M EC-003No. of Printed Pages : 12

MASTER OF ARTS (ECONOMICS)

co Term-End Examination

June, 2010O

MEC-003 : QUANTITATIVE TECHNIQUES

Time : 3 hours Maximum Marks : 100

Note : Answer the questions from each section as directed.

SECTION - A

Answer all the questions from this section : 2x20 =40

1. A competitive firm has the following productionfunction :

y=f (x) = 400x + 60x2 — 6x3

Where y= output, x = input. The firm faces anoutput price of P=10 and an input price ofW = 5440.

Write a profit function of this firm in termsof output and input prices and the inputlevel.

What is the profit maximising level of inputfor this firm ? Verify that the input levelyou choose is the profit maximising point.

Find the marginal product (MPx) of thevariable input.

Verify that P(MPx)=W at the profitmaximising input level.

OR

MEC-003

1 P.T.O.

What are the differences between open andclosed input-output models ?

An economy has two sectors, agricultureand manufacturing. The input-outputcoefficients for these sectors are given as :

Output SectorInput Sector

Agriculture Manufacturing

Agriculture 0.1 0.5Manufacturing 0.2 0.25

If the final demands for these sectorsare 300 and 100 units respectively,determine the gross output for the twosectors.

If the input coefficients for labour ofthe two sectors are 0.5 and 0.6respectively, determine the total unitsof required labour.

2.

What is Bayes theorem ? Explain how would youmake use of the results of this theorem to derivethe law of total probability.

OR

Define the standard error of a statistic. Explainhow it is helpful in testing of hypothesis anddecision making.

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SECTION-B

Answer all the questions from this section : 4x12=48

3. The following data are available for an industrywhich produces three products A,B and C.

ProductRequired time (hrs) Profit

per unitAssembly FinishingA 10 2 80B 4 5 60C 5 4 30

Industry's capacity 2000 1009

Write the compact linear programmingmodel using the above information.

Derive the optimal solution of the model byusing simplex method.

OR

Distinguish between the characteristics of first andsecond order difference equations. Give examplesof economic problems that are solved with thehelp of each category of such equations.

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3 P.T.O.

4. (a) Consider the following national incomedetermination model :

Y=C+I +G

C=a+b (Y —T)

T=d+ty

Where

Y = national income

C = Consumption expenditure

T = Tax collection

If you are given that Y,C and T areendogenous variables ; I and G areexogenous variables and t is the income taxrate, using cramer's rule solve the model forendogenous variables.

(b) Solve the equation

OR

dy _ X2 - y2

dx 2 xy

A production function is given as

—2(axi X2 - bx i2 — cx2 )

ax1 + bx2

Determine its degree of homogeneityand derive the marginal products ofx1 and x2.

Show that marginal products derivedare homogenous of degree zero. Whatmeaning will you describe to such afeature of the production function ?

MEC-003 4

5. Assume that on an average one telephone numberout of 15 is busy. Find the probability that if 6randomly selected telephone numbers are pickedup,

not more than three are busy

at least three of them are busy

OR

A sample survey was conducted to see whetherthere is any significant difference in the sales bytwo salesmen (A and B) in a district. Thefollowing data have been obtained from survey.

A BNo. of Transaction 20 18Average value of transaction (Rs. 000) 170 205Standard deviation (Rs.000) 20 25

What conclusion can be reached on the differenceof sales by A and B ? (Table value at 5% levelof significance for the test of difference is givenas 1.9)

6. A problem in statistics is given to 5 students Al,A2, A3, A4 and A5. Their chances of solving it

1respectively, are 1 1 1 1

—2 , 3 , 4 , —5 and —6 . What is the

probability that the problem will be solved ?

OR

Explain the relevant considerations of making achoice between one-tailed and two-tailed tests.How would you determine the level of significancein the above tests ?

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5 P.T.O.

SECTION-C

Answer all the questions from this section : 2x6=12

7. Estimate the regression equation of Y on X fromthe following data :

X 1 2 3 4 5Y 2 5 3 8 7

OR

Find the expected value E(X) and Var(X), whereX is the outcome when we roll a fair die.

8. Write short notes on any two of the following :Monotone functionEigen value and eigen vector

(c) Rank of a matrix

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cchY97 ( 312.1Fr )

ti^lia r

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RTITI : 3 Vz4 31A 3�w : 100

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4. n1 8 -

{A u s 7x9#7v9Sri .01 2x20=40

1. ciq I IFF{ 3-01-K (-no-r t :

y=f (x) = 400x +60x2 — 6x3

,=4r y= 3c-41qt x=31-1q-H74-04 3c41C-f

P=10 .2.TT 3-17q9I -11=M W =5440.

z-eq-g, Iff2TT 341-q-RI tcIt -97 -N4"t

Iffffti I

aTfr 3011q-r err -141(.?

