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Homework 1 Sol

# Homework 1 Sol - Econ3101 Section 003 Intermediate...

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Econ3101 - Section 003 Intermediate Microeconomics Xavier Vinyals-Mirabent Due: Tuesday, February 8th, 2011. Solutions to Homework 1. 1

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1. A consumer has preferences for two goods. Her preferences satisfy Axioms 1 through 4 as discussed in class. 0 5 10 0 5 10 v A v B v C v D v E (a) Plot and label the following bundles: A (2,10) B (6,2) C (0,4) D (8,10) E (4,6) (b) Assume A is indiﬀerent to B ( A B ). On a single line, list all the bundles in descending order of preference using ( ± ) to denote strict preference and ( ) to denote indiﬀerence between adjacent pairs. In other words, use the form: A ± B ± C ± D ± E Answer: D ± E ± A B ± C , or D ± E ± B A ± C . 2
2. Consider an economic agent who has preferences that are represented by the utility function: u ( x,y ) = xy (a) for each pair of bundles A and B, indicate whether A ± B , A B , or A B (but of course change the letters according to the bundles you are comparing). A B A(4,7) B(7,10) B ± A C(8,4) D(2,8) C ± D E(7,3) F(6,9) F ± E G(10,10) H(9,6) G ± H (b) Using the bundles in (a.), make a list that orders the bundles according to the agent’s preferences. Start with the most preferred bundle and end with the least preferred bundle using ± or (e.g. A ± B ± C ± D ± E ± F ± G ± H ). Answer: G ± B ± F H ± C ± A ± E ± D (c) Consider a bundle C = ( 1 2 ) ,y ), where C contains one-half of a unit of good x and some amount of a good y. If the consumer is indiﬀerent between C and the bundle (1,1), how much of good y does the bundle C contain? Answer: C (1 , 1) ⇐⇒ u ( 1 2 ) = u ( 1 , 1 ) q 1 2 · y = 1 · 1 1 2 · y = 1 y = 2 3

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3. Consider the following four consumers/agents ( C 1 ,C 2 3 4 ) with the following utility functions: Consumer Utility function C 1 u ( x,y ) = 3 x + 2 y C 2 u ( ) = x 1 3 y 2 3 C 3 u ( ) = max (3 ) C 4 u ( ) = min (2 x, 2 y )
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Homework 1 Sol - Econ3101 Section 003 Intermediate...

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