No.
of Printed Pages : 8 MEC-003
M. A. (ECONOMICS)
(MEC)
Term-End Examination
June, 2020
MEC-003 : QUANTITATIVE TECHNIQUES
Time : 3 Hours Maximum Marks : 100
Note : Answer the questions from each Section as
directed.
Section—A
Note : Answer any two questions from this Section.
2 x 20 = 40 .
1. A monopolist produces two commodities A and
B. His demand function is Qi = 40 + P2 – 2Pi
and Q2 = 15 – P2 + Pi . Pi and P2 are prices and
Qi and Q2 are quantities of A and B. Let the
cost function of the monopolist be
C = Q + Q 1 4Q2 + Ql . Find his profit
maximising output and prices. Also, find the
Hessian matrix.
P. T. 0.
[2] MEC-003
2. The input coefficient matrix of an economy is
given by
0.0 0.3 0.3
A = 0.3 0.1 0.1
0.2 0.4 0.0
and the final demand matrix
180
D = 20
90
Find the level of output.
3. (a) Consider the aggregate production function
Q= Ka. , where Q, K and L are all
functions of time. Depict and solve for the
time path of capital output ratio.
(b) Solve :
(t + 2y) dy + (y + dt2 ) dt = 0
4. (a) State and explain Bayes' theorem.
(b) Calculate P(B/A) if P(A/B) = 1/4, P (A) = 2/5
1/2 using Bayes' theorem.
31 MEC-003
Section—B
Note : Answer any five questions from this
Section. 5 x 12 = 60
5. Show that in a Poisson distribution, the mean
and variance are equal.
6. Suppose we roll a die and are told that the
number is odd. What is the probability that it
was 5?
4 1 —1
7. Find the inverse of 0 3 2
3 0 7
8. Estimatr se regression equation of x on y from
the data given below :
x y
5 8
8 6
3 11
10 8
5 9
9. (a) Find dy I dx when :
y = log (ex + 3)
1
=
IX2 a2
P. T. 0.
[ 41 MEC-003
(b) Find the total differential given :
xl
y=
x1 + x2
10. Solve the following linear programming
problem using the simplex method :
Max. :
Z = 55x2 + 45x1
Subject to :
6x1 + 4x2 5 120
3x1 + 10x2 S 180
?. 0, x2 0.
11. For 150 beams of a particular type, the mean
and standard deviation were found to be
8.5 mm and 0.5 mm respectively. Test if the
observed mean differs significantly from 8 mm.
12. Write short notes on the following :
(i) Kuhn-Tucker condition
(ii) Taylor's expansion
5 MEC-003
MEC-003
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thin RTr
19', 2020
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air : SAch TIM 4 7igirf-4-4r 3rn
WPT—W
wiz : wr 1-*---4Y 4} VrA71
2 x 20 = 40
1. 1 Writ/W(1' AV A '211 B ac Inca cmcri
tl dkicti 1717 41(14 swikf: Q 1 = 40 + P2 — 2P1
utrrQ2 = 15 P2 ± P1 ti fie? P2 7(.1
A afR B t 4;144 -ffeir Q1 ati Q2 ART st+of:
.sick 411,111t W4ifTft 1T *1 Wir
rerWRI a5T mid
410-1 C = Q2 + Q1 c12 +Q? *1 stmt; alftWdli
WIT drits•t 494 alTWFM f i*ffizM
loco AT airireff 4' at
P. T. O.
[6] MEC-003
2. R-W alter IT iii alKIff 1j111TW a-170:0-
0.0 0.3 0.3
A = 0.3 0.1 0.1
0.2 0.4 0.0
3117 alfatr Trig *item :
180
D= 20
90
dicbr ac41q f Tiff airWi-Mff a-AT
3. () *iabei Loorf Q = L1-a Ka 'R Th-9T-t
WT— Q, K ati-t L 1:11# chid
Loci-1 do us 39cfrul -wr <bid 72./
311Weffa 1;ci W-ARI
(u) f :
(t + 2y) cly + (y + dt2 )dt = 0
4. (Ti) " -1 5TT si 4 g cic1I U 3-fri -314-4
Wirq71
P (B/A) Thl-N7 7:fR
P (A/B) = 1 / 4, P (A) = 2 / 5 IT
P (B) = 1 / 2 cl ,st 31* 3trzlITT Th11771
7 MEC 003
-
• ITTIT-75
: Tcr iwt irt-a srn
5 x 12 = 60
5. T41f-Rfq Ti WERT( dimert * atk
fcritur -*RR lac ti
6. 4iiia f'W RW Rim Qm4 -ER fatm itgrr ti
*Err kiNiogir t N haft '5' t ?
7. $T alTalg air*fau .4) ,414 :
4 1 -1 -
0 3 2
30 7
8. ftiMk1rivd 3 * x TR
sin 4414-1-1 ahvi auchri-f '4NIZ :
x y
5 8
8 6
3 11
10 8
5 9
9. (V) lict Wff
dx
(i) y = log(ex +3)
1
(u) )1- 4x2 a2
P. 7 O.
[8 MEC-003
t-lchrf ara-0. ;11c1 -1f1-
47 :
()
xl
Y=
x1 + x2
qq trATI:n.
10. rti4c a+r rgrtT T mil4r
wrem Tru W-mg :
aftwaR :
Z = 55x 2 + 45;
srfreArd :
6; + 4x2 < 120
3; + 10x2 S 180
xi a 0, x2 a 0
11. "RW mcbit 150 Mit Aliff ITN 3117
1 -11111 rcirld4 sto-tql: 8.5 fit 4kt ail't 0.5
1-1dk trrg TR ti trftwi -4-F-A7 fqc 9zrr arcau
*Efff 8 4-1et 1:11-0 W-1 t fiT9
12. r1 4 -irrirtld c TITkit71 e.t+iruiqi fafiuR :
(i)
(ii) acct fd-RIR
540
MEC-003
