currency war currency war known competitive condition international affairs countries seek gain trade advantage countries causing exchange rate currency fall relation exchange rate country currency falls exports competitive countries imports country expensive effects benefit domestic industry employment receives boost demand domestic foreign markets price increases import goods cost foreign travel unpopular harm citizens purchasing power countries adopt similar strategy lead general decline international trade countries historically competitive rare countries generally preferred maintain high value currency countries generally allowed market forces work participated systems managed exchanges rates exception occurred currency war broke 1930s countries abandoned gold standard great depression currency attempt stimulate economies effectively pushes unemployment overseas trading partners quickly period considered adverse situation concerned unpredictable changes exchange rates reduced overall international trade according brazilian minister finance global currency war broke view echoed numerous government officials financial journalists world senior policy makers journalists suggested phrase currency war extent hostility exceptions commentators agreed currency war generally concluded states engaging possible competitive mix policy tools including direct government intervention capital controls indirectly countries experienced undesirable upward pressure exchange rates took ongoing arguments notable dimension episode conflict united_states china january measures announced japan expected currency sparked concern possible second 21st century currency war breaking time principal source tension china versus japan versus late february concerns new outbreak currency war issued statements committing avoid competitive european central bank launched fresh programme january intensification discussion currency war background absence intervention foreign exchange market national government authorities exchange rate country currency determined general market forces supply demand point time government authorities intervene market time time achieve specific policy objectives maintaining balance trade competitive advantage international trade reasons intentional adverse consequences historically rarely preferred strategy according economist richard cooper writing substantial traumatic policies government adopt resulted cries outrage calls government replaced lead reduction citizens standard living purchasing power reduced buy imports travel abroad add pressure interest payments international debt expensive debts foreign currency discourage foreign investors 21st century strong currency commonly seen mark prestige associated weak governments country suffering high unemployment wishes pursue policy export led growth lower exchange rate seen early 1980s international monetary fund proposed potential solution developing nations consistently spending imports earn exports lower value home currency raise price imports making exports cheaper tends encourage domestic production raises employment gross domestic product effect immediate marshall condition seen attractive solution unemployment options like increased public spending ruled high public debt country balance payments deficit help correct reason preferring common emerging economies maintaining relatively low exchange rate helps build foreign exchange reserves protect future financial crises mechanism state wishing check appreciation currency work constraints prevailing international monetary system 1930s countries relatively direct control exchange rates actions central banks following collapse woods system early 1970s markets substantially increased influence market forces largely setting exchange rates increasing number countries state central bank intervene markets effect sells currency buy cause value currency fall practice common states managed exchange rate regime directly common tends lead fall value currency central bank directly buy foreign assets method authorities simply talk value currency future action discourage betting future rise little effect finally central bank effect lowering base rate interest limited effect end world war central banks set base rate according needs domestic economy country authorities wish prevent appreciation market forces upwards pressure currency retain control interest rates usually case need capital controls place conditions arise impossible trinity practice central bank tries potential actual recession increasing money supply domestic economy printing money domestic economy open market operations promise destroy newly created money economy improves order avoid inflation widely response financial crises began especially united_states united_kingdom lesser extent bank japan central bank claim policy administration denied currency objectives implementing practice act country currency indirect ways firstly encourage bet currency decline value secondly large increase domestic money supply lower domestic interest rates lower interest rates countries practising creates conditions carry trade market participants engage form borrowing currency country practising lending country relatively high rate interest effectively selling currency international markets increase supply currency push value october expectations markets high united_states japan soon embark second round prospects join certain early november united_states launched second round expected federal reserve additional billion available purchase financial assets prompted widespread criticism china germany brazil united_states try currency consideration effect resulting capital emerging economies leading figures critical countries governor people bank china said given challenges facing united_states chinese vice finance minister suggested help revival global economy president barack_obama defended saying help economy grow good world japan launched second round lesser extent united_states britain launch additional international conditions required currency war widespread currency war occur large proportion significant economies wish far happened global economic individual currency involve corresponding rise value currency corresponding rise generally spread country huge economy substantially rise individual currency tend small normal times countries content accept small rise value currency worst indifferent world suffering recession low growth pursuing strategies depend favourable balance payments nations begin competing conditions small number countries begin intervening trigger corresponding prevent deterioration export historical overview going classical period governments currency reducing value methods included reducing percentage gold coins precious metals gold 19th century proportion world trade occurred nations low exchanges rates generally matter great concern seen means help currency motivated desire increase domestic money supply ruling authorities wealth especially needed finance wars pay debts notable example substantial occurred napoleonic wars nations wished compete economically typically practiced involved attempts boost exports limiting imports rarely means favoured method protect home industries current account controls late 18th century especially great_britain 19th century world largest economy increasingly rival theory free trade held best way encourage prosperity allow trade occur free government imposed controls value money gold standard widely adopted global economy sufficiently integrated competitive occur little opportunity following end countries experienced recession immediately returned gold standard conditions currency war place currency war occur great_britain trying raise value currency pre war levels effectively countries wished market members gold standard rejoined standard work successfully pre war widespread competitive currency war great depression great depression 1930s countries abandoned gold standard widespread high unemployment common policy frequently described neighbour countries compete export unemployment effects soon offset corresponding cases barriers trading partners nations gain enduring advantage exact starting date 1930s currency war open debate principal parties great_britain france united_states 1920s generally coinciding interests france supported britain efforts raise sterling value market forces collaboration aided strong personal friendships nations central especially britain norman america benjamin strong early death soon wall street crash france lost faith sterling source value begun selling heavily markets britain perspective france longer playing rules gold standard instead allowing gold increase money supplies expanded economies reduced trade france began building gold factors contributed sterling crises september year great_britain substantially took pound gold standard years global trade disrupted competitive currency war 1930s generally considered ended monetary agreement woods era end world war woods system semi fixed exchange rates meant competitive option design objectives systems architects additionally global growth generally high period little incentive currency war possible conditions allow currency war place points period countries generally contrasting priorities point states simultaneously wanting currency war break occasions countries desperately attempting cause prevent states countries market forces undesirable downwards pressure examples include great_britain black wednesday tiger economies asian crises mid-1980s united_states desire significantly able secure cooperation major economies plaza accord free market influences approached 1990s advanced economies increasingly transition emerging economies moved view best leave running economies markets intervene correct substantial current account deficit asian crisis asian economies ran critically low foreign reserves leaving forced accept harsh terms accept low prices forced sale assets shattered faith free market thinking emerging economies generally began intervening value low enhanced ability pursue export led growth strategies time building foreign reserves better protected crises currency war resulted advanced economies accepted strategy short term benefits citizens buy cheap imports enjoy higher material standard living current account deficit grew substantially consensus view free market policy makers like chairman federal reserve paul treasury secretary deficit major reason worry popular concern example chorus executives trade union mid ranking government officials speaking perceived unfair trade practices china concerns soon partially global economy china able abandon dollar allowing substantial appreciation increasing exports dollar later established financial crises began reduce china export orders michael peter david described new economic relationship emerging economies woods competitive conditions required currency war returned severe economic seeing global trade year decline widespread concern advanced economies size increasingly joined emerging economies viewing export led growth ideal strategy march international operation reached peak london summit economist warn dangers competitive coined phrase competitive non appreciation september brazilian finance minister announced world midst international currency war numerous financial journalists agreed view financial times telegraph evans journalists linked announcement recent countries seeking exchange rate including china japan colombia israel switzerland analysts jim asserted fears currency war exaggerated september senior policy makers managing director tim secretary