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MEC712S-MATHEMATICAL ECONOMICS-1ST OPP-NOV 2025 |
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nAm I BI A un IVE RS ITV
OF SCIEnCE Ano TECHnOLOGY
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: NOVEMBER 2025
DURATION: 3 HOURS
PAPER: THEORY
MARKS: 100
FIRST OPPORTUNITY EXAMINATION QUESTION PAPER
EXAMINER(S)
MR EDEN TATE SHIPANGA
MODERATOR:
MR. GEBHARD LUCKY SHIGWEDHA
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 1 125 Marks!
Consider the following simple one commodity market model:
Q = b -aP
(a, b > 0)
[demand]
Q = -d + cP
(c, d > 0)
[supply]
I. Find the Equilibrium Price P* and Quantity Q*?
(10)
2. Use partial derivative to find the effect of the parameters (a, b, c and d) on the equilibrium quantity? (15)
Question 2 [25 Marks]
Formulate a closed economy national income model (IS-LM analysis model) system of equations. Where
consumption and demand for money is considered to be strictly increasing function of income [a fraction of
income (0 < Cy < 1 and Ly > 0)] , tax is ignored (or tax does not exist), investment and demand for
money is said to be strictly decreasing function of rate of interest Ur < 0 and Lr < 0) and Government
spending and Money supply are exogenously determined as G0 and M2. Analyse the comparative statics of
the model to find the effect of expansionary fiscal and monetary policy on the equilibrium level of income
and interest rate?
(25)
Question 3 125 Marks]
Give the input matrix and the final demand vector
0.05 0.25 0.34]
A= [00..3139
0.10
0.38
0.12
0
d
=
1800]
[
200
900
(a) Explain the economic meaning of the elements 0.33 , 0 and 200
(9)
(b) Explain the economic meaning (if any) of the third column sum
(3)
(c) Find the solution output levels by Cramer' s rule
(13)
Question 4 125 Marks]
I. Optimise the following function , a) find the critical value for the first order condition and b) the high-order
Hessian:
y = 4xf - 7X1 - X1Xz + Bx~ - Sxz + 2XzX3 + 4x~ + 2x3 - 4X1X3
(15)
2. Use discriminants to determine whether each of the following quadratic function is positive or negative definite:
(10)
TOTAL MARKS: 100
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nAmlBIA un1VERSITY
OF SCI En CE An □ 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: NOVEMBER 2025
DURATION: 3 HOURS
PAPER: THEORY
MARKS: 100
FIRST OPPORTUNITY EXAMINATION QUESTION PAPER
EXAMINER(S)
MR EDEN TATE SHIPANGA
MODERATOR:
MR. GEBHARD LUCKY SHIGWEDHA
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)