Week 4: Where Does Comparative Advantage Come From?

Size: px
Start display at page:

Download "Week 4: Where Does Comparative Advantage Come From?"

Transcription

1 Wk 4: Whr Dos Coparativ Advantag Co Fro? In Wk 3, w larnd that a country xports goods in which it has a coparativ advantag and iports goods in which it has a coparativ disadvantag. This bgs th qustion o what dtrins a country s coparativ advantag and disadvantag. This not addrsss this qustion. Coparativ Advantag is not a Fixd roprty First o all, it should b notd that a country s coparativ advantag is not a ixd proprty. On th contrary, goods in which a country has a coparativ advantag chang ovr ti, with attndant changs in its trad structur. Figur 1. Coodity coposition o Japans trad: Food Export Txtil & apparl Chical & tal products Machinry Othr products 0% 20% 40% 60% 80% 100% Iport Food & raw atrials Crud & proccssd nrgy products Txtil & apparl Chical & tal products Machinry Othr products 0% 20% 40% 60% 80% 100% (Sourc) Yaazawa & Yaaoto (1979) and Ministry o Financ, Trad Statistics o Japan. 1

2 Figur 1 illustrats how Japan s trad structur has changd ovr th past 140 yars. In th id-1850s, Japan trinatd its isolationist policy and startd trading activly with wstrn countris. Japan s ajor xport goods in th lat Edo and arly Miji priods wr ood and raw txtil atrials such as silk yarn. Alost vrything ls was uncoptitiv in wstrn countris or not producd at all. This situation did not last long, howvr. Japan s balanc o trad in ood and raw atrials quickly turnd ro positiv to ngativ whil light anuacturs, such as cotton cloths, porclain and glasswar, rgd as nw xport goods. Although ths products raind ajor orign-xchang arnrs until th arly post- World War II ra, xports o achinry, such as autoobils, startd to grow rapidly in th 1960s. Whil achinry accounts or th ajority o Japan s xports vn today, th shar o achinry in its iports has also risn rcntly, thanks in part to a surg in iports o IT quipnt and othr lctronic products ro othr Asian countris. According to Figur 1, it ss that Japan s coparativ advantag has shitd ro agricultur to light anuacturs and ro light anuacturs to achinry during th past 140 yars. Now th qustion is what brought about ths changs. Who is Copting with Who? Obviously, tchnology is an iportant actor bhind coparativ advantag. As th tchnology o a ir or an industry progrsss, so dos its productivity, aking that ir or industry or coptitiv in th world arkt. As w will discuss blow, howvr, th thory o coparativ advantag suggsts that th natur o coptition acing individual irs is not ncssarily what th anagrs o ths copanis hav in ind. In Wk 3, w considrd a situation in which th ollowing rlationship holds or autarky prics in Japan and th USA: (1). In th abov inquality, and rprsnt th yn prics o ood and achinry in Japan whil and ar th dollar prics o ths goods in th USA. According to (1), th USA has a coparativ advantag in ood production and Japan has a coparativ advantag in achinry production. (1) is quivalnt to (synonyous with) th ollowing inquality rlation, (2) which copars th rlativ pric o ood in Japan and th USA with that o achinry in th two countris. In Wk 3, w also ound that th yn/dollar xchang rat ust satisy a crtain condition or ach country to xport on good and iport th othr good. Th ood prics in th two countris ar qualizd whn = in which stands or th xchang rat dind as th pric o on dollar in yn. Lt us writ th valu o th xchang rat that satisis this condition as, that is, (3). Whn th actual xchang rat riss abov (so that on dollar costs or than yn), Japans ood bcos chapr than Arican ood and xportd to th USA. Whn it alls blow S, Arican ood bcos chapr than Japans ood and xportd to Japan. W can siilarly din th xchang rat at which th pric o achinry is qualizd btwn th two countris as 2

3 Using th xprssions in quations (3) and (4), w can rwrit (2) as (4)., (5) which tlls us th rang o valus that th yn/dollar xchang rat is likly to tak. I th actual xchang rat is highr than, both ood and achinry ar xportd by Japan; i th xchang rat is lowr than, both goods ar xportd by th USA. As discussd in th Wk 3 not, howvr, ths situations ar abnoral and will b corrctd soonr or latr by dand-supply dynaics in th orign xchang arkt. In th long run, th xchang rat is xpctd to sttl at a valu btwn and, at which ood is xportd by th USA but achinry is xportd by Japan. As long as (5) holds, at no xchang rat is thr a situation in which Japan xports ood and th USA xports achinry. But what i Japans arrs or ood anuacturs ar unhappy about this situation and want to b an xportr? Th only thing that thy can do by thslvs is to iprov thir own productivity and rduc th prics o thir products. I alls suicintly, (2) and (5) chang to and (6), in which cas Japan xports ood and iports achinry. (7) As w saw in Figur 1, Japan did xport a lot o ood during th 19 th cntury but barly dos so today. It should b notd, howvr, that this is not ncssarily bcaus Japans arrs and ood anuacturrs hav raind idl and hav not ad ort to iprov thir productivity. 1 Which o (2) and (6) holds in practic dpnds not only on th Japans ood pric, but also on th othr thr prics. Evn i Japans arrs cut thir prics, thy ay rain unabl to xport i, or xapl, Japans achinry irs succd in cutting thir prics by a largr proportion. This iplis that Japans arrs ar copting not only with Arican arrs but also with Japans (and Arican) achinry anuacturrs, whos action ay hav a largr ipact on whthr thy nd up bing xportrs or iportrs. Coparativ Advantag and Factor roportions Tchnology is not th only dtrinant o prics. Th pric o a good rlcts not only th cost o raw atrials and intrdiat inputs but also that o labor and othr production rsourcs. In conoics, rsourcs that ar usd or th production o a good, but do not physically bco part o th inal product, ar calld actors o production. Exapls o actors o production ar land, physical capital (buildings and quipnt) and labor. Labor includs unskilld workrs and skilld workrs o which th lattr bodis spciic skills and knowldg that ar usul or advancd tasks. Factors o production hav two iportant proprtis that ar rlvant to coparativ advantag. First, th stocks (aounts) o so actors o production ar ixd or changs only slowly ovr ti, whras th stocks o othr production actors can b incrasd rapidly through conscious invstnt. Land and unskilld labor 1 As will b discussd in Wk 5, howvr, th Japans govrnnt havily protcts dostic arrs. It is likly that this protction has waknd Japans arrs incntiv to iprov thir productivity. 3

