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# Gauhati University 2007 B.A Economics Mathematical Methods for Economic Analysis - Question Paper

Monday, 21 January 2013 11:05Web

2007
ECONOMICS
THIRD PAPER
(Mathematical Methods for Economic Analysis)
Full Marks: 80
Time: three hours
The figures in the margin indicate full marks for the ques.

1. ans the subsequent 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 2 equality constraints
( ) c x x g one 1 two one =
State the necessary and sufficient conditions of maximization.
(d) Distinguish between" mixed strategy and dominated strategy.
2. ans any 4 of the following:
a) provided the demand function
Where Q is volume demand and P is price. find consumer's surplus when
p= 16.
b) "Imposition of specific sales tax not only modifications the usual
equilibrium condition of a monopolist but also outcomes in a smaller
output and higher price.” Justify the above statement using
optimization technique.
c) A technology matrix is provided as under:
Steel Coal
Steel 0.4 0.1
Coal 0.7 0.6
Labour five 2

Determine the equilibrium price if wage rate is Rs 10 per Labour Day.
(d) Formulate a general transportation issue to linear programming where there
are 3 factories for production and 5 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. find the
rate of tax which will maximize total tax revenue of the government.
{f} Distinguish ranging from static and dynamic input-output models with examples.
3. ans any 3 of the following: 8×3=24
a) obtain out the general method of solution of a game where there are 2 players
having m strategies every in the case of mixed strategies.
b) Under joint production, a perfectly competitive fIrm sells 2 products ql and q2
at prices Rs 10 and Rs 15 per unit of output respectively. The joint cost function
of the firm is provided by
C=4qt 2+2q2
2 +4qlq2
obtain profit maximizing output levels ql and q2 and maximum profit.
(c) provided the national income model
Y = C+I0 +G0
C=a+b(Y-T) (a>0,1>b>0)

T= dY (0
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 subsequent

dy/dy+2x = 0

with initial condition y(0) = 5.
(e) Let the demand function of a firm under monopolistic competition be provided by
P = 118 -3Q+4.A
where P is price, Q is volume and A is advertisement expenditure. If the total
cost function is provided by C = 4Q2 +10Q + A, obtain the value of A, Q and P that
maximizes the profit of the firm.
4. ans any 2 of the following: 12×2=24
(a) (i) obtain the optimal strategies for the participants in a two-person zerosum
game with the subsequent profit matrix :{4 -2}
{-3 1}
What is the value of the game?
(ii) What is Nash equilibrium? discuss with a suitable example.
(b) provided the demand and supply functions for cobweb model:
Qdt = 10 -2Pt
Qst = -5 +3Pt-1
obtain 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 provided

Q=5 K 1/2 L 1/2

obtain 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 