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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”
a Want © CNnodpe
5
S.EXISTENCE OF WALRASIAN ( *. UNIQVENESS OF
—— eee ( EYNIGVENESS OF () GL BASIC FRAMEWORK M how scarce reuren
EQuieiberA Ly & wotrasian s WALRASIAN EQUILIBRIA \ SS cue atLocoURd. beter.
L Equillin vim wit NOT TH mouy eG watranvan \ 4 v & exogenous agenb of economy
be muitipici a coe” : :
Rot of nore oxsienea: SMMP eve | 2F aptirol biealds equation & ik nek TBE Ag ana
TOL endanonen> ae oy Set of supicient \ and equiviei, nok quai) be Ona 5b T of OD inwal allocation oy endownent
Carly 224 2021) coraitions ¢ 2OEee \ bo eg ig both unique digosert, goods on ba. * Ce, 02.89)
Lge LMA EFL) qwalapia a gtk oe . Commodi, Gr en. vk 5 '
* ie * t=O. ean ean yuuion hoe sane unity > if inibial alloceton i Grajarencen of each agony Fy
? a guncs thot at WRUIFASION Equiliiemum SA eens L TGSSUNe piepenDs wt eprerenttbl
46 = Ly Cpr if 25 70 por au penece subs, —agtiocation und ae
“LR <pa Ben ao WE inauivikuictla, cond ad OLN pi py ae preerenan at srt / | © dary an exchange economy, no reducoar
2. if , hae smetly guasi- qulimion gr® « Comey + serengl | @ weir -azpined groperey rights
FP 2pus both cmaure ——concare (cancer) pagent, \ %Y aecasion monatone, ten ws f | © maret por every commodity (eg. oven cuanaw
ae interior pain , but + gyorg, eC Cong budget Une ik unique WE | @ tveryore & apni r
diperens points Ngiy mone’ ij we ‘ pyore pre tare!
© Goods ae vivauous
© Aguntis usitiog oniy depends on goods bey commune
otler Up ube prce pouch gor them
@ No srameccon coss tm trade )
@ every induct is (A¥ONL Lcomplyl © tranribre prejeren>
~ hoor optimat bundle st. budget constrain 9» unreativo’ curupaptcl
LECTURE 2: WAURASIAN Ua@ mame clear -n0 man damand of suphly
EQUIUBRIUM IN PURE EXCHANGE
AX 9,
luting BYnc, then O Wording
EQuidomnum ry bai se
bo
For 1x2 economign Xai ch
(goody «2 Consunen) -—|
Or EdgQuortIn YOM put
Reperend set op seo, “|
Xo é nor en
a
invial but ip chy 6,
ae Bing &
Front ERE Suycaence
Pty, ConobiBons volte,
4 en mutnpllciny
36 noOre has Cy We GUN G bRrevownk
ihante tb KEK OveRGrd ANON OA
» AS conmunption
aocabons tha = & mecsion op good B Ss an a
clear tHe movie of secre > Lar Ene, oe Exeass demand a dijerent sa anna” hnoue
noe ence Large 84 ton wptiow then exeon furcoon i < pace oleae, PRL &
- otal: good - i Zp) = Zier Xulp)> Eun Cie oxtocen
trntontat geod Pere ends damand zip? degX On cig
> veroced | geod 2 M . . vig Lp) ~ve, , Ardownent
~ iwDOl endowrert 4 WE Betrod £00 Computing Hen fen ac ip domank > 1.2. WALRASIAN EQUILIGRIUM
Should b2 on budget Une Walaa equiion o mee aie ~Tarua 0 And paces G tnahivide ae
Pn Consumer, ote, + 20)=6, ten A ote damon ucts once, iILUGL hoo epecere
L mona maven cacy 58g comune —butlget constraimt; — dat wealth 6p
s une GL ate snpuned :