4 blong to th orr catgory whras capital and skilld labor ar clarly o th lattr typ. Sinc th stocks o capital and skilld labor ar vry low in poor countris but incras progrssivly in th procss o conoic dvlopnt, th stocks o capital/skilld labor rlativ to thos o land/unskilld labor tnd to b highr in rich countris. Th othr iportant charactristic o actors o production is that individual industris ak us o ths actors in dirnt proportions. Agricultur is land-intnsiv in th sns that it rquirs proportionatly or land than othr production actors in coparison to othr industris (.g., srvics). Siilarly, light anuacturing is highly intnsiv in unskilld (or si-skilld) labor whil th achinry and pharacutical industris ar or intnsiv in capital and high-skilld labor than ar othr industris. Tabl 1. Factor intnsity and ndownts in rprsntativ industris and countris Industry/country Land, unskilld labor Capital, skilld labor Agricultur/ood products 〇 Light anuacturs Havy/high-tch anuacturs 〇 Dvloping countris 〇 Advancd countris 〇 Tabl 1 suarizs th rquirnt and availability o th two typs o production actors in rprsntativ industris and countris. According to this tabl, th rsourc ndownt o dvloping countris is unsuitd to havy/high-tch anuacturs whil that o advancd countris is not suitabl or th production o ood and light anuacturs. Although dvloping countris ay b abl to produc havy/high-tch anuacturs, th scarcity o capital and high-skilld labor is likly to driv up th cost o producing ths goods. In advancd countris, th production o land and un-/si-skilld labor-intnsiv goods, such as ood, will b xpnsiv bcaus o th rlativ scarcity o ths rsourcs. To th xtnt that this is th cas, poor countris will hav a natural coparativ advantag in ood and light anuacturs (such as apparl) whil rich countris is likly to hav a coparativ advantag in havy and high-tch anuacturs. To xain th accuracy o this prdiction, Figur 2 plots data on GD pr capita and th shars o light anuacturs and achinry in total xport arnings or a larg nubr o countris. According to this igur, th shar o light anuacturs is vry high in so low- and iddl-inco countris but invariably low in rich countris. In contrast, th shar o achinry tnds to b largr in high-inco countris, coniring that ths countris hav a coparativ advantag in capital- and skill-intnsiv products. In Figur 2, howvr, thr ar a handul o countris whos inco lvl is rlativly low but whos shar o achinry xports is high, such as Vitna, th hilippins and Mxico. Ths countris ar not, howvr, xcptions to th principl o coparativ advantag. Ths countris ar dply intgratd into intrnational production ntworks and srv as th bass or inal assbly oprations or orign ultinational copanis (MNCs). For xapl, th hilippins iports a lot o capital- and tchnology-intnsiv lctronic coponnts (such as siconductors) ro advancd countris and xports IT quipnt that incorporats ths coponnts. To th xtnt that this is th cas, what th hilippins xports is not th whol IT quipnt but only th un-/si-skilld part o it. W will hav an opportunity to xain intrnational production ntworks and global valu chains as part o our discussion o orign dirct invstnt (FDI) and MNCs in Wk 8. 4

5 Shar in total xports (%) Figur 2. Th inco lvl and th coposition o xports (2015) hilippins Mxico Light anuacturs Machinry 60 Singapor 40 Vitna 20 Nw Zaland 0 2,000 20, ,000 GD pr capita (in dollars, 2011) (Nots) Light anuacturs includ txtils and apparl, lathr products, wood and papr products. Export shars ar calculatd by xcluding nrgy and inral rsourcs ro th total xport valu. Countris that dpnd havily on nrgy/inral rsourc xports or whos population is sallr than on illion ar xcludd. GD pr capita is adjustd or intrnational dirncs in prics and asurd in trs o dollars as o (Sourc) CEII/Burau van-dijk, Chl Databas ( chl). Suggstd Radings: Rinrt, Chap. 3; Sawyr & Sprinkl, Chap. 4. 5

+ f. e f. Ch. 8 Inflation, Interest Rates & FX Rates. Purchasing Power Parity. Purchasing Power Parity

+ f. e f. Ch. 8 Inflation, Interest Rates & FX Rates. Purchasing Power Parity. Purchasing Power Parity Ch. 8 Inlation, Intrst Rats & FX Rats Topics Purchasing Powr Parity Intrnational Fishr Ect Purchasing Powr Parity Purchasing Powr Parity (PPP: Th purchasing powr o a consumr will b similar whn purchasing

More information

First derivative analysis

First derivative analysis Robrto s Nots on Dirntial Calculus Chaptr 8: Graphical analysis Sction First drivativ analysis What you nd to know alrady: How to us drivativs to idntiy th critical valus o a unction and its trm points

More information

Two Products Manufacturer s Production Decisions with Carbon Constraint

Two Products Manufacturer s Production Decisions with Carbon Constraint Managmnt Scinc and Enginring Vol 7 No 3 pp 3-34 DOI:3968/jms9335X374 ISSN 93-34 [Print] ISSN 93-35X [Onlin] wwwcscanadant wwwcscanadaorg Two Products Manufacturr s Production Dcisions with Carbon Constraint

More information

The Open Economy in the Short Run

The Open Economy in the Short Run Economics 442 Mnzi D. Chinn Spring 208 Social Scincs 748 Univrsity of Wisconsin-Madison Th Opn Economy in th Short Run This st of nots outlins th IS-LM modl of th opn conomy. First, it covrs an accounting

