HW 1
Econ4001.02
Intermediate Microeconomics - Homework 1
Maryam Saeedi
Due Tuesday, February 3, 8am
Please answer all parts to all questions. Do so neatly and scan the document on Dropbox. If you have appropriate softwares you can answer the questions in pdf editor. You are welcome to work with classmates on homework but remember to note who you worked with at the top of the cover page. Please refer to the syllabus regarding the homework policy.
1
1. A consumer has preferences for two goods. Her preferences satisfy Axioms 1 through 4 as discussed in class.
10
5
0
0
5
10
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. 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 as, e.g., in the form A ≻ B ≻ C ∼ D ≻ E.
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.
A
B
(4, 7) (7, 10)
(8, 4)
(2, 8)
(7, 3)
(6, 9)
(10, 10) (9, 6)
b. Using the bundles in (a), make a list that orders the bundles according to the agent’s preferences.
Start the descending list with the most preferred bundle and end with the least preferred bundle.
(For example, as before: A ≻ B ≻ C ∼ D ≻ E)
c. Consider a bundle C = ( 12 , y), where C contains a half unit of good x and some amount of good
y. If the consumer is indifferent between bundle C and the bundle (1, 1), how much of good y does the bundle C contain?
3. Consider the following four consumers (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) = min(3x, y) u(x, y) = min(2x, 2y)
On the appropriate graph below, draw each consumer’s indifferent curves through the following points: (2,2), (4,4), (6,6) and (8,8).
C1
C2
10
Intermediate Microeconomics - Homework 1
Maryam Saeedi
Due Tuesday, February 3, 8am
Please answer all parts to all questions. Do so neatly and scan the document on Dropbox. If you have appropriate softwares you can answer the questions in pdf editor. You are welcome to work with classmates on homework but remember to note who you worked with at the top of the cover page. Please refer to the syllabus regarding the homework policy.
1
1. A consumer has preferences for two goods. Her preferences satisfy Axioms 1 through 4 as discussed in class.
10
5
0
0
5
10
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. 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 as, e.g., in the form A ≻ B ≻ C ∼ D ≻ E.
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.
A
B
(4, 7) (7, 10)
(8, 4)
(2, 8)
(7, 3)
(6, 9)
(10, 10) (9, 6)
b. Using the bundles in (a), make a list that orders the bundles according to the agent’s preferences.
Start the descending list with the most preferred bundle and end with the least preferred bundle.
(For example, as before: A ≻ B ≻ C ∼ D ≻ E)
c. Consider a bundle C = ( 12 , y), where C contains a half unit of good x and some amount of good
y. If the consumer is indifferent between bundle C and the bundle (1, 1), how much of good y does the bundle C contain?
3. Consider the following four consumers (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) = min(3x, y) u(x, y) = min(2x, 2y)
On the appropriate graph below, draw each consumer’s indifferent curves through the following points: (2,2), (4,4), (6,6) and (8,8).
C1
C2
10