MASTER OF ARTS (ECONOMICS) Term-End Examination June, 2010 MEC-003 : QUANTITATIVE TECHNIQUES SECTION - A

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1 No. of Printed Pages : 12 M EC-003 MASTER OF ARTS (ECONOMICS) co O Term-End Examination June, 2010 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 production function : y=f (x) = 400x + 60x2 6x3 Where y= output, x = input. The firm faces an output price of P=10 and an input price of W = Write a profit function of this firm in terms of output and input prices and the input level. What is the profit maximising level of input for this firm? Verify that the input level you choose is the profit maximising point. Find the marginal product (MPx) of the variable input. Verify that P(MP x)=w at the profit maximising input level. MEC P.T.O.

2 What are the differences between open and closed input-output models? An economy has two sectors, agriculture and manufacturing. The input-output coefficients for these sectors are given as : Output Sector Input Sector Agriculture Manufacturing Agriculture Manufacturing If the final demands for these sectors are 300 and 100 units respectively, determine the gross output for the two sectors. If the input coefficients for labour of the two sectors are 0.5 and 0.6 respectively, determine the total units of required labour. 2. What is Bayes theorem? Explain how would you make use of the results of this theorem to derive the law of total probability. Define the standard error of a statistic. Explain how it is helpful in testing of hypothesis and decision making. MEC-003 2

3 SECTION-B Answer all the questions from this section : 4x12=48 3. The following data are available for an industry which produces three products A,B and C. Product Required time (hrs) Profit Assembly Finishing per unit A B C Industry's capacity Write the compact linear programming model using the above information. Derive the optimal solution of the model by using simplex method. Distinguish between the characteristics of first and second order difference equations. Give examples of economic problems that are solved with the help of each category of such equations. MEC P.T.O.

4 4. (a) Consider the following national income determination 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 are endogenous variables ; I and G are exogenous variables and t is the income tax rate, using cramer's rule solve the model for endogenous variables. (b) Solve the equation dy _ X2 - y2 dx 2 xy A production function is given as 2 (axi X2 - bxi 2 cx2 ) ax1 + bx2 Determine its degree of homogeneity and derive the marginal products of x1 and x2. Show that marginal products derived are homogenous of degree zero. What meaning will you describe to such a feature of the production function? MEC-003 4

5 5. Assume that on an average one telephone number out of 15 is busy. Find the probability that if 6 randomly selected telephone numbers are picked up, not more than three are busy at least three of them are busy A sample survey was conducted to see whether there is any significant difference in the sales by two salesmen (A and B) in a district. The following data have been obtained from survey. A B No. of Transaction Average value of transaction (Rs. 000) Standard deviation (Rs.000) What conclusion can be reached on the difference of sales by A and B? (Table value at 5% level of significance for the test of difference is given as 1.9) 6. A problem in statistics is given to 5 students Al, A2, A3, A4 and A5. Their chances of solving it 1 1 respectively, are 2 1, 31, 14, 5 and 6. What is the probability that the problem will be solved? Explain the relevant considerations of making a choice between one-tailed and two-tailed tests. How would you determine the level of significance in the above tests? MEC P.T.O.

6 SECTION-C Answer all the questions from this section : 2x6=12 7. Estimate the regression equation of Y on X from the following data : X Y Find the expected value E(X) and Var(X), where X is the outcome when we roll a fair die. 8. Write short notes on any two of the following : Monotone function Eigen value and eigen vector (c) Rank of a matrix MEC-003 6

7 cchy97 ( 312.1Fr ) ti^lia r 1,1, #.-003:,c; g ut rakze RTITI : 3 Vz4 31A 3w : 100 adz : q,.5 r.?//t-tit mq-f 6ci 4).1 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 +60x 2 6x3,=4r y= 3c-41qt x=31-1q-h c41C-f P=10.2.TT 3-17q9I -11=M W =5440. z-eq-g, Iffffti I Iff2TT 341-q-RI tcit -97 -N4"t 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 'ER P(MPx) = w. MEC-003 P.T.O.

8 r<99--a--ffg mrd I---q-T-P-Tr 4 TN -R--4 laf-hf u r 4-A1 31-Kiff-dc-1< -Tifffit otrochr 4 : z-etrq -)--q 4 ci iil c Fra- 4-1q rcipihni *Tr IV: T100 LTT e cal T11413 c 4-ii<-1 T 311*-1ff q < T4- wr 31-r-<-F $114-RI: e al N11 31F4T4WdT -4 dt? 2. 3r1:1-4.q,Efr *-1-544tq.kuli4A rvti-r 314 Tilur-q-dr ;1-o:1-F-7-174? 3TEIVT 4-111* ed. q *. I -4 f-*-:ft mierenc-qq r Zic-q t y rr fa-f11-9-r--*-4r 4 f*--{zr m*r dqq1411 MEC-003 8

9 - s 779.M517-4 : 4x12=48 3. a-131)' A, B 3i C dr-li qi ci alc,1 Lo, -Tag ri titf 14 "4 IIdmltl krit : 3cgiq 3TEWEIW 1:11:14 ( Tft ) Vrff TWI kle-4 \AI 4 tfl rs1111 9T1I A B C ql 0 agrat :*Tr III l ohr 31KR 3f-d-rrra- 01, rt-i Lic; 01ti rcirtt (a) 11 A-iT7 TT 3T1117 TITri9Ti ql1c1 ci.) I -SifdlTrff r TRI)T1 3TV4T A cqkfon ,t uif 1-1fa71-Erd-r q F 10 I 7X111 *44-114)*u1 fm-r Trin:ErrA.)cir t? dqikur MEC P.T.O.

10 4. (a).t-{ 717 atri f9-9117t SIR 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.TIG t 3-TRT obt t -1=R t -F a1-)-71a t 3 11dr4 (b) tis-i chtu f oh dy x2 y2 dx 2xy ac-lik-f 41(1-r f-d-q7 : (axi x2 bx? cx3) axi + bx2 TriffiTffi Tlfa TIT x 1 3T x 2 j1 4-11cf ql1cf cf.: I T4TN rah 39 i TnTrfa dcliiq-f ohl 3-Trcr qzfr 771 t i t dclik MEC

11 5. -RH Fet) '6.1-f '1 &Rf Th-d-eff t I t4-4 6 Lb) r iat ilqi=o4) Farq 4 14 t qki 3Tr-*-'ffu d-114 : cl RI7f, * "R?f 11' T it-d-q-si gri A p-14 S1R-1 fwzr t1 c -k-ta4i(a,b)61trehl t61 4 la 1 1-1q ti.w-4i aftra' a II-Iti 4itee-4 ( s.r1h T. ) fcimic1-1 ( Ii T.) A B TPTT1 TE(T fite0 +If? (5% 41ft-d1 t chl ziyt c q4-41-ff 1.9 t I) 6. 41Tf fd7t6174 A 1, A2, A 3, A4 37 A 5 I 1Th4 TITR7I1 t 75.1([7qk 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 wffi Tft 6:11 t? trthruff 4 3Trcr TrP-f-*--dr tclt -Tr fiqit-oi F.4 sicrir -t71? MEC P.T.O.

12 - (As "k Mfi 2x6= fT* 3-1MTR -ER Y X 'TT SlcI f =4,; : X Y TETaT if X ffu -cifff *-* fruiP4 *rfqa 141-ff E(X) 2-TT Var(X) 1 31-r* R5a re ufui q f f : 41( r$TN-- (c) I) 3 d i oh rds#144 MEC