Gauhati University 2007 B.A Economics Mathematical Methods for Economic Analysis(THIRD ) - Question Paper

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
(0 1)
( ) ( 0,1 0)
0 0
= < <
= + - > > >
= + +
T dY d
C a b Y T a b
Y C I G
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
+ 2x = 0
dy
dy
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 :




- 
- 1
2
3
4
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 K L 2
1
2
1
= 5
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, YO

Earning:   Approval pending.