Can snow when NOT g WE: ; FYING @ JUNC O} prea, og) purction Fe Xi lp) . ee
85 damn WE 2 Calculak goon damonst € Rey is total vent FR = PO + Bs Cis
oT ¢| J) Find pea vector that suives demanded by comunen [ ree HRM wealth = value
eS Ug Lao damon — elon damand Of eveny good = O (220) @ pune of price, * Px ip 6} endownent
In WOUGsicL ak é
a has. tuatienn CME); > Bch Cormuner solve
ek j—— a= j
/| a ee & tora. WE ny Oe to clatke Wain $’ Law You hae a pice vector -
excep ioe? Mule oF thot YOUr anseer C whee Geryord maximils Wainy Murinrisd bon Prada
Suppty & & Pra veor Les. xp) OL agents Dib OM individuals Utividg +6. budget constraint fume) >
geek a Kae wh ane ie aa. damondr hove lecelly ron~ ank mare claw MANE [X1) sb. PX epee
. _ Builrivon paca d SAHARA prepeencs , » pts WE pie vector rex "
o AS both poland ait not equad, Vvettoy 1% alt te vale op excon xe ae d-dimansional veoon shou
mashed de ad cwar, go ie matics excpt Om OCT equals = ~WE allocation FENN” for every
pet a watarion quod, cao s — Of p.2(p) 20) carmen gpomal. bune gpod, terar demented equals
EQuilomum Piro, Cen maalet dopend cr price vector goto suppued a e@angmy
pos 7 mune Oe Ca cuurtty a Beats eadownorad
BUicling extension example
Lure WARd w bud exterin, “3.3. THE COASE THEOREM LLWHAT ARE EXTERNALITIES ?
but it courts negate exe natiby Lows ould hove | 20;
on Sam ane caso shadow cr t “compe noone = come tuned
On his Swiiming pooh N=) Need Sam with AS long as
Rnowig Laura's Payment at property ngnty
9.0.2.MISSING MARKETS benef > Sams Ware = oot aie wert depnedk
7
FF an enternatity is aM An ex ternoctity occur wen
The COSL ov KORDA that @ penons wei-being on
SRC a third party who & firmly producton capabiliy
Did nov choose to incur thot — ts aiectiy apeded by ve
Seken. i . - -
‘GeqeNGM ssches wakes cost gors ns and. Vee cue litle CO% cr behofe __/ 288008 Of ober consumer
. 7 can , Critria. for theorem no transac . & OF firing
externality a ‘missing mohet’ a9 aa ES ost, hon opicient Posibe externality = the change
ice estabishos am market for tle Grew apyecread Sutconk will be reaciedt MOkky eCpient beter oy Ly Negative exdernadity =
hegarbre oxternatity Change makes recperve
waghour gow » Poltusion VL Ono wearth eppects - people nat > 2.FAILURE OF wore of. *
intervendion, tex —, VOUCHOSS KO cancowe wnung pune 50 Fish auersion WELFARE THEOREMS
WO4 inepricienc becor-e a NA compet injormation— NECTARE THEOREMS welfare teolems peril
since payers cil Bire’s pr in ‘ ' a p ahibe,
cae for social cove eet & Xo So. we assume piste Te show senethin, L 1% PENG OF exten
Hey reach eppcient Outcone . >
nego cy vp - US NOT pareto optiniaL, ampie - Andy har e4=(0)2)
BING an altemadtive thas — AURA Preferences Ue =x ay Xy,~Lep
7 INGHRS i wateasian 50 US likes A When fich smoney
3.21 EFFICIENCY THROUGH
eee
POLLUTION VOUCHER §mtkeT Fon
SSS ee POLLUTION VOUCHERS |
LECTURE 6:
