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Problem set 5 Solutions_Peter

# Problem set 5 Solutions_Peter - Question 1:a Heueeheldie...

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Unformatted text preview: Question 1 :a: Heueeheldie prnlﬂem: nrair'llilhe'r +5121 e: E.i. Ellen +1sz :19! Lagrangian ie I. =1EILha] —I5'.h.u':! —A:192—3EI:L'-_ —.l.rr!g: Fiat-order enndhinhe are "I. 'll] 1 = ——3|:|I’r={| 5'01] 1"] EL E “I 5'35: _ e:_ _ EL — =192—2ﬂ —.1.xn=ll at m ' :b] Ere-:11 the fun t'a'n FDCe. §:—:=El=rtltz=3:t"_ euh intn 1he budget enne1rain1 111 = '5 .11: = '13 Refer tn :Graph Lh]. :e‘: ftlarginal rare ef t'i'eetimiinn between gnnd 1 and 2 ie HU— «ix! MESH: — T: = ——'= —ﬁ . -.:2 Ex] It meane that if the enneumgrinn nf fnnri [£1] deereaeee '51: 1 unit. the enhe'ihigrinn nf elethihg :ag‘: has in inereaee by i uni1e in order tn hia'ae ihe heuehnld maintain i1t utilit]; '.e‘.'el. Hi] The :rela1ie-hehig 'eent'eeh the [agrangian multiplier ti: and marginal uiilit}; efgnnde is given by the Enllnwing equatinn: 1‘ ME; Jeri-’2 F'] 3:! {liven 1he np1inral ehniee ran .11 and m. we can eaieula1e ,5. as: A _ i _ 5' _ 1 ' 21'] ' Ear; ' 1: Therefore the marginal urilit}; nf heueehelri ihennre at rhe ng1inral ehniee is J'J' euh inte 1he budget eens1rain1 a; 5.375 '_' 16.125 H H :e‘: ILineier ihe eaneunzpﬁeh tax. ihE uiilit}; of the household is L’G-j'mi::1:":f-='lﬂ]n i —IS'.nlE as 33.4.? where subscript IS“ indie-sues the eemeumpiien taxation eeheme. Under the Jump sum tax. “19 utilit}; of the heueehelu ie L’lell': :1:":': = IEI 1:15.375 +61h1ISJEEI Fti SEE-[l 1.I.'here subscript L indlea1es the eemeumptien taxation scheme. 1.. Nate iha1 u-Lllx'fm'ﬂ- :.- ch-:-m1:xll:l. 1hereﬁure ihE haueeheld. ie 'ueiier of under the lump sum taxaiinn scheme. Refer to :Graph 1e]. The labelling is: Eehemee Budget Line Litilitj.‘ Le‘.'e] Optmal Che-ice Ihi1ia'. .‘1 U :1 Coneumpiinn tax l: D} B Lump sum tax is If; I? Here 1ha1 i, and 13 intersects at pein1 3 ID- nzahe sure that get‘erhmem raises the eame eembunt of revenue from the tin: taxation pregra me. I1 ie eh'riu U-EIj.‘ that L: :: UL .'.~ L’C. ...
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