Intermediate Microeconomics: Solutions to Homework
Econ3101 - Section 006 Intermediate Microeconomics
Xavier Vinyals-Mirabent Due: Wednesday, February 1st, 2012.
Solutions to Homework 1.
1
1. A consumer has preferences for two goods. Her preferences satisfy Axioms 1 through 4 as discussed in class. A v D v
10
E v 5 C v
B v
0 0 5 (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. 10
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) C(8,4) D(2,8) E(7,3) F(6,9) G(10,10) H(9,6)
B C F G
A D E 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
1 (c) Consider a bundle C = ( 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 ,y 2 1 2
= u 1, 1 √ 1·1
·y =
1 2
·y =1 y=2
3
3. Consider the following four consumers/agents (C1 , C2 , C3 , C4 ) with the following utility functions: Consumer C1 C2 C3 C4 Utility function u(x, y) = 3x + 2y 1 2 u(x, y) = x 3 y 3 u(x, y) = max(3x, y) u(x, y) = min(2x, 2y)
On the appropriate graph below, draw each consumer’s indifference curves through the following points: (2,2), (4,4), (6,6), (8,8) (*Note- this means you should draw an
Xavier Vinyals-Mirabent Due: Wednesday, February 1st, 2012.
Solutions to Homework 1.
1
1. A consumer has preferences for two goods. Her preferences satisfy Axioms 1 through 4 as discussed in class. A v D v
10
E v 5 C v
B v
0 0 5 (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. 10
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) C(8,4) D(2,8) E(7,3) F(6,9) G(10,10) H(9,6)
B C F G
A D E 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
1 (c) Consider a bundle C = ( 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 ,y 2 1 2
= u 1, 1 √ 1·1
·y =
1 2
·y =1 y=2
3
3. Consider the following four consumers/agents (C1 , C2 , C3 , C4 ) with the following utility functions: Consumer C1 C2 C3 C4 Utility function u(x, y) = 3x + 2y 1 2 u(x, y) = x 3 y 3 u(x, y) = max(3x, y) u(x, y) = min(2x, 2y)
On the appropriate graph below, draw each consumer’s indifference curves through the following points: (2,2), (4,4), (6,6), (8,8) (*Note- this means you should draw an