treasury reported saying chances genuine currency war breaking low early october warning risk currency war real suggested help resolve trade underlying conflicts currency said weapons solution lead bad situation domestic solution global problem considerable attention focused programmes china china pressure allow appreciate june october china allowed appreciation concerns western observers china intervention heavy pressure fixed abandoned june meeting appreciated slowly pressure september appreciated relatively prior september congressional hearings discuss measures force suggested china united_states winning currency war holding pushing value euro emerging economies martin wolf economics leader writer financial times suggested advantages western economies taking approach china recent years far biggest competitive advised measures spark trade war better tactic use targeted capital controls china prevent buying foreign assets order previously suggested daniel director centre european policy studies contrasting view published october paper chinese economist arguing win currency war japan chance china focus instead broader structural adjustments november seoul summit discussion currency war dominated seoul summit little progress resolving issue half analysts financial press widely reported currency war ended entered speaking july told financial times conflict ongoing investor confidence global economic outlook fell early august suggested currency war entered new phase followed renewed talk possible round days august switzerland japan push value september opening speech united_nations debate article financial times brazilian president called currency war ended increased use floating greater cooperation solidarity major economies exchange rate policies set good having individual nations gain advantage march said brazil experiencing undesirable upwards pressure currency finance minister saying country longer play fool allow away competitive announcing new measures aimed limiting appreciation real june real fallen substantially peak dollar able begin anti appreciation measures currency war mid january japan central bank signaled intention launch open ended bond buying programme likely resulted short lived intense period alarm risk possible fresh round currency war numerous senior central finance ministers issued public warnings deputy chairman russia central bank later joined including park finance minister south_korea president held view period intense count competitive genuine currency war real possibility japan economy minister said bank japan bond buying programme intended combat weaken early february president mario agreed monetary policy like undertaken deliberately cause statement hint action euro continues appreciate saw value european currency fall considerably mid february statement affirmed advanced economies commitment avoid currency war initially read markets endorsement japan actions later suggested like japan tone language specifically linking policies like expressed desire commentators asserted new round competitive occurs harmful global economy analysts stated japan planned actions long term interests rest world incident economist barry suggested countries start intervening boost growth world wide effects similar semi coordinated global monetary expansion analysts expressed skepticism risk war breaking chief currency brown brothers advising real currency war remains remote possibility february statement issued meeting finance ministers central bank governors moscow affirmed japan face high level international criticism planned monetary policy remark endorsed fed chairman ben managing director said recent concerns possible currency war paul echoed view central bank unconventional monetary policy best understood shared concern boost growth currency war suggested rising stock markets imply market players generally agree central bank actions best understood monetary competitive analysts continued assert ongoing tensions currency remain currency war trade war significant risk central bank officials ranging new_zealand switzerland china fresh statements possible analyses published currency scoring countries potential undertake intervention measuring relative intention weaken currency capacity ratings based country economy export growth real effective exchange rate scope country weaken currency damaging economy january indonesia thailand malaysia chile sweden willing able intervene new_zealand march concerns currency war diminished november journalists analysts warned possible fresh outbreak likely principal source tension appeared shift time versus china versus japan versus germany late october treasury officials criticized germany running excessively large current account surplus acting drag global economy currency war september journalists commentators financial sector raised prospect currency war time intended means boost states especially japan motivated means counter threat president mario denied intent engage competitive currency war month programme launched january european central bank lowering value euro programme official objectives speculation new represents currency war especially analysts working markets david example managing director bank america lynch stated growing consensus market participants states engaging currency war financial times editorial claimed rhetoric currency war august china partially weakening export figures previous month drop export caused loss major export countries including japan germany currency drastically previous operations sparked new round asian including vietnam comparison 21st century currency war 1930s episode outbreak competitive began occurred global economic important difference 2010s period international traders better able exchange rate sophisticated financial markets second difference later period invariably effected nations expanding money supplies creating money buy foreign currency case direct creating money domestic economies nations try net effect exchange rates cancel leaving largely unchanged effect remain collaborative intent berkeley barry wilson suggested net effect similar semi coordinated monetary expansion help global economy james united_nations conference trade development warned october fluctuations exchange rates causing corporations scale international investments comparing situation currency war 1930s evans daily_telegraph suggested new currency war beneficial countries suffering trade noting 1930s big surplus countries severely impacted competitive began suggested overly tactics damage status dollar global reserve currency ben chairman federal reserve drew comparison competitive inter war period referring gold france america helped sustain large trade caused pressure trading partners contributing great depression stated example 1930s implies pursuit export led growth ultimately succeed implications strategy global growth stability taken account february davies financial times emphasized key difference 1930s 21st century countries carried increases import tend international trade uses term currency war meanings related competitive book currency wars chinese economist song term somewhat contrary sense refer alleged practice lend emerging market countries speculate emerging state currency trying force value wishes states government book john uses term refer efforts state monetary authorities protect currency simple criminals agents foreign governments trying currency cause excess inflation home government wishes jim book currency wars making global crisis argues consequences fed attempts prop economic growth devastating american national security book largely concerned currency war competitive uses broader definition term policies cause inflation currency war policies seen warfare monetary assets favor effects rising inflation international trade offset policies tend country exports competitive foreign countries review book publishers weekly said book contributions later day war game simulation held applied physics laboratory warfare analysis laboratory argues financial attack destroy confidence dollar view fed policy confidence dollar lead chaos global financial markets reviews said view world currently going currency war based competitive occurred 1960s 70s culminated nixon decision dollar gold standard followed included german roosevelt dollar gold demonstrates competitive race instruments sort warfare writes characterized federal reserve policy calls extensive theoretical work negative interest rates achieved expense countries offers view continued dollar ultimately lead collapse asserts come widespread abandonment worthless inflated instrument provides possible scenarios future including collaboration variety emergence world central bank forceful return gold standard emergency powers based legal regime author emphasizes questions matters policy choice different historically term refer competition japan china preferred tender parts asia years leading second sino japanese war


substitute check united_states substitute check called image replacement document instrument united_states represent digital reproduction original paper check payment instrument substitute check maintains status legal check lieu original paper check authorized united_states law check clearing 21st century act check act instead presenting original paper checks financial institutions payment processing centers transmit data substitute check settlement process united_states federal reserve system clearing deposit based private agreement member financial institutions operates uniform commercial code substitute checks recognized legal checks long instruments meet specific requirements requirements include faithful reproduction paper check instrument bank financial institution created substitute check financial institution transferred presented check clearing process substitute checks subject existing federal state check laws regulations specific consumer rights affect acceptance instruments substitute check subject existing state federal check laws check act takes precedence laws regulations instrument specifications standards standards committee standards development committee american national standards institute maintains promotes supports technical financial standards procedures delivery transactions financial products services include image replacement documents financial instruments american national standard covers specifications content processing quality image replacement documents specifically certain standards exist paper checks apply image replacement documents standards include magnetic ink printing external processing code field use specifications image format image exchange specifications electronic exchange check image data domestic draft standard trial use electronic exchange check image data eligible payment items check act paper checks check like instruments eligible substitute checks including consumer personal checks commercial business checks money orders traveler checks cash advance convenience checks tied credit charge card accounts controlled checks drafts addition government treasury checks check act permits financial institution commercial bank credit union check collection process remove original paper check forward collection return process paper check substitute check requiring existing agreement bank deposit paying bank elimination paper checks clearing process saves banking treasury management industries handling transporting storing costs financial institution original paper check substitute check financial institution store archive paper check return paper check customer according state law later