# ECON 5005 Dalhousie University Quantitative Tools of Economics Discussion

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Economics
EXAMINATION
Semester 1 – Main, 2019
ECON5005 Quantitative Tools for Economics
For Examiner Use Only
EXAM WRITING TIME:
2 hours
10 minutes
Q
Mark
1
2
3
EXAM CONDITIONS:
This is a CLOSED book examination – no material permitted
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During reading time – writing is not permitted at all
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6
MATERIALS PERMITTED IN THE EXAM VENUE:
(No electronic aids are permitted e.g. laptops, phones)
7
Calculator – non-programmable
8
MATERIALS TO BE SUPPLIED TO STUDENTS:
Answer sheet: UNSW Generalised (150)
9
INSTRUCTIONS TO STUDENTS:
Answer all multiple choice questions in Part A by marking the computer cards
provided. Unanswered, incorrect or multiple answers are given a mark of zero. Do
not cross on the computer cards.
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10
reflect your work. Answers with no explanation receive zero credit.
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15
Allocate your time wisely: do the questions that are easier for you first.
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Please tick the box to confirm that your examination paper is complete.

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Total ________
Page 1 of 12
PART A
MULTIPLE CHOICE QUESTIONS
ANSWER ALL 15 QUESTIONS BY MARKING
THE COMPUTER CARDS PROVIDED
1) Determinant of the following matrix
is
a) -15
b) 10
c) -10
d) 0
2) Consider utility function
expressed as
a)
b)
c)
d)
, then its elasticity can be
3) Compute
a) 48
b) -48
c) 9.6
d) None of the above
4) Function
is
a) Convex
b) Concave
c) Both convex and concave
d) Neither convex nor concave
Page 2 of 12
5) At what values of x and y function
constraint
a) x=1, y=0 and x=0, y=1
is maximized subject to a
b) x=1, y=1
c) x=0.5, y=0.5
d) Function f does not have a global maximum
6) Function f is defined as
, find
a)
b)
c)
d)
7) Function f is defined as
function is
a) Convex
b) Concave
c) Neither convex nor concave
d) Constant
. On the interval
this
8) Preferences of a representative consumer over goods x and y can be written
down as the following utility function
a)
b)
c)
d)
Page 3 of 12
, find
9) At what values of x and y function
constraint
a) x=1, y=2
is minimized subject to a
b) x=5, y=0
c) x=0, y=0
d) Function g does not have a global minimum
10) Function
is
a) Increasing
b) Decreasing
c) Neither increasing nor decreasing
d) Constant
11) The value of the integral
is equal to
a)
b) 0
c) 108
d)
12) Find rank of the following matrix:
a) 3
b) 2
c) This matrix has no rank
d) 1
13) Consider the supply and demand equations
and the initial
condition
, then long run values of prices and quantities are:
a) P=5, Q=10
b) P=6, Q=9
c) P=3.2, Q=11.8
d) Not defined as the system is unstable
Page 4 of 12
14) Determinant of the matrix
is
a) 0
b) -12
c) 12
d) -15
15) GDP growth of China is described by the difference equation
given that
find the equilibrium value of Chinese GDP
a) 1
b) 2
c) 8
d) There is no equilibrium
Page 5 of 12
,
PART B
QUESTION 1. [5 points]. Sketch the graph of
Show you steps: i.e., What are the x- and y-intercepts? What are the critical points?
Which part of the graph is increasing/decreasing? Which part of the graph is
concave/convex?
Page 6 of 12
QUESTION 2. [6 points]. Use the Lagrangian method to maximize
such that
. Find the optimal
point, the value of the Lagrange multiplier and the value of the function at the optimal
point
Page 7 of 12
QUESTION 3. [6 points]. Calculate the integral.
Page 8 of 12
QUESTION 4. [6 points]. Use the Kuhn-Tacker conditions to maximize
such that
.. Find the optimal point and the value of the function
at the optimal point.
Page 9 of 12
QUESTION 5. [6 points]. Matrices A and B are given as:
Find
Page 10 of 12
QUESTION 6. [6 points]. Invert the following matrix:
Page 11 of 12
END OF EXAMINATION
Page 12 of 12
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Semester 2 2017
Practice Final
Page 1 of 7
Semester 2 2017
Page 2 of 7
PART A
MULTIPLE CHOICE QUESTIONS
#
1)   Derivative of 𝑒 ” \$%
#
a) 𝑒 ” \$%
is

#
b) 2𝑒 ” \$%

#
𝑒 ” + 1   𝑥
#

#
-.
c) 𝑒 ” \$%
d) 𝑒 ” \$%
#
2x +   𝑒 ”
#
x / +   𝑒 ”
2)   Rank of the matrix
a)
b)
c)
d)

1 2
4
2
2 4
is
2 1
1 1
3
1 1
2 1
7
1
2
3
4
3
3)   Evaluate -. 𝑥 + 3 𝑥 + 1 3.5 𝑑𝑥
a) 3
b) 0
c) 16
d) 9
“#
4)   Function & is
%
a)   Convex
b)   Concave
c)   Constant
d)   Neither convex nor concave
5)   Consider function 𝑓 𝑥, 𝑦 = 𝑥 + 2𝑒𝑦 − 𝑒 ” − 𝑒 / −1
(or equivalently −1 −21/2 (or equivalently −21/2 2 (or equivalently 2 ’ changes to ‘ −2
Notice that the sense has been reversed at this stage because we have divided by a negative
number.
M01_JACQ4238_08_SE_C01.indd 34
6/17/15 11:10 AM
35
SECTION 1.2 FURTHER ALGEBRA
You should check your answer using a couple of test values. Substituting x = 1 (which lies to the
right of −2, so should work) into both sides of the original inequality 2x + 3 −4
(c) 3 x + 1
(b) 7x + 3 ≤ 9 + 5x
(c) x − 5 > 4x + 4
(d) x − 1 7x + 24
(d) 3 +
x

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