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MEC721S- MATHEMATICAL ECONOMICS- 2ND OPP- NOV 2023 |
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nAmlBIA unlVERSITY
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: JANUARY 2024
DURATION: 3 HOURS
PAPER:THEORY
MARKS: 100
SECOND OPPORTUNITY EXAMINATION QUESTION PAPER
EXAMINER(S)
MR EDEN TATE SHIPANGA
MODERATOR:
DR R. KAMATI
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 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]
Consider the following microeconomic model.
Qd = D(P, Yo)
Q5 = D(P, T0)
[Dp < O; Dy0 > OJ
[Sp > O; Sr0 < 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 3 f25 Marks)
Give the input matrix and the final demand vector
0.05 0.25 0.34]
A= [0.33 0.10 0.12
0.19 0.38 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 [25 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 - X1X2+ Bx~ - Sx2 + 2X2X3+ 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