More information

Chapter 13 Aggregate Supply

Chapter 13 Aggregate Supply Chaptr 13 Aggrgat Supply 0 1 Larning Objctivs thr modls of aggrgat supply in which output dpnds positivly on th pric lvl in th short run th short-run tradoff btwn inflation and unmploymnt known as th Phillips

More information

dr Bartłomiej Rokicki Chair of Macroeconomics and International Trade Theory Faculty of Economic Sciences, University of Warsaw

dr Bartłomiej Rokicki Chair of Macroeconomics and International Trade Theory Faculty of Economic Sciences, University of Warsaw dr Bartłomij Rokicki Chair of Macroconomics and Intrnational Trad Thory Faculty of Economic Scincs, Univrsity of Warsaw dr Bartłomij Rokicki Opn Economy Macroconomics Small opn conomy. Main assumptions

More information

Diploma Macro Paper 2

Diploma Macro Paper 2 Diploma Macro Papr 2 Montary Macroconomics Lctur 6 Aggrgat supply and putting AD and AS togthr Mark Hays 1 Exognous: M, G, T, i*, π Goods markt KX and IS (Y, C, I) Mony markt (LM) (i, Y) Labour markt (P,

More information

4. Money cannot be neutral in the short-run the neutrality of money is exclusively a medium run phenomenon.

4. Money cannot be neutral in the short-run the neutrality of money is exclusively a medium run phenomenon. PART I TRUE/FALSE/UNCERTAIN (5 points ach) 1. Lik xpansionary montary policy, xpansionary fiscal policy rturns output in th mdium run to its natural lvl, and incrass prics. Thrfor, fiscal policy is also

More information

Chapter 14 Aggregate Supply and the Short-run Tradeoff Between Inflation and Unemployment

Chapter 14 Aggregate Supply and the Short-run Tradeoff Between Inflation and Unemployment Chaptr 14 Aggrgat Supply and th Short-run Tradoff Btwn Inflation and Unmploymnt Modifid by Yun Wang Eco 3203 Intrmdiat Macroconomics Florida Intrnational Univrsity Summr 2017 2016 Worth Publishrs, all

More information

The van der Waals interaction 1 D. E. Soper 2 University of Oregon 20 April 2012

The van der Waals interaction 1 D. E. Soper 2 University of Oregon 20 April 2012 Th van dr Waals intraction D. E. Sopr 2 Univrsity of Orgon 20 pril 202 Th van dr Waals intraction is discussd in Chaptr 5 of J. J. Sakurai, Modrn Quantum Mchanics. Hr I tak a look at it in a littl mor

More information

Pipe flow friction, small vs. big pipes

Pipe flow friction, small vs. big pipes Friction actor (t/0 t o pip) Friction small vs larg pips J. Chaurtt May 016 It is an intrsting act that riction is highr in small pips than largr pips or th sam vlocity o low and th sam lngth. Friction

More information

Chemical Engineering 412

Chemical Engineering 412 Chical Enginring 4 Introductory Nuclar Enginring Lctur 6 Nuclar Radiation Typs Ky oints Typs of cay Na roprtis athatical scriptions Cavats cay Charts (KNOW HOW TO USE!) Nuclar Equation for cay -Valus for

More information

Calculus Revision A2 Level

Calculus Revision A2 Level alculus Rvision A Lvl Tabl of drivativs a n sin cos tan d an sc n cos sin Fro AS * NB sc cos sc cos hain rul othrwis known as th function of a function or coposit rul. d d Eapl (i) (ii) Obtain th drivativ

More information

On Certain Conditions for Generating Production Functions - II

On Certain Conditions for Generating Production Functions - II J o u r n a l o A c c o u n t i n g a n d M a n a g m n t J A M v o l 7, n o ( 0 7 ) On Crtain Conditions or Gnrating Production Functions - II Catalin Anglo Ioan, Gina Ioan Abstract: Th articl is th scond

More information

Inflation and Unemployment

Inflation and Unemployment C H A P T E R 13 Aggrgat Supply and th Short-run Tradoff Btwn Inflation and Unmploymnt MACROECONOMICS SIXTH EDITION N. GREGORY MANKIW PowrPoint Slids by Ron Cronovich 2008 Worth Publishrs, all rights rsrvd

More information

Part 7: Capacitance And Capacitors

Part 7: Capacitance And Capacitors Part 7: apacitanc And apacitors 7. Elctric harg And Elctric Filds onsidr a pair of flat, conducting plats, arrangd paralll to ach othr (as in figur 7.) and sparatd by an insulator, which may simply b air.

More information

perm4 A cnt 0 for for if A i 1 A i cnt cnt 1 cnt i j. j k. k l. i k. j l. i l

perm4 A cnt 0 for for if A i 1 A i cnt cnt 1 cnt i j. j k. k l. i k. j l. i l h 4D, 4th Rank, Antisytric nsor and th 4D Equivalnt to th Cross Product or Mor Fun with nsors!!! Richard R Shiffan Digital Graphics Assoc 8 Dunkirk Av LA, Ca 95 rrs@isidu his docunt dscribs th four dinsional

More information

Exchange rates in the long run (Purchasing Power Parity: PPP)

Exchange rates in the long run (Purchasing Power Parity: PPP) Exchang rats in th long run (Purchasing Powr Parity: PPP) Jan J. Michalk JJ Michalk Th law of on pric: i for a product i; P i = E N/ * P i Or quivalntly: E N/ = P i / P i Ida: Th sam product should hav

More information

Calculus concepts derivatives

Calculus concepts derivatives All rasonabl fforts hav bn mad to mak sur th nots ar accurat. Th author cannot b hld rsponsibl for any damags arising from th us of ths nots in any fashion. Calculus concpts drivativs Concpts involving

More information

Higher order derivatives

Higher order derivatives Robrto s Nots on Diffrntial Calculus Chaptr 4: Basic diffrntiation ruls Sction 7 Highr ordr drivativs What you nd to know alrady: Basic diffrntiation ruls. What you can larn hr: How to rpat th procss of

