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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 → 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.]

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.4: Linear Transformations
Problem 34EQ
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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.]
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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