Solutions
Player 1
Consider the following game:
A
B
C
Player 2
D
E
7, 6
5, 8
5, 8
7, 6
0, 0
1, 1
F
0, 0
1, 1
4, 4
a. Find the pure strategy Nash equilibria (if any).
Player 1
8.1
A
B
C
Player 2
D
E
7, 6
5, 8
5, 8
7, 6
0, 0
1, 1
F
0, 0
1, 1
4, 4
Best repli
15.2 Suppose that a firms marginal and average costs are constant and equal to c, and
that demand satisfies P = a - bQ, a > 0, b > 0 .
a. Calculate the profit maximizing price-quantity combination for a monopolist, as
well as profit.
The profit maximizing
Solutions for Week 3
6.1
Heidi receives utility, two goods m and s, according to the utility function:
U ( m, s) = m s
a. Show that increases in the price of m will not affect the quantity of s purchased.
The demand function was derived in example 5.3 (an
4.10
Consider the Cobb-Douglass utility function U ( x, y ) = x a y a - 1 , where 0 a 1.
a. Calculate the indirect utility function.
From example 4.1,
x* =
aI
b I (1 - a )I
, y* =
=
px
py
py
Substituting into the utility function:
V ( px , py , I ) U ( x
2.1
[10 pts] Suppose U ( x, y ) = 4 x 2 + 3 y 2 .
a. Calculate U /x, U /y
U ( x, y ) = 4 x 2 + 3 y 2
U x = 4 (2 x ) + 0 = 8 x
U y = 0 + 3(2 y ) = 6 y
b. Evaluate these partial derivatives at x = 1, y = 2 .
Ux = 8 x = 8 = 8
1
U y = 6 y = 6 2 = 12
c. Write
Consider a world consisting a monopolist selling a good a price p and quality s and of
identical consumers with preferences given by the utility function:
qs - p if consumer buys
U =
otherwise
0
The monopolist chooses p and s. The unit cost of production
73-252: Advanced Microeconomic Theory
Tepper School of Business
Carnegie Mellon University
Fall 2008
Final
Name: _
Andrew ID: _
1. [15 points] For the following utility functions, determine if the underlying preferences
are convex. For each, state whether
Econ 73-253
Fall 2009 - Mini 1
Prof. Daniele Coen-Pirani
Practice Final Exam
Exercises in the nal exam will be of similar level of di culty as these practice exercises. The nal
exam is closed-books and closed-notes. You will have 3 hours of time.
Exercise
Econ 73-253
Fall 2009 - Mini 1
Prof. Daniele Coen-Pirani
Suggested Solution Problem Set #5
Exercise #1 [70 pts.]. Exercise 12.6, page 434. The exercise starts with The handmade snubox
industry. (10 points per subpoint).
.
We have 100 rms with short-run to
Econ 73-253
Fall 2009 - Mini 1
Prof. Daniele Coen-Pirani
Suggested Solution to Problem Set #4
Exercise #1 [40 pts.]. Exercise 10.5, page 352. The exercise starts with A rm producing
hockey sticks. (5 points per subpoint).
.
(a) In the SR we have k = 100.
Econ 73-253
Fall 2009 - Mini 1
Prof. Daniele Coen-Pirani
Suggested Solution to Problem Set #3
Exercise #1 [30 pts.]. Consider the following utility function:
U (x; y ) = x + ln y
and assume that I > px :
(a) [5 pts.] Compute the Marshallian demand functio
Econ 73-253
Fall 2009 - Mini 1
Prof. Daniele Coen-Pirani
Suggested Solution Problem Set #2
Exercise #1 [75 pts.]. Exercise 4.7 page 134 of the textbook (15 points per subpoint).
(a) See Figure 1.
(b) The Cobb-Douglas expenditure function is:
p
E (px ; py
Econ 73-253
Fall 2009 - Mini 1
Prof. Daniele Coen-Pirani
Suggested Solution Problem Set #1
Exercise #1 [30 pts.]. Exercise 3.3 page 106 of the textbook (10 points per subpoint).
(a) Utility function
U (x; y ) = xy:
The marginal utilities are
Ux = y; Uy =
Econ 73-253
Fall 2009 - Mini 1
Prof. Daniele Coen-Pirani
Problem Set #5
As indicated on Blackboard, this problem set is due on THURSDAY, October 8, at the end of class.
Please consult the syllabus on the policy for homework assignments handed in late. The
Econ 73-253
Fall 2009 - Mini 1
Prof. Daniele Coen-Pirani
Problem Set #4
As indicated on Blackboard, this problem set is due on THURSDAY, October 1, at the end of class.
Please consult the syllabus on the policy for homework assignments handed in late. The
Econ 73-253
Fall 2009 - Mini 1
Prof. Daniele Coen-Pirani
Problem Set #3
As indicated on Blackboard, this problem set is due on THURSDAY, September 24, at the end of
class. Please consult the syllabus on the policy for homework assignments handed in late.
Econ 73-253
Fall 2009 - Mini 1
Prof. Daniele Coen-Pirani
Problem Set #2
As indicated on Blackboard, this problem set is due on Tuesday, September 15, at the end of class.
Please consult the syllabus on the policy for homework assignments handed in late. T
Econ 73-253
Fall 2009 - Mini 1
Prof. Daniele Coen-Pirani
Problem Set #1
As indicated on Blackboard, this problem set is due on Tuesday, September 8, at the end of class.
Please consult the syllabus on the policy for homework assignments handed in late. Th