization problem M(p, y) = min x -U(x) s.t. p1 · x1 + ... + pn · xn < y where U:Rn → Ris continuous. Prove that the function M(p, y) : Rn + x R+ → R is quasi-concave. [Hint: the subscript + means that all elements of a vector are nonnegative and at least one is strictly larger than zero.]
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 minimization problem M(p, y) = min x -U(x) s.t. p1
· x1 + ... + pn · xn < y where U : Rn → R is continuous. Prove that
the function M(p, y) : R n + x R+ → R is quasi-concave. [Hint: the
subscript + means that all elements of a vector are nonnegative
and at least one is strictly larger than zero.]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc541b931-ed61-4d49-baa7-c070b3f98219%2F913bb482-b019-4f3f-9298-dca57106f08b%2Fj83b8cf_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the minimization problem M(p, y) = min x -U(x) s.t. p1
· x1 + ... + pn · xn < y where U : Rn → R is continuous. Prove that
the function M(p, y) : R n + x R+ → R is quasi-concave. [Hint: the
subscript + means that all elements of a vector are nonnegative
and at least one is strictly larger than zero.]
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