SECTIONA
Answerall EIGHTquestionsfromthissection(5markseach).
1.Considerthestrategic-formgamebelowwithtwoplayers,1 and 2. Solve the
game by iteratively eliminating dominated strategies.
2.Consider an economy with two goods, x and y with prices px and py, respec-
tively. We observe the following choices made by Rob: if px > py he chooses to
consume only y, and if py > px he chooses to consume only x. Suggest a utility
function for Rob that represents preferences consistent with the given data.
3.Consider a market for used cars. There are many sellers and even more buyers.
A seller values a high quality car at 800 and a low quality car at 200. For any
quality, the value to buyers is m times the value to sellers, where m > 1. All
agents are risk-neutral. Sellers know the quality of their own car, but buyers
only know that 2/3 of the cars are low quality and the remaining 1/3 of them
are high quality. For what values of m do all sellers sell their used cars?
4.If the price elasticity of supply is zero, a tax on suppliers will raise the market
price. Is this true or false? Explain your answer.
5.AmalconsumespizzasandalsoconsumesgoodOwhichisacompositeofall
othergoods.Hisincome-consumptioncurveisaverticallineasshowninthe
picturebelow.PizzamightbeaGiffengoodforAmal.Isthistrueorfalse?
Explainyouranswer.
6.Anindividualconsumestwogoodsandherpreferencessatisfynon-satiation.It
followsthatatleastoneofthetwogoodsmustbeanormalgood.Isthistrueor
false?Explainyouranswer.
7.Underfirst-degreepricediscrimination,amonopolistproducestheefficientout-
put.Isthistrueorfalse?Explainusinganappropriatediagram.
8.Severalgeneratorspollutetheenvironmentbyemittingcarbondioxide.Gener-
atorshavedifferentcostsofreducingcarbonemissions.Thegovernmentwants
toputacapontotalemissions.Puttingacaponeachgeneratorismoreefficient
comparedtoissuingtradeableemissionspermitstoeachgenerator.Isthistrue
orfalse?Explainyouranswer.
SECTIONB
AnswerTHREEquestionsfromthissection(20markseach).
9.(a)Considerthefollowingsimultaneousmovegamewithtwoplayers
Considerthepurestrategiesofplayer1.NotethatA1doesnotdominate
B1,andB1doesnotdominateA1.Isitpossibleforamixedstrategyof
player1tobeadominantstrategy?Explain. [5marks]
(Hint:Foranymixedstrategyof1tobeadominantstrategy,itmustdom-
inatebothA1andB1.Isthispossible?)
(b)Forthefollowingextensive-formgame:
i.IdentifythepureandmixedstrategyNashEquilibria. [5marks]
ii.IdentifyallSubgamePerfectNashequilibria. [5marks]
isanequilibriumoftheinfinitelyrepeatedgameinwhich(C,C)isplayed ineveryperiod.Youranswermuststatethestrategiesoftheplayersclearly.
[5marks]
2
consumingtheunitofqualityqatpricet.Ifhedecidesnottobuy,hegetsa utilityofzero.θcantaketwovaluesθ1=1andθ2=4.
(a)Supposethesellercanobserveθ.Derivetheprofitmaximizingprice-quality
pairsofferedwhenthetypeisθ1=1andwhenthetypeisθ2=4.
[6marks]
(b)Provethatthefullinformationprice-qualitypairsarenotincentivecom- patibleifthesellercannotobserveθ. [7marks]
(c)Supposethesellercannotobserveθ,andsupposehedecidestosetq1=
1/4andq2=4.Calculatetheoptimalvaluesoft1andt2suchthatboth
typesparticipate,typeθ1=1takesthecontract(q1,t1)andtypeθ2=4
takesthecontract(q2,t2). [7marks]
[Hint:writedowntheparticipationconstraintoftypeθ1andtheincentive
constraintoftypeθ2andsolvefort1andt2.]
11.Supposetwofirms(1and2)selldifferentiatedproductsandcompetebysetting
prices.Thedemandfunctionsare
q1=7−P1+
and
q2=7−P2+
P1
2
Firmshaveazerocostofproduction.
(a)FindtheNashequilibriuminthesimultaneous-movegame.Alsofindthe
quantitiessoldbyeachfirm. [5marks]
(b)Findthesubgame-perfectequilibriumif1movesbefore2.Alsofindthe quantitiessoldbyeachfirm. [5marks]
(c)Calculatetheprofitsofthetwofirmsforthecaseinpart(b).Whichfirm getsahigherprofit,thefirstmoverorthesecondmover? [5marks]
(d)Brieflyexplaintheintuitionfortheresultinpart(c). [5marks]
12.Ariskneutralprincipalhiresariskaverseagenttoworkonaproject.The
agent’sutilityfunctionis
V(w,ei)=√w−g(ei),
wherewiswage,g(ei)isthedisutilityassociatedwiththeeffortleveleiexerted
ontheproject.
Theagentcanchooseoneoftwopossibleeffortlevels,eHoreL,withassociated
disutilitylevelsg(eH)=2,andg(eL)=1.Iftheagentchooseseffortlevel
eH,theprojectyields20withprobability3/4,and0withprobability1/4.Ifhe
chooseseL,theprojectyields20withprobability1/4and0withprobability3/4.
Thereservationutilityoftheagentis0.
Let{wH,wL}beanoutput-contingentwagecontract,wherewHisthewage
paidiftheprojectyields20,andwListhewageiftheyieldis0.Theagent
receivesafixedwageifwH=wL.
(a)Ifeffortisobservable,whicheffortlevelshouldtheprincipalimplement?
Whatisthebestwagecontractthatimplementsthiseffort? [8marks]
(b)Supposeeffortisnotobservable.Whatistheoptimalcontractthatthe
principalshouldoffertheagent?Whateffortleveldoesthiscontractim-
plement? [8marks]
(c)Explaininwordswhytheprincipal’spayoffdiffersacrossthecasescon- sideredinparts(a)and(b)above. [4marks]