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Posted Date: 13 Jun 2009      Posted By:: Papori Gogoi    Member Level: Gold    Points: 5 (Rs. 1)

# 2007 Gauhati University M.A Economics Economics Dept., Previous Examination, 2007, Third Paper Question paper

 Course: M.A Economics University/board: Gauhati University

2007
ECONOMICS
THIRD PAPER
(Mathematical Methods for Economic Analysis)
Full Marks: 80
Time: 3 hours
The figures in the margin indicate full marks for the questions
1. Answer the following questions: 2×4=8
a) Show that the determinant of a triangular matrix is equal to the products of the
diagonal elements.
b) Why is it necessary to add a constant term while integrating a function?
c) A function y = f(x1x2) has to be maximized subject to two equality constraints
( ) c x x g 1 1 2 1 =
State the necessary and sufficient conditions of maximization.
(d) Distinguish between" mixed strategy and dominated strategy.
2. Answer any four of the following:
a) Given the demand function
Where Q is quantity demand and P is price. Obtain consumer's surplus when
p= 16.
b) "Imposition of specific sales tax not only changes the usual
equilibrium condition of a monopolist but also results in a smaller
output and higher price.” Justify the above statement using
optimization technique.
c) A technology matrix is given as under:
Steel Coal
Steel 0.4 0.1
Coal 0.7 0.6
Labour 5 2
( ) c x x g 2 2 2 1 =
P Q
2
3
60 - =
Determine the equilibrium price if wage rate is Rs 10 per Labour Day.
(d) Formulate a general transportation problem to linear programming where there
are three factories for production and five destinations to supply the products.
(e) In the competitive market model
D=16-2P
S = -4 +2(P- t}
where D, S, P and t denote demand, supply, price and sales tax rate. Obtain the
rate of tax which will maximize total tax revenue of the government.
{f} Distinguish between static and dynamic input-output models with examples.
3. Answer any three of the following: 8×3=24
a) Find out the general method of solution of a game where there are two players
having m strategies each in the case of mixed strategies.
b) Under joint production, a perfectly competitive fIrm sells two products ql and q2
at prices Rs 10 and Rs 15 per unit of output respectively. The joint cost function
of the firm is given by
C=4qt 2+2q2
2 +4qlq2
Find profit maximizing output levels ql and q2 and maximum profit.
(c) Given the national income model
) 1 0 (
) 0 1 , 0 ( ) (
0 0
< < =
> > > - + =
+ + =
d dY T
b a T Y b a C
C Y G I
where Y, C, T, 10 and Go denote income, consumption, income tax, investment
and government expenditure respectively. Solve the above model using Cramer's
rule.
(d) Solve the following
0 2 = + x
dy
dy
with initial condition y(0) = 5.
(e) Let the demand function of a firm under monopolistic competition be given by
P = 118 -3Q+4.A
where P is price, Q is quantity and A is advertisement expenditure. If the total
cost function is given by C = 4Q2 +10Q + A, find the value of A, Q and P that
maximizes the profit of the firm.
4. Answer any two of the following: 12×2=24
(a) (i) Find the optimal strategies for the participants in a two-person zerosum
game with the following profit matrix :



 -
- 1
2
3
4
What is the value of the game?
(ii) What is Nash equilibrium? Explain with a suitable example.
(b) Given the demand and supply functions for cobweb model:
Qdt = 10 -2Pt
Qst = -5 +3Pt-1
Find the inter-temporal equilibrium price and also determine whether you will get
stable equilibrium.
(c) A producer desires to minimize the cost of production
C= 16K +4L
where K and L are capital and labour respectively subject to the production
function given
L K Q 2
1
2
1
5 =
Find out the equilibrium combination of inputs (K and L) in order to minimize the
cost of production when output Q=40.
(d) Maximize f = 2X + 5Y
subject to
X+4Y24
3X + Y  21
X+Y9
X, YO

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