AP “ealue of P Supp > Fixed aston oo
mse ate y ‘ 4 eae conic’ of
cia! VA "Ehemalts 7 sxe v Ob EXTERNALITIES Andy > Xeve See cohen 7 Lone WE is not
Social Sopely cecal , me PRN: Z 4 IC cures age Parety eppciont
Pn praducton, 1 Ot Pree ; Py depend en bob’5 °
two Nw) NC. . ConsumpHN. deus Bob doen't
east nt wind Pama > incerrde LOv Pitre Ineye (negative Wark, tke into crount
tn Ge 2 ¥ c In POLLUTIOU REDUCING TECH CONSUMPTION % #AE nagarire exiemalty
ie / So thy Can wel their peemit SATERNALITY) She pukiion analy whan
> Govt can cop amount of poltunon eS ‘ Vn. Smoning
produud hy issuing pod number of 7 For ee cones
pour vouclen Rnown av “ernolen’ Sgane PETE EPC EME 5 . ,
3.1.2 PLGOUVIAN a pollution TOME ecemciido, <7 Z.POSSIBLE GOVERNMENT ~ Negotre produccen
A. permit, mae quantisy is ee Sore ae
id ier
SUBSIDY? ty SLLPIGOUVIAN TAL poducd thie = INTERVENTIONS —— externauey example
Subsidy of Candy’ AIAX 0, e mse social aphmum we wit comidore? ““porroed Frey producing the :
b Ay Pp - > si f Pe Pc ic “ rRaInet trarysoming a i Consumpdicn g cod pole,
Pe Pm [=> ~~ Corrects) ; capt For postie® iApucs (2-5 meta, pLastic) tHe bland Wi Ch mats
conects por’ 8 Overpreducten Sapp’. euternavy, w ; ' ~
Career fe \ vee en mY XEIDAUEY, BS into treadmills CrUs0e WON of)
cay PENS Way Re GRIN Im Guan bby Lyle piter polluier, thon puts negate loge a:
ty posite eueinaliby — fe Remand PrOodued than entemnaliry. 730 firm soley prigite
ec leinadiny pa > CONRGE Qumnndy _ Stak optimum, Gq ip giv benepib society by onakary POR witheus
He dadtucignt Los rm mathe qm GE Ay a Jb rie BW ae e) " thinring about
s marginal social bnent co) ope m oe Eppicitant sociad / c net. peop a and negABe Exim
above demand cure, Gm However: Hard por govt t calculak optimum wier, Soy Sapp ROGTENES “tren On Curae °
18 C00 low cand sociaa Size Of EKER AbiDy ; Mme piremy May oie Qiks positcre Laso WE is NOT
OPM iy MgLeY Oe POU mod, but CU ae taxed tHe iane nS Hemaat — DIALIROMA GE pare? oppmad
caigd Oy, NEGATIVE Eviconanty®
|.1 FORMAL DEFINITION OF WALRASIAN
Wt PRU Tach agent has |
- 5 1s Preperences Uz lx)
Fundamentals “r 2, Endowment » €e
Production econamy : 3. shares » (Scrm mem
oD = consuner
2. FIRST FUNDAMENTAL, 3. SECOND_ FUNDAMENTAL THEOREW
THEOREM OF WELFARE OF WELFARE ECONOMIC Ss
ECONOMICS oy)
% an allocation ig ponsiblery
4 (cry) is & Pareto epncient allocation, if
GYAN preperences convex, Connhuous ¥ loceuly
1. Ail pOduCHON seH ae tahan preaneee vets Qe convex, clowed x sanapy] f° = goods “>? each pimn has producton
feasibie gor each MEM, Ere2 disposat ems set of pinnae fee Ym ©
Yom E¥m So Tren Cx)y> is Wautrasian Equilievium allocation! S Each comsuney hae A arrasian Equiibnum ©
2. Markets cedar: nee wee Th pitti edad clue Gone @ taple (p, x,y) Such that!
Fie Ky = Zee *2ye Sustained oo & mica tsPh4 ee damand < endounenct + © EACH consumer solve, UMP.
