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.]

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.]

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter2: Mathematics For Microeconomics

Section: Chapter Questions

Problem 2.7P

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