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NAMIBIA UNIVERSITYOF SCIENCE AND TECHNOLOGY

FACULTY OF HEALTH ANDAPPLIED SCIENCES

DEPARTMENT OF MATHEMATICS ANDSTATISTICS

QUALIFICATION: BACHELOR OF ECONOMICS

QUALIFICATION CODE: 07BECO LEVEL: 5

COURSE CODE: MFE511S COURSE NAME: MATHEMATICS FOR ECONOMISTS 1A

SESSION: JUNE 2018 PAPER: THEORY

DURATION: 3 HOURS MARKS: 100

FIRST OPPORTUNITY EXAMINATION QUESTION PAPER

EXAMINER(S) MRSS. MWEWA,J AMUNYELA,S HEELU(DI)

MODERATOR: DRA. S. EEGUNJOBI

INSTRUCTIONS

1. Answer ALL the questions in the booklet provided.

2. Show clearly all the steps used in the calculations.

3. All written work must be donein blue or black ink and sketches must

be donein pencil.

PERMISSIBLE MATERIALS

1. Non-programmable calculator without a cover.

THIS QUESTION PAPER CONSISTS OF 8 PAGES(Including this front page)

Question 1 (1 mark each = 5 marks)

For each of the following statements, indicate whether True or False in your answer

booklet

1.1. The polynomial 9x*y’z— 6x’y + llx'y + 4y°z has a degree of 6

12 log,(x+y)=log,x+log, y

1.3 A non-linear function has no gradient

1.4 If y=e’, then Y _9dx

. Lo b b15 The vertex of a quadratic function is given as 74 -—

a 2a

Section 2(2 marks each = 20 marks)

For each of the following indicate your best answerin the answer booklet provided

2.1

2.2

2.3

How manytermsdoesthe expression 2x(-4x"y) have?

A. 3 B. 2 G. 1 D. 4

-7x (x

Simplify (ytleaving your answerwithpositive indices.

5 \-4

4 | | 43A. x B. Th C. 3 D. x

Michelle borrowed NS$3r° + 5r*+ 187 + 20 from herbrother. If she paid back

NS3r°+ 2r? — 2r + 11, how much more money doesshestill owe her brother?

A. NSO B. NS 37? +20r +9

c NS 6r°+7r? +20r4+31 D. NS -3r? +20r-—9

Page 2 of 8

2.4

2.5

2.6

2.7

A.

Whichofthe following is a function?

{ive|4t | VAL | Jo}

&

ol

“y¥

Ty 1

|

Tuli farms produces lemons and the domestic demand and domestic supply curves

for lemonsin this economyare givenby: P=20-+0 and P=24+-0

The calculated equilibrium price and quantity will be:

A. P = N$2.00; Q = 4lemons B. P=N$5.00; Q = 30 lemons

C. P = N$2.50; Q = 45 lemons D. P = N$1.00; Q = 50 lemons

Which equation is the same as y = 4(2)*?

A. 4y=2* 8. y=2™ ff. y=2* po y=8

6 .If log, 64=_x is equal to:

0.04 B. 32 Ge 53.33 D. 147

Page 3 of 8

2.8 Refer to the graph below:

Aggregateconsumption(C)

Aggregate income (¥) 2.8.1 The consumption function equation will be equal to

A.

B.

G

D.

C = 140 +0.5Y

C = 80 + 0.6Y

C = 60 + 0.7Y

C = 60 + 0.4Y

2.8.2 From the graph above the value of the autonomous expenditure multiplieris

2.9

A.

B.

C

D.

k =0.3

k = 0.7

k = 3.33

k=1

Whensolving for the “x” in the equation ax* +bx+c =0, the solution(s) represent:

990p> the x — coordinateofthevertex of the quadratic function y=ax? +bx+c

the maximum valueof ‘x’

the x - intercepts of y=ax’ +bx+c

the x - coordinates of the y — intercept

Page 4 of 8

Section 3 (3 marks each = 15 marks)

For each of the following indicate your best answerin the answerbooklet provided

3.1

3.2

3.3

3.4

2Determine the expanded form of log yv4y—

(3y—2)