An ailocanon Goy)is “ vaohe. Font eon Blom SROHE mak UL Sb. Pee Spee
Pareto epicient if & is feasipe > more cledting. ES um Pe Yen
YA odber poasibe alloca non > FOr an input i ouiget © Each given scive propre maX+
eno cesar it concn Qy ou : . ters we Psd
1 vith. 9) 2 wlry) ve Awan a) LECTURE 5: WALRASIAN EQUILIGRIUM Pecoromy | @ AL mavkets clear 1A
2.3) with ujit9 7 uy ey apee sermoe AND WELFARE THEOREMS IN 2mm dedin lex, o30, aye) oe
a ECONOMIES WITH PRODUCTION, "" oo
* For an output? Total goods feral goods
amouns dananctecl= . abeady in economy
Amount ia economy Excess damon vector
onginally plus amoint AA
producd by pars
G re Fundlament Theorem is ip ail
consumed hare locally nen- sanaed A
preprences, chen any WalrasAn Equitonm \. 1.3 WORKED EXAMPLE fOromy wee
See ee md
1S Pareto afi Chee 9 ame i
: i DIAGRAMS FOR AMC. eb Anay: 226.6) Bre] oayouns fm)
Snes presences Ug= xk wc% i i
Gob! 29 =(i2,0) ped ae 7 fob duns > L2METHOD FOR «te alp) <0 = een supply
Fim 2 Ane prod set ¥.2 (yer lyco.que-y.t FINDING + ig 2tp) >O = excess de meena
~N 4928 Yi ike a eee .
L : WALRASILA Finding, Walroui dn equilinun
Tuma ped see R= LyEm ly co, we Fy |
; ' , EQUILIBRIUM O Gading co price vettor
- Fires produces @ Consuneh opbmal bundle st. budget # 5 pm P
© Prog max prod vectors + Profits on 22vo-proapt consoraint , . ain a so that [Sip ;
for a i Con propa line andy solkes unPy indy Ua txade tt, act L Find, prop maximising prod *e erat (2ip) 20) (no exces
, “m gf eee Reps) st o tftar S Cpe The netic — Wet Of each Firm, Ym Op) ‘. ov supply
wipy> fy emivso, ye=-4} bap. nah (non een PT egual w eccchale-and PEORL Pe Yrntp) Pie walms’ haw hos
A Greed radeon», > BP Ye weeps 2 2. Find each consumer opernal Ankh pp PO Wy thon ip
ais r Pi rpe + Xa lp) = (44 oe Ben res ap + BF bund St. budget Constraint, ci fp) markets cluar ir au
vpor . . pe pe rel . oat Pe Ged oO, 3. Write dowa Maher cWanng markets burt ont, they
Fem: Ya@p)= apt ap. Gi CEE) 5] masmet caring se B,1p)=0 v 226pkO conditions 2(p)=O 1 check muse alse cane in the
So propit of: ph ) pr weld A\L@ WE of Prices P2 OD ant demands: oe eee Got clay Fingi mourhet too
7 . fF) = x . fea ga” a vector Pa n
Te =P. Yip= p (Ze) pe (& pr MARKETS “Xp = (6,6) en? Ht BY au mashed mere
sp 2t:3. IN-WORK BENEFITS
>
Most pirmy prowdé \L, Govt tax INTERVENTIONS
PUbUC goods gor Syste encourages
Beir employer firms to spend mot ©
MOMMY on compensahng
empioyse) with
in-work, penggre
& Paying employees
hgher wage b oppoytunioy
Wst OF pubic Qpads
Ly makes Liems moe competive XK -
ia, 2 labour sroutheet wa | SUBSIDIES S ut gor provinen endl
24:2 TIEGOUT EQUILI CRUE
Xo ip we howe of diperent
local prond2s of goods thot
canbe non rve.uous Or only
only partially nvalrow and
exCuudabu to thot that haven't
paid gor them, then can Roe,
is
Compeb oon amongst dugerent \ocad)
poviden of these goods SEG: spore
Qntres WICH Of 2 OOM
24. PROVIDIN G PUBLIC GOODS “i, £80 mores wl
GY GUNDLING 265, 7h were
WE @ good i> AGr-exclUdabe,podue 2.3.1. DEMAND CURVES
raped meena
Subsidies re comect:
public goods lat, govt revtla
G But govts rere Morey — ching Help
fron taken wiih credits .