More information

Empirical Relationships among Lepton and Quark Masses

Empirical Relationships among Lepton and Quark Masses Epirical Rlationships aong Lpton and Quark Masss Alan Brakston 887 Wst Knickrbockr Driv, Sunnyval, CA 94087 Abstract W driv pirical rlationships aong lntary frion asss basd on rlativly sipl ponntial forula

More information

Elements of Statistical Thermodynamics

Elements of Statistical Thermodynamics 24 Elmnts of Statistical Thrmodynamics Statistical thrmodynamics is a branch of knowldg that has its own postulats and tchniqus. W do not attmpt to giv hr vn an introduction to th fild. In this chaptr,

More information

Gradebook & Midterm & Office Hours

Gradebook & Midterm & Office Hours Your commnts So what do w do whn on of th r's is 0 in th quation GmM(1/r-1/r)? Do w nd to driv all of ths potntial nrgy formulas? I don't undrstand springs This was th first lctur I actually larnd somthing

More information

22/ Breakdown of the Born-Oppenheimer approximation. Selection rules for rotational-vibrational transitions. P, R branches.

22/ Breakdown of the Born-Oppenheimer approximation. Selection rules for rotational-vibrational transitions. P, R branches. Subjct Chmistry Papr No and Titl Modul No and Titl Modul Tag 8/ Physical Spctroscopy / Brakdown of th Born-Oppnhimr approximation. Slction ruls for rotational-vibrational transitions. P, R branchs. CHE_P8_M

More information

Molecules and Covalent Bond

Molecules and Covalent Bond Molculs and ovalnt ond Qustion Papr 1 Lvl IGSE Subjct hmistry (0620/0971) Exam oard ambridg Intrnational Examinations (IE) Topic toms, lmnts and compounds Sub-Topic Molculs and covalnt bonds ooklt Qustion

More information

1 Minimum Cut Problem

1 Minimum Cut Problem CS 6 Lctur 6 Min Cut and argr s Algorithm Scribs: Png Hui How (05), Virginia Dat: May 4, 06 Minimum Cut Problm Today, w introduc th minimum cut problm. This problm has many motivations, on of which coms

More information

The pn junction: 2 Current vs Voltage (IV) characteristics

The pn junction: 2 Current vs Voltage (IV) characteristics Th pn junction: Currnt vs Voltag (V) charactristics Considr a pn junction in quilibrium with no applid xtrnal voltag: o th V E F E F V p-typ Dpltion rgion n-typ Elctron movmnt across th junction: 1. n

More information

3.2.3 Molecules and Covalent Bonds

3.2.3 Molecules and Covalent Bonds Sav My Exams! Th Hom of Rvision For mor awsom GSE and lvl rsourcs, visit us at www.savmyxams.co.uk/ 3.2.3 Molculs and ovalnt onds Qustion Papr Lvl IGSE Subjct hmistry (0620) Exam oard ambridg Intrnational

More information

ph People Grade Level: basic Duration: minutes Setting: classroom or field site

ph People Grade Level: basic Duration: minutes Setting: classroom or field site ph Popl Adaptd from: Whr Ar th Frogs? in Projct WET: Curriculum & Activity Guid. Bozman: Th Watrcours and th Council for Environmntal Education, 1995. ph Grad Lvl: basic Duration: 10 15 minuts Stting:

More information

Search sequence databases 3 10/25/2016

Search sequence databases 3 10/25/2016 Sarch squnc databass 3 10/25/2016 Etrm valu distribution Ø Suppos X is a random variabl with probability dnsity function p(, w sampl a larg numbr S of indpndnt valus of X from this distribution for an

More information

Adding Angular Momenta

Adding Angular Momenta Adding Angular Monta Michal Fowlr, UVa /8/07 Introduction Considr a syst having two angular onta, for xapl an lctron in a hydrogn ato having both orbital angular ontu and spin Th kt spac for a singl angular

More information

Brief Introduction to Statistical Mechanics

Brief Introduction to Statistical Mechanics Brif Introduction to Statistical Mchanics. Purpos: Ths nots ar intndd to provid a vry quick introduction to Statistical Mchanics. Th fild is of cours far mor vast than could b containd in ths fw pags.

More information

Lecture 37 (Schrödinger Equation) Physics Spring 2018 Douglas Fields

Lecture 37 (Schrödinger Equation) Physics Spring 2018 Douglas Fields Lctur 37 (Schrödingr Equation) Physics 6-01 Spring 018 Douglas Filds Rducd Mass OK, so th Bohr modl of th atom givs nrgy lvls: E n 1 k m n 4 But, this has on problm it was dvlopd assuming th acclration

More information

Maxwellian Collisions

Maxwellian Collisions Maxwllian Collisions Maxwll ralizd arly on that th particular typ of collision in which th cross-sction varis at Q rs 1/g offrs drastic siplifications. Intrstingly, this bhavior is physically corrct for

More information

MACROECONOMIC ANALYSIS IN THERMODYNAMIC MODEL REVIEW BY USING FUZZY STATISTICS

MACROECONOMIC ANALYSIS IN THERMODYNAMIC MODEL REVIEW BY USING FUZZY STATISTICS I J A B E R, Vol. 13, No. 2, (2015: 639-648 MACROECONOMIC ANALYSIS IN THERMODYNAMIC MODEL REVIEW BY USING FUZZY STATISTICS Sutanto *, Purnai Widyaningsih * and Ririn Stiyowati Abstract: Application of

More information

Physics. X m (cm)

Physics. X m (cm) Entranc xa 006-007 Physics Duration: hours I- [ pts] An oscillator A chanical oscillator (C) is ford of a solid (S), of ass, attachd to th xtrity A of a horizontal spring of stiffnss (constant) = 80 N/

More information

EXST Regression Techniques Page 1

EXST Regression Techniques Page 1 EXST704 - Rgrssion Tchniqus Pag 1 Masurmnt rrors in X W hav assumd that all variation is in Y. Masurmnt rror in this variabl will not ffct th rsults, as long as thy ar uncorrlatd and unbiasd, sinc thy

More information

Labor Productivity by Country and Good United States Shirts 10 shirts/day 6 shirts/day Food 30 bushels/day 2 bushels/day. 2bushels.

