MEC-003 QT 2014

MEC-003No. of Printed Pages : 7 MASTER OF ARTS (ECONOMICS) Term-End Examination December, 2014 MEC-003 : QUANTITATIVE TECHNIQUES Maximum Marks : 100 Time : 3 hours Note : Answer the questions from each sections as directed. SECTION - A Answer any two questions from this section. 2x20=40 1. Given the demand and supply for cobweb model as : Qdt = 18 - 3 t and Qst - 3 + 4Pt-i (a) Find the inter temporal equilibrium price and determine whether the equilibrium is stable. (b) Establish the stability condition of Samuelson's multiplier accelerator model. (a) Write down the distribution functions of the 2. Binomial distribution and Poisson distribution. When is a Poisson distribution an approximation of Binomial distribution ? Obtain the mean and variance of the Binomial and Poisson distribution. (b) Write down the properties of a normal distribution. For a standard normal distribution, write the density function. MEC-003 1 P.T.O. (b) contrast these values with those that would be achieved under profit maximisation. determine the total labour that would be required. His cost and demand functions are C = 500 + 4q + 8q2 and P = 304 — 2q. SECTION . (a) Solve graphically Sub to Min C = 0. 6. 2 successive draws of 3 balls are made without replacement.3. 5. A revenue maximising monopolist requires a profit of at least 1500. 4.B Answer any five questions from this section. X2 > 0 (b) Why does the solution occur at the corner point only ? Give reasons.10 0. (a) determine his output level and price.20 0. determine the gross output of the two sectors. Find the probability that the first drawing will give 3 black balls and the second 3 blue balls.6x1 + .x2 10x1+ 4x2 > 20 5x1 + 5x2 20 2x1 + 6x2 > 12 Xi. The input-output coefficients of these sectors are given as : Output sector Agriculture Industry Input sector Agriculture Industry 0. (a) What are the difference between open and closed input-output models ? (b) An economy has 2 sectors agriculture and industry. (ii) If the input coefficients for labour of the two sectors are 0. 5x12=60 A bag contains 8 blue balls and 5 black balls.50 and 0.25 If the final demand of these sectors are (i) 300 and 100 respectively. MEC-003 2 .60 respectively.50 0. Using + x3 the Hession matrix check whether the extreme value(s) is/are maximum or minimum.- MEC-003 3 P.7.X1 X2 4x2 x1X3 12. 10. Explain the method of maximum likelihood for estimating the value of a population parameter. (c) State properties of point estimators. 4 1 —1 Find inverse of 0 3 2 3 0 7 9. Find the extreme values of : 2 + 2 . .. When we roll a die and are told that the number is even ? What is the probability that it was 4 ? 11. 8.O. Maximise z = 45x1 + 55x2 6x1 +4x2<-120 Sub to 3x1 +10x2-L:180 x2 ?.T. (a) What is sampling distribution ? (b) State control limit theorem. Solve the following Linear Programming Model in x1 and x2. 2 2 z = 2X1 . Htur 711I .: 37filwff-T3-fw. 111(1-1 fff4 I 3TI4E7 fit fT2rfff t ? f-g-Erq 3. 2014 7114111-003 : isiktfur %fuze iglullti-lch TP:FT : 3 Eir4 *a.R.0 I (b) 14-11-11 31-E4E7 FcR)tic14 fffd I M.TthlTTi 1.b -5fEdtri7 #RITM TI'T-Rit-9-9-r 2.-003 rti aph-fm.*. Qdt =18 — 3Pt (a) -grTi-r 2x20=40 3-1-FL-M -TxT-R Qst = — 3 +4Pt _ i #7ff pfd 7ficr cf-) I q 1. (a) tcg 7174i-31T4-69'( 3lT4E.H14-11-q 3T14-Ci MEC-003 (41C1-1 f974 I 4 4-11-Ich .:100 FigTvti.# F-47 z1-1 - (b) Ttg-07 #27-67:rf ? Thrrw-T.tH v-r/Y 6/1 14/ VITT 14Tri fwt 9-79f -k 6-7R I 1-1115-AK1 1.711 .It6t ATTff AT Y.9.) trftalT tf.. 4To Trly I tr-0 -Icf")10 t ?TV at{ ensi.)? $3T143-TEqff 9114-Rf: qrq c f-*-ff4 0.50 3117 0.50 371)7 0.60 t c 311-477W-d-f il411? Tcb. MEC-003 5x12=60 mio 8 -141 3IY{ 11.4T-rt chef-t-ch4 1500 31714 31fT*71:1 -WT4 t I 3TIt 1NId 3t-{f 41(1-1 Tichlt C = 500 + 4q + 8q2-ff2TT P=304 —2q I -W11:rd3-4F-07 c I (a) 3tichl (b) goof 311g1W-dl:f H Ti 311 c1Tsi m1 4-11-qc-11 tr{ 31-19-1ft7 4-11-4 -# chZ I .20 0. .25 ciq7#"A't3-0:17 chi 31tffigiltrf #t 300 AT looT*-tirtt TTFT cI I if. 3-11 5 Rt-) -4-tt 1141 P.3.O. TrTsf Tdirr Trti 0.T.731 ftt ITN -9-7t3clt f74 I 5.10 0.-1(-1 51c4 Tr7 t . (a) 31917 3j 377 3-TgT9-37rg 51F1HI 14 31---T I ict) 310:1-d74114t dc4lqct) #qtTrisf 3-1177dFT (b) T1WR : "qt44 31-gi #-I• 37-1:17 #9' (i) 4. . 9. 1 31-11:rF (1411 crii 31firwair 3Traff (a) fq-1 4(sii TM 2.6. fT-Tft f*711. 1 rarq 8. *Riff 7417 ra. (a) 71TITIFER ch I -c171 1a` chi : ctA : C =0.20 2x1+ 6x2 > 12 x1.6x1+ x2 10x1+4x2 ?.-9--1rr MEC-003 6 .71:1FTE MI10 . rcli)t1c11(1 -01 'TT f qchcll 11. mite-11:1H 3iftrwair t Trr .1 1 mR4-1 TIN 71id chi : 2 z = 2x1 — X1x2 4x22 x1 x3 + x3 + 2 . clqi ti+i 11 374a-ff 4 1 —1 0 3 2 3 0 7 t? SIT 3r4zr t-z4 (b) 13 f4- (c) 10. x2 > 0 (b) 7.ft I 3 :1-k '4' ? 7r 9h 1.20 5x1+5x2 ?. 12. 3-Ti-Wr—d7 cbsk *-1 .120 3x1 + 10x2 180 0. 71:1-FIT x1 79-11 x2 I 3Nal=f kik qTql-9 : MEC-003 : z = 45x1 + 55x2 6x1 + 4x2 . x2 .0 7 .ft§fT -5413719. 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