-afg "r* 3-TFT gitr f-*-zrr J i q r 31-rq-rff

33-F4*--d-rt 111 ark cb) r t

-11-FT-4-d1 3-Tr q-ra- *:(fd- zrg (MPx) 711d

fq-ur 3117ff t-c.R 'ERP(MPx) = w.

MEC-003 P.T.O.

3117 31-r<99--a--ffg mrd4-114

342I---q-T-P-Tr 4 TN -R--4 laf-Hfu r 4-A1

31-Kiff-dc-1< -Tifffit otrochr 4 :

z-eTrq -)--q31-Fra- 4-1q

c1 4 rcIPIHNI

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T11413 c 4-ii<-1 T 311*-1ff

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MEC-003 8

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s 779.M517-4 : 4x12=48

3. a-131)' A, B 3i C dr-li qi ci alc,1 Lo, -Tag

ri ti tf 14 "4 IIdmltl kriT :

3TEWEIW 1:11:14 ( Tft ) Vrff TWI3cgiq

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A 10 2 80

B 4 5 60

C 5 4 30

2000 1009ql 0 agraT

31:*Tr III l ohR 31KR 3f-d-rrra-

01,

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14-q F 10 I 7X111 *44-114)*u1 fm-r

3101--Trin:ErrA .)cir t? dqikur

MEC-003

9 P.T.O.

4. (a) .t-{ 717 aTRI f9-9117T SIR1 411-1 -N--4R cf; :

Y = C+I +G

C =a+b (Y —T)

T=d+ty

Y =Trtzf

C = -3-c[A-rf oq4,

T = oh

Y, C, T cM-Ift ff -t at I 2.TIGt 3-TRT obt t -1=R t -F9-74

-51a1-)-71a t 3 11dr4

dy x2 y2(b) tis-i chtu f oh

• dx 2xy

34-21-7

ac-LIK-f 41(1-r f-d-q7 :

(axi x2 — bx? — cx3)

TriffiTffi Tlfa TIT

x1 3T x2 j1 4-11cf ql1cf cf.: I

T4TN rah 39 i TnTrfa dcLiiq-f 410-11 ohl

771 t i t dcLIK

3-Trcr qzfr

—axi + bx2

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5. -RH Fet) 15 4 74 1 '6.1-f '1 &Rf Th-d-eff t I t4-4 6Lb) r iat ilqi=o4) Farq 4 14 t qki3Tr-*-'ffu d-114 :

cl RI7f ,

* 44 -4 474 "R?f 11'11

3111-4T

it-d-q-si gRI•A p-14 S1R-1 fWZR 14-41t1 c•-k-tA4i(A,B)61trehl t61 4

A B

20 18la 1 1-1 q ti.W-4I

170 205aftra' a II-Iti 4itee-4 ( s.r1H T. )

20 254-11-111 fcimiC1-1 ( Ii T.)

3TPTT1 TE(T fitE0 +If ? (5% 41ft-d1 t chlziYt c116 0111 q4 -41-ff 1.9 t I)

6. 41Tf fd7T6174 A 1 , A2, A3, A4 37 A5 I 1Th4

TITR7I1 t 75.1([7qk1 1 1 1 1

trr4 Tfi.Tir—d-0 WITT: 71, 5 7 t I *t-1

-41,111 Mt 414 chl *frr-q--dr

-ffqr Likl-fuff 4 =.1i-r wffiTft 6:11 t? trthruff 4 3Trcr TrP-f-*--drtclt -Tr fiqit-oi F.4 sicriR -t71?

MEC-003

11 P.T.O.

-

(As "k Mfi

7. 9 3-1fT* 3-1MTR -ER Y X 'TT SlcI4411-1-f

=4,; :

X 1 2 3 4 5Y 2 5 3 8 7

3TETaT

2x6=12

if X 319-54-ffu -ciFff *-*-4 --111-fruiP4

*rfqa 141-ff E(X) 2-TT Var(X) 1 31-r*-6-9.

8. 4R5a re ufui q f f :

41(1-1

31-719. 1 31-r$TN--

(c) I) 3 d i oh rds#144

MEC-003 12