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Questions › DSE › DSE 2012 › Q45
2 marksMathematics › Concavity, convexity and quasi-concavity › Quasi-concavity and quasi-convexityHardabout 4 min

DSE 2012 Question 45: Concavity, convexity and quasi-concavity

f(x,y)=x+y+xyf(x,y)=x+y+xyf(x,y)=x+y+xy where x,y∈ℜ++x,y\in\Re_{++}x,y∈ℜ++​. For c∈ℜ++c\in\Re_{++}c∈ℜ++​, let us define, L={(x,y)∈ℜ2∣f(x,y)≤c}L=\{(x,y)\in\Re^{2}\mid f(x,y)\le c\}L={(x,y)∈ℜ2∣f(x,y)≤c}, U={(x,y)∈ℜ2∣f(x,y)≥c}U=\{(x,y)\in\Re^{2}\mid f(x,y)\ge c\}U={(x,y)∈ℜ2∣f(x,y)≥c}, I={(x,y)∈ℜ2∣f(x,y)=c}I=\{(x,y)\in\Re^{2}\mid f(x,y)=c\}I={(x,y)∈ℜ2∣f(x,y)=c}. Which of the above sets are convex?

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f(x,y)=x+y+xy where x,y∈ℜ₊₊. For c∈ℜ₊₊, let us define, L={(x,y)∈ℜ²| f(x,y)≤ c}, U={(x,y)∈ℜ²| f(x,y)≥ c}, I={(x,y)∈ℜ²| f(x,y)=c}. Which of the above sets are convex? (A) L (B) U (C) I (D) All of them

Also written as: f(x,y)=x+y+xy where x,y in Re_(++). For c in Re_(++), let us define, L={(x,y) in Re^2| f(x,y)<= c}, U={(x,y) in Re^2| f(x,y)>= c}, I={(x,y) in Re^2| f(x,y)=c}. Which of the above sets are convex?

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

What this question tests

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

The weaker shape conditions defined by upper or lower level sets.

TestStop has 8 past-paper questions on this subtopic; the nearest in year are below.

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