TRENT UNIVERSITY
DEPARTMENT OF ECONOMICS
ECON 3250H
ASSIGNMENT #2
Dr. M. Arvin XXXXXXXXXX
DATE GIVEN: Wednesday, October 13, 2021.
DUE DATE: Beginning of class on Wednesday, November 17, XXXXXXXXXXAs your
course outline states: “late penalty is 20% for each day or part thereof for
which the assignment is late.” You have five weeks to complete this assignment.
Please complete your assignment in ink or type it. Questions 1 and 2 are each
worth 50 marks.
1. Consider a household’s utility function
4/32
4/1
XXXXXXXXXX −−= qqu
where )2,1( =iqi is quantity consumed of good i . Suppose unit price
of good 1 and good 2 are $5 and $4 , respectively. The budgeted income
of the household is $129.
i) By setting up a constrained optimization problem and using a
Lagrangian function find the optimal quantity consumed of goods
1 and 2.
ii) Verify that your second-order condition is satisfied. (Note:
answers lacking final simplification and appropriate substitution
will be penalized.)
iii) Without performing another optimization, comment on the change
in the level of the consumer’s maximized utility if she has a
udgeted income of $130 instead.
2. Suppose you are studying in an American university. Suppose it is late in
the semester and you have two exams left. You must decide how to
allocate your working time during the study period. After eating, sleeping,
exercising, and maintaining some human contact, you have 12 hours each
day in which to study for your exams. You have figured out that your
grade in Mathematical Methods and Chemical Methods take the form of
M)3/4( and C2)3/4( , respectively. M is the number of hours per
day spent studying for Mathematical Methods and C is the number of
hours per day spent studying for Chemical Methods.
i) By setting up a constrained optimization problem and using a
Lagrangian determine the optimal number of hours per day spent
studying for each course if you wish to maximize your grade point
average. If you follow this strategy, what will your grade point
average be? (Notes: Suppose GPA is an average standing
determined out of six. You may assume your second-order
condition is satisfied. That is, you do not have to show it.)
ii) Without performing another optimization problem, comment the
impact on your grade point average if you study time increases by
one hour each day.
iii) Now suppose your marks production function changes to M
for Mathematical methods and to C2 for Chemical methods.
is a parameter measuring how much you concentrate during
your study time. By totally differentiating your F.O.Cs. and
performing comparative statics, comment on the impact of a rise in
on your optimal M and C . (Note: you may assume your
second-order condition is satisfied. That is, you do not have to
prove that it is satisfied.)