Calicut University 2009 B.A Economics ch, VI – Optional (vi) : Mathematical - Question Paper

I. select the accurate ans. Write only the alphabet.

1) Which theory made use of General Equilibrium framework ?
a) Linear programming b) Input-output table c) Game theory

2) TV 2nd order condition of profit maximisation is
a) 0 2
2
<
?
? p
x
b) 0 2
2
>
?
? p
x
c) 0 2
2
<
?
? p
x

3) The nature of apparent real income in slutsky formula is
a) decreasing b) increasing c) constant

4) The elasticity of supply for the function s = 100 – 5p2 at p =3.
a) Less than 1 b) 1 c) More than one

5) At q = 2, the function x2 – 2x – 7, is ___________
a) decreasing b) increasing c) stationary (5×1=5 Marks)

II. State actual or False :
6) Saddle point is a different name for dominant equilibrium.
7) Product differentiation is a feature of monopoly.
8) Expansion path is the locus of the optimal input combinations as the output
level modifications input prices remaining constant.
9) Lagrangian multiplier is unconstrained optimisation technique.
10) The Engel curve for an inferior good is negatively sloped. (5×1=5 Marks)

III. Fill in the blanks :

11) ___________ of a provided matrix is the new matrix found by interchanging its
rows and columns.
[Transpose, Determinants]
12) _________ is that the price derivative of a demand function can be decomposed
into an income effect and substitution effect.
[Euler's Theorem/Slutsky Equation]
13) _______ measures the rate at which substitution ranging from factors takes place.
[Elasticity of substitution/Marginal rate of substitution]
14) Perfect price discrimination is also termed as _________
[First degree discrimination/Third degree discrimination]
15) ___________ developed input-output model.
[Robinson/Leontieff] (5×1=5 Marks)

IV. describe any 4 of the subsequent :
16) Saddle point.
17) Market equilibrium.
18) Budget line.
19) Returns to scale.
20) Quadratic formula. (4×1=4 Marks)

V. ans any 7 of the subsequent not more than half a page.
21) elaborate the assumptions of input-output model ?
22) discuss Prisoner's dilemma.
23) discuss consumer's surplus.
24) From the demand function X = 80 – 4P – P2, determine price elasticity of
demand when P = 5.
25) Differentiate y = (x2 + 3) (2x3 + 4x).
26) If the total cost is TC = 50 + 10q + 25q2. obtain the avg. Cost and Marginal
Cost when q = 2.
 -3- 1264
27) obtain the equilibrium price and volume
P Q (demand function)
8
7
= 50 -
P Q (sup ply function)
4
3
=15 + .
28) Determine which kind of returns to scale is the subsequent production function
Q = 2K + 3L + KL.
29) Distinguish ranging from primal and dual.
30) discuss price effect. (7×3=21 Marks)

VI. ans any 6 of the following, every not more than 1 page.
31) Examine the subsequent function for its maxima or minima and determine its
value
C = 2x2 – 12x + 40.
32) discuss CES production function.
33) discuss economic interpretation of time margin function.
34) Solve the LPP by graphic method :
Maximise Z = 3x1 + 4x2
Subject to x1 + x2 < 6
2x1 + 4x2 < 21
x1, x2 > 0
35) The cost function of a monopolist is
TC = 500 + 20q2
The demand function is P = 400 – 20q. What is the profit maximising output ?
36) Production function is provided by k k
k
Q two 12
3
2
3
= - + + . Beyond what points
do diminishing returns do exist ?
37) discuss Ridge Lines.
38) discuss dynamic input-output model.
39) State and prove Adding-up Theorem.
40) The supply function for a commodity P = two + Q2. obtain the producer's surplus
when price is Rs. 18. (6×5=30 Marks)

VII. ans any 3 of the subsequent not exceeding 3 pages every.
41) discuss Cobweb Model.
42) obtain firm's equilibrium and cost function if the production function is Cobb-
Douglas function.
43) discuss constrained optimisation. Optimise the function z = 2x3 + 3x2 – 2x2y2
subject to x + y = 10.
44) The demand function of a monopolistic firm is
P = 8000 – 4q
LAC = 8000 – 7q + 0.002q2.
obtain profit maximising price and output.
45) Production function is provided by 2
1
2
1
Q= 2K L . presume that K = 9, P = six and
wage rate (w) = 2. Determine optimal volume of labour. If wage rate is increased
to Rs. 3/-, obtain the optimal volume of labour.
46) discuss Simplex method of Linear Programming. (3×10=30 Marks)

Earning:   Approval pending.