 |
MFE511S - MATHEMATICS FOR ECONOMISTS 1A - 1ST OPP - JUNE 2022 |
|
|
1 Page 1 |
▲back to top |
p
NAMIBIA UNIVERSITY
OF SCIENCE AND TECHNOLOGY
FACULTY OF HEALTH, APPLIED SCIENCES AND NATURAL RESOURCES
DEPARTMENT OF MATHEMATICS AND STATISTICS
QUALIFICATION: BACHELOR OF ECONOMICS
QUALIFICATION CODE: 07BECO
LEVEL: 5
COURSE CODE: MFE511S
COURSE NAME: MATHEMATICS FOR ECONOMISTS 1A
SESSION: JUNE 2022
DURATION: 3 HOURS
PAPER: THEORY
MARKS: 100
EXAMINER
FIRST OPPORTUNITY EXAMINATION QUESTION PAPER
MR G. S. MBOKOMA, MR F.N. NDINODIVA, MRS A. SAKARIA
MODERATOR:
MR I.D.0 NDADI
INSTRUCTIONS
Answer ALL the questions in the booklet provided.
Show clearly all the steps used in the calculations.
All written work must be done in blue or black ink and sketches must be done in pencil.
Decimal answers must be rounded to 4 decimals places
PERMISSIBLE MATERIALS
1. Non-programmable calculator without a cover.
THIS QUESTION PAPER CONSISTS OF 3 PAGES (Including this front page)
|
|
2 Page 2 |
▲back to top |
QUESTION 1 (25 marks)
1.1 Simplify the following expressions.
1d
(= a+b
2a-2b
- 2aa+—b2= b - >b*2.b-2)a?/\\b(1 -)a1
[6]
1.1.2
antt+9
3r-144
[4]
1.1.3 log, 8171 + log, 36 — log, V42
[5]
1.2 Solve each of the following equations without using a calculator:
1.2.1 log,x —loggx =4
[5]
aa (5) |»
[5]
QUESTION 2 (25 marks)
2.1 Rite-Cut riding lawnmowers obey the demand equation p = —=x + 1070. The cost of
producing x lawnmowers is given by the function C(x) = 110x + 6000.
2.1.1 Express the revenue function, R as a function of x.
[2]
2.1.2 Express the profit, P as a function of x.
[3]
2.1.3. Use a vertex approach to find the value of x that maximizes profit, hence find the
maximum profit?
[5]
2.1.4 What prices should be charged to maximise profit?
[2]
2.2 The Income Determination model for a 3-sector economy is given as
Y=C+I+G;C=C,+bY, I=1,, G=120
Where Y = Income,C = Consumption,I = Investment and G
= Government expenditure
With the above information determine showing all necessary steps
2.2.1 the reduced form of Y
[5]
2.2.2 the numerical value of income, Y given that:
C, = 220, b=0.55, I, =110
(3]
For this same economy, the LM (money market) model is given by
M,=500; M,=L,+L,, L, =0.2Y +200 and L, =150-—200i
2.2.3. With this additional information determine the interest rate i for this
economy
[3]
2.2.4 Calculate the autonomous expenditure multiplier for this economy
2
|
|
3 Page 3 |
▲back to top |
QUESTION 3 (25 marks)
3.1 The demand function for a certain commodity is p(x) = 10 — 0.001x, where p is
measured in N$ and x is the number of units. The total cost of producing x items is
C(x) = 50 + 5x.
By using a derivative approach, determine the level of production that maximises the
profit?
[8]
3.2 A firm’s production function is Q(L,K) = L’K%, so that the MP, = BL*-1K® and
MPx = aLP K*}, Leta = = and B= - Let the slope of the isocost line be — and let
w = N$4 an=dNr $ 27.
3.2.1 Find the marginal rate of technical substitution (MRTS).
[3]
3.2.2 What is the lowest cost at which it can produce 1080 units?
[8]
3.3
Use implicit differentiation to determine B aye the implicit function
3x° + 5xy* —4y’ = 8x’ and determine the slope of this curve at (1,1).
[6]
QUESTION 4 (25 marks)
4.1 Determine the following integrals:
411 f (2-2Vx?) dx
[4]
4.1.2 fe? dt
[4]
4.2 An investment flow is /(t) = 900¥t, where t is measured in years.
4.2.1 Calculate the total capital formation during the first four years?
[5]
4.2.2 Calculate the total capital formation from the end of the second year to the
beginning of the beginning of the sixth year.
[5]
4.2.3. Find an expression for the total capital formation during the first N years and
hence find the year in which the total capital formation reaches NS 16 200.
[7]