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Questions › DSE › DSE 2020 › Q30
4 marks, −1Mathematics › Concavity, convexity and quasi-concavity › Testing concavity and convexityModerateabout 3 min

DSE 2020 Question 30: Concavity, convexity and quasi-concavity

Given a non-empty set C⊆RnC\subseteq\mathbb{R}^nC⊆Rn, for every p∈R+np\in\mathbb{R}^n_+p∈R+n​ let c(p)∈Cc(p)\in Cc(p)∈C satisfy p⋅c(p)≤p⋅cp\cdot c(p)\le p\cdot cp⋅c(p)≤p⋅c for every c∈Cc\in Cc∈C. Then the function e:R+n→Re:\mathbb{R}^n_+\to\mathbb{R}e:R+n​→R given by e(p)=p⋅c(p)e(p)=p\cdot c(p)e(p)=p⋅c(p) is

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Given a non-empty set C⊆ℝⁿ, for every p∈ℝⁿ₊ let c(p)∈ C satisfy p· c(p)≤ p· c for every c∈ C. Then the function e:ℝⁿ₊→ℝ given by e(p)=p· c(p) is (A) linear (B) convex (C) concave (D) quasi-convex

Also written as: Given a non-empty set C subseteq R^n, for every p in R^n_+ let c(p) in C satisfy p* c(p)<= p* c for every c in C. Then the function e:R^n_+->R given by e(p)=p* c(p) is

Concavity, convexity and quasi-concavity has come up 39 times in 6 exams since 2006.

What this question tests

This question is on Testing concavity and convexity, part of Concavity, convexity and quasi-concavity in Mathematics.

Checking concavity or convexity from a definition, derivatives or operations that preserve it.

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Practise Concavity, convexity and quasi-concavityMore on Testing concavity and convexity

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