Labor Productivity by Country and Good United States Shirts 10 shirts/day 6 shirts/day Food 30 bushels/day 2 bushels/day. 2bushels. Fall 010 Econ 455 Anwr to Problm St Harvy Lapan 1. Conidr a Ricardian modl o comparativ advantag. Thr ar two countri, th U.S. and. Each country can produc two good, hirt (S and ood (F. Aum th US ha 1000

More information

Matrix Algebra of Regional Input-Output Analysis Tim Tyrrell University of Rhode Island March 16, 2002

Matrix Algebra of Regional Input-Output Analysis Tim Tyrrell University of Rhode Island March 16, 2002 Matrix Algbra of Rgional nput-output Analsis i rrll nivrsit of Rhod sland March 16, 2002 his not was writtn in ordr to clarif th calculations and assuptions ad in rgional input-output analsis that lad

More information

4 x 4, and. where x is Town Square

4 x 4, and. where x is Town Square Accumulation and Population Dnsity E. A city locatd along a straight highway has a population whos dnsity can b approimatd by th function p 5 4 th distanc from th town squar, masurd in mils, whr 4 4, and

More information

CS 361 Meeting 12 10/3/18

CS 361 Meeting 12 10/3/18 CS 36 Mting 2 /3/8 Announcmnts. Homwork 4 is du Friday. If Friday is Mountain Day, homwork should b turnd in at my offic or th dpartmnt offic bfor 4. 2. Homwork 5 will b availabl ovr th wknd. 3. Our midtrm

More information

Unit 7 Charge-to-mass ratio of the electron

Unit 7 Charge-to-mass ratio of the electron Unit 7 Charg-to-ass ratio of th lctron Kywords: J. J. Thoson, Lorntz Forc, Magntic Filds Objctiv: Obsrv th rsults of lctron ba influncd by th agntic fild and calculat th charg-to-ass ratio of th lctron.

More information

Chemistry 342 Spring, The Hydrogen Atom.

Chemistry 342 Spring, The Hydrogen Atom. Th Hyrogn Ato. Th quation. Th first quation w want to sov is φ This quation is of faiiar for; rca that for th fr partic, w ha ψ x for which th soution is Sinc k ψ ψ(x) a cos kx a / k sin kx ± ix cos x

More information

Ch. 24 Molecular Reaction Dynamics 1. Collision Theory

Ch. 24 Molecular Reaction Dynamics 1. Collision Theory Ch. 4 Molcular Raction Dynamics 1. Collision Thory Lctur 16. Diffusion-Controlld Raction 3. Th Matrial Balanc Equation 4. Transition Stat Thory: Th Eyring Equation 5. Transition Stat Thory: Thrmodynamic

More information

Problem Set 6 Solutions

Problem Set 6 Solutions 6.04/18.06J Mathmatics for Computr Scinc March 15, 005 Srini Dvadas and Eric Lhman Problm St 6 Solutions Du: Monday, March 8 at 9 PM in Room 3-044 Problm 1. Sammy th Shark is a financial srvic providr

More information

A Dual De nition for the Factor Content of Trade and its E ect on Factor Rewards in US Manufacturing Sector

A Dual De nition for the Factor Content of Trade and its E ect on Factor Rewards in US Manufacturing Sector A Dual D nition for th Factor Contnt of Trad and its E ct on Factor Rwards in US Manufacturing Sctor Aglos Dlis Thofanis P Mamunas 2 Univrsity of Nottingham Univrsity of Cyprus Abstract In this papr, rst

More information

a 1and x is any real number.

a 1and x is any real number. Calcls Nots Eponnts an Logarithms Eponntial Fnction: Has th form y a, whr a 0, a an is any ral nmbr. Graph y, Graph y ln y y Th Natral Bas (Elr s nmbr): An irrational nmbr, symboliz by th lttr, appars

More information

Quasi-Harmonic Phonon Dynamics of Potassium Fluoride

Quasi-Harmonic Phonon Dynamics of Potassium Fluoride Intrnational Journal o Enginring Rsarch and Dvlopnt -ISSN: 78-67X, p-issn: 78-8X Volu, Issu 8 (Sptbr ), PP. 5-56 Quasi-Haronic Phonon Dynaics o Potassiu Fluorid D.M Srivastava,.K. Yadav and S.K. Singh

More information

A Propagating Wave Packet Group Velocity Dispersion

A Propagating Wave Packet Group Velocity Dispersion Lctur 8 Phys 375 A Propagating Wav Packt Group Vlocity Disprsion Ovrviw and Motivation: In th last lctur w lookd at a localizd solution t) to th 1D fr-particl Schrödingr quation (SE) that corrsponds to

More information

CO-ORDINATION OF FAST NUMERICAL RELAYS AND CURRENT TRANSFORMERS OVERDIMENSIONING FACTORS AND INFLUENCING PARAMETERS

CO-ORDINATION OF FAST NUMERICAL RELAYS AND CURRENT TRANSFORMERS OVERDIMENSIONING FACTORS AND INFLUENCING PARAMETERS CO-ORDINATION OF FAST NUMERICAL RELAYS AND CURRENT TRANSFORMERS OVERDIMENSIONING FACTORS AND INFLUENCING PARAMETERS Stig Holst ABB Automation Products Swdn Bapuji S Palki ABB Utilitis India This papr rports

More information

Some Inequalities for General Sum Connectivity Index

Some Inequalities for General Sum Connectivity Index MATCH Counications in Mathatical and in Coputr Chistry MATCH Coun. Math. Coput. Ch. 79 (2018) 477-489 ISSN 0340-6253 So Inqualitis for Gnral Su Connctivity Indx I. Ž. Milovanović, E. I. Milovanović, M.