destroy paper check legal requirements properly prepared substitute check considered legal equivalent original paper check accepted payment proof payment manner original check substitute check adhere following requirements recognized legal equivalent original check substitute check accurately represent information depicted original paper check time financial institution check including names courtesy legal amounts endorsements information details substitute check accurately represent line original check substitute check bear legend legal copy check use way use original check financial institution provide substitute check provided financial institution removes original paper check forward collection return process paper check substitute check financial institution truncated original check follow standards capture check images data produces substitute check image statements include series pictures images original paper checks substitute checks original checks images checks posted online recognized legal substitute checks unlike substitute check check presented check clearing process settlement check adhere strictly requirements substitute checks check act substitute checks considered legal checks substitute checks subject existing check laws regulations laws regulations govern substitute checks united_states include funds availability act article instruments article bank deposits collections uniform commercial code variety state federal regulatory laws federal laws affect substitute checks include federal reserve regulations provide substitute check case fraud duplicate payments caused settlement substitute check original check creating substitute check state law federal law provision conflicts check act check act takes precedence extent inconsistencies laws provisions clearing process forward collection process substitute check processed forward collection external processing code position line required example forward collection process substitute checks involves following steps financial institutions process deposits federal reserve system original paper check presents financial institution financial institution bank referred bank deposit stamps endorsement rear original check bank captures image original check line data check bank removes original check clearing process uses check image data electronic endorsement electronic endorsements create substitute check bank check image line data captured original check paying bank bank settlement agreement exists bank bank exchange check images data bank provide original check legal equivalent substitute check bank paying bank bank uses check image data information substitute check received bank process item normal course settlement settlement process bank provides copy substitute check customer wrote original check includes information substitute check customer monthly periodic statement financial institution forward collection return process financial institution creates substitute check settlement return process checks substitute check returned unpaid insufficient funds bounced check paying bank bank stamps item non sufficient funds reason return case bank line identify substitute check according routing number financial institution dollar substitute check bank information return strip strip carrier document financial institution unpaid substitute check paying bank returns unpaid substitute check routing process bank handling bank receives returned substitute check financial institution issues charge notice customer deposited offered check settlement external sources standards committee financial industry standards statement check adoption october anatomy substitute check federal reserve financial services ways use check march electronic check clearing house organization forward collection return processes substitute check substitute checks development processing quality standards electronic check clearing house organization identify parts substitute check forward collection return processes included end document


result convex geometry applications mathematical economics describes addition sets space addition defined addition sets members example adding set consisting zero yields set consisting zero related results provide answer question sum sets close convex set defined convex line segment joining points set example solid disk formula convex set circle formula line segment joining distinct points formula circle suggests number summed sets exceeds dimension space sum approximately convex introduced step proof states upper bound distance sum convex hull convex hull set smallest convex set contains distance zero sum convex bound distance depends dimension shapes sets number sets shapes sets determine bound distance average sets convex hull increases infinity bound decreases zero sets uniformly bounded size upper bound decreased alternatively lloyd jon published economist ross investigating existence economic studying kenneth arrow paper studied economy non convex sets replaced convex hulls proved economy closely quasi original economy proved quasi optimal properties true proved exist convex economies following paper results widely central results convex economic theory good large economies non example quasi closely approximate economy results general form major achievements postwar economic theory wrote roger topic non convex sets economics studied nobel lloyd won prize arrow robert paul paul topic convex sets economics emphasized robert applications probability theory theory explain successful solution problems sums functions law averages random sets proved convex sets introductory example example contained interval real numbers convex implies point sum real number distance convex interval non convex set equals half distance average sum convex hull half distance sets added average sum fills convex hull maximum distance average convex hull approaches zero average includes depends following definitions results convex geometry real spaces real space dimensions given coordinate system point identified ordered pair real numbers called coordinates conventionally denoted points plane added coordinate wise point multiplied real number coordinate wise generally real space finite dimension viewed set real numbers operations defined addition real number finite dimensional spaces operations addition real number defined coordinate wise following example plane convex sets real space non set defined convex pair points point line segment joins example solid disk formula convex circle formula contain line segment joining points formula non convex set contained interval convex example solid cube convex hollow example crescent shape non convex set convex definition depending author formally set convex points real number unit interval point member mathematical induction set convex convex combination members belongs definition convex combination space weighted average set non negative real numbers satisfying equation definition convex set implies intersection convex sets convex set generally intersection family convex sets convex set particular intersection sets set convex convex hull real space convex hull minimal convex set contains intersection convex sets cover convex hull set defined set convex combinations points example convex hull set closed interval real numbers contains end points convex hull unit circle closed unit disk contains unit circle addition real space sum non sets defined set formed addition element wise sets example principle mathematical induction sum finite family non sets set formed element wise addition convex hulls sums addition respect operation taking convex hulls specifically real space convex hull sum sum convex hulls result holds generally consequence principle mathematical induction finite collection sets statements preceding identity implies point lies convex hull sum sets lies sum convex hulls sets definition addition expression means selection points convex hulls sets representation selection points depends chosen sum point representation point states dimension number needed sets choice depends point representation formula belongs convex hull fewer sets belongs remaining sets formula sets depends particular point represented implies example point sum real number dimension real space conversely characterizes dimension finite dimensional real spaces space natural number number dimension exactly holds finite dimensional spaces prove bounds distance sum convex hull sum states squared distance point sum original sum bounded sum squares largest sets smallest spheres sets bound independent number sets states bound distance sum convex hull distance zero sum convex bound distance depends dimension shapes sets number sets exceeds inner radius inner radius set defined smallest number point convex hull sphere radius contains convex hull contains inner radius reduce upper bound stated states squared distance point sum original sum bounded sum squares largest inner sets states upper bound distance sum sets convex hull sum distance sum convex hull measurement non set simplicity distance called non set respect measurement bound non sum depends largest inner sets bound depend number sets example distance convex interval non convex set equals half bound non average decreases number increases example distance averaged set convex hull half distance shapes sets determine bound distance average set convex hull number increases infinity bound decreases zero sets uniformly bounded size fact bound non average set decreases zero number increases infinity inner bounded number original proof established existence representation provide computing representation similar given arrow abstract elegant proof extended different appeared unpublished papers published method computing representation given sum point proof provides weaker bound original result elementary proof finite dimensional space found book applications estimating gap problems zero sum games applications enables researchers extend results sums convex sets sums general sets need convex sums sets arise economics mathematical probability theory mathematical sciences non important feature applications economics economics consumer preferences defined goods basket represented non negative coordinates represent quantities goods set indifference curve defined consumer consumer indifference curve contains consumer regards equivalent pair indifference curve consumer prefer basket basket passes indifference curve consumer preference set relative indifference curve union indifference curve consumer prefers indifference curve consumer preferences convex preference sets convex optimal basket goods occurs budget line supports consumer preference set shown means optimal basket highest possible indifference curve given budget line defined terms price consumer income set optimal function prices function called consumer demand preference set convex price consumer demand convex set example unique optimal basket line segment non convex preferences preference set non convex prices determine budget line supports separate optimal example imagine lion costs eagle zoo budget eagle lion suppose zoo keeper views animal equally valuable case zoo purchase lion eagle course contemporary zoo keeper want purchase half eagle half lion griffin zoo keeper preferences non convex zoo keeper prefers having animal having strictly convex combination consumer preference set non convex prices consumer demand connected disconnected demand implies behavior consumer discussed indifference curves purchases thought possessing character convex origin regions concave forced conclusion portions convex origin regarded possessing