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Economics

EXAMINATION

Semester 1 – Main, 2019

ECON5005 Quantitative Tools for Economics

For Examiner Use Only

EXAM WRITING TIME:

2 hours

READING TIME:

10 minutes

Q

Mark

1

2

3

EXAM CONDITIONS:

This is a CLOSED book examination – no material permitted

4

During reading time – writing is not permitted at all

5

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.

11

10

Answer Part B in the space provided, NOT answer book. Your answers should

reflect your work. Answers with no explanation receive zero credit.

12

13

14

15

Allocate your time wisely: do the questions that are easier for you first.

16

17

Please tick the box to confirm that your examination paper is complete.

18

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

SHORT ANSWER QUESTIONS

ANSWERS WITHOUT EXPLANATION RECEIVE ZERO CREDIT

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

Advice

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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