A. log y’ —4log3y—4log2 +log,/4y—1

B. 2logy+ log(4y-1)- 4log3y~2)

LC. logy’ J/4y—1-log(3y—-2)4

D. Noneof the above

Steeples CC estimates that its weekly profit, m, in hundreds of dollars, can be

approximated by the formula z =—3x° +6x+10 , where x is the numberof units

produced per week, in thousands. The numberof units the company should

produceper weekto earn maximum profit and the maximum weekly profit will be

A. 1000 units; NS1300 B. 3000 units; NS100

C. 1000 units; NS600 D. 2000 units; NS1100

A firm with total costs TC = 50 + 3Q for Q units of output, whichsells its output

at price p = $5 will break even at level of production of

50 50 50 45A. Q=F B. f=" C. Q= > D. Q=—

The derivative of y = xe** andits value at x = 0 will be

d. 2A. = 2xe 30 B. ay =e" +2xe"*:]

dx dx

C. D _ oo4124 D. ® _ oy eesdx dx

Page 5 of 8

53.4 [oe —~—43x dx is equal to

x

5 : 33 2 39 2A. Mytae? +6 B. 3x° —-—+2x7 ++€C3x 3x

5 3 3C. x ———+2x7 +C D. 3x8 +42x? $C

3x 3x

3.5 The average cost function of producing x units of a productis given as

AC (x) =0.1x’ —3x+60. Determine the marginal cost function and the marginal

cost of producing the 50*item.

A. MC(x)=0.2x-3; $7 B. C(x) =0.1x’ +60; $310

C. MC(x) =0.3x? —6x +60; $510 D. C(x) =0.1x” -3; $247

Section 4(60 marks)

Showall the necessary calculations and steps in your answer bookletfor the following

questions:

4.1 The income determination model of an economyis given below with an

income tax T incorporated into the income determination modelgivenas:

Y=C+iI, C=C,+5Y,, Y,=Y-T, I=,

Where Y = income; C = consumption; I = investment; and

Y, is disposable income

By showingall the necessary steps determine:

4.1.1 the reduced form of Y [5]

4.1.2 the numerical value of income, Y given that

C, =85, I,=30, T=20, b=0.75 [2]

Page 6 of 8

For this same sector, the LM model (money market) is represented by:

Transaction — precautionary demandfor moneygiven by

L, =0.2Y

And the speculative demand for money represented by

EL, = 750-250:

Where M, =1L,+L, at equilibrium and the supply of moneyis fixed at 7, = 800

4.2

4.3

4.1.3. Determine the interest rate i for this sector. [4]

Consider a production function with three inputs:

1 i_— K°?75 H°®

v A

WhereA is the level of technology, K is the capital (the number of machines), L is

labour (the numberof workers), and H is the human capital (the numberof college

degrees amongthe workers).

4.2.1 Show thatif capital (K) and labour (L) are both doubled, and the human

capital (H)is tripled, then the newlevel of production Q, will be

QO, =2.550 [5]

4.2.2 \f there are 300 units of capital (K) available, 150 units of labour (L) and 100

units of human capital (H) and thelevel of technology is 0.25, what will be

the level of productionfor this function? [2]

Determine the derivatives of the following functions with respect to their

independentvariables

4.3.1 Q= p(3p-2e°”) [4]

432 y=2 7 [5]x+l1

Page 7 of 8

4.4

4.5

4.6

4.7

4.8

Given that the demandfunctionfor a firm manufacturing wall clocks is given as

P(q) =120-—3q andthetotal cost function as TC (q) =120+36q +1.2q’, determine:

4.4.1 the costthis firm will incur if no wall clocks are produced [2]

4.4.2 the revenue functionforthis firm [1]

4.4.3 the profit function forthis firm [2]

4.4.4 the numberofwall clocks that need to be produced to maximize profit

(confirm this profit function yields a maximum using derivatives) [6]

4.4.5 the maximum profit [2]

1 2Consider the Cobb-Douglas production outputfunction is given asO =3AK3L?,

60. a0determine —and — [4]

OK OL

dy2, 2. — at (11Given that *” +* Y=4Y fing the value of dy ~ (Lb) [6]

Evaluate the following integral [5]

i 1i(i2» +4x° Na. x

Find the revenue function R(q) given the marginal revenue MRfunction [5]

MR = 250+ 60g —-18q’

END OF EXAMINATION!

‘3

i435CALMAND

GOOD LUCKWITH THE EXAM!

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