importance essentially detected occur demand variation price leading abrupt jumping point straight line rotated reveal existence measure depth concave portions indifference curves dimensional exist forever remain obscurity difficulties studying non convex preferences emphasized paul wrote non eternal darkness according nonetheless non convex preferences illuminated sequence papers journal political economy main contributors particular paper discussed approximate sums non convex sets papers stimulated paper lloyd martin considered consumer preferences introduced concept approximate papers paper influenced notion quasi robert paper contemporary economics previous publications non economics collected kenneth arrow gave undergraduate enrolled arrow graduate advanced mathematical economics course term paper studied general artificial economy non convex preferences replaced convex hulls economy price aggregate demand sum convex hulls consumers demands ideas interested lloyd jon proved eponymous private correspondence reported published paper publication applied proved economy general closely quasi original economy number agents exceeds dimension goods proved exists quasi prices following properties quasi prices consumers choose optimal preferred meeting budget constraints quasi prices economy good market supply equals demand quasi prices nearly clear markets original economy upper bound distance set economy set quasi original economy followed established aggregate allocation fictitious economy generated taking convex hulls consumption production sets allocation real economy bounded way independent number economic agents average agent experiences intended actions significance number agents goes infinity following paper results widely economic theory roger summarized economic implications key results obtained assumption remain approximately relevant circumstances fails example economies large consumption preference destroy standard results results general form major achievements postwar economic theory wrote topic non convex sets economics studied nobel arrow robert paul paul topic convex sets economics emphasized robert results featured economics literature general theory public economics including market failures game theory mathematical economics applied mathematics results influenced economics research measure integration theory mathematical explain large problems non nearly solved methods convergence stated convex problems encouraged use methods convex applications sums functions theory relies following definitions functions function set pairs arguments function real valued function set points real valued function defined convex function convex set example function convex absolute value function function pictured non convex interval problems problems objective function sum functions argument example problems linear given problem optimal solution fix optimal solution min minimum value problem consider optimal solution problem convex hulls taken functions optimal solution limit sequence points problem course given optimal point sum points original small number analysis published explain apparent problems despite non problems young mathematician surprised success convex methods problems known non convex problems solution dual problem problem need provide useful information solving problem problem convex satisfy qualification problem function non convex nonetheless solution dual problem provided close problem optimal value analysis explained success methods convex large problems despite non functions later authors argued produced approximately convex aggregate problem functions non convex crucial step publications use encouraged use methods convex applications sums functions probability measure theory convex sets studied probability theory point convex hull non finite dimensional space expected value simple random takes values consequence non set collection expected values simple valued random equals convex hull equality implies results useful probability theory direction probability theory provides tools examine convex sets generally results specifically results widely theory random sets example prove law large numbers central limit large principle limit results avoid assumption random sets convex probability measure finite measure applications non measure theory theories volume measures enables inequality bounds volume sums terms volumes sets volume set defined terms measure defined space advanced measure theory prove states range measure convex traditional term range alternatively image set values produced function measure valued measure example probability measures defined space product function measure defined event economics bang bang control theory statistical theory called continuous counterpart called


david david born april american economist vice chairman federal reserve served assistant secretary treasury domestic finance administration united_states president george bush left federal reserve join fund long term capital management remained private finance following collapse early life david born april david wife memphis tennessee father worked auburn university president university arkansas david raised arkansas brother sister left arkansas yale went study finance mit school management earned mit accepted position faculty harvard business school expert financial crises career immediately market crash president reagan tapped nicholas united_states senator chairman read chair presidential task force market mechanisms later known commission recruited harvard business school professor robert commission executive director turn enlisted harvard faculty colleague associate director report presidential task force market mechanisms commission inquiry stock market crash october known black monday months helped assemble nearly people produce report provided official record caused crash offered recommendations fix deficiencies market report laid blame derivatives trading portfolio insurance mechanisms focus generated went serve secretary treasury savings loan crisis deepened turned assistant secretary treasury develop plan resolve crisis plan enacted congress august financial institutions reform recovery enforcement act created dispose failed assets ultimately sold billion assets failed approach model banking resolution plans sweden thailand remained popular congress president appointed president bush assistant secretary treasury domestic finance treasury wrote paper high yield debt received inaugural smith prize bush nominated year term federal reserve board governors fill vacancy left resignation robert seen fed resident intellectual background professor finance economics resigned join john new fund long term capital management term come close resignation viewed unexpected joined business week termed dream team financial experts academics including nobel robert roger author genius failed rise fall long term capital management argued prospective investors presence celebrity caused investors trading partners exercise addition added firm following fund collapse dissolution left worked financial services companies career government effectively ended collapse chief economist fund asset management


iranian reform plan iranian targeted plan persian known reform plan passed iranian parliament january government described plan biggest surgery nation economy half century important iran recent economic history goal reform plan replace subsidies food energy total targeted social assistance accordance year economic development plan free market prices year period reform plan important broader iranian economic reform plan according government approximately billion year spent energy prices billion prices fuel goods including bread sugar rice cooking oil medicine experts believe direct subsidies billion depending oil prices system inherited iran iraq war era abolished iran largest gasoline consumers world ranking second united_states consumption car government reform years making reasons iran supreme leader backed government latest reform plan objectives iran largest provider fuel subsidies world iranian experts agree subsidies encourage waste goods including production sector ranging gasoline bread stopped way subsidies stated goal reform iran economy increase productivity new bring slump long government plans replace subsidies targeted social assistance consequences economic reform plan iran vulnerable sanctions reduce fuel imports reform plan save money iranian people end dollar year percent fuel production iran smuggled abroad daily subsidies iran long gas prices world cents cents implementation plan reduce waste fact according official data higher income strata population enjoyed subsidies poor subsidies reduction reduce air pollution reducing car traffic finally plan increase social justice targeted social assistance according official data richest households benefits times gasoline subsidies overall implementation plan increase productivity efficiency iran economy economic growth oil exports capita income things equal implementation implementation bill entity established duly authorized governmental company targeting subsidies organization saved government distributed follows strata iranian society government disposal compensate increased costs safety net remaining directed improving efficiency utility fuel energy production infrastructure public transportation development industry farming plan commence energy fuel utilities year goods start second year start cuts coincide beginning second half iranian year time gas plan come end march iranian parliament approved billion budget allocation subsidies oil price set billion barrel respectively according vice president parliamentary affairs iran reforms save percent country budget iran wants save billion subsidies years iranian parliament approved billion budget based barrel oil price bill factors billion price cuts totals add rounding double counted items note numbers billion dollars income data according recently member iranian household received average year subsidies oil natural gas compared typical annual income year iran department statistics announced million live absolute poverty line million live relative poverty line president says implementation targeted system unemployment poverty iran years data collection administration said earlier able different payment amounts different people end forms distributed asking report income assets property question remains government verify information gathered self reporting people chosen report information administration categorized people income lower middle higher implementation reform plan clear form compensation distributed direct cash goods concern accuracy government information family september iran statistics bureau announced implementation delayed month collecting information financial situation households opening bank accounts plan revision later government announced revised plan lack reliable data personal ease economic loss lost subsidies government indicated distribute person month month general population starting december price adjustments government took control deciding prices rise year long cuts gasoline refined products natural gas electricity water food sugar rice cooking oil bread health education billion dollars annually estimates indicate government increase existing prices average times achieve lower target times maximum target according expect price lift energy product prices times previous levels prices higher eventually according plan type consumption agricultural industrial civil considered setting energy prices plan implemented proportion geographical regions warm regions