More information

Random Process Part 1

Random Process Part 1 Random Procss Part A random procss t (, ζ is a signal or wavform in tim. t : tim ζ : outcom in th sampl spac Each tim w rapat th xprimnt, a nw wavform is gnratd. ( W will adopt t for short. Tim sampls

More information

Figure 1: Closed surface, surface with boundary, or not a surface?

Figure 1: Closed surface, surface with boundary, or not a surface? QUESTION 1 (10 marks) Two o th topological spacs shown in Figur 1 ar closd suracs, two ar suracs with boundary, and two ar not suracs. Dtrmin which is which. You ar not rquird to justiy your answr, but,

More information

Design Guidelines for Quartz Crystal Oscillators. R 1 Motional Resistance L 1 Motional Inductance C 1 Motional Capacitance C 0 Shunt Capacitance

Design Guidelines for Quartz Crystal Oscillators. R 1 Motional Resistance L 1 Motional Inductance C 1 Motional Capacitance C 0 Shunt Capacitance TECHNICAL NTE 30 Dsign Guidlins for Quartz Crystal scillators Introduction A CMS Pirc oscillator circuit is wll known and is widly usd for its xcllnt frquncy stability and th wid rang of frquncis ovr which

More information

Unit Workbook 1 - Level 5 ENG U49 Lean Manufacturing 2018 UniCourse Ltd. All Rights Reserved. Sample

Unit Workbook 1 - Level 5 ENG U49 Lean Manufacturing 2018 UniCourse Ltd. All Rights Reserved. Sample Parson BTEC Lvl 5 Highr Nationals in Enginring (RQF) Unit 49: Lan Manufacturing Unit Workbook 1 in a sris of 4 for this unit Larning Outco 1 Coon Princis of Lan Manufacturing Pag 1 of 12 1.1 Lan Manufacturing

More information

ME 300 Exam 1 October 9, :30 p.m. to 7:30 p.m.

ME 300 Exam 1 October 9, :30 p.m. to 7:30 p.m. CIRCLE YOUR LECTURE BELOW: First Na Last Na 10:0 a.. 1:0 p.. Naik Gor ME 00 Exa 1 Octobr 9, 014 6:0 p.. to 7:0 p.. INSTRUCTIONS 1. This is a closd book and closd nots xaination. You ar providd with an

More information

A central nucleus. Protons have a positive charge Electrons have a negative charge

A central nucleus. Protons have a positive charge Electrons have a negative charge Atomic Structur Lss than ninty yars ago scintists blivd that atoms wr tiny solid sphrs lik minut snookr balls. Sinc thn it has bn discovrd that atoms ar not compltly solid but hav innr and outr parts.

More information

(1) Then we could wave our hands over this and it would become:

(1) Then we could wave our hands over this and it would become: MAT* K285 Spring 28 Anthony Bnoit 4/17/28 Wk 12: Laplac Tranform Rading: Kohlr & Johnon, Chaptr 5 to p. 35 HW: 5.1: 3, 7, 1*, 19 5.2: 1, 5*, 13*, 19, 45* 5.3: 1, 11*, 19 * Pla writ-up th problm natly and

More information

Collisions between electrons and ions

Collisions between electrons and ions DRAFT 1 Collisions btwn lctrons and ions Flix I. Parra Rudolf Pirls Cntr for Thortical Physics, Unirsity of Oxford, Oxford OX1 NP, UK This rsion is of 8 May 217 1. Introduction Th Fokkr-Planck collision

More information

1.2 Faraday s law A changing magnetic field induces an electric field. Their relation is given by:

1.2 Faraday s law A changing magnetic field induces an electric field. Their relation is given by: Elctromagntic Induction. Lorntz forc on moving charg Point charg moving at vlocity v, F qv B () For a sction of lctric currnt I in a thin wir dl is Idl, th forc is df Idl B () Elctromotiv forc f s any

More information

The following information relates to Questions 1 to 4:

The following information relates to Questions 1 to 4: Th following information rlats to Qustions 1 to 4: QUESTIN 1 Th lctrolyt usd in this ful cll is D watr carbonat ions hydrogn ions hydroxid ions QUESTIN 2 Th product formd in th ful cll is D hydrogn gas

More information

Will the true marginal investor please stand up?: Asset prices with immutable security trading by investors. Peter L. Swan

Will the true marginal investor please stand up?: Asset prices with immutable security trading by investors. Peter L. Swan Will th tru arginal invstor plas stand up?: Asst prics with iutabl scurity trading by invstors by Ptr L. Swan School of Businss, Univrsity of Sydny Octobr 4, 2001 (Prliinary draft, conts wlco) ABSTRACT

More information

Content Skills Assessments Lessons. Identify, classify, and apply properties of negative and positive angles.

Content Skills Assessments Lessons. Identify, classify, and apply properties of negative and positive angles. Tachr: CORE TRIGONOMETRY Yar: 2012-13 Cours: TRIGONOMETRY Month: All Months S p t m b r Angls Essntial Qustions Can I idntify draw ngativ positiv angls in stard position? Do I hav a working knowldg of

More information

Linear-Phase FIR Transfer Functions. Functions. Functions. Functions. Functions. Functions. Let

Linear-Phase FIR Transfer Functions. Functions. Functions. Functions. Functions. Functions. Let It is impossibl to dsign an IIR transfr function with an xact linar-phas It is always possibl to dsign an FIR transfr function with an xact linar-phas rspons W now dvlop th forms of th linarphas FIR transfr

More information

Partial Derivatives: Suppose that z = f(x, y) is a function of two variables.

