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MEC712S-METHEMATICAL ECONOMICS- 2ND OPP-JAN 2025 |
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n Am I BI A unIVE Rs ITY
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 2025
DURATION: 3 HOURS
PAPER:THEORY
MARKS: 100
SECOND OPPORTUNITY EXAMINATION QUESTION PAPER
EXAMINER($)
MR EDEN TATE SHIPANGA
MODERATOR:
DR R. KAMAT!
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 I [25 Marks[
Consider the following Microeconomic market model, where A is the level of technology.
Q = D(P, Y)
[Dp < O,Dy > O]
Q = S(P,A)
[Sp > O; SA > O]
Analyse the comparative statics of the model to find the effect of the level of technology and Income on the
equilibrium quantity and price simultaneously.
(25)
Question 2 125 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 pa1tial derivative to find the effect of the parameters (a, b, c and d) on the equilibrium quantity?
(15)
Question 3 [25 Marks!
1. Use Jacobian determinants to test the existence of functional dependence between the paired functions.
a)
Y1 = 3xf + Xz
Yz = 9xt + 6xf(x 2 + 4) + x 2 (x 2 + 8) + 12
(5)
b)
Y1 = 3xf + 2x?
Yz = Sx1 + 1
(5)
ii. Optimise the following function, a) find the critical value for the first order condition and b) the high-order
Hessian:
(15)
Question 4 125 Marks]
= 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: 100