Adam Smith Business School
Subject of Economics
Degree of MA(SocSci)/BAcc/BSc/MA
Degree Exam
Mathematical Methods for Economics, ECON4074
Thursday, 28 April 2022, 9:15 to Friday, 29 April 2022, 9:15
Exam duration: 1 hour and 30 minutes
How to complete this exam:
Students should answer Section A (Questions 1-5) on Moodle. Students should answer 2 of 3
questions in Section B. Students should answer 1 of 2 questions in Section C.

Instructions to students:
Read the exam student guidance below carefully.
For this exam, the required number of questions is 5 in Section A, 2 in Section B, and 1 in
Section C.


1. Advice on the contents of the exam and technical support
If you have questions about the contents of this paper, or you require technical
assistance, please contact our virtual invigilation team at the University of Glasgow
Helpdesk https://www.gla.ac.uk/help or on +44 (0)141 330 4800.
An academic member of staff will be available to answer questions about the
examination as they would normally at the beginning of the exam. Technical
support will be available 24 hours per day. To ensure timely responses and that all
students receive the same information, you should not contact academic staff
directly but instead use the Helpdesk.
2. You are about to sit an online assessment
The duration of this exam is 1 hour and 30 minutes. Where uploading of files is
required you will have 30 minutes to upload your answer files.
3. Time adjustments for students with disabilities
If you have been assessed through the University’s Disability Service as needing time
adjustments in exams, your additional time allowance has been configured in
Moodle for each exam.
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When planning your time, and where required, you should allocate time to
download the exam paper and to upload your answers to Moodle at the end of the
exam. For students instructed to do so, you should allow time to submit your exam
script on Turnitin within the exam period. Please report any technical difficulties
experienced as soon as possible via https://www.gla.ac.uk/help.
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Please check that you have uploaded the CORRECT FILE, that it is readable and is the
version that you want to be marked; if you use a word-processing package other
than Word, you are advised to convert and upload as a pdf.
Lastly please ensure you upload files to the correct course Moodle assignment.



Late submissions
This exam has been configured to ‘auto-submit’ uploaded file(s) at the end of the
scheduled exam time. If you have not submitted your completed answers by this
time you should submit via: business-school-assessment@glasgow.ac.uk.
Submissions made direct to School/RI in the two hours following the end of the
scheduled exam time will be treated as ‘late’ and will be graded ‘H’. Any submissions
made beyond this time will be treated as non-submissions.



7. Declaration of Academic Integrity
The following information is very important – your degree may be at risk if you do
not adhere to these instructions:
• You must not communicate with any other person about these examination
questions during the period in which you can submit your answers
• You must follow any instructions on your examination paper regarding use of
resources such as internet sources, books, notes or any other material that
would not normally be allowed in examinations on campus.
• The work you submit must be entirely your own effort and must demonstrate
your understanding rather than reproduce text from notes, slides, books, or
online sources (which is plagiarism)
• You must not submit answers you have discussed with or copied from others,
and you must not copy from notes you have prepared with or shared with
others. If your answers are similar to those of any other candidate(s) you will
both/all be suspected of collusion and referred to Student Conduct
• This declaration incorporates the University’s Declaration of Originality which
applies to all academic work (see below).

Declaring that the work is your own
Before viewing the exam paper, you must check the box in the Exam Section of the Moodle page to
agree to both this declaration and the University’s Declaration of Originality. You will be unable to
access the exam
Section A (25%)
This section (Questions 1-5) is administered via Moodle.
Section B (50%)
Students should choose 2 of 3 questions in this section.
Question 6 (25%)
(a) (12.5%) Consider the following matrix :
=
(

−1
√2
⁄ 0 1
√2
⁄
1 0
−1
√2
⁄ )

Find value of , , and such that = −1.
(b) (12.5%) Consider the following matrix :
= (
0 1
0 1
−2 1
)
Find all values of such that the set of all pairs (, ) for which the linear system Ax=0 has
multiple solutions, i.e. the set
= {(, )| ℎ = 0 ℎ }
forms a linear subspace.

Question 7 (25%)

Find a value of the parameter such that 2 is an eigenvalue of the following matrix. Then, for this
value of , find all the remaining eigenvalues and eigenvectors. Do the eigenvectors form a basis?
= (
1 2 0
1 2 1
0 2
)

Question 8 (25%)
(a) Differentiate the function :ℝ2 → ℝ defined by
(, ) = (ln( + 2))
⋅cos()
2+2
(b) Observe the set
= {(, ) ∈ ℝ ∣ ≥ 2 − 1 and ≤ 4 − −}

Is bounded / closed / open / compact / convex?

Section C (25%)
Students should choose 1 of 2 questions.
Question 9 (25%)
(a) (12.5%) Find the global minima and maxima of the function :ℝ → ℝ defined by
() =
− 3
2 − 6 + 14

(b) (12.5%) Observe :ℝ2 → ℝ defined by
32 − 2 − ⋅ 3 − 4 + 2
where ∈ ℝ, > 0 is fixed. Find all local and global extrema of ; explain how your answers
depends on .
Question 10 (25%)
Maximize the function :ℝ2 → ℝ
(, ) = ( + 3)α ⋅ ( + 3)1−α
where 0 < < 1, subject to
(, ):= ( + 3)2 + ( + 3)2 ≤ , ≥ 0, ≥ 0
where > 18.