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MEC712S-MATHEMATICAL ECONOMICS-2ND OPP-DEC 2025 |
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nAmIBIA untVERSITY
OF SCI En CE Ano TECH n OLOGY
FACULTY OF MANAGEMENT SCIENCES
DEPARTMENT OF ECONOMICS, ACCOUNTING AND FINANCE
QUALIFICATION: BACHELOR OF ECONOMICS
QUALIFICATION CODE: 12BECO
LEVEL: 7
COURSE CODE: MEC712S
COURSE NAME: MATHEMATICAL ECONOMICS
SESSION: DECEMBER 2025
DURATION: 3 HOURS
PAPER: THEORY
MARKS: 100
SECOND OPPORTUNITY EXAMINATION QUESTION PAPER
EXAMINER(S)
MR EDEN TATE SHIPANGA
MODERATOR:
MR. GEBHARD LUCKY SHIGWEDHA
INSTRUCTIONS
4. Answer ALL the questions.
5. Write clearly and neatly.
6. Number the answers clearly.
PERMISSIBLE MATERIALS
4. PEN,
5. PENCIL
6. CALCULATOR
THIS QUESTION PAPER CONSISTS OF 2 PAGES (Including this front page)
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.Question 1 f25 Marksl
Consider the following microeconomic model.
Qd = D(P, Yo)
Q5 = D(P, T0)
[Dp < O; Dv0 > OJ
[Sp > O; STo < OJ
Where Y0 is income and T0 is the tax on the commodity.
Analyse the comparative statics of the model to find the effect of change in Income and Tax on the
equilibrium Q and P?
(25)
Question 2 125 Marks!
I. Solve the following system of equations using Cramer's rule
(15)
a)
= 8X1 - X2 16
= 2X2 + SX3 = 5
2X1 - 3X3 7
b)
= 7X1 - 3X2 - 3X3 7
2X1 + 4X2 + 3X3 = 0
= -2X2 -X3 2
2. Use Jacobian determinants to test the existence of functional dependence between the paired
functions.
a)
Y1 = 3xf + Xz
Y2 = 9xt + 6xf(x2 + 4) + Xz(x2 + 8) + 12
(5)
b)
Y1 = 3xf + 2xJ
Y2 = Sx1 + 1
(5)
Question 3 f25 Marks]
I. In a three-industry economy, it is known that industry I uses 20 cents of its own product, IO cents of
commodity III and 60 cents of commodity 11 to produce a dollar' s worth of commodity I. Industry II
uses IO cents of its own product, 30 cents of commodity III and 50 cents of commodity I to produce a
dollar' s wo1th of commodity II. While industry III uses none of its own product and commodity I, but
uses 20 cents of commodity II in producing a dollar's worth of commodity 111. The open sector
demands N$ 2,000 billion of commodity I, N$ 500 billion of commodity II and 1500 billion of
commodity III.
a) Write out the input matrix, and the specific systems of equations for this economy.
(5)
b) Find the new output level when final demands increase bylO¾, 40% and 20%, respectively . (15)
c) Work out the required primary input for this economy
(5)
Question 4 125 Marks!
I. Maximize profits using Kuhn-Tucker conditions, rr = 64x - 2x 2 + 96y - 4y 2 - 13 Subject to the
production constraint x + y $ 36
(15)
2. Given y = xf + 6x? + 3x~ - 2x1 x2 - 4x2 x3 use the Discriminants to determine whether quadratic
function is positive or negative definite:
(10)
TOTAL MARKS: I00