Download ALLAMA IQBAL OPEN UNIVERSITY, ISLAMABAD (Department of

ALLAMA IQBAL OPEN UNIVERSITY, ISLAMABAD
(Department of Economics)
WARNING
1.
PLAGIARISM OR HIRING OF GHOST WRITER(S) FOR SOLVING
THE ASSIGNMENT(S) WILL DEBAR THE STUDENT FROM AWARD
OF DEGREE/CERTIFICATE, IF FOUND AT ANY STAGE.
2. SUBMITTING ASSIGNMENT(S) BORROWED OR STOLEN FROM
OTHER(S) AS ONE’S OWN WILL BE PENALIZED AS DEFINED IN
“AIOU PLAGIARISM POLICY”.
Course: Mathematics for Economists (803)
Semester: Autumn 2016
Level: M.SC Economics
Total Marks: 100
Pass Marks: 40
ASSIGNMENT No. 1
(Units: 1–4)
Q.1
Elucidate the ingredients of mathematical model with examples. Also discuss
various kinds of variables.
Q.2
Give the following model: Y= C+1o + G
C = a + b (Y – To), G = gY
(a) Identify the endogenous variables
(b) Give the economic meaning of the parameter ‘g’
(c) Find the equilibrium national income
Q.3
Use Crammer’s rule to solve the following equation systems:
a)
8x1-x2=16
(b)
-x1+ 3x2 +2x3= 24
2x2+ 5x3 = 5
x1 + x3 = 6
2x2+ 3x3 = 7
5x2 – x3 = 8
Q.4
Discuss with the help of examples the applications of derivatives in economic
theory.
Q. 5
Use the Jacobian determinants to test the existence of functional dependence
between the paired functions.
(a)
y1 = 3x 21 + x2
y2 = 9x41+ 6x21 (x2 + 4) + x2 (x2 + 8) + 12
(b)
y1 = 3x12 + 2x22
y2 = 5x1 + 1
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ASSIGNMENT No. 2
(Units: 5–9)
Total Marks: 100
Pass Marks: 40
Q.1
Find the derivatives using the implicit function derivative technique for the
following functions
(a)
F (x, y) + 3x2y – 5xy2 + 3xy – 4x + 9y – 10
(b)
F (x, y) = x2 + y2 – 9
Q.2
Describe in detail the formulas for calculating simple growth rate, compound rate
and average compound rate of growth.
Q.3
A monopolist sell two goods have its demand functions as:
X = 25 – 0.5PX and y = 30 - PY
The joint cost function is:
C = x + 2xy + y2 + 20
Find the quantity of each good where the cost of monopolist is minimum
(a) The price charge for “x” and “y”
(b) The profit of monopolist
Q.4
Explain the difference between concave function and strictly concave function,
convex and strictly convex function.
Q.5
If C = 45x2 + 90 x y + 90y2 while the production quota is 2x + 3y = 60
(a)
Find quantities where costs are minimized.
(b)
Check second order conditions with Boarder Hessian Determinant.
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