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MEC721S- MATHEMATICAL ECONOMICS- 1ST OPP- NOV 2023 |
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nAmlBIA UnlVERSITY
OF SCIEnCE Ano TECHn OLOGY
FACULTY OF MANAGEMENT SCIENCES
DEPARTMENT OF ACCOUNTING, ECONOMICS AND FINANCE
QUALIFICATION: BACHELOR OF ECONOMICS
QUALIFICATION CODE: 12BECO
LEVEL: 7
COURSE CODE: MEC712S
COURSE NAME: MATHEMATICAL ECONOMICS
SESSION: NOVEMBER 2023
DURATION: 3 HOURS
PAPER: THEORY
MARKS: 100
FIRST OPPORTUNITY EXAMINATION QUESTION PAPER
EXAMINER(S)
MR EDEN TATE SHIPANGA
MODERATOR:
DR R. KAMATI
INSTRUCTIONS
1. Answer ALL the questions.
2. Write clearly and neatly.
3. Number the answers clearly.
PERMISSIBLE MATERIALS
1. PEN,
2. PENCIL
3. CALCULATOR
THIS QUESTION PAPER CONSISTS OF 2 PAGES (Including this front page)
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Question 1 [25 Marksl
1. Solve the following system of equations using Cramer's rule
(15)
a)
= 8X1 -X 2 16
2X2 + SX3 = 5
2X1 - 3X3 = 7
b)
= 7X1 - 3X2 - 3X3 7
= 2X1 + 4X2 + 3X3 0
= -2X 2 -X 3 2
2. Use Jacobian determinants to test the existence of functional dependence between the paired
functions.
a)
Y1 = 3xf + Xz
y 2 = 9xt + 6xf (x 2 + 4) + x2 (x 2 + 8) + 12
(5)
b)
Y1 = 3xf + 2xf
y2 = Sx1 + 1
(5)
Question 2 [25 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 II 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 worth 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 III; and the open sector demands N$ 1,000 billion of commodity I, N$ 2,000 billion of commodity II and
500 billion of commodity III
a) Write out the input matrix, and the specific input matrix equation for this economy. (5)
b) Find the solution output levels?
(15)
c) Work out the required primary input for this economy
(5)
Question 3 [25 Marksl
1. Optimise the following function, using a) Cramer's rule for the first order condition and b) the Hessian for the
second-order condition:
(10)
y = Sxf - 7x 1 - x 1x 2 + Bx? - 6x 2 + 4x 2 x3 + 6xl + 4x 3 - Sx1x 3
2. Maximize utility u = xy + x, subject to the budget constraint 6x + 2y = 110 by a) finding the critical values
i , y and X,b) use the Hessian bordered.
(15)
Question 4 [25 Marks I
Maximise profits using Kuhn-Tucker conditions, rr = 54x - x 2 + 76y - 3y 2 - 12 subject to the production
constraint x + y $ 35
(25)
TOT AL MARKS: I 00