No. of Printed Pages : 12 MASTER OF ARTS (Economics) Term-End Examination June, 2012 MEC-001

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1 No. of Printed Pages : 12 MASTER OF ARTS (Economics) Term-End Examination June, 2012 MEC-001 MEC-001 : MICRO ECONOMIC ANALYSIS Time : 3 hours Maximum Marks : 100 Note : Attempt questions from each section as per instructions given under each section. SECTION - A Answer any two questions form this section. 2x20=40 1. Consider a world with two agents, A and B. There are two goods 1 and 2. The utility functions of A and B are given as U A = X.?" XA2 and UB = XB1 XB2 Their initial endowments are WA =(1,2) and WB =(2,1) (a) Draw the Edgeworth Box for the agents considering their initial endowments and commodity consumptions. Lr.) p (b) Find the contract curve through your Lc) CD Edgework Box. (c) Find the demand functions of A and B for prices Pi,P2 and incomes ma of A and mb of B. (d) Find the competitive equilibrium price P* and equilibrium allocation ()CAP A2,X*B1, X*B2) of this economy. MEC P.T.O.

2 2. A monopoly insurance company provides accident insurance to two types of customers; low risk and high risk, for whom the probability of an accident is 0.25 and 0.5. There are customers in the groups of low and high risks in equal number. Without insurance, each customer's wealth is 16 if there is no accident but zero if there is an accident. Customers utility function of wealth is given as u(w) =. The insurance company cannot identify the type of customer's when they apply for insurance contract. The company plans to offer two contracts; First, a payout of 8 in case there is an accident and requires the customer to pay a premimum of 7. Second,.a payout of 16 in case an accident happens but requires customers to pay a premiiim of 10. (a) Determine for the low risk and high risk customers which if any, of these contract they will buy. (b) Calculate the insurance company's expected profit if it offers these contracts. comment how does the company would like to screen its customers with these contracts. 3. (a) What do you mean by a pure public good? (b) There are only two individuals A and B in an economy. Their respective marginal valuation curves for a public good, x, are given by MVA = 100 2x and MVB = 25 x. The marginal cost of providing the public good is given by MC = x. Find the socially efficient quality of public goods. MEC-001 2

3 4. A consumer's utility function is given as U(x, y) = In (x +2y -Y± 2 ) Where x and y are two goods of consumption. (a) Find the indirect utility function of the consumer. (b) Examine if Roy's law is satisfied by the consumer's demand function for y. (c) Find the expenditure function of the consumer e(p,u) where price of x =1 and price of y=p. (d) Find the Hickrian demand function by (p,u) for commodity y, where the price of x is 1 and the price of y is p. MEC P.T.O.

4 SECTION - B 5. Answer any four questions from this section. 4x10=40 (a) How would you differentiate a static game from that of a dynamic game? (b) Suppose the following game is played for a infinite number of periods. If the players are discounting the future at the rates of 8A and 6B respectively, find the conditions under which they sustain the outcome (2,2) in every period. Player A Player B Low High Low (1, 1) (4, 0) High (0, 4) (2, 2) 6. Sita expects her future earnings to be worth Rs 100. If she falls ill, her expected future earning will be Rs 25, There is a belief that she may fall ill 2 with probability of -3 while the probability of remaining in good health is 3. Let her utility function be given as u(y)= y Suppose that an insuranne company offers to fully insure sita against loss of earnings caused by illness against an actuarially fair premimum. MEC-001 4

5 (a) (b) Will Sita accept the insurance Explain What is the maximum amount that Sita would pay for the insurance? 7. Suppose that two identical firms produce bal.: bearings. Their total costs are given by CJi and C2 = 30 Q7 where Qi =out put_ of firni fori =1, 2. The inverse demand curve is given by P =150 Q where Q= Q7. Find the Courn.ot equilibrium quantities, price and profits of the firms. 8. Why would you prefer Pareto's approach t welfare analysis over that of Pigou? EI.aboraie your view points. 9. (a) Explain how and in what circumstances markets would lead to a Pareto efficient allocation of resources? (b) Why does the existence of public goods make it impossible or unlikely that markets would lead to a Pareto-efficient allocation of resources? Why would you say Boumol's model of sales maximisation is. an alternative theory of firm? Which features of his model may be considered to support your view points? Explain your answer. MEC P.T.O.