consume electricity summer cold regions consume gas winter finally time consumption peak peak hours consumption demand low high taken consideration starting april iran consumers hit wave rising prices touched laundry food items cooking oil rice eggs dairy products april price food consumer products risen cases latest official data comparing prices second week april corresponding period showed dairy products rose cent red meat cent rice cent beans cent vegetables cent sugar cent vegetable oil cent price chicken nearly consumption patterns october consumption petroleum gas gasoline diesel cut despite fact million cars added iran fleet increased use compressed natural gas fuel cars reportedly played role according government oil products consumption managed consumption gasoline increased million day reforming consumption pattern figure fallen million day november government reported reform plan saved iran billion economic structural adjustments reforms target major sources price iranian economy likely lead major restructuring economic sectors banking sector iran viewed potential removal subsidies plan expected direct impact banks experts believe following launch subsidies reform plan electricity industry undergo significant changes appealing private investors cement industry iran economic sectors hit hardest iran following reform plan iranian cement factories energy inefficient notwithstanding possible adjustment prices government implementation taxi delivery truck drivers adversely affected recent gas price increase experts believe removal subsidies likely adverse impact automotive sector years major element pressure producers unchanged exchange regime central bank iran puts imported products advantage failing compensate relative increase production costs domestic producers second phase second phase starting june half funds energy food subsidies allocated people remaining industrial sector approved parliament government pay extra cash month general population people earning month comfortable income level iran july announced implementation second phase suspended awaiting adjustments government raising inflation april finally fall parliament approved plan drop million percent system instead reported iran population million million registered receive cash hand outs effects criticism according earlier critics half billion passed compensation poorer iranian society eligible person month way near inflation rates critics government goes range inflation rise economy international monetary fund predicted moderate rise inflation percent january official inflation rate stands percent cost living iran according research center rise percent administration contends negative effects projections based date models according western reports cash payments denied opponents regime distribution phase accused government violating law implementing plan earned cut subsidies months implementation paid people compensation return says reported reform plan needs adaptation fine tuning citizens separate questions public policy issues government legitimacy hailed iran economic reform asked iran expertise transferred countries economist intelligence unit praised iran subsidies reform plan positive effect economy iran head council criticized government failing money saved restructuring government subsidies compensate government says allowed producers adjust prices given free loans energy subsidies cases recent years income inequality iran declined different measures effect reforms example income fell february february government earned billion implementing reform plan according world bank october members parliament voted favor reform high inflation exacerbated sanctions iran consequently growth consumption products rebounded iran started second phase targeted plan president petrol prices raised far target price consequence fuel smuggling gasoline imports increased iran government reported second phase reform plan continue originally planned according sixth year development plan reform plan extended iranian parliament approved cuts million changes government end monthly cash payments person government employees income month citizens receive social welfare government reluctant comply unfair allegedly despite risk running large budget


racial wage gap united_states united_states despite efforts equality proponents income inequality races whites asian americans highest average income followed latino americans african americans native americans variety explanations differences proposed differing intelligence access education experience discrimination topic highly controversial civil rights act passed illegal employers based race income flattened passage act wage gap minority groups narrowed absolute difference white wages percentage white wages mid-1970s time progress racial minorities slowed stopped reversed median weekly wage african american hispanic workers percent percent white workers respectively asian workers median wage percent white workers overall minority women wages comparison white women better minority men wages compared white men knowing wages races useful understanding overall racial inequality united_states integral role wages play wages labor market primary source income families america income socio demographic status indicator important understanding building wealth causes studies wage gap minority races united_states revealed number factors contribute differences wages observed white americans americans races factors contributing wage gaps races degree affect race varies factors common races educational education influential wage factor contributes racial wage gap varying education levels races lead different wages racial groups education affects wages allows access higher status offer greater earnings mary waters studied decrease black white wage gap 1940s 1970s found primary reason decrease wage gap education gap blacks whites education different groups equal wage gaps decrease disappear distribution way races distributed affects racial wage gap white asian americans highest median concentrated professional executive managerial blacks american indians black hispanic workers likely work blue collar service jobs tend concentrated lower wage skilled jobs operators laborers higher paying precision production craft jobs categories distribution varies women races white asian women likely work managerial professional black hispanic american indian women likely work service certain races likely lower paying jobs gaps median races arise study conducted kenneth couch mary found distribution blacks white improved 1990s black male percent likely employed manager white male percent likely work professional occupation increased percent respectively despite improvement distribution differences exist blacks whites black male likely white male work lower skills jobs likely white male work high paying jobs united_states economy 1970s 1980s caused shift income distribution united_states joined global market economy outcomes occurred possessed financial human capital education succeeded new economy money skills offer short supply possessed labor fare cheap physical labor global market new economy formed united_states manufacturing exported affected adversely group americans lowest section education distribution section minority groups increase overall wage inequality created new economy lower demand physical labor affected minorities economic restructuring served create structural barriers improvement education skills united_states shift economy lead greater income education groups uneven distribution minorities jobs overall increase wage inequality led wage gap whites minorities increase geographic distribution distance jobs location minorities homes affects ability minorities find profitable work found manufacturing jobs central cities 1980s negatively affected wage gap blacks whites blacks live cities foreign birth person minority race born united_states worse native born terms wages worst affected men women japan china filipino women study long found positive effect economic outcomes second generation immigrants children immigrants foreign born believe means specific traits immigrant parents beneficial economic success children client wage gaps blacks whites compared observed depend social networking success tend largest racial success depend type clients served tend racial difference attributed employee assignment white employers minority employees serve minority clients implications employee black real estate agent example served black clients neighborhoods resulting lower sales commissions way employee identified social form discrimination contributes wage gap discrimination human capital skills factors contributing racial wage gap taken account researchers find portion racial wage gap unexplained attribute factor race differences wages solely race racial discrimination use statistical controls ask given person background characteristics level education region residence gender marital characteristics earnings equivalent person different racial ethnic group differences emerge taken evidence racial discrimination research found wage employment discrimination blacks native americans discrimination found larger contributing factor black wages wages races study conducted found individual attributes human capital region account half black white wage gap additional percent different blacks whites remaining portion wage gap accounted individual distribution factors thought discrimination discrimination based race found research seventy percent employers study found racially biased blacks blacks found lower wages whites working industry white earn higher wages regardless native immigrant suggesting possible discrimination based skin color additionally employers openly admit blacks workers inner city study found hiring found discrimination labor market blacks whites credentials receive jobs rate specific races wage gaps identified races united_states research found size causes wage gap differs race instance median black male worker earns percent median white male worker median hispanic male worker earns percent understand fully accurately subject racial wage gap united_states useful look different races individually understand causes outcomes unique black history black americans united_states characterized social control domination wealth black white america history long relationship groups country white americans required pay enslaved centuries slavery abolished racist groups like led engage outright violence black businesses race riot churches 16th street baptist church bombing schools pillars black society worst individuals died wealth passed present form inheritance historical business investment civil rights act forbade employers basis race earliest greatest influences black white wage gap act economic prosperity 1960s contributed rising black wages increased education blacks increased returns education weekly wages average black male percent average white male risen percent percent improvement decades ending legal segregation mid-1970s black white wage gap continued narrow mid-1970s progress wage equality greatly slowed black white wage gap decreased average percent year 80s increased percent year 1990s black white wage gap decreased percent year proportional decrease accompanied decrease absolute difference black white wages analyses uncovered underlying influences improvements black white wage gap decades progress 1970s 1990s percent wage gap convergence attributed changes black education experience employment distribution influenced convergence decades factors identified contributing decreases wage gap