nHlTllBlH UNIVERSITY

OF SCIENCE nnu TECHNOLOGY

FACULTY OF HEALTH AND APPLIED SCIENCES

DEPARTMENT OF MATHEMATICS AND STATISTICS

QUALIFICATION: BACHELOR OF ECONOMICS

QUALIFICATION CODE: 07BECO LEVEL: 5

COURSE CODE: MFESllS COURSE NAME: MATHEMATICS FOR ECONOMISTS

SESSION: JULY 2017 PAPER: THEORY

DURATION: 3 HOURS MARKS: 100

SECOND OPPORTUNITY EXAMINATION QUESTION PAPER

EXAMINER MRS S. MWEWA

MODERATOR: DR A. 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 done in blue or black ink and sketches must

be done in pencil.

PERMISSIBLE MATERIALS

1. Non-programmable calculator without a cover.

THIS QUESTION PAPER CONSISTS OF 3 PAGES (Excluding this front page)

'

MATHEMATICS FOR ECONOMlSTS (MFESllS) 2ND OPPORTUNITY EXAMINATION ‘JULY 2017‘

Show all your solutions to the following questions fully, clearly and neatly in the answer

booklet provided.

Question 1125 marks)

1.1

1.1.1

1.1.2

1.1.3

1.2

1.2.1

1.2.2

1.2

simplify the following without the use of a calculator:

1 3 11_

2__ 2+_ 2_2 2

+r 3

2196] 49119 3m 6117 ()

6x2x"3 —(22‘x )_1 (4)

imam—m

2J§+3JE‘5’

Solve the following equations

2—fl+—6=—— (4)4 3—1

210g7 2 + log7 x = log7 32 (4)

The demand function for Lilly’s handbags is given as

Hd =100—p+31+§Where, p is the price of handbags, I is consumer income and A is the advertising

budget of the company. The supply of the handbags by the company to the

consumers is given by the function

Hx=40+2p

Find the equilibrium price and quantity for the handbags sold on the market if

1 = $20; A = $60. (5)

2ND OPPORTUNITY EXAMINATION JULY 2017':"

MATHEMATICS‘FO‘R ECONOMISTS (M FE511$)

Question 2 (18 marks}

2.1 A two sector economy given as Y = C+I, has the following prevailing conditions:

C =10 +0.8Y;I = 70—60igM, = 0.2Y;MW =190—100i;Ms = 250

Note that C is the level of consumption, I the investment, Mt the transaction Precautionary

demand for money and MW the speculative demand for money and Md = M, +MW

2.1.1 Derive the IS schedule for this economy (2)

2.1.2 Derive the LM schedule for this economy (2)

2.1.3 Determine the level of income, Y and the rate of interest, i that will concurrently

bring equilibrium to this 2-sector economy (6)

2.1.4 Calculate the levels ofC, 1, MI, and MW, at the equilibrium level of income and

interest rate computed in 2.1.3 (8)

Question 3 {17 marks)

Poppii makes Herero dresses for a select clientele. In the relevant range of her production,

she can produce dresses according to the production function

D : ASo.35M0.65

Where D is her output (number of dresses per week), A is the level of technology, S is the

number of sewing - hours that she works in a week and M is the amount of material in

metres that she uses per week.

Poppii values her sewing-hours at N$15 per hour and she pays N$50 per metre of material.

She is currently working 50 hours per week and using 80 metres of material per week.

3.1 Determine how many dresses 3 week Poppii is producing in a week with level of

technologyA = 0.2 (4)

3.2 If Poppii decides to increase her sewing hours by 5% by what percentage will her

output increase? (4)

3.3 Calculate how much it costs Poppii to make one dress if each dress requires 10 hours

of labour to make and 12 metres of material (3)

3.4 Determine the marginal productivity of sewing-hours and the marginal productivity

of material if the amounts are 50 hours and 80 metres respectively. (A = 0.2) (6)

2ND'0PPORTUNITY EXAMINATION Jun/20.17 ,i-MATHEMAncs FOR ECONOMISTS (MFESllS)

Question 4 (15 marks)

Omega manufactures calculators and the weekly production cost of the calculators is given

by: C(x) =25x+750

And the weekly revenue R(x) resulting from the sale of these x units is given by

R (x) = 340x — 2.25x2

4.1 What will be the total cost when there is no production? (2)

4.2 Derive the profit function for these calculators (2)

4.3 Determine and confirm the number of calculators that will maximize profits for

Omega (5)

4.4 What is the maximum profit Omega will make? (3)

4.5 What will be the marginal cost of producing the 110th calculator? (2)

Question 5 (12 marks)

5.1 if \/y—3—xy+2y=4x3 Find % (6)x

5.2 if xyz +x2y=2;determine d_y at (1,—2)dx

(5)

Question 6 (13 marks)

6.1 Integrate J(15x4 +15e“ +x\/;)dx (4)

6.2 The daily marginal cost function for Emcee shirt production is C'(x) = 3 —2x+x2

dollars per unit and x denotes the number of shirts produced. It has been determined that

the daily fixed costs is N$200. Find the cost that Emcee will incur in producing the first 50

shirts. (9)

END OF EXAMINATION

GOOD LUCK