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MFE511S - MATHEMATICS FOR ECONOMISTS 1A - 2ND OPP - JULY 2022 |
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e
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: JULY 2022
DURATION: 3 HOURS
PAPER: THEORY
MARKS: 100
SECOND OPPORTUNITY/SUPPLEMENTARY EXAMINATION QUESTION PAPER
EXAMINER
MR G. S. MBOKOMA, MR F.N. NDINODIVA, MRS A. SAKARIA
MODERATOR:
MR I.D.0 NDADI
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
PERMISSIBLE MATERIALS
1. Non-programmable calculator without a cover.
THIS QUESTION PAPER CONSISTS OF 4 PAGES (Including this front page)
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QUESTION 1 (25 marks)
1.1 For each of the following statements, indicate whether True (T) or False (F)
1.1.1 |./(x — 2) =|(-x2)|
[1]
1.1.2 log, (=) =log,x —1
[1]
1.1.3 lim5=5
[1]
6-0
1.1.4 Ifa? + b*? =1andx? + y? = 2, then (ax + by)? + (ay — bx)? =2
[1]
1.1.5 Q =0.001K°?3L°7® is a strict Cobb-Douglas production function
[1]
1.2 Determine the degree of the polynomial.
(9x? y3z)?- Sa6ax2ayp * 1ixtyz® + (4xy?z)3
[3]
+b) —2?
2
on
207
2
1.3.
Simplify the expression a (a+ab+yace+bc x4 faab—+b+ace Be 2t a ; -Sc c
[5]
l 24x
1 8x 2
1.4
Solve the following indicial equation in x : (=20)
“(520 ]
=
[4]
1.5 Evaluate li. m —x?—-4
[3]
x-2 x-
1.6 Use first principle of differentiation to evaluate < ifye= xt
[5]
QUESTION 2 (30 marks)
2.1
Assume an income tax T with a proportional component tf incorporated into an
income determination model Y = C +],
C=Cot=b To Y +tYm , Y, n =T Y —-T, =I
where Cy = 42, Ip = 15, To = 10, b = 0.375 andt = 0.2
2.1.1 Determine the reduced form of this model
[5]
2.1.2 Determine the numerical value of Y
[2]
2.2 Given that Q, = —5 + 3p and Qg = 10 — 2p, determine the equilibrium price and
quantity
[5]
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2.3 The Investment-Savings (IS) and Liquidity Preference — Money Supply (LM) models
of acertain 3-sector economy, Y = C +1 +G, economy compose the following:
C=100+0.8%,;
I =50-25i
G=T=50
= ¥—T
M“ =Y —25i.....demand
= 200.......... supply
Derive the JS and LM equations and hence determine the equilibrium levels of
income and rate of interest, where P = 2.
[8]
2.4 A firm uses labour (L) and machines (K) to manufacture their products. The cost of
labour is NS 40 per unit and the cost of using a machine is NS 10.
2.4.1 Derive the budget line of the firm.
(2]
2.4.2 Sketch a budget line for this firm, showing the combinations of (L,K) with total
cost of NS 400, label the budget line with (C,).
[3]
2.4.3 On the same graph, sketch another budget line with total cost of NS 200, label
it with (C2)
[3]
2.4.4 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~°°".
3.1.1 Find the marginal product of labour?
[5]
3.1.2 AtZ = 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 Given the production
Q=K*4+2L
3.2.1 Determin. e the margin: al products of adeQ and rdsQ
[4]
3.2.2. Showthat MRTS 2= k7 andgy KK~20 4+L1 2h8a— 2Q
[5]
3.3. Determine 2, if 2x3 — 3y?+ 7xy =0
[5]
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QUESTION 4 (20 marks)
4.1 Determine the following integrals:
4.1.1 f-vtdt
(3]
4.1.2 [> e7* dx
[5]
4.2 Assume that the rate of an investment is given by the function /(t) = 6Vt. Compute the
total capital accumulation (K) between the 1* and 5" years? [Hint: K = fJ(t)dt] [6]
4.3 The marginal revenue of a company is given MR = 100 + 20x + 3x?, where x is an
amount of good in units sold for a period. Find the total revenue function at (x = 2)
when total revenue is equal to 260?
[6]