Test code: ME I/ME II, Syllabus for ME I, Matrix Algebra: Matrices and Vectors, Matrix Operations.

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1 Test code: ME I/ME II, 005 Syllabus for ME I, 005 Matri Algebra: Matrices ad Vectors, Matri Operatios. Permutatio ad Combiatio. Calculus: Fuctios, Limits, Cotiuity, Differetiatio of fuctios of oe or more variables, Ucostraied optimizatio, Defiite ad Idefiite Itegrals: itegratio by parts ad itegratio by substitutio, Costraied optimizatio of fuctios of a sigle variable, Theory of Sequece ad Series. Liear Programmig: Formulatios, statemets of Primal ad Dual problems. Graphical Solutios. Theory of Polyomial Equatios (up to third degree). Elemetary Stattics: Measures of cetral tedecy; dpersio, correlatio, Elemetary probability theory, Probability mass fuctio, Probability desity fuctio ad Dtributio fuctio.

2 Sample Questios for ME I (Mathematics), 005 For each of the followig questios four alterative aswers are provided. Choose the aswer that you cosider to be the most appropriate for a questio ad write it i your aswer book.. X B(, p) ~. The maimum value of Var (X) (A) 4 ; (B) ; (C) ; (D).. The fuctio (A) dcotiuous at = 0; (B) cotiuous but ot differetiable at = 0; (C) differetiable at = 0; (D) cotiuous everywhere but ot differetiable aywhere.. If A =, the 00 5 A + A 0 0 (A) ; (B) ; (C) ; (D) oe of these The maimum ad miimum values of the fuctio f ( ) = + +.5log e, over the iterval,4, are (A) ( + log e,.5 log e ); (B) ( + log e. 5, 0); (C) ( + log e, 0); (D) ( + log e. 5, -.5 log e ).

3 5. Let α ad β be the roots of the equatio p + q = 0. Defie the sequece = α + β. The + give by (A) p q ; (B) p + q ; (C) q p ; (D) q p. + be twice differetiable at = 0, f (0) = f (0) = 0, f ( ) f () + f (4) ad f ( 0) = 4. The the value of Lt 0 6. Let f :[, ] R (A) ; (B) ; (C) ; (D) oe of these. 7. For e < (A) less tha log < <, log (C) greater tha. e e ; (B) greater tha ; (D) greater tha, but less tha ;, but less tha 8. The value of the epressio (A) a ratioal umber lyig i the iterval (0,9) ; (B) a irratioal umber i lyig i the iterval (0,9) ; (C) a ratioal umber lyig i the iterval (0,0) ; (D) a irratioal umber lyig i the iterval (0,0).

4 9. Cosider a combiatio lock costig of buttos that ca be pressed i ay combiatio (icludig multiple buttos at a time), but i such a way that each umber pressed eactly oce. The the total umber of possible combiatio locks with buttos ( A ) 6 ; ( B ) 9 ; ( C ) 0 ; ( D ). 0. Suppose the correlatio coefficiet betwee ad y deoted by R, ad that betwee ad (y + ), by R. The, ( A ) R > R ; ( B ) R = R ; (C ) R < R ( D ) oe of these.. The value of ( + ) d (A) 0; (B) -; (C) ; (D) oe of these.. The values of 0 Π = subject to ad are (A) (0,) ; (B) (8,5) ; (C) (,) ; (D) oe of the above. 4

5 Syllabus for ME II (Ecoomics), 005 Microecoomics: Theory of cosumer behaviour, Theory of producer behaviour, Market forms (Perfect competitio, Moopoly, Price Dcrimiatio, Duopoly Courot ad Bertrad) ad Welfare ecoomics. Macroecoomics: Natioal icome accoutig, Simple model of icome determiatio ad Multiplier, IS LM model, Moey, Bakig ad Iflatio. Sample questios for ME II (Ecoomics), 005. (a) A divible cake of size to be divided amog (>) persos. It claimed that the oly allocatio which Pareto optimal allocatio (,,.., ). Do you agree with th claim? Briefly justify your aswer. (b) Which of the followig trasactios should be icluded i GDP? Eplai whether the correspodig epediture a cosumptio epediture or a ivestmet epediture. (i) (ii) (iii) Mr. Ramgopal, a private ivestmet baker, hires Mr. Gopi to do cookig ad cleaig at home. Mr. Ramgopal buys a ew Maruti Esteem. Mr. Ramgopal flies to Kolkata from Delhi to see Durga Puja celebratio. 5

6 (iv) (v) Mr. Ramgopal directly buys (through the iteret) 00 stocks of Satyam Ltd.. Mr. Ramgopal builds a house.. Roses, oce i full bloom, have to be picked up ad sold o the same day. O ay day the market demad fuctio for roses give by P = α - Q (Q umber of roses ; P price of a rose). It also give that the cost of growig roses, havig bee icurred by ay ower of a rose garde log ago, ot a choice variable for him ow. ( a ) Suppose, there oly oe seller i the market ad he fids 000 roses i full bloom o a day. How may roses should he sell o that day ad at what price? ( b ) Suppose there are 0 sellers i the market, ad each fids i h garde 00 roses i full bloom ready for sale o a day. What will be the equilibrium price ad the umber of roses sold o that day? (To aswer th part assume α 00). ( c ) Now suppose, the market served by a large umber of price takig sellers. However, the total availability o a day rema uchaged at 000 roses. Fid the competitive price ad the total umber of roses sold o that day.. Lami a poor agricultural worker. Her cosumptio basket compres three commodities: rice ad two vegetables - cabbage ad potato. But 6

7 there are occasioally very hard days whe her icome so low that she ca afford to buy oly rice ad o vegetables. However, there ever ares a situatio whe she buys oly vegetables ad o rice. But whe she ca afford to buy vegetables, she buys oly oe vegetable, amely the oe that has the lower price per kilogram o that day. Price of each vegetable fluctuates day to day while the price of rice costat. Write dow a suitable utility fuctio that would represet Lami s preferece patter. Eplai your aswer. 4. Cosider a simple Keyesia model for a closed ecoomy without Govermet. Suppose, savig proportioal to icome (y), margial propesity to ivest with respect to y 0. ad the system iitially i equilibrium. Now, followig a parallel dowward shift of the savig fuctio the equilibrium level of savig foud to icrease by uits. Compute the chage i the equilibrium icome. 5. Cosider a IS LM model. I the commodity market let the cosumptio fuctio be give by C = a + b Y, a>0, 0< b <. Ivestmet ad govermet spedig are eogeous ad give by I 0 ad G 0 respectively. I the moey market, the real demad for moey give by L = ky gr, k> 0, g >0. The omial moey supply ad price level are eogeously give at M 0 ad P 0 respectively. I these relatios C, Y ad r deote cosumptio, real GDP ad iterest rate respectively. (i) Set up the IS LM equatios. (ii) Determie how a icrease i the price level P, where P > P 0, would affect real GDP ad the iterest rate. 7

Noah Williams Economics 312. University of Wisconsin Spring Midterm Examination Solutions 1 FOR GRADUATE STUDENTS ONLY

Noah Williams Economics 312. University of Wisconsin Spring Midterm Examination Solutions 1 FOR GRADUATE STUDENTS ONLY Noah Williams Ecoomics 32 Departmet of Ecoomics Macroecoomics Uiversity of Wiscosi Sprig 204 Midterm Examiatio Solutios FOR GRADUATE STUDENTS ONLY Istructios: This is a 75 miute examiatio worth 00 total