201Spring2011HW2SOLUTIONS

# 201Spring2011HW2SOLUTIONS - Solutions to Problem Set 2...

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Solutions to Problem Set 2. University of Waterloo, Microeconomic Theory 201, Spring 2011. Question 1. Ying°s preferences satisfy the following indi/erence relations and strict pref- erence relations: (2 oranges, 1 apple) ° (2 orange, 0 apples) (2 oranges, 0 apples) ± (0 oranges, 2 apples) (0 oranges, 2 apples) ° (1 orange, 1 apple) (1 orange, 1 apple) ° (1 orange, 0 apples) (1 orange, 0 apples) ± (0 oranges, 1 apple) (0 oranges, 1 apple) ° (0 oranges, 0 apples) Ying°s preferences are also transitive, complete and re±exive. a) In a carefully labeled diagram, depict a set of possible indi/erence curves for Ying that go through the following points: (0 oranges, 1 apple) (1 orange, 0 apples) (1 orange, 1 apple) (0 oranges, 2 apples) (2 oranges, 0 apples) 1

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b) Do Ying°s preferences exhibit diminishing marginal rate of substitution between apples and oranges? Explain. No. Ying prefers combinations among which she is indi/erent ((0 oranges, 2 apples) and (2 oranges, 0 apples)) to the average of these combinations (1 orange, 1 apple). Note: Diminishing marginal rate of substitution requires that Ying°s preferences are convex. However, Ying is indi/erent between the combinations (0 oranges, 2 apples) and (2 oranges, 0 apples) and prefers both of these combinations over the average of these combinations which is (1 orange, 1 apple). In other words, Ying prefers either of two extreme combinations among which she is indi/erent over the average of these combinations. This implies that Ying°s preferences are not convex which in turn implies that Ying°s preference do not exhibit diminishing marginal rate of substitution. c) If the price of an orange is \$1 and the price of an apple is \$1 might Ying ever buy 2 oranges and 0 apples? Explain. Yes. If Joan only has \$2 to spend, according to her preferences she is better o/ by consuming either (0 oranges, 2 apples) or (2 oranges, 0 apples) than any other combination that she can a/ord. The other a/ordable combinations are (1 orange, 1 apple), (0 oranges, 1 apple), (1 oranges, 0 apple) and (0 orange, 0 apple) when the price of an orange is \$1 and the price of an apple is \$1 and Joan only has \$2. d) If the price of an orange is \$2 and the price of an apple is \$1 might Ying ever buy 1 apple and 1 orange? Explain. No. At these prices (1 apple, 1 orange) costs \$2+\$1 = \$3 and with \$3 Joan could purchase (0 oranges, 2 apples), which Joan strictly prefers (0 oranges, 2 apples) over (1 apple, 1 orange). ² 2
Jen°s preferences satisfy the following indi/erence relations and strict preference relations: (2 oranges, 1 apple) ° (1 orange, 1 apple) (1 orange, 1 apple) ° (2 oranges, 0 apples) (2 oranges, 0 apples) ± (0 oranges, 2 apples) (0 oranges, 2 apples) ° (0 orange, 1 apple) (0 oranges, 1 apple) ± (1 orange, 0 apples) (1 orange, 0 apples) ° (0 orange, 0 apple) Jen°s preferences are also transitive, complete and re±exive.

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