convergence include shifts industry demand greater relative deterioration skills blacks rising overall male wage inequality decline black white wage gap 1990s greatest years potential experience decreased percent year kenneth couch mary report study black white wage inequality decreases result greater diversity reductions differences decade century wage gap fluctuated terms ratio black white wages percent percent percent percent absolute difference black white wages decreased period black americans number million total population median black male income compared median white non hispanic male income progress wage inequality blacks passage civil rights acts inequality discrimination exist study conducted major reports black white men similar competitive performance ratings racial wage differences increase decrease found black wages white wages industry factors race considered black hourly wage white hourly wage percent higher black hourly wage controlled human capital education skills difference decreased percent attributed percent difference racial discrimination calculated wage differences found blacks hour whites private sector public sector statistical found human capital region marital status account percent wage gap difference additional percent wage gap attributed differences blacks whites percent wage gap model black women experience wage equality comparison white women black men white men mid-1970s wages black white women equal black women wages decreased percent relative white women wages difference emerged attributed increase white women labor force following mid-1970s suggested white women began working advantages black women differences labor force attachment disappeared revealing racial wage gap overall wage gap appeared black white women earnings black women college degrees surpassed white women college degrees understanding earnings black women recently recognized important area research role black women traditionally terms family income black married couples typically relied women earnings races percentage single parent female maintained families highest black population hispanic hispanic minority group united_states composed million individuals consists regard wages groups wages lower non hispanic whites largest hispanic group consisting million people individuals mexican origin followed million people puerto rican origin million people cuban origin median income lower whites higher median wages african americans compared african americans general population relative wages fallen attributed demand educated workers gap educational supported fact college educated hispanic men relative wages changed little time unlike research findings black minority finding largest contributing factor wage gap skill characteristics especially education increased education seen contribute decreased wage gap college educated hispanic men wages approximately percent earned college educated white males percent higher wages earned college educated black males college educated hispanic women earn approximately percent college educated white women earn slightly earnings college educated black women despite improvement wages educational educated hispanic men return education non hispanic men comparable study conducted census data income controlled age education english language ability state metro residence found wage gap percent existed compared non additionally discrimination hispanic men women found study employers san_diego chicago skills educational major contributing factor wage gap differences education levels hispanic explain differences wages typical trend wages hispanic best puerto worst severely comparison blacks american indians george attributes group differences factors nature migration decision individuals migrated united_states political economic reasons incentives immigrants adapt labor market hispanic persons united_states physical human capital specific country origin easily transferred united_states labor market human capital investments united_states order labor market argues hispanic groups united_states economic reasons political reasons incentive acquire human capital united_states faster groups faster acquisition human capital results better economic progress higher wages relative success attributed fact invest united_states education labor market skills faster greater degree hispanic groups recognizes main reasons hispanic migration united_states political reasons argues political refugees incentive acquire human capital migrate economic reasons lower incentive leads education gaps seen whites greatly contributes observed wage gap based analysis hispanic wages past decades concludes differing incentives factors puerto rican immigrants wait years process reflected wages mexican immigrants wait years hispanic women like black women experienced greater success wage equality relative males race hispanic women education levels high school associate degrees earnings white women information positive broader examination hispanic women wages reveals inequality exists 1990s hispanic women time earnings fell real terms difference attributed mainly differences educational asian living america asian americans minority united_states median income higher whites assuming pacific counted separate race median income asian males compared median income non hispanic white males asian american men highest earning racial group hour asian american men earned white american men hour earning white americans counterparts similarly asian american women earned white american women asian groups united_states high wages certain asian groups fared better united_states labor market longer established china japan philippines india higher median wages household income southeast asian refugees vietnam groups median income non hispanic whites hand median income close national average blacks indian americans currently highest median household income ethnic group united_states americans lowest explanation higher wages greater average educational 1990s percent total male population college degree percent asian indian men percent filipino men percent chinese men college degree higher educational masks fact wage gap exists whites whites earn categories factors controlled whites comparable jobs american indian american indian minority studied minority groups united_states median family income american indians approximately percent median family income families median household income native americans compared total population making second race average african americans wage gap attributed large human capital differences debate discrimination affects wage gap private public sector employment racial wage gap blacks whites observed differ public private sectors analysis difference hour found blacks whites private sector percent difference contrast smaller difference hour found public sector percent difference percent blacks work public sector evidence suggests wages based primary individual qualifications percent blacks employed private sector assertion found valid additionally larger percentage wage gap found accounted human capital characteristics educational potential years experience public private sector effect encountered private sector black males higher absolute wages increase status lower wages relative whites status found public sector policy discussion solutions eliminate racial wage gap proposed eliminate races race research identified different wage gaps sources wage gaps different minorities suggesting public policies affect different minorities different ways effective strategies account unique circumstances race group douglas offers solutions alleviate wage inequality greater investments education elimination racial segregation notes economy physical labor offer suffer argues investments education especially higher education result higher rates economic growth lower income inequality eliminating racial segregation argues divides races exist broken including income segregation accomplish abolition racial segregation argues simple enforcement legislation place fair housing act home mortgage disclosure act community act required group specific policies focus education language helpful employment opportunities specific policies dependent research wage gaps groups tackle wage inequality specifically companies random job national state local levels suggested study find wage inequality past way actively monitor presence racial wage gap companies limitations criticisms racial wage gap evaluating understanding causes consequences racial wage gap races important understanding racial inequality united_states wage gap encompass aspects inequality useful understood conjunction types example mary waters note types important understanding inequality united_states including health demographic measures infant mortality rates life disability ethnic racial groups differ rates residential segregation overall wealth exposure crime toxic access power upper reaches society racial wage gap aspect inequality united_states criticism racial wage gap noted scholars racial wage gap fails account people certain race unemployed examining median reflect growing racial butler hypothesis states skilled members society ones likely working suggesting wage gap account overall difference wages races analysis black white wage gap accounted unemployment found unemployment included calculation weekly wages convergence convergence percentage went percent percent


mathematical economics mathematical economics application mathematical methods represent theories analyze problems economics convention applied methods refer simple geometry differential integral difference differential matrix mathematical programming methods advantage claimed approach allowing theoretical relationships simplicity mathematics allows form meaningful wide ranging complex subjects easily expressed informally language mathematics allows specific positive claims controversial contentious subjects impossible mathematics economic theory currently presented terms mathematical economic models set stylized simplified mathematical relationships asserted clarify assumptions implications broad applications include problems goal household business firm policy maker static analysis economic unit household economic system market economy modeled changing comparative change induced change factors dynamic analysis tracing changes economic system time example economic growth formal economic modeling began 19th century use differential represent explain economic behavior utility early economic application mathematical economics mathematical discipline half 20th century introduction new techniques period second world war game theory greatly use mathematical economics rapid economics alarmed critics discipline noted john robert friedrich criticized broad use mathematical models human behavior arguing human choices mathematics history use mathematics service social economic analysis dates 17th century mainly german universities style instruction emerged dealt specifically detailed presentation data related public administration fashion term statistics time small group professors england established method reasoning figures things relating government referred practice political sir william petty wrote length issues later concern taxation velocity money national income analysis numerical rejected abstract mathematical petty use detailed numerical data john influence time petty works largely ignored english scholars economics began earnest 19th century economic analysis time later called classical economics subjects discussed means importantly von isolated state develop explicit