nAmIB lA UnIVERSITY OF SCIEnCE AnD TECHnOLOGY

FACULTY OF HEALTH AND APPLIED SCIENCES

DEPARTMENT OF MATHEMATICS AND STATISTICS

QUALIFICATION: BACHELOR OF ECONOMICS

QUALIFICATION CODE: 07BECO LEVEL: 5

COURSE CODE: MFE511S COURSE NAME: MATHEMATICS FOR ECONOMISTS

SESSION: JULY 2016 PAPER: THEORY

DURATION: 3 HOURS MARKS: 100

SECOND OPPORTUNITY EXAMINATION QUESTION PAPER

EXAMINER

MODERATOR:

MRSS. MWEWA

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 5 PAGES (Excluding this front page)

l·

MFE511S 2ND OPPORTUNITY EXAM 12016

Question 1(3marks each = 24 marks)

1.1 The function f(x) = 3x3- 4x2 + 10 implies that

A. f(1}=10 B. f'(x) = 9x2 - 8x + 10 C. f"(x) = 18x-8 D. ['(2) = 20

1 2 1 2 h . y = -x +4x-10 as 2

A. a maximum point where x = 4 B. a minimum point where x = 4 c. a maximum point where x = -4 D. a minimum point where x = -4

1.3 For the demand function Q1 = ＱＰＭＹｾ＠ + ｾ＠ +0.01Y which of the following

statements are true?

A.

B.

c.

D.

b'Q1 =-9+P +0.01Y b'P. 2

I

b'Ql =-9 ｢Ｇｾ＠

b'QI =P b'P 2

2

b'Ql =-0.01 b'Y

1.4 A firm with total costs TC =50+ 3Q for Q units of output, which sells its output at price P = 5, breaks even at the output level:

A.

c.

Q = 50/3

Q = 50/2

B.

D.

1.5 The value x-4 may also be written as:

B. Vx 1

C. -(x)4

Q= 50/8

Q = 45/3

D -4x .e

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MFE511S 2ND OPPORTUNITY EXAM 12016

1.6 An integral may be interpreted as:

A. The inverse of the objective function.

B. The Lagrangian multiplier.

C. The area under a curve.

D. A monotonic function

1.7 Consider a four-sector economy described by the following parameters

and answer questions 1.7.1 and 1.7.2:

G = 2000 X - M = 500 I= 1300 T = 1000 C = 1000 + 0.8(Y - T)

Where G is government expenditure, (X- M) is net exports, I is the

level of planned investment, Tare lump-sum taxes on income, C is

household consumption and Y- Tis disposable income

1.7.1 The level of autonomous consumption and the MPC in this economy are,

respectively:

A. 1000 and 0.8 B. 800 and 0.8 C. 1200 and 5 D. 1000 and 5

1.7.2 The equilibrium level of income is: A. $22500 B. $20000 c. $16250 D. $26250

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MFE511S 2ND OPPORTUNITY EXAM 12016

Question 2 (2marks each=lOmarks)

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

2.1 J200 -m = s.fi

2.2 If y = axk, then dy = akxk-I dx

2.3 J;F + -1)' ｾ｡Ｂ＠2.4 In the simple Keynesian model, the expenditure multiplier is equal to

1

1-MPC

2.5 The vertex of a quadraticfunction is given as (;a;J[;a]J

Question 3(66 marks)

3.1 Without the use of a calculator solve the equation:

(5)

3.2 Find the level of income Yand the rate of interest i that will

simultaneously bring equilibrium to the economy given that the level of

consumption (C), investment (I), the speculative demand for money

( Mw), and the transaction-precautionary demand for money ( M1

) are

defined by:

(8)

Ms =1000, C=950+0.75Y, 1=310-125i,

Mw = 264 -175i and Mt = 0.15Y;Ms = Mw + Mt

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MFE511S 2ND OPPORTUNITY EXAM 12016

3.3 Raggs Ltd is a clothes manufacturer, determines that its demand

function for suits is given as p = 150 - 0. Sx. This manufacturer also

determines that its cost function is given as C(x) = 4000 + 0. 25x2

3.3.1 Derive the revenue function R(x)

3.3.2 Derive the profit function n(x) for the suits

3.3.3 Calculate how many suits must be produced and sold in order to

(1)

(2)

maximize profits? (Confirm profit function yields a maximum) (8)

3.3.4 What is the maximum profit? (2)

3.3.5 What unit price must be charged per suit in order to realise this

maximum profit?

3

3.4 A production output function is given as Q, = AK0·75 i5 .

3.4.1 Does the given production function qualify to be a Cobb-Douglas

function? State reasons

(3)

(2)

3.4.2 Determine the cost of production output Q, if the cost of technology is

N$25.00, cost of capital is N$60.00 and the cost of ｬ｡｢ｯｵｲｾ＠ of the cost 4

of the capital

3.4.3 If the cost of capital and the cost of labour in the original

Production function are both quintupled (times 5), show that the

new level of production Q2 will be

(4)

(6)

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MFE511S 2ND OPPORTUNITY EXAM 12016

3.5 Given that:

3.5.1 (6)

3.5.2 1 5 . dZ

Z =-log4t--e0.4' fmd-

4 2 I df (5)

3.5.3 (9)

3.6 Compute the following integral f( 6x2 + 18x5 + ｾ［＠ )dx (5)

END OF EXAMINATION

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