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MPE781_T2_2018_QBs PartA:MicroeconomicsandMacroeconomics Question1: Assumethatafirminaperfectlycompetitivemarketcansellitsproductfor$35(iepriceperunitof output).Furthermore,itfacesthefollowingcosts: Output(Q) TotalCost 0 25 1 50 2 100 3 120 4 155 5 190 6 250 7 390 a) Calculate Total revenue (TR),Marginal Cost (MC), Fixed Cost (FC), Variable cost (VC) and AverageCost(AC). b) Whatistheprofitmaximizingoutputlevel? c) Isthisfirmismakingaprofitorlossatprofitmaximizingoutputlevel?Explain. d) Doyouthinkthefirmwillcontinueitsproductionintheshortrun? e) Whatwillbethelong-runpriceinthismarket? Question2: Assume the current price of corn chips is $2 per packet. The demand elasticity is 1 (ignoring the negative sign) and current consumption (i.e. quantity demanded) is 40 million packets per week. Suppose that the manufacturer raises the price of corn chips to $4 per packet. a) Derive the demand equation. b) What will happen to weekly consumption as price increases to $4? c) Suppose the supply equation is P=2+Q. Find out the market equilibrium price and equilibrium quantity. d) Given the above supply and demand equations, calculate the surpluses for both consumer and producer. e) Now suppose the supply curve shifts and the equation of new supply curve is P=4+Q. Do you think market exist? Question3: Supposethatthedemandequation:P=10–Qandsupplyequation:P=Q. a. Calculatetheequilibriumpriceandquantity. b. Calculatetheconsumersurplus,producersurplusandtotalsurplusat equilibrium. c. Supposethegovernmentimposesataxof$2foreachunitbought.Derivethe newequilibriumpricethatconsumerspay,thepricethatfirmsreceive,and quantity. d. Calculatethedeadweightlossofthistax. e. Inadiagram,showtheequilibriuminpartaandtheequilibriuminpartc;and theareasthatyoucomputedinpartbandd. Question4: Consider perfect competition, a non-discriminating monopoly and a perfectly discriminatingmonopoly. a. Comparingandcontrasttheequilibriumpriceandquantityineachofthemarket structureandidentifyforeachmarketstructurewhetheritisefficientorresults indeadweightloss. b. Whydogovernmentscontrolcertainmonopolies?Provideatleastonerealworld exampleinsupportingyourargument. c. Whydogovernmentscreatecertainmonopolies? Question5: Usingasimpleexample,explaintheComparativeAdvantageTheoryandhowCountriescanbenefit frominternationaltrade.Whattypeofeconomicpolicydoesthistheorycallfor? Question6: Assume that Bob can either type 6 pages per hour or bake 2 cakes. His wife Mary can type 12 pages per hour or bake 4 cakes. a) What is comparative advantage? Explain. b) Calculate the comparative advantage of each person in the above example. c) In this example, do you think that complete specialization is possible? Explain. d) WilltherebeanytradebetweenBobandMary? Question7: Theelasticitydemandplaysacrucial role indetermining the incidenceof taxbetweenbuyersand sellers.Explainwithproperdiagram(s). Question8: Starting from an above full employment equilibrium, briefly explain with the aid of a diagram, the short-run effect on the price level and real GDP of an open market purchase of securities by the central bank. Does such an action lower real GDP in the long run? Question9: What is deflation? Discuss the appropriate government policies to deal with a problem of deflation; and also provide diagram (s) and at least one real world example in supporting your argument. Question10: Using theAS/ADmodel,discuss the likely impactof the followingeventswithproper diagram(s): a) Anincreaseinpetrolprice(startingfromthefull-employmentlevel). b) Ariseinthegeneralpricelevel(startingfrombelowthefull-employmentlevel). c) Theworldeconomyenters intoarecession(starting fromthe full-employment level). d) TheRealEstatebusinessinAustraliabooms(startingfromthefull-employment level). Question11: Twoprisoners,AandB,allegedtobeconspiratorsinacrime,areputintoseparate rooms.Apoliceofficergoesintoeachroomandsays: Ifyourpartnerconfessesandyouconfessalso,youwillonlyget3yearsinprison. Ifyourpartnerremainssilentandifyouaresilentalso,youwillget1yearinprison. However,ifyourpartnerconfessesandyouremainsilent,youwillget5yearsinprison. Butifyourpartnerremainssilentandyouconfess,youwillbeoutin0.3years. a. IfprisonerAconfesses,whatwouldbethebeststrategyforprisonerB? b. IfprisonerAdoesnotconfess,whatwouldbethebeststrategyforprisonerB? c. DefineNashequilibrium:whatistheNashequilibriumforthisquestion? Question12: Doesaminimumwagelawalwaysleadtounemployment?Whendoestheminimum wagelawleadtoanefficientoutcomeinacompetitivelabourmarket?Explainwithan appropriatediagram. Question13 Supposethatthedemandequation:P=12–Qandsupplyequation:P=2Q. a. Calculatetheequilibriumpriceandquantity. b. Calculatetheconsumersurplus,producersurplusandtotalsurplusat