abstract models behavior order apply tools mathematics model farmland use represents example marginal analysis work largely theoretical mined data order attempt support comparison contemporaries built economic models tools applying previous tools new problems new scholars trained mathematical methods physical sciences economics advocating applying methods subject described today moving geometry mechanics included presented paper general mathematical theory political economy providing outline use theory marginal utility political economy published principles political economy declaring subject science mathematical simply deals quantities expected collection statistics price quantities permit subject presented exact science preceded followed expanding mathematical representations economic problems roots economics built tools discipline utility arguing individuals sought maximize utility choices way described time thought utility units known francis considered modern mathematical economics professor mathematics developed mathematical treatment market condition defined competition sellers treatment competition published mathematical principles wealth referred assumed sellers equal access market produce goods cost assumed goods seller vary output based output market price determined total quantity supplied profit firm determined output unit market price profit function respect quantity supplied firm left system linear simultaneous solution gave quantity price profits contributions economics neglected decades eventually influenced models represent non cooperative games today solution given nash work preceded modern game theory years provided solution later called partial attempted discussion economy theory general competitive behavior economic actor considered production consumption originally presented separate models exchange included solution resulting system linear non linear general time general solution expressed system attempts produced famous results economics law second principle method considered highly mathematical time commented length fact review pure elements pure economics law introduced theoretical answer problem determining solutions general different modern constructed modern assumed money spent goods good sold market price good buyer dollar basket goods starting assumption markets markets cleared reached conditions market clear easiest markets considered texts market goods market money markets reached state additional goods conversely money enter exit second market state statement proof existence solutions general commonly today illustrate market clearing money markets undergraduate level roughly french meant serve practical expression general marketplace auction goods prices market participants wait satisfy personal reservation prices quantity desired remembering auction goods reservation price desired basket goods buyers satisfied given market price transactions occur market clear price surplus shortage exist word describe directions market takes settling high low prices different goods price agreed goods process appears dynamic presented static model transactions occur markets practice markets operate manner francis introduced mathematical elements economics explicitly mathematical essay application mathematics moral sciences published adopted economic behavior allowing outcome decision converted change utility assumption built model exchange assumptions individuals self interested individuals act maximize utility individuals free independently party given individuals set solutions individuals maximize utility described contract curve known box technically construction person solution problem developed arthur contract curve box generally set solutions problem actors referred core economy devoted considerable effort insisting mathematical appropriate schools thought economics helm economic journal published articles criticizing mathematical rival researchers including robert anderson noted mathematical economics articles focused forth tax responses producers noticed monopoly producing good supply demand class economy airplane plane flies sets seats fly actually lower price seen consumer tax applied common sense traditional numerical analysis indicate insisted results achieved mathematical suggested assumption continuous demand function change tax resulted predictions later showed correct result price result tax occur demand function large changes tax rate modern mathematical economics array new mathematical tools differential differential convex sets theory deployed advance economic theory way similar new mathematical methods earlier applied physics process later described moving mechanics differential analyzed treating decisions economic actors attempts change given goods preferred sets treated efficient optimal equivalent term exchanges occur actors individual better making individual worse proof commonly informally ascribed adam smith invisible hand hypothesis statement formal assertion known fundamental welfare economics models lacked generation mathematical economics landmark treatise foundations economic analysis paul identified common mathematical structure multiple fields subject building previous work alfred marshall foundations took mathematical concepts physics applied economic problems broad view example comparing principle drives fundamental premise mathematical economics systems economic actors modeled behavior described like system extension followed work previous century extended significantly approached problems applying individual utility aggregate groups comparative compares different states change variable methods book provided foundation mathematical economics 20th century linear models restricted models general formulated john von unlike earlier versions models von inequality constraints model expanding economy von proved existence fixed point von model expanding economy considered matrix pencil von sought probability positive number solve equation inequality systems expressing economic efficiency model probability represents prices goods probability represents intensity production process run unique solution represents rate growth economy equals interest rate proving existence positive growth rate proving growth rate equals interest rate remarkable achievements von von results viewed special case linear programming von model uses study von model expanding economy continues interest mathematical interests economics input output economics russian born economist built model input output analysis material balance tables constructed soviet followed earlier work model described system production demand processes described changes demand economic sector influence production practice estimated simple models address economically interesting questions production economics technologies produce constant proportions regardless price reducing value models understanding economies allowing parameters estimated relatively easily contrast von model expanding economy allows choice techniques estimated technology mathematical mathematics mathematical mathematical programming refers selection best element set available alternatives simplest case problem involves real function selecting input values function computing corresponding values function solution process includes satisfying general necessary sufficient conditions problems specialized function input generally includes finding best available element function given defined domain use variety different techniques economics closely linked agents economy influential definition describes economics science study human behavior relationship ends scarce means alternative uses problems run modern economics explicit economic technical constraints utility problem dual problem expenditure problem given level utility economic problems theory consumers maximize utility subject budget constraints firms maximize profits subject production functions input costs market demand economic studied theory key ingredient economic principle tested data newer developments occurred dynamic programming modeling risk uncertainty including applications portfolio theory economics information search theory properties entire market system stated mathematical terms fundamental welfare economics arrow model general discussed problems formulaic solution sufficiently complex require numerical methods solution aided software complex allow methods solution particular general models entire economy linear programming profoundly affected earlier considered equality constraints mathematical received nobel prizes economics conducted notable research linear programming kenneth arrow robert paul robert acknowledged george deserved share nobel prize linear programming conducted research programming won nobel prize notably addition arrow linear linear programming developed aid allocation resources firms industries 1930s russia 1940s united_states berlin linear programming plan shipment supplies prevent berlin soviet blockade programming extensions inequality constraints achieved albert tucker considered problem minimize formula formula subject formula formula formula formula formula function formula formula formula functions formula inequality constraints formula formula formula functions formula equality constraints allowing inequality constraints tucker approach classic method allowed equality constraints tucker approach inspired research including treatment inequality constraints theory programming particularly satisfactory applied convex problems enjoy convex theory convex particularly strong convex functions arising linear programming convex analysis daily operations research scheduling power plants planning production schedules factories routing routes flights planes crews optimal control economic dynamics allows changes economic time including dynamic systems problem finding optimal functions changes studied optimal control theory second world war frank variations end following richard work dynamic programming english translation earlier work optimal control theory extensively economics addressing dynamic problems especially economic growth stability economic systems textbook example optimal consumption saving crucial distinction control models applications optimal control theory include finance production example functional analysis course proving existence optimal model economic growth john von introduced functional methods include economic theory particular fixed point theory fixed point following von program kenneth arrow formulated abstract models economic convex sets fixed point theory introducing arrow model proved existence proved efficient general need unique models space represented dual space represented prices russia mathematician developed economic models partially ordered spaces emphasized quantities prices renamed prices determined abbreviated russian difficulty discussing prices soviet_union finite dimensions concepts functional analysis illuminated economic theory particularly role prices normal supporting convex set representing production consumption possibilities problems describing time uncertainty require use infinite dimensional function spaces agents choosing functions processes differential decline rise john von work functional analysis broke new ground mathematics economic theory left advanced mathematical economics fewer applications differential particular general general convex geometry theory differential approach differential failed establish existence decline differential exaggerated differential graduate training applications differential returned highest levels mathematical economics general theory practiced set