数理经济学代写 EC301代写 经济学考试代考 经济学代写
619EC301 Test 数理经济学代写 You have 90 minutes plus 15 minutes reading time. During the reading time, you may write on the question paper but not inside your answer booklet. You have 90 min...
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代写经济学问题集 I. Suppose F(x, y) := x1/2 y1/2 and g(x, y) = x2 + y2 . A. Draw A := {(x, y)|g(x, y) ≤ 1} and B := {(x, y)|F(x, y) > 1}. (8 pts)
Due: Wednesday, April 8, 2:00pm online.
Points Possible: 100.
Suppose F(x, y) := x1/2 y1/2 and g(x, y) = x2 + y2 .
A. Draw A := {(x, y)|g(x, y) ≤ 1} and B := {(x, y)|F(x, y) > 1}. (8 pts)
B. Are A and B convex? A well-drawn figure is sufficient. (8 pts)
C. Are A and B strictly convex? A well-drawn figure is sufficient. (8 pts)
D. Are A and B disjoint? Explain. (8 pts)
E. Can A and B be separated by a hyperplane? Explain. If yes, provide such a hyperplane. (8 pts)
Show that the budget set B := {(x, y)|x + 2y ≤ 4, x, y ≥ 0} is convex, but not strictly convex. (9 pts)
Show that if a set A ⊂ Rn is open and convex, then it must be strictly convex. (8 pts)
A. Show by (counter)example (a well-drawn figure is sufficient) that the convexity of both A and B are typically required to ensure this result. That is, show that if either of A or B is nonconvex then there may be no separating hyperplane. (8 pts)
B. Construct an example of disjoint non-convex that can be separated. Does this contradict the separating hyperplane theorem? Explain. (8 pts)
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