Fall 2009 Econ 810: Microeconomic Theory
Solutions to Assignment 4
1. (i) Deriving the Lagrangian etc., the Marshallian demands for A are:
xAi (p; m) =
m1
1
2 /[ p + p ]
pi
1
2
while that for B (using the well-known formula for Cobb-Douglas functions):
m
Econ 810: Microeconomic Theory
Solutions to Assignment 2
1. From Assignment 1, individuals lifetime utility if he saves is given
the
I +s(1+rs )
1
by: 1/4 1/4 [ I s +
].
(1+i)
2
(1+ 2 (1+i)]
Optimizing this gives s = [2 I [ r )2rs ) r )(1+i)] .
(1+ s +(1
Econ 810: Microeconomic Theory
Solutions to Assignment 3
1. (i) Here, F (x) = 0 for x < 1, F (x) = x+1 for x [1, 1] and
2
F (x) = 1 for x > 1.
G(x) = 0 for x < 0, G(x) = x for x [0, 2] and G(x) = 1 for x > 2.
2
G(x) = 0 < F (x) = x+1 for x [1, 0].
2
G(x)
Econ 810: Microeconomic Theory
Assignment 2
Due Date: Thursday, 15th October 2009, in class.
1. In Assignment 1, Q.4, you considered the saving and borrowing decisions of an individual who lives for two periods and has the utility function:
1/4 1/4
1/4 1/
1
Fall 2009 Econ 810 Midterm Examination
Tuesday, 27 th October 2009, 1:00 - 2:15 p.m. Total points: 50
Answer all questions.
1. [10 pts] Dene a consumers indirect utility function, v (p; m), and show that it is
e
0
00
e
e
e
quasi-convex in prices i.e. gi
Econ 810: Microeconomic Theory
Assignment 1
Due Date: Thursday, 25 September 2014, in class.
1. Mr. Smiths preferences over goods 1, 2 are represented by the
utility function:
(1 2 ) =
1 2
1 2
0
0 1
X
= 1
=1
(i) Find his Marshallian demand function for
Econ 810: Microeconomic Theory
Assignment 1
Due Date: Thursday, 1 st October 2009, in class.
1. Mr. Smiths preferences over goods 1, 2, ., n are represented by the
utility function:
u(x1 , x2 , ., xn ) = x + x + . + x ,
1
2
n
x1 , x2 , ., xn 0,
0<1
(i) Fi
Econ 810: Microeconomic Theory
Assignment 2
Due Date: Thursday, 9th October 2014, in class.
1. Take a consumer with the following indirect utility function (over 2
goods): (p; ) = 2(1 2 )
+
Suppose the price of good 1 drops from its current level 1 = 10
Fall 2009 Econ 810: Microeconomic Theory
Assignment 4
Due Date: Friday, 13th November 2009 (by 3 p.m.).
1. Consider the following two goods and two consumers (2 X 2) exchange
economy. Preferences and endowments are described by:
uA (x1 , x2 ) =
x1 + x2 ,
Econ 810: Microeconomic Theory
Assignment 3
Not required to be handed in.
1. Consider a competitive market for good 1 in which there are 100 consumers, all with the utility function over goods 1 and 2 given by:
(1 2 ) =
1
1
ln(1 ) + ln(2 )
4
4
The price o
Fall 2009 Econ 810: Microeconomic Theory
Assignment 5
Due Date: Tuesday, 1 st December 2009, in class.
1. Consider the following simultaneous move game. Look for strategies that
are strictly dominated (may also be by mixed strategies) for either player;
e
Econ 810: Microeconomic Theory
Assignment 5
Due Date: Thursday, 27th November 2014, in class.
1. Consider the following model of bidding for a government project with incomplete information. There are 2 rms who are each interested in obtaining
the project
1
Econ 810 Final Examination
Wednesday, 7 December 2011, 9:00 a.m. - 12:00 noon. Total points: 100
Answer ALL questions. Be sure to explain/justify all your steps. You will be wellrewarded for completeness in answers, but not for making points way o the m
1
Fall 2010 Econ 810 Midterm Examination
Tuesday, 26 th October 2010, 11:30 - 12:50 p.m. Total points: 50
Answer all questions.
1. [12 pts] Consider a competitive rm that uses n inputs to produce a single output
according to the production technology f (x
1
Fall 2014 Econ 810 Midterm Examination
Tuesday, 21 October 2014, 1:00 - 2:20 p.m. Total points: 50
Answer all questions.
1. [8 pts] Suppose the consumption bundle minimizes the consumers expenditure
at prices p, subject to the utility constraint 0 Show
1
Econ 810 Final Examination
Monday, 13 December 2010, 9:00 a.m. - 12:00 noon. Total points: 100
Answer ALL questions. Be sure to explain/justify all your steps. You will be wellrewarded for completeness in answers, but not for making points way o the mar
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Fall 2011 Econ 810 Midterm Examination
Wednesday, 26 October 2011, 1:00 - 2:20 p.m. Total points: 50
Answer all questions. Some hints are given at the bottom of the exam.
1. [22 pts] Lee has the following utility function over goods and :
1
ln +
2
(i)
Econ 810: Microeconomic Theory
Assignment 6
Not required to hand in
1. Consider the following simultaneous-move 3 X 3 game between players
and . The rst element in any square represents the payo to
and the second element, the payo to .
20 30
60 15
50 70
Fall 2014 Econ 810: Microeconomic Theory
Assignment 4
Due Date: Thursday, 13th November 2014, in class
1. [GE with intertemporal considerations] Consider an exchange
economy with three consumers, and and one physical good
Each consumer lives for two peri
Fall 2009 Econ 810: Microeconomic Theory
Solutions to Assignment 6
1. (i) Suppose rm 20 s pricing strategy as a function of her cost c is given
by the increasing continuous function p(c).
By announcing a price r, the probability that rm 1 with cost c1 wil
1
Econ 810 Final Examination
Wednesday, 10 th December 2008, 9:00 a.m. - 12:00 noon. Total points: 100
Answer ALL questions. Be sure to explain/justify all your steps.
1. [10 pts] A consumer who cares only about goods X1 , X2 and X3 has the following
Hick