equilibrium. c. Supposethegovernmentimposesataxof$3foreachunitbought.Derivethe newpricethatconsumerspay,thepricethatfirmsreceive,andquantity. d. Calculatethedeadweightlossofthistax. e. Inadiagram,showtheequilibriuminpartaandtheequilibriuminpartc;and theareasthatyoucomputedinpartbandd. PARTB:STATISTICS Question1. Thefinalexammarksfor10studentstakingMPE781aregivenasfollow: 9858347867 a)Calculatethemean,medianandmode. b)Calculatethefirstquartile,thirdquartile,andinterquartilerange.Interpretthese values. c)Calculatethesamplestandarddeviationandinterpretthisvalue. d)Whatisthemainadvantageofthesamplestandarddeviationoverthesample varianceasameasureofvariability? Question2. Eachpartnerinasampleof10marriedcoupleswasaskedhowhappyeachis intheir ownmarriageonscale1to100.Theratingsbythesecouples(husband,wife)were: (60,50), (70,65), (80, 81), (80,79), (80,85), (40,35), (50, 55), (60,55), (65,65),(65,60). a) Just by looking at the responseswithout doing any formal calculation, can youarriveatanyconclusionabouttherelationshipbetweenthehusbandand wiferesponses?Explainyouranswer. b) Calculatethesamplecovarianceandinterprettheresult. c) Calculatethesamplecoefficientofcorrelationandinterprettheresult. Question3. Define?asthenumberofheadsobservedinanexperimentthatflipsabalanced coin3times.Calculate: a)Theexpectedvalueof?. b)Theprobabilitythat? = 2. c)Theprobabilitythat? ≥ 2. Question4. Arealestatedeveloperisinterestedintherelationshipbetweenthepriceofhousesin MelbourneandtheirdistancetotheCBD.Usingdatacollectedfromrealestateagents, heperformedthefollowingsimplelinearregressionmodel: ?! = ?! + ?!?! + ?! , wherethedependentvariable(?)isthepriceofhouses(measuredinthousandsof Australiandollars);theexplanatoryvariable(?)isthedistancetotheCBD(measuredin km);?!and?!areunknownparameters;and?isthedisturbanceterm.Theregression resultsaregiveninthefollowingTable. Table:ExcelOutputforLinearRegressionModel RegressionStatistics RSquare 0.4615 Standard Error 137.1313 Observations 10 Coefficients Standard Error tStat P-value Intercept 865.87 A 16.30 0.00 Distance -14.75 3.01 B 0.00 a)WhatarethevaluesofAandB? b)Whatistheinterpretationofthetwoparameterestimates?Dotheycorrespondto yourexpectation? c)WhatarethepredictedpricesforahouseinBurwood,whichis15kmfromtheCBD andahouseinYarraGlen,whichis60kmfromtheCBD?Arethesepredictionsreliable? d)IsthispredictionofaboveTablereliable?Explain. Question5. Astatisticianisinterestedintherelationshipbetweenthesalaryofgraduatesfroma Masterprogramatauniversityandthenumberofyearsaftertheirgraduation.Using datafromarandomsurveywithrecentgraduates,heperformedthefollowing simplelinearregressionmodel: ?! = ?! + ?!?! + ?!, wherethedependentvariable(?)isthesalaryofthegraduates(measuredin thousandsofAustraliandollars);theexplanatoryvariable(?)isthenumberofyears aftergraduation;?!and?!areunknownparameters;and?isthedisturbanceterm. TheregressionresultsaregiveninthefollowingTable. Table:ExcelOutputforLinearRegressionModel RegressionStatistics RSquare 0.8643 Standard Error 9.4531 Observations 30 Coefficients Standard Error tStat P-value Intercept 40.73 3.62 11.24 0.00 Years 6.42 0.48 13.35 0.00 a)Whatconclusionscanyoureachabouttherelationshipbetweensalaryand numberofyearsaftergraduation? b)Whatisthepredictedsalaryforapersoninthesurveyin2012,whograduated fromtheMasterprogramin2008?Commentbrieflyonhowsafeyouthinkitisto relyonthisprediction. c)Findandinterpretthevalueofthestandarderroroftheestimate. d)Whatassumptionshavebeenemployedinordertoobtaintheseregressionresults USEFULSTATISTICSFORMULAE SampleMean:? = !! ! !!! ! SampleVariance:?! = !!" !!! = !!!! !! !!! !!! = !! !! !!! !!!! !!! ??? = ?! − ? !!!!! = ?!!!!!! − ??! SampleStandardDeviation:? = ?! SampleCovariance:??? ?,? = !!"# !!! = (!!!! ! !!! )(!!!!) !!! = !!!!!!!! ! !!! !!! ???? = (?! − ?!!!! ) ?! − ? = ?!?! − ???!!!! SampleCoefficientofCorrelation:? = !"#(!,!) !!!! = !!"# !!" !!" GeneralAdditionRuleofProbability:? ? ?? ? = ? ? + ? ? − ?(? ??? ?) GeneralAdditionRuleforDisjointEvents:? ? ?? ? = ? ? + ? ? ConditionalProbability:? ? ? = !(! !"# !) !(!) GeneralMultiplicationRule:? ? ??? ? = ? ? ? ? ? = ? ? ? ?(?) GeneralMultiplicationRuleforIndependentEvents:? ? ??? ? = ?(?)? ? ExpectedValueofaDiscreteRandomVariable:? = ? ? = ?!? ?!!!!! VarianceofaDiscreteRandomVariable:?! = [?! − ?(?)]!? ?!!!!! = ?! !? ?!!!!! − [? ? ]! Z-valueinaNormalDistribution:Z = !!! ! StandardDeviationoftheSampleMeans:σ! = ! ! ThePredictedLineforSimpleLinearRegressionEquation:?! = ?! + ?!?! ?! = !!"# !!" = (!!!! ! !!! ) !!!! !!!! !!!!! and?! = ? − ?!? CoefficientofDetermination:?! = !"#!"$$%&' !!" !" !"#$%&! !"!#$ !"# !" !"#$%&! = !!" !!" = !!!! !! !!! !!!! !!!!! StandardErroroftheEstimate:?!" = !!" !!! = !!!!! !! !!! !!! Source:Berensonetal.(2010).