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# Homework 1 Answers - ECO 301 Intermediate Microeconomics...

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ECO 301: Intermediate Microeconomics Marco A Castaneda Homework 1: Answers 1. ANSWER a) Explain what it means for preferences to be (i) transitive, (ii) convex, and (iii) strictly monotone. i. Formally, the preferences of a consumer are transitive if, for any consumption vectors A, B, and C, we have A B and B C imply A C Intuitively, if the consumer prefers A to B and B to C, then the consumer must prefer A to C if the preferences are transitive. This is the basic assumption on the consistency of preferences. ii. Formally, the preferences of the consumer are convex if, for any consumption vectors A, B, and C and any number α [0,1], we have A C and B C imply α A + (1 – α )B C Intuitively, if the consumer prefers A to C and B to C, then any linear combination of A and B should be preferred to C if the preferences are convex. This implies the preferences exhibit a decreasing marginal rate of substitution. You should be able to interpret this assumption graphically. iii. Formally, the preferences of the consumer are strictly monotone if, for any consumption vectors A and B, we have A is “strictly preferred” to B whenever it has more of at least one commodity X Y B C A E D F

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and no less of any other commodity. Intuitively, preferences are
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