DU MA Economics
Topic:- DU_J18_MA_ECO
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Let R be the set of real numbers and f: R ? R be a continuous and concave function. Which of the following statements is correct?
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[Question ID = 6976]
- If f must be concave [Option ID = 27896]
- -f must be concave [Option ID = 27895]
- f + f must be concave [Option ID = 27898]
- f o f must be concave [Option ID = 27897]
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Correct Answer :-
f + f must be concave [Option ID = 27898]
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The maximum value of f(x, y) = (xy)1/2, subject to x = y and |x| + |y| = 1, is
[Question ID = 6977]
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- 1 [Option ID = 27901]
- 1/2 [Option ID = 27902]
- 0.25 [Option ID = 27899]
- 0.5 [Option ID = 27900]
Correct Answer :-
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0.5 [Option ID = 27900]
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Consider an exchange economy with two agents, 1 and 2, and two goods, X and Y. Each agent's consumption set is R2+. The endowments of agents 1 and 2 are (10,1) and (0,9) respectively. (In any commodity bundle, the first entry is a quantity of X and the second one is a quantity of Y.)
If a > c, or a = c and b > d, then Agent 1 strictly prefers bundle (a, b) to (c, d).
If b > d, or b = d and a > c, then Agent 2 strictly prefers bundle (a, b) to (c, d).
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Which of the following allocations is a competitive equilibrium allocation?
[Question ID = 7047]
- 1 gets (10, 1) and 2 gets (0,9) [Option ID = 28179]
- None of the above [Option ID = 28182]
- 1 gets (10, 10) and 2 gets (0,0) [Option ID = 28180]
- 1 gets (5,5) and 2 gets (5,5) [Option ID = 28181]
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Correct Answer :- Full Marks Given to all the candidates
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Let R be the set of real numbers and let D be the set of functions d: R×R?R that satisfy the following properties for all x, y, z ? R:
- d(x,y) = 0
- d(x, y) = 0 if and only if x = y
- d(x,y) = d(y, x)
- d(x,z) = d(x, y) + d(y, z)
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Which of the following is not a function in D?
[Question ID = 6975]
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- d(x,y) = min{|x -y|, 1} [Option ID = 27893]
- d(x,y) = { 0, if x = y 1, otherwise [Option ID = 27892]
- d(x,y) = { 0, if xy= 1 1, otherwise [Option ID = 27894]
- d(x,y) = |x-y| [Option ID = 27891]
Correct Answer :-
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d(x,y) = { 0, if |x - y| = 1 1, otherwise [Option ID = 27894]
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Let f: [0,1] ?R be twice differentiable. Suppose that the line segment joining the points (0, f(0)) and (1, f(1)) intersects the graph of f at a point (a, f(a)), where 0<a<1. Then,
[Question ID = 6980]
- there exists z ? [0,1] such that f'(z) = 0. [Option ID = 27912]
- there exists z ? [0, 1] such that f"(z) = |f(1)-f(0)|. [Option ID = 27914]
- there exists z ? [0, 1] such that f"(z) = f(1) - f(0) [Option ID = 27911]
- there exists z ? [0, 1] such that f"(z) = 0. [Option ID = 27913]
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Correct Answer :-
there exists z ? [0, 1] such that f"(z) = 0. [Option ID = 27913]
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Consider the matrix
A =
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