Partial Derivatives: Suppose that z = f(x, y) is a function of two variables. Chaptr Functions o Two Variabls Applid Calculus 61 Sction : Calculus o Functions o Two Variabls Now that ou hav som amiliarit with unctions o two variabls it s tim to start appling calculus to hlp us solv

More information

Differentiation of Exponential Functions

Differentiation of Exponential Functions Calculus Modul C Diffrntiation of Eponntial Functions Copyright This publication Th Northrn Albrta Institut of Tchnology 007. All Rights Rsrvd. LAST REVISED March, 009 Introduction to Diffrntiation of

More information

TP A.31 The physics of squirt

TP A.31 The physics of squirt thnial proof TP A. Th physis of squirt supporting: Th Illustratd Prinipls of Pool and Billiards http://illiards.olostat.du y David G. Aliator, PhD, PE ("Dr. Dav") thnial proof originally postd: 8//7 last

More information

A Prey-Predator Model with an Alternative Food for the Predator, Harvesting of Both the Species and with A Gestation Period for Interaction

A Prey-Predator Model with an Alternative Food for the Predator, Harvesting of Both the Species and with A Gestation Period for Interaction Int. J. Opn Problms Compt. Math., Vol., o., Jun 008 A Pry-Prdator Modl with an Altrnativ Food for th Prdator, Harvsting of Both th Spcis and with A Gstation Priod for Intraction K. L. arayan and. CH. P.

More information

Need to understand interaction of macroscopic measures

Need to understand interaction of macroscopic measures CE 322 Transportation Enginring Dr. Ahmd Abdl-Rahim, h. D.,.E. Nd to undrstand intraction o macroscopic masurs Spd vs Dnsity Flow vs Dnsity Spd vs Flow Equation 5.14 hlps gnraliz Thr ar svral dirnt orms

More information

The Frequency Response of a Quarter-Wave Matching Network

The Frequency Response of a Quarter-Wave Matching Network 4/1/29 Th Frquncy Rsons o a Quartr 1/9 Th Frquncy Rsons o a Quartr-Wav Matchg Ntwork Q: You hav onc aga rovidd us with conusg and rhas uslss ormation. Th quartr-wav matchg ntwork has an xact SFG o: a Τ

More information

A. Limits and Horizontal Asymptotes ( ) f x f x. f x. x "±# ( ).

A. Limits and Horizontal Asymptotes ( ) f x f x. f x. x ±# ( ). A. Limits and Horizontal Asymptots What you ar finding: You can b askd to find lim x "a H.A.) problm is asking you find lim x "# and lim x "$#. or lim x "±#. Typically, a horizontal asymptot algbraically,

More information

What are those βs anyway? Understanding Design Matrix & Odds ratios

What are those βs anyway? Understanding Design Matrix & Odds ratios Ral paramtr stimat WILD 750 - Wildlif Population Analysis of 6 What ar thos βs anyway? Undrsting Dsign Matrix & Odds ratios Rfrncs Hosmr D.W.. Lmshow. 000. Applid logistic rgrssion. John Wily & ons Inc.

More information

HIGH-ENERGY EMISSION FROM THE PROMPT GAMMA-RAY BURST Dafne Guetta 1 and Jonathan Granot 2

HIGH-ENERGY EMISSION FROM THE PROMPT GAMMA-RAY BURST Dafne Guetta 1 and Jonathan Granot 2 Th Astrophysical Journal, 585:885 889, 2003 March 10 # 2003. Th Arican Astronoical Socity. All rights rsrvd. Printd in U.S.A. HIGH-ENERGY EMISSION FROM THE PROMPT GAMMA-RAY BURST Dafn Gutta 1 and Jonathan

More information

General Notes About 2007 AP Physics Scoring Guidelines

General Notes About 2007 AP Physics Scoring Guidelines AP PHYSICS C: ELECTRICITY AND MAGNETISM 2007 SCORING GUIDELINES Gnral Nots About 2007 AP Physics Scoring Guidlins 1. Th solutions contain th most common mthod of solving th fr-rspons qustions and th allocation

More information

8 Equilibrium Analysis in a Pure Exchange Model

8 Equilibrium Analysis in a Pure Exchange Model 8 Equilibrium Analysis in a Pur Exchang Modl So far w hav only discussd dcision thory. That is, w hav lookd at consumr choic problms on th form s.t. p 1 x 1 + p 2 x 2 m: max u (x 1 ; x 2 ) x 1 ;x 2 Th

More information

First order differential equation Linear equation; Method of integrating factors

First order differential equation Linear equation; Method of integrating factors First orr iffrntial quation Linar quation; Mtho of intgrating factors Exampl 1: Rwrit th lft han si as th rivativ of th prouct of y an som function by prouct rul irctly. Solving th first orr iffrntial

More information

Answer Homework 5 PHA5127 Fall 1999 Jeff Stark

Answer Homework 5 PHA5127 Fall 1999 Jeff Stark Answr omwork 5 PA527 Fall 999 Jff Stark A patint is bing tratd with Drug X in a clinical stting. Upon admiion, an IV bolus dos of 000mg was givn which yildd an initial concntration of 5.56 µg/ml. A fw

More information

10. Limits involving infinity

10. Limits involving infinity . Limits involving infinity It is known from th it ruls for fundamntal arithmtic oprations (+,-,, ) that if two functions hav finit its at a (finit or infinit) point, that is, thy ar convrgnt, th it of

More information

NEW APPLICATIONS OF THE ABEL-LIOUVILLE FORMULA

NEW APPLICATIONS OF THE ABEL-LIOUVILLE FORMULA NE APPLICATIONS OF THE ABEL-LIOUVILLE FORMULA Mirca I CÎRNU Ph Dp o Mathmatics III Faculty o Applid Scincs Univrsity Polithnica o Bucharst Cirnumirca @yahoocom Abstract In a rcnt papr [] 5 th indinit intgrals

More information

Magnetic vector potential. Antonio Jose Saraiva ; -- Electric current; -- Magnetic momentum; R Radius.