6 SECTION - C Answer all the questions from this section. 2x10= Write short notes on any two of the following : (a) Public goods (b) Rawl's theory of justice (c) VNM utility function 12. Differentiate between (any two) : (a) Moral hazard and Adverse selection (b) Shepherd's lemma and Hotelling's lemma (c) First and third degrees of price discrimination. MEC-001 6

7 7.4.t-ooi 71T7. ( ankrrw) Trita TAT Tr, : Tgzi 311*TM clq qui wig : 3 oo alferw-d-4 3fW : 100 5)2" : sim viva( Tri4 u-d-(.1.11p 4 3rkr- 1 2x20=40 1. faqir 4 t atrfik aifirw-df t, A *B I 3 t qgq. 1 3l 2 ill I d-14, sn4ikr: ua = xai xa2 3 ub = xbi x82 ti 34 9-rtfw Ofd ẉitef WA = (1,2) 47 WB =(2,1) t I (a) 3-14) ti4fd ct)) ZrfilliT ei),siitaff 317NTKITT 1:71c1?-f WF err Fc171 I (b) 31:r.:31efef SIT fqi 3-1c fR I (c) *714 A AT B*1:fiTT a 6111R, /it Pi* P2 al:pi 4,144 -ffen MA 3th MB afir*--diaff 3Trzr -Rrtt (d) i atefardrtt*tertillt09. ch sicf P* 311T 374E9. (X*Ai, X*A2,X*Bp X*B2) WI I MEC P.T.O.

8 2. -cr*--15-1thlt ticit 13T-6-4 V1-6-1T t ; 17ff-*- f9-pi 7)-t111 ak,) t I 9-f 1441TW-0 so-ri: 0.25 and 0.5 t I -71Ett F4 chei titsq I t I rci -I I ci14 74-cr-q-r t 'TT u.((o),r7 I ath c t,4 Tf-cr--t d4 H711,-no-f 4TM1f-11 3a4-1q et A741dr T -- t97:17 ;17T- t. 17,:r *! C f")1 t I A. 7 U 4-T 3 7,7 ;4) % e. f all d1 ti 11# 10-7: r-q9. ;dl t f--*-q 16 3-T5-117 (a) 711d rch -7gT 711T- R:ft F ti7t4 17-6T -F-*-74 trio17# --t4 (b) ITT ttit "WE 314N-d -ottit 3T-1-4.eff ch-k I ff %ft -grewq 74 *cit Act )ik cpitcnkur t 3. (a) t> fa-714 wciailch trq-r21 Err 310 t? (b) i-W4T-2,1T 14q1:4 A *13 t I x viicni co, 91-)4-11: MVA =100 2x 72TT MVB = 25 x e I k-1147ftt oi+id ash t; MC = x I Vq 3-1-f-*-07 chki MEC-001 8

9 4. 31:TINT f t: U (x, y) = In (x + 2y -Ȳ:-) x3thytt:rziw[qw t1 (a) 3714WIT st) 7 c4 (b) Fen ITT y f' -41-Trr tft1 F.-Ng 7-07 t- I (c) tirqx.wiwiti-fflff 211yriffptt -3111)-Wff cig ash e (p,u) c I (d) y twi ciiq1 1:111'T by (p,u) grq x =m =13 y fi =P I MEC P.T.O.

10 WT+T- Zd dti(.f14 I 4x10=40 5. (a) 31Tt1 Ict)1:9-1tWV -A ICt410-Ict) 7 A. -14)( ;1? (b) e---- d 3T-A-z4 7w -to -1 ITT ifdicer.w1 6A ' 21T SEI TtI ciehltf W.{ t I 3ff Tr f W 3Tḻfz1 14 (2, 2) TrITRIN %TIM cilt t (0 4;1) I ft~m!s1 -A -1.-f 314 -B 14-i 3" (1,1) (4,0) (0,4) (2,2) 6. t if-atzr zu-a. z, z TT Wcd111 R-W 41 11IT 3t14 ti:fri 6-A t ViTwr 3117 TER2T TilTraraT 3 t d4t.1 ildr 4.)oi U (y) = i X11 i ci:o4-11 4di 3TRE t 414 t at i rz) al-11tr -411,-qui.113 tvg-ritri-t. r -wt t (a) r 401 zig. 4 HI r R? t,+-ww I (b) -Tt aftrwa ai Ti (qc "r 1Tfali:ftt ITT-4 MEC

11 7. i 41(,) t t Id t I C1=30 Q1 and C2 =30 Q2,316 Qi =I Q' 1: q1 3-fr{ i =1, 2 fd-atf 1:67 ash P=150-Q Q = Q/ + Q2 I ItTru, 141-1T t Lags T T r rcik;tiuf rcirq qt17:1ḏt T? ( I 9. (a) e411tm et) rebq ita# 4 at cht-f 51ch1t 111ft 4th%Ta. 31-r-4a7 i 3f TfLCT -cfrcrt I (b) TR1211 TTF-T-9Ofd, GUAR Itt Wf 37-4TffVFI T Rm.{ Wahlt 31-# Wif Ti-Er c 31fkwaTr fa-wa ixf-d-rrri 3-1--d-rrN Tff t? 3TrEr fa-9-r -aftz -5faTrri ichl fa 34 t? 3T 3rIt ceirni MEC P.T.O.

12 14PT - TT %WI 5Ik 11 f 37R t/zi 2x10= frs re.uanqi t-4 (a) sal 1* 1:1-q2i (b) tf-( q feria (c) (VNM) dt-qprif 12. fwt t 1)- 73:1,3 ch (a) rc g-g 47 fa-r-1-ff q1 (b) "WF 1;11:14 TR.wr Tr-gr (c) 1; T Tdtzl chlre. -NATi MEC