PROVISION
provide geod dUkectly
UP CROWDING OUT
Govt coud prod = prvate provision, >
.&
urprovision Of So to get Quant
procdud every
marker neyiciency
LECTURE 2:
thor don
3.POSSIBLE GOVERMENT —
Ly 3.2. GOVERNMENT
gers could seep Hr >
PUBLIC GOODS
\.WHAT ARE PUGLIC GCoDs ?
a
Corse ae 5 RvObrous: ig De sane Unit Op that
© 7 ee 16 file qook cannot be comuned by
hott ena progucing multiple eonsunes or Lema SOW HAreal
g hase tee asod ig dopiota bw resource, ent ~
power tp exclude other i $ pero 4 ony
peopee pom consumung Biuke amount avaiable)
Unee
L, good / Pubic 900d US NONn- excrcable
> PrIVELR Sood is / and non-riValrous
exttudabw + nvalrouy (2g. prrewories, sees Vigivic)
2-9. chottes jrood)
> Z.INEFFICIENCY OF THE FREE MARKET AND
THE FREE ~RIDER PROBLEM ip Anoly Ue alone au
— _ appmat demanol ¢s
2.1 ROUSEROLD PUBLIC G6 Paiete YP lene , Sine
. only him rete te ly
MODEL. se each individual has Gn anh plage
sO CONVO O
feopia shout ahowe m+ Yy & Te » 1B Andy Ue wrth
and can spend on 4 Srey 0b, Hee is te
pase good Cinesting JAR Pe ws rape “ABER EFT -
it by bundting © in with oeler 2x0 Wabie in howe impOveneres) igood. jot both hae ine mabe we
goods se Ropin uring to pay gor te Pn Price. Aa ig Or On pRVale geod (spend Pioneer’ fren -vid On super!
x lA ocedake % aS rs CONS “on 0} ui
Lindaht eguitibnivs ie |Rapegae public goods] on Vemvewes dive < aaa an
Out al ual individual dormand if - . or
me Asie : Aggie gas foe
> cA ecowut {iden t lee soot \ a Rayos neack sonetning — Lo Houremouier would
as coun’t pce ; NT adh ae a » benepit ig Hey coordinard ar cuotcemt where
pi “ 4 & - ‘ dl : a : -
discrmminate o> tity { 3 | 7 z 5 REED, obkvait | both conmbiue mort publicgood than in NE
dont Brow each ade : AAR IACRAGE one od .
ranges dbeandh \ Quornicy | FOUR on Mnaarginal OM atiie ther On, POM Where Bost Responses intersect bb le Nash
Buse ere ge wilingnass to PRY, SO in rin Equilibrium
2.32, LINDAHL eQUiLipRiuM yerscal sum of ee a wirmauad [MER ean ome.
When gook ts pubuc good, Mca aR OR ony When godda ue,“ 2.2,FIREWORKS EXAMPLE 2. neighhoun, Andly fob deeds hows many
everyOre fOLeEA SAre quamhd4- pnvate, NE part TG They cae. op Le PRewolk4 wo set OY on NYE ‘utes
a SCP CRA oubwone otal no. of prrewore we oy: "Uae Ca * lise one - +f
2 Appa a ' . 5 4 “4 : Ca tly
WRYORE Giywice prices As ‘publicrass’ op b= bat Le fudges convydint: CatCg +f Sma tig
+ Benevount soci at PLonnee csp) good. increase, gap toda of am | Gocan pind epicient el 9 preworra
WhO Row evenongs Gerard ¥ ehenn WE x PART i goure mei i thor oe oe, “bine wher wih
Supply ciutes Uppciont ovicore increas ubtity - so Can DRAGS ustudy erin Bcd Me j Ry
na , t 4 ; ion ‘ ‘abo =
* BcieAY QUAN whet as Do incentt t gree Ade PE ere eer ore Wie goed Diuon Of ; : -t