# 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(x1x

**2)**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.

**(**Distinguish between" mixed strategy and dominated strategy.

**d)****2.**ans any 4 of the following:

**a)**provided the demand function

Where Q is volume demand and P is pric

**e.**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.

**(**Formulate a general transportation issue to linear programming where there

**d)**are 3 factories for production and 5 destinations to supply the products.

**(**In the competitive market model

**e)**D=16-2P

S = -4 +2(P- t}

where D, S, P and t denote demand, supply, price and sales tax rat

**e.**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.

**(**provided the national income model

**c)**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.

**(**Solve the subsequent

**d)**dy/dy+2x = 0

with initial condition y(0) = 5.

**(**Let the demand function of a firm under monopolistic competition be provided by

**e)**P = 118 -3Q+4.A

where P is price, Q is volume and A is advertisement expenditur

**e.**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)****(**obtain the optimal strategies for the participants in a two-person zerosum

**i)**game with the subsequent profit matrix :{4 -2}

{-3 1}

What is the value of the game?

**(**What is Nash equilibrium? discuss with a suitable example.

**i****i)****(**provided the demand and supply functions for cobweb model:

**b)**Qdt = 10 -2Pt

Qst = -5 +3Pt-1

obtain the inter-temporal equilibrium price and also determine whether you will get

stable equilibrium.

**(**A producer desires to minimize the cost of production

**c)**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.

**(**Maximize f = 2X + 5Y

**d)**subject to

X+4Y<24

3X + Y < 21

X+Y<9

X, Y

Earning: Approval pending. |