310-1 Winter 2008 PS2 Brief Answers

310-1 Winter 2008 PS2 Brief Answers - Economics 310-1...

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Economics 310-1 Problem Set 2—Brief Answers Winter 2008 1, 2. See handout. 3. a) C = 6. c) Yes, convex. d) 1) MU G / P G = MU C / P C and 2) P C C+ P G G = I. . These yield C = 10.5 and G = 5.75. 4. a) MU x = 2xy 2 , MU y = 2x 2 y, MRS = y/x. As x increases and y decreases, the MRS becomes smaller so the IC’s are convex. b) MU x = y 1/2 /2x 1/2 MU y = x 1/2 /2y 1/2 , MRS = y/x. They are the same—the utility functions in a) and b) are monotonic transformations (increasing functions) of one another. c) MU x = y 2 , MU y = 2xy, MRS = y/2x. Convex. d) MU x = 5, MU y = 3, MRS = 5/3. IC’s are linear. e) MU x = 2x + 2y, MU y = 2x + 2y, MRS = 1. IC’s are linear. Note: U = x 2 + 2xy + y 2 = (x+y) 2 . So, U and W = x + y have the same IC’s. 5. x = 25, y = 10. 6. x = 25, y = 10. 7. The utility function of # 5 is the utility function of # 6 squared. That is, they are monotonic transforms (increasing functions) of one another. Thus, the values of x and y that maximize utility will be the same in the problems. 8.
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310-1 Winter 2008 PS2 Brief Answers - Economics 310-1...

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