500359 Microeconomics Tutorial Exercises 3 (2019-20) (1).doc - 500359 \u2013 MICROECONOMICS \u2013 2019\/20 Class Exercises Problem Set 3 1 The following

500359 Microeconomics Tutorial Exercises 3 (2019-20)...

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500359 – MICROECONOMICS – 2019/20 Class Exercises Problem Set 3 1 The following questions relate to the axioms of consumer theory: (i) If a consumer chooses bundle (X 1 , Y 1 ) when bundle (X 2 , Y 2 ) is available, is it right to conclude that (X 1 , Y 1 ) (X 2 , Y 2 )? [Hint: Are the two bundles necessarily on different indifference curves?] (ii) When it comes to dessert, given two options B 1 and B 2 , Calvin always prefers the largest dessert with the most ice cream. Is this preference relation (a) transitive? (b) complete? [Hint: Can you represent all possible bundles with indifference curves that satisfy the axioms?] (iii) Can an indifference curve that satisfies all the axioms cross itself? See Figure 1. [Hint: Compare bundles A and B.] (iv) Prove, using a diagram, that if preferences are monotonic a diagonal line though the origin will intersect each indifference curve exactly once. [Hint: Proof by contradiction helps i.e. what shape must indifference curves be for the line from the origin to cross them more than once? Do these indifference curves represent monotonic preferences?] Figure 1 Y X A B
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