 |
MFE511S - MATHEMATICS FOR ECONOMISTS 1A - 1ST OPP - JUNE 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, STATISTICS AND ACTUARIAL SCIENCES
QUALIFICATION: BACHELOR OF ECONOMICS
QUALIFICATION CODE: 07BECO
LEVEL: 5
COURSE CODE: MFESllS
COURSE NAME: MATHEMATICS FORECONOMISTSlA
SESSION: JUNE 2023
DURATION: 3 HOURS
PAPER:THEORY
MARKS: 100
EXAMINER
FIRSTOPPORTUNITY EXAMINATION QUESTION PAPER
MR G. S. MBOKOMA, MRS A. SAKARIA
MODERATOR:
MR E. MWAHI
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.
4. Decimal answers must be rounded to 4 decimals places
PERMISSIBLEMATERIALS
1. Non-programmable calculator without a cover.
THIS QUESTION PAPER CONSISTS OF 3 PAGES (Including this front page}
1
|
|
2 Page 2 |
▲back to top |
QUESTION 1 (30 marks)
1.1 Simplify the following expressions.
1.1.1
-a-2(+-a+-abb-)+xa2-c--+c-b2-c +---a
2+ab-ac-bc
a+b+c
2a 2 -ac-c 2
a2-c 2
[7]
1.1.2
14 n+4+ 7n+3xzn+3
13x14n- 1 +14n
[S]
1.1.3 log 2 5 x log 3 ..Jsx log 5 3
[4]
1.2 Solve each of the following equations:
f - 1.2.1 log 3 [ (1og½y
3 log½y + 5] = 2
[8]
= 1.2.2 4x 2 + 5x - 6 0 (use completion of squares method)
[6]
QUESTION 2 (25 marks)
2.1 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:
C = 100 + 0.75Yd; yd = Y - T
I= 50 - 25i
G = T = 50
ILMI
Md = Y - 25i ..... demand
= M5 250 .......... supply
Derive the IS and LM equations and hence determine the equilibrium levels of
income and rate of interest.
[10]
2.1 Consider the following production function for bus transportation in a city:
where , L = Labour input in worker hours
F = Fuel input in gallons
K = Capital input in number of busses
Q = Output in millions of bus mileage
and the estimate of the various parameters using historical data given as:
a= 0.012; /31 = 0.45; /32 = 0.35; /33 = 0.20
2
|
|
3 Page 3 |
▲back to top |
2.2.1
2.2.2
2.2.3
2.2.4
Define a
[2]
State with reason what type of returns to scale are present in this production
function.
[4]
Suppose that number of busses increases by 12%. By what percentage will output
increase?
[4]
Assume that labour hours= 8 hours, the fuel input= 11500 litres, and number of
buses= 60, what will be the total mileage output for these buses?
[S]
QUESTION 3 (20 marks)
3.1 The demand function for a certain commodity is p(x) = 10 - 0.00lx, where p is
measured in N$ and x is the number of units. The total cost of producing x items is
C(x) = 50 + Sx.
By using a derivative approach, determine the level of production that maximises the
profit?
[10]
3.2 Given the production
Q = K2 + 2L2
!; 3.2.1 Determine the marginal products of and :~
= - = 3.2.2 Show that MRTS + 2i and K-aaQ L-aaQ 2Q
K
K
L
3.3 Use implicit differentiation to determine dy for the implicit
dx
3x 3 + 5xy 2 -4y3 = 8x 2 and determine the slope of this curve at (1, 1).
[2]
[3]
function
[S]
QUESTION 4 (25 marks)
4.1 Determine the following integrals:
4.1.1 f c3+zx_;;d4xx+1)
[6]
[S]
4.2 The supply functions of for bailes of vintage clothes from Angola is given (in N$) by
= = S(x) x 2 + 10x, and the demand function (in N$) by D(x) 900 - 20x - x 2 .
4.2.1 Find the (Q, P) point at which supply and demand are in equilibrium
[4]
4.2.2 Find the consumer surplus
[S]
4.2.3 Find the producer surplus
[S]
.................................................... END OF EXAMINATION ................................................... .
3