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MEC712S-METHEMATICAL ECONOMICS-1ST OPP-NOV 2024 |
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n Am I BI A u n IVE RS ITV
OF SCIEnCE Ano TECHnOLOGY
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 2024
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 Marks!
Given a is non-income tax, is income tax, 8 is marginal propensity to consume, y is autonomous consumption, Y
(national income), Io(investment) and Go(government expenditure)
I. Formulate the equations needed to find the reduced form of equilibrium income (Ye).
(5)
2. Do a comparative static to find the effect of income tax, non-income tax and government spending on
equilibrium income.
(15)
3. If~= 0.2; a= 20; y =80; 8 = 0.25; Io= 45; Go= 50, find the effects of lump sum tax increase by$ I billion?(5)
Question 2 [25 Marks!
I. Solve the following system of equations using Cramer's rule
X1 = 0.2X1 + 0.3X2 + 0.2X3 + 10
X2 = 0.4X1 + 0.lX2 + 0.2X3 + 5
X3 = 0.1X1 + 0.3X2 + 0.2X3 + 6
2. Solve the following system of equations using Cramer's rule
(10)
= 8X1 -X 2 16
2X2 + SX3 = 5
2X1 - 3X3 = 7
Question 3 [25 Marks]
I. In a three-industry economy, it is known that industry I uses 30 cents of its own product, 40 cents of commodity
Ill and 20 cents of commodity II to produce a dollar's worth of commodity I. Industry II uses I 5 cents of its
own product, 35 cents of commodity III and 45 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 25 cents of commodity II in
producing a dollar's worth of commodity III. The open sector demands N$ 1,000 billion of commodity I, N$
800 billion of commodity II and 1200 billion of commodity III.
a) Write out the input matrix, and the specific systems of equations for this economy.
(5)
b) Find the solution output levels by Cramer's rule.
(15)
c) Work out the required primary input for this economy
(5)
Question 4 125Marks!
I. Optimise the following function, a) find the critical value for the first order condition and b) the high-order
Hessian:
y = 4xf - 7X1- X1X2+ Bxi - Sx2 + 2XzX3+ 4x~ + 2x3 - 4X1X3
(15)
2. Use discriminants to detennine whether each of the following quadratic function is positive or negative
definite:
a) y = Sxf - 6X1X2+ 3x} - 2X2X3+ Bxf - 3X1X3
(5)
b) y = xf + 6x} + 3xf - 2x1x2 - 4x2x 3
(5)
TOT AL MARKS: 100