Economic policy final exam (in 2020 we did few small tests and then this whole exam) PDF

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1 EP FINAL EXAM July 10, 2020. This exam consists of Part A and Part B. To get full points both parts must be answered. Questions with an * may be the more difficult ones.Part A (31 points). Theme: Externalities(I ) Pollution(a) Explain formally why there is a negative externality in the model of a ...

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EP#FINAL#EXAM#July#10,#2020.# This#exam#consists#of#Part#A#and#Part#B.# To#get#full#points#both#parts#must#be#answered.# Questions#with#an#*#may#be#the#more#difficult#ones.# # ! !

Part#A#(31#points).!Theme:!Externalities! ! (I)!!Pollution! ! (a) Explain!formally!why!there!is!a!negative!externality!in!the!model!of!a! polluting!firm!and!a!consumer.! (b) Still!referring!to!the!model!of!polluting!firm!and!a!consumer,!explain! formally!why,!as!the!consumer!preferences!change!such!that!he/she! dislikes!pollution!more!(while!the!technology!remains!unchanged),!the! Pareto!efficient!level!of!pollution!decreases.! ! ! (II)!Risk!taking!by!banks! ! (a) Present!the!model!of!a!bank!choosing!a!more!risky!rather!than!a!less! risky!project,!assuming!that!each!of!the!two!projects!has!four!possible! outcomes.! (b) Explain!why!there!is!a!negative!externality!in!this!situation!and!how! this!externality!can!be!removed!by!means!of!government!regulation.! ! (III)!Prisoner’s!Dilemma!Game! ! (a) Present!the!Prisoner’s!Dilemma!Game,!the!concept!of!a!strictly! dominant!strategy!and!the!concept!of!a!Nash!Equilibrium.!In!what! sense!is!there!a!negative!externality!in!this!game?! (b) Present!a!version!of!the!Prisoner’s!Dilemma!Game!where!player!B! always!(i.e.!no!matter!the!strategies!chosen!by!A!and!B)!gets!a!smaller! prison!term!than!A,!but!where!nonetheless!the!outcome!is!the! inefficient!one!where!both!confesses.! (c) Present!a!variant!of!the!Prisoner’s!Dilemma!Game!where!player!A!has!a! strictly!dominant!strategy,!but!where!B!does!not!have!a!strictly! dominant!strategy!and!where!the!Nash!equilibrium!is!not!Pareto! efficient.!Is!there!still!a!negative!externality!in!this!game?*! ! ! ! !

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! ! Part#A#(31#points).!Themes:!Pareto!Efficiency!and!Fairness! ! (I)!!Measuring!Inequality! ! (a) How!does!one!construct!a!Lorenz!curve!for!a!country?!Illustrate.!How!is! the!Gini!coefficient!defined?!Sketch!a!case!of!two!countries!with! different!Lorenz!curves!but!the!same!Gini!coefficient.! (b) Explain!how!the!life!cycle!model!can!be!used!to!argue!that!even!if!there! is!income!inequality!as!measured!by!the!Gini!coefficient,!there!is! fundamentally!no!inequality.! (c) Present!a!numerical!example,!in!terms!of!incomes,!with!two!countries!A! and!B,!each!with!three!inhabitants,!and!where!country!A!has!higher! average!income!but!also!higher!inequality!than!country!B.! ! (II)!Insurance! ! (a) What!do!we!mean!by!an!actuarially!fair!insurance!contract?!Explain!and! illustrate!the!case!where!an!insurance!company!offers!a!pooling! contract!with!full!insurance!to!two!types!of!agents,!a!low!risk!and!a!high! risk,!and!where!both!types!accept.!! (b) Explain!why!the!contract!from!(a)!is!Pareto!efficient,!however!not! actuarially!fair!for!any!of!the!two!types.! ! ! (III)!Pareto!Efficiency!!in!the!!Edgeworth!Box!! ! (a) Present!the!Edgeworth!box!and!the!definition!of!a!Pareto!efficient! allocation!in!it.!Illustrate.! (b) What!do!we!mean!by!a!fair!allocation?!Suppose!that!both!agents!have! the!utility!function!U(x1,x2)!=! 𝑥" 𝑥# !and!that!Agent!!A!has!the!initial! endowment! 𝜔%" , 𝜔%# = (2,3),!while!agent!B!has!the!initial! endowment! 𝜔-" , 𝜔-# = 2,1 .!Find!the!Pareto!set!for!this!case!as!well! as!a!fair!allocation!and!illustrate.!Why!is!the!fair!allocation!unique?! (c) With!the!utility!functions!and!numbers!from!(b),!construct!a!so!called! Utility!Possibility!Frontier!(UPF)!as!follows:!on!the!first!axis!is!the! utility!of!agent!A!and!on!the!second!axis!is!the!utility!of!agent!B.!Now,! for!each!Pareto!efficient!allocation!indicate!the!utility!level!for!each! agent,!which!then!constitutes!the!UPF.!If!the!government!uses!a! Maximin!social!welfare!function,!which!point!will!it!choose!on!the!UPF?! Illustrate.*! ! !

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