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bing sabe Roprete atObi uw % a Repsenvabuey 7 Sersunge woh 5 CONSUMER OPTIMISATION Lexicog caphic” arty 7 fue, 4 SL NECESSARY AND SUPFICIENT CONDITIONS The prepecence “eeponws cos can agord - Z yi Ramen % HEC NE wh cep . 22 implies x%= 9 repierenied by bi, puncte ae eas ult “7 max We) ie, ae 7 7" wmphes % wilieg Fine | conwfaing J PT t+ Py SM Ty, (ADS mean & 7 Ly ge a Le KOR ip gor y Function & implies 8 Lesa a } ~ bey pair or KOR Us P where slope of (C= slope op AC : a Beene Lees non-sasaver of" Kunde, guasi concOre ‘Slope of BC is price ramio - Le { BEA mean ie Swppcient Condition for aLows me or MOT Fey, — ie wper arel Pe {set of venien wae A eoneti6ok x=3 commodiba tw he 9 4 Feb ae Conds * Slope OF ICs rRS 2 MY: —, marginal whl! i . por 224 i a 5 m RLS gor every TAU, — fovral by dipereanictiyf tre GO TUBA op bods e@27u@) “cer or cobb Dougan ux zine wet cack MANSY oe Sines wee Bin -yue) \_, 5 & roctt nonseniatio G Any iactearing Optimal bundle i god tos aad when APR and ‘se suppcient Tonaction of Ue reprerent L. gee * exp conaseon ee FTL nae Weta Neocon goo 2" oR my ae uv ho be 2. PREFERENCES : ithe aie é “ G & is eee prejrence Y dapna, weer Low indliperence HeLawion pepiene over | (80 > bat won't Alwaiga work FeAFECT commembirrs WO ta)= mia Ee, 4x} ee eee > COmek prepOHeAdd> : corsunen Cremer her’ compan Utiuties bundles 2 BATIONALITY SZ Deir average % goods 2 otenes O Compiatenass ~ the S++ two comen tv «Strictly convex peperencey | conuner Cin alway For every EX, ip xy x Fae compart Pe wich X# %, len bof any bundle. KEN a weighed * auectg® AR a (l-w\ ESE LECTURE 1: O Teansinviay ~ ig XeY anh Yue ten Kz Row Sarictly pepe ree ol. i . ly prepe. rererences cut st yh 3 a os Monotone ip Strongly monotone if | gin ou T consunytion Jor ncieae the amount af YI ve You contune of day ore ob every eek gook without decrearing | MOE & herser | Sean be Ue consumpron op ! of &ny utter good _ A wearenod to local} hon Sadao SARECAP OF CONSUMER Thelt ——SSSSZ e~ Budget consoaint Giver the et of bundy comune STATEMENTS SS with bork the sabgied, iets rAbORAL Commuter | Ome Where A i tne aka ‘bundia’ « ‘bundle of &% good” Assure buy constraint is Okt UReOW > aihiney L CONSUMPTION SET AND BUDGET SS Wu ak alway con aor AeA G COnmimprion pet is charged the ¢ cormumpds &~ RE OL goods sure eros Equation is’. wee asnamptn. consuned can & goo B+ + GSM urrounded- —— OMune \ * ; . Re apppee bound gor ig we ove , Walrasian budget Containt /eet consuming» godt 1 goods ten connmpben, & set of puncte cur Consunes CON « apiniteey dinsibe~ CRO AREA (6,25) € Kool Erg EM | ary t Rebl ne. of goods ee is the posite orthant ch be Comune To solve wie Lagrangian or setimas-pna Les tekrecr sugstiTutes find vhichd opting 24 PROVING ANd o1seeSunuce ALPROVING AND 0Isp2GvinGe Ly To prove a seaermrent of foim ADB | Gor rend te Show i hada th every | act (X anh Y) > or a YY not (X or YY = noe (x) ASB ue Say A and B we _— tm each othe, ADB Ace al 16] ak At ay 2.2. THE CONTR APOSITIVE wo CoruGpositie is lagicat twin of & statment To disprove a mor pent of A> 6, you read t pind Qn exampia whee AO te but Bh PAUe Wanye 8 ACB Se Ais SUBSET is Cnet Brace A of becouse ty ae equivalent to each etler Taking conbapesrive of the contraposithe get back te onginal stabenent es ContrOposible of Ag? Lo bg LHD XZ $ Ran CONDMOpOSE OF xLtaxcy similar 2.3 Wa and NEGATION Prooe by comvadicton, _Z/ GY peau A moana Z sg nears ke Yor au ov oy ‘fer Hele dovint | there exists’ emg) ey - 29. Y¥X7O near, for au x grenier than 0 not Xe Negaion for tk stagnent Ve € A, LEG con une dy xEA = x EB aad not — SN&atonop thd y axeA, st. c€B ws WhCK mom ‘thee, d0em’s gut Gr © wy NOTADOR » Ti'Rox whick u in & » E245 an element of" Sut nob « Gis a subset og* in B (xépn ox) © FE -% eat a subnet op” 
