 |
MFE511S - MATHEMATICS FOR ECONOMISTS 1A - 2ND OPP - JULY 2023 |
|
|
1 Page 1 |
▲back to top |
nAmlBIA unlVERSITY
OF SCIEn CE Ano TECHn OLOGY
FACULTYOF HEALTH, NATURAL RESOURCESAND APPLIEDSCIENCES
SCHOOLOF NATURALAND APPLIEDSCIENCES
DEPARTMENT OF MATHEMATICS, STATISTICSAND ACTUARIALSCIENCES
QUALIFICATION: BACHELOROF ECONOMICS
QUALIFICATION CODE: 07BECO
LEVEL: 5
COURSECODE: MFESllS
COURSENAME: MATHEMATICS FOR ECONOMISTS lA
SESSION:JULY 2023
DURATION: 3 HOURS
PAPER:THEORY
MARKS: 100
SECONDOPPORTUNITY/SUPPLEMENTARYEXAMINATION QUESTION PAPER
EXAMINER
MR G. S. MBOKOMA, MRS A. SAKARIA
MODERATOR:
MR E. MWAHI
INSTRUCTIONS
1. Answer ALLthe 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.
4. Decimal answers must be rounded to 4 decimals places
PERMISSIBLEMATERIALS
1. Non-programmable calculator without a cover.
THIS QUESTION PAPERCONSISTSOF 4 PAGES(Including this front page)
1
|
|
2 Page 2 |
▲back to top |
QUESTION 1 (30 marks)
1.1 Determine the degree of the polynomial.
[3J
1.2 Simplify the following expression
1.2.1 4x 2 -2x(I+2x)-2x(I-y)-2xy
[3J
¼[ 1.2.2
log (a 2 + 9a )- log (a+ 9)]
[4J
(p-q )-2111'11+(11- )111'
1.2.3 -----,-
X p-q
[SJ
( p _ q t-111J-
l 2+x
l2
Hx
1.3 Solve the following indicial equation in x: ( ) x ( ) = I
[SJ
[ 20
20 ]
1.4 Evaluate lim -x-3 -4x
[SJ
x---+z x-z
1.5 Use first principle of differentiation to evaluate dy if y = x 2 + 1
[SJ
dx
QUESTION 2 (25 marks)
2.1 A total cost function is given as C = a(bh+2) where a, b, d, and hare quantities
l+dh
produced. Make h the subject of the formula and then evaluate h when a = 20, c = 10,
d = 1 and b = .
[7J
4
2.2 The Investment-Savings (IS) and Liquidity Preference - Money Supply (LM) models of
a certain 3-sector economy, Y = C +I+ G, economy compose the following:
[m
C=I00+0.8r:,;
I= 50-25i
G=T=50
r:,=Y-T
ILMI
M" = Y - 25i .....demand
M-'
- p = 200..........supply
Derive the IS and LM equations and hence determine the equilibrium levels of
= income and rate of interest, where P 2.
[8J
2
|
|
3 Page 3 |
▲back to top |
2.3 A firm uses labour (L) and machines (K) to manufacture their products. The cost of
labour is N$ 40 per unit and the cost of using a machine is N$ 10.
2.3.1 Derive the budget line of the firm.
[2]
2.3.2 Sketch a budget line for this firm, showing the combinations of (L,K) with total
cost of N$ 400, label the budget line with (C1 ).
[3]
2.3.3 On the same graph, sketch another budget line with total cost of N$ 200, label
it with (C2 )
[3]
2.3.4 Discuss your observations between the two-budget lines.
[2]
QUESTION 3 (25 marks)
= 3.1 A firm's short-run production function is given by Q Le- 0·0ZL.
3.1.1 Find the marginal product of labour?
[5]
= 3.1.2 At L 50, determine whether the firm's maximes its production level?
[3]
= 3.1.3 What will be the production output at L 50 ?
[3]
3.2 The daily production function of a small-scale shoe manufacturer is given by
Q = ~3K 2 + 2[} , where L is the labour input measured in daily work hours and K is the
cost of capital investment measured in thousands of dollars and Q represents the daily
production of shoes.
3.1.1 Determine the marginal productivity of capital and the marginal
productivity of labour
[4]
3.1.2 Calculate the MRTSof the productions of shoes if workers put in 8 hours per
day and cost of capital is N$ 4.
[5]
= 3.3 Determine dy, if 2x 3 - 3y 2 + 7xy 0
[5]
dx
QUESTION 4 (20 marks)
4.1 Determine the following integrals:
4.1.1 I(x3 +2xi4x+lr
[5]
f3 -x
4.1.2 e2 dx
[5]
-2
3
|
|
4 Page 4 |
▲back to top |
I
4.2 The revenue and cost rates of a mining exploratory company are R'(t) = 14-t 2 and
I
C'(t) =2 + 3t 2 respectively, where the time t is measured in years and R and C are
measured in millions of dollars.
4.2.1 How long should the exploration be continued to obtain the maximum profit? [4]
4.2.2 Calculate the maximum profit for this company .
[6]
...................................................... END OF EXAMINATION .................................................. .
4