humorous designation 1960s 1970s stephen led revival use differential mathematical economics particular able prove existence general earlier writers failed novel mathematics category general differential associated use differential analysis include advances changed traditional narrative history mathematical economics following von celebrated abandonment differential game theory john von working theory games broke new mathematical ground extending functional methods related convex sets fixed point theory economic analysis work avoided traditional differential maximum operator apply non functions continuing von work cooperative game theory game lloyd martin influenced economic research politics economics example research fair prices cooperative games fair values voting games led changed rules voting accounting costs public works projects example cooperative game theory designing water distribution system southern sweden setting rates dedicated telephone lines usa earlier theory bounded range outcomes special cases example monopoly contract curve box von results similarly weak following von program john nash fixed point theory prove conditions problem games generate unique solution game theory adopted fundamental aspect experimental economics economics information economics industrial organization political economy given rise subject mechanism design called reverse game theory private public policy applications ways improving economic efficiency incentives information sharing nash john received nobel memorial prize economic sciences work non cooperative games awarded work repeated games later work extended results methods modeling agent based economics agent based economics ace named field relatively recent dating 1990s published work studies economic processes including economies dynamic systems interacting agents time falls complex systems corresponding agent based models agents real people objects modeled interacting according rules micro level interactions create patterns space time rules formulated predict behavior social interactions based incentives information theoretical assumption mathematical agents markets replaced restrictive agents bounded adapting market forces ace models apply numerical methods analysis computer based complex dynamic problems conventional methods find ready use starting specified initial conditions economic system modeled evolving time constituent agents repeatedly interact respects ace characterized culture dish approach study economy contrast standard modeling methods ace events driven solely initial conditions exist ace modeling includes agent adaptation autonomy learning similarity overlap game theory agent based method modeling social interactions dimensions approach include standard economic subjects competition collaboration market structure industrial organization transaction costs welfare economics mechanism design information uncertainty method said benefit continuing improvements modeling techniques computer science increased computer capabilities issues include common experimental economics general comparison development common framework resolving open questions agent based modeling ultimate scientific objective method described test ing theoretical findings real world data ways permit supported theories time researcher work building appropriately work gone economics course 20th century articles core journals economics exclusively written result material transmitted journals relates economic theory economic theory continuously abstract mathematical assessment mathematical techniques employed core journals showed decrease articles use geometric representations mathematical survey economic journals finds articles published lacked statistical analysis data lacked displayed mathematical expressions numbers margin page world wars advances mathematical statistics trained led proposed discipline advancing economics mathematics statistics economics statistical methods economics mathematical economics statistical features application linear time series analysis economic data coined word helped found society journal student published probability approach asserted precise statistical analysis tool mathematical theories economic actors data complex sources linking statistical analysis systems economic theory commission foundation 1930s 1940s earlier work roots modern traced american economist henry moore moore studied agricultural productivity attempted fit changing values productivity plots corn crops curve different values moore errors work choice models limitations use mathematics accuracy moore models limited poor data national accounts united_states time models production static published dynamic moving model designed explain business cycles periodic variation supply demand curves known model formal model later nicholas largely credited exposition application classical economics presented simple geometric terms elementary mathematical mathematical economics conventionally makes use matrix economic analysis order powerful claims difficult mathematical tools tools formal study mathematical economics contemporary economic theory general economic problems involve mathematics practical way attacking solving alfred marshall argued economic problem expressed solved treated means mathematical work economics increasingly dependent mathematical methods mathematical tools employs sophisticated result mathematics considerably important professionals economics finance graduate programs economics finance require strong undergraduate preparation mathematics admission reason attract increasingly high number applied apply mathematical principles practical problems economic analysis economics related issues economic problems defined integrated scope applied mathematics integration results economic problems stylized models clear assumptions predictions modeling informal adam smith wealth nations formal rigorous mathematical broadly speaking formal economic models classified continuous practical level modeling applied areas economics evolved independently models formulated processes model economically values time based statistics test processes estimate parameters world wars developed representation stationary processes terms models trend jan applied time series analysis economic data contemporary research time series statistics consider additional stationary processes moving average models general models include arch models arch models non mathematical models purely example models involved aspect social choice theory involving financial example coordinates specific forms functional relationships cases economic predictions model merely assert direction movement economic functional relationships sense example price item increases demand item decrease models use dimensional instead functions models occasionally example scenario planning possible future events played example non numerical decision tree analysis models suffer lack precision classification according mathematics subject classification mathematical economics falls applied mathematics classification category game theory economics social sciences classifications game theory codes mathematical economics codes handbook mathematical economics series currently volumes distinguishes mathematical methods economics areas economics volumes mathematics employed source similar distinction new dictionary economics subject entries subject index includes mathematical entries vol mathematical economics listed problem comparative linear models economics mathematical methods listed variations theory general convex programming optimal control widely system economics includes mathematical methods subject classification codes originated journal economic literature classifying new books articles relevant categories listed simplified miscellaneous codes reproduced classification codes mathematical methods new dictionary economics 2nd uses codes classify entries corresponding links new online category fewer page similar google searches mathematical methods following general mathematical methods programming models mathematical simulation modeling general techniques programming models dynamic analysis existence stability conditions techniques simulation modeling input output models general models game theory general cooperative games games dynamic games evolutionary games repeated games theory matching theory criticisms defences mathematics complicated economics friedrich contended use formal techniques projects scientific appropriately account limitations faced real economic agents interview economic historian robert stated guess scientific approach began penetrate soon dominate profession past thirty years came invention mathematical analysis kinds considerable improvements age data sophisticated use data strong feeling data laden science data laden undertaking virtue sheer sheer sheer look journal page bears certain resemblance science central activity looks scientific understand think genuine approaches universal law resembling science different science stated economics naturally lend mathematical exposition testing predictions mathematical economics philosopher discussed scientific standing economics 1940s 1950s argued mathematical economics suffered words economics mathematical theory mathematical economics ceased rely relied mathematical according assumptions tested experiment observation assumptions explored consequences consistency assumptions sharing concerns assumptions economics generally mathematical economics declared assumptions unrealistic proposed judging economic models performance match assumptions reality mathematical economics form pure mathematics considering mathematical economics wrote general theory great fault symbolic pseudo mathematical methods system economic analysis assume strict independence factors involved lose authority hypothesis ordinary discourse manipulating know time words mean heads necessary reserves qualifications adjustments shall later way complicated partial pages assume large proportion recent mathematical economics merely initial assumptions rest allow author lose sight real world maze symbols defense mathematical economics response criticisms paul argued mathematics language repeating thesis economics language mathematics necessary representing substantive problems mathematical economics led conceptual advances economics particular gave example writing people ingenious grasp complex parts language mathematics ordinary individuals fairly easily aid mathematics state mathematical economics deserves support like forms mathematics particularly neighbors mathematical mathematical statistics increasingly theoretical computer science mathematical economics mathematical sciences history theoretical advances regularly contributed reform applied branches economics particular following program john von game theory provides foundations describing applied economics statistical decision theory games nature general theory industrial organization decade rise internet mathematical experts computer scientists worked problems line services contributions mathematics cooperative game theory games robert concluded mathematical economics core infrastructure contemporary economics economics longer fit conversation piece ladies gentlemen technical subject like technical subject attracts people interested technique subject bad inevitable case kid technical core economics infrastructure political economy consult reference contemporary economics looking enlightenment world today led technical economics history mathematical prominent mathematical include limited following century birth 19th century 20th century