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Reg. No. : ................................. Name : .....................................

B.A. Supple. Degree Examination, August/September 2009 Part  III : Group (iii)  Economics Paper  VI : Optional (vi)  MATHEMATICAL ECONOMICS (New Scheme  2005 Admission Onwards) Time : 3 Hours

Max. Marks : 100

Instruction : Answers may be written either in English or in Malayalam. I. Choose the correct answer. Write only the alphabet. 1) If A =

, then A2 is a













a) unit matrix c) diagonal matrix

b) null matrix d) none of these

examquestionpapers.com 2) Price elasticity of demand is given by a) 

b)

G

p



.

F

q



c)

F

p



.

G

q



F

.

d)

q



F

 p

q

.

G

p

p

3) Marginal cost curve is the slope of a) TR c) AC

b) TC d) None of these

4) The Engel curve for a Giffens good is a) positively sloped c) zero sloped

b) negatively sloped d) none of these

5) A linear function is in the form a) y = a + bx + cx2 c) y = axn

b) y = a + bx d) y = ax

(5×1=5 Marks) P.T.O.

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II. State true or false : 6) Input output analysis was first developed by Cobb Douglas. 7) Two indifference curves intersect at the equilibrium point. 8) A monopolist follows price discrimination. 9) Order of a matrix is given by Â&#x2018;nÂ&#x2019; coloumns. 

m



when a matrix is arranged in Â&#x2018;mÂ&#x2019; rows and

n

10) Cobweb model explains that todayÂ&#x2019;s output is determined by yesterdayÂ&#x2019;s price. (5Ă&#x2014;1=5 Marks) III. Fill in the blanks : 11) When AC falls (MC is above AC, MC is below AC) 12) Transpose of the matrix A =

is





examquestionpapers.com 



!





1

4

1

3

 ,





2





3

2









"



4

 

13) The derivative of the function y = 2x2 + 3x Â&#x2013; 4 is (4x2 + 3, 4x + 3) 14) PrisonerÂ&#x2019;s dilemma is a special case of (Game theory, Input output analysis) 15) A general demand curve is always (monotonically increasing, downward sloping or decreasing)

(5Ă&#x2014;1=5 Marks)

IV. Define any four of the following : 16) ConsumerÂ&#x2019;s surplus 17) Variable 18) Marginal cost 19) First order condition for profit maximisation 20) Determinant of a matrix.

(4Ă&#x2014;1=4 Marks)

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V. Answer any seven of the following in not more than half a page. 21) Linear Programming. 22) Production possibility curve. 23) Properties of indifference curve. 24) Relation between TC, MC and AC. 25) Distinguish between primal and dual. 26) Cross elasticity of demand. 27) Returns to scale. 28) Find the value of the determinant

!

"















29) Explain the assumptions of the input-output analysis. 30) Income effect according to the Indifference curve analysis.

(7×3=21 Marks)

VI. Answer any six of the following each not more than one page.

examquestionpapers.com

31) Graphically illustrate the Slutsky demand curve.

32) A monopolist firm has the following total cost and demand function C = aQ2 + bQ + c; P = . What is the profit maximising output level when the firm is assumed to fix output ? 





3

33) Derive the first order derivative for consumers utility maximisation in the indifference curve analysis. 34) Derive the equilibrium condition of a perfectly competitive firm. 35) Given the demand function X = 25  4P + P2, where X is the demand for commodity at price P, find elasticity of demand ed .

36) The demand and supply laws are Pd = (6  x)2 and Ps = 14 + x respectively. Find the consumers surplus if demand and supply are determined at pure competition. 37) Explain the Cobb-Web model. 38) Explain saddle point solution. Distinguish between simple and mixed strategy in oligopoly.

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39) Define (i) a scalar matrix (ii) a zero matrix (iii) sum of two matrices when it exists. 40) Examine the following for maximum and minimum values x3 + y2  4x + 8y.

Z= "

(6×5=30 Marks)

!

VII. Answer any three of the following not exceeding three pages each. 41) Given A2 + B2 = (A + B)2 where =



and B =



)







>



find a and b. 



















42) Solve the following LP by simplex method. Maximise

Z = x1 + 2x2 + 3x3  x4

Subject to

x1 + 2x2 + 3x3 = 15 2x1 + x2 + 5x3 = 20

examquestionpapers.com x1 + 2x2 + x3 + x4 = 10

and xj



0 (j = 1, 2, 3, 4)

43) Find the demand vector D which is consistent with the output vector #

0 





X=



2

0

.

3

0

.

2 

, when the input-output coefficient matrix is A =





.





.



0

.

4

0

.

1

0

.

2



&



0

.

1

0

.

3

0

.

3

















44) Explain the General Linear Programming Problem with example. 45) If the demand law is P = 12  5Q and total cost is C =  Q3 + 3Q2 , determine the change in the price due to imposition of sales tax of 20%. Find the corresponding profit. Determine the price if government grants subsidy (instead of imposing tax) of 10% per unit of output. What will be the profit if a sales tax of 10% is imposed ? 46) State and prove properties of Cobb Douglas production function. (3×10=30 Marks) __________________

Branch Paper - VI Optional (vi) - Mathematical Economics (New Scheme - 2005 Admission Onw

d) P.T.O. a) c) Reg. No. : ................................. Name : ..................................... F G G F F G F q p ....