Magnetic vector potential. Antonio Jose Saraiva ; -- Electric current; -- Magnetic momentum; R Radius. Magnti vtor potntial Antonio Jos araiva ajps@hotail.o ; ajps137@gail.o A I.R A Magnti vtor potntial; -- auu prability; I -- ltri urrnt; -- Magnti ontu; R Radius. un agnti ronntion un tru surfa tpratur

More information

Hydrogen Atom and One Electron Ions

Hydrogen Atom and One Electron Ions Hydrogn Atom and On Elctron Ions Th Schrödingr quation for this two-body problm starts out th sam as th gnral two-body Schrödingr quation. First w sparat out th motion of th cntr of mass. Th intrnal potntial

More information

UNTYPED LAMBDA CALCULUS (II)

UNTYPED LAMBDA CALCULUS (II) 1 UNTYPED LAMBDA CALCULUS (II) RECALL: CALL-BY-VALUE O.S. Basic rul Sarch ruls: (\x.) v [v/x] 1 1 1 1 v v CALL-BY-VALUE EVALUATION EXAMPLE (\x. x x) (\y. y) x x [\y. y / x] = (\y. y) (\y. y) y [\y. y /

More information

Classical Magnetic Dipole

Classical Magnetic Dipole Lctur 18 1 Classical Magntic Dipol In gnral, a particl of mass m and charg q (not ncssarily a point charg), w hav q g L m whr g is calld th gyromagntic ratio, which accounts for th ffcts of non-point charg

More information

Math 34A. Final Review

Math 34A. Final Review Math A Final Rviw 1) Us th graph of y10 to find approimat valus: a) 50 0. b) y (0.65) solution for part a) first writ an quation: 50 0. now tak th logarithm of both sids: log() log(50 0. ) pand th right

More information

VALUING SURRENDER OPTIONS IN KOREAN INTEREST INDEXED ANNUITIES

VALUING SURRENDER OPTIONS IN KOREAN INTEREST INDEXED ANNUITIES VALUING SURRENDER OPTIONS IN KOREAN INTEREST INDEXED ANNUITIES Changi Kim* * Dr. Changi Kim is Lcturr at Actuarial Studis Faculty of Commrc & Economics Th Univrsity of Nw South Wals Sydny NSW 2052 Australia.

More information

Physics in Entertainment and the Arts

Physics in Entertainment and the Arts Physics in Entrtainmnt and th Arts Chaptr VI Arithmtic o Wavs Two or mor wavs can coxist in a mdium without having any ct on ach othr Th amplitud o th combind wav at any point in th mdium is just th sum

More information

Extraction of Doping Density Distributions from C-V Curves

Extraction of Doping Density Distributions from C-V Curves Extraction of Doping Dnsity Distributions from C-V Curvs Hartmut F.-W. Sadrozinski SCIPP, Univ. California Santa Cruz, Santa Cruz, CA 9564 USA 1. Connction btwn C, N, V Start with Poisson quation d V =

More information

Give the letter that represents an atom (6) (b) Atoms of A and D combine to form a compound containing covalent bonds.

Give the letter that represents an atom (6) (b) Atoms of A and D combine to form a compound containing covalent bonds. 1 Th diagram shows th lctronic configurations of six diffrnt atoms. A B C D E F (a) You may us th Priodic Tabl on pag 2 to hlp you answr this qustion. Answr ach part by writing on of th lttrs A, B, C,

More information

Problem Set 4 Solutions Distributed: February 26, 2016 Due: March 4, 2016

Problem Set 4 Solutions Distributed: February 26, 2016 Due: March 4, 2016 Probl St 4 Solutions Distributd: Fbruary 6, 06 Du: March 4, 06 McQuarri Probls 5-9 Ovrlay th two plots using Excl or Mathatica. S additional conts blow. Th final rsult of Exapl 5-3 dfins th forc constant

More information

Chapter 8: Electron Configurations and Periodicity

Chapter 8: Electron Configurations and Periodicity Elctron Spin & th Pauli Exclusion Principl Chaptr 8: Elctron Configurations and Priodicity 3 quantum numbrs (n, l, ml) dfin th nrgy, siz, shap, and spatial orintation of ach atomic orbital. To xplain how

More information

Title: Vibrational structure of electronic transition

Title: Vibrational structure of electronic transition Titl: Vibrational structur of lctronic transition Pag- Th band spctrum sn in th Ultra-Violt (UV) and visibl (VIS) rgions of th lctromagntic spctrum can not intrprtd as vibrational and rotational spctrum

More information

EEO 401 Digital Signal Processing Prof. Mark Fowler

EEO 401 Digital Signal Processing Prof. Mark Fowler EEO 401 Digital Signal Procssing Prof. Mark Fowlr Dtails of th ot St #19 Rading Assignmnt: Sct. 7.1.2, 7.1.3, & 7.2 of Proakis & Manolakis Dfinition of th So Givn signal data points x[n] for n = 0,, -1

More information

Economics 201b Spring 2010 Solutions to Problem Set 3 John Zhu

Economics 201b Spring 2010 Solutions to Problem Set 3 John Zhu Economics 20b Spring 200 Solutions to Problm St 3 John Zhu. Not in th 200 vrsion of Profssor Andrson s ctur 4 Nots, th charactrization of th firm in a Robinson Cruso conomy is that it maximizs profit ovr

More information

REGISTER!!! The Farmer and the Seeds (a parable of scientific reasoning) Class Updates. The Farmer and the Seeds. The Farmer and the Seeds

REGISTER!!! The Farmer and the Seeds (a parable of scientific reasoning) Class Updates. The Farmer and the Seeds. The Farmer and the Seeds How dos light intract with mattr? And what dos (this say about) mattr? REGISTER!!! If Schrödingr s Cat walks into a forst, and no on is around to obsrv it, is h rally in th forst? sourc unknown Phys 1010

More information

Network Externalities, Competition, and Trade: East Asian Perspectives

Network Externalities, Competition, and Trade: East Asian Perspectives Ntwork Extrnalitis, Comptition, and Trad: East Asian Prspctivs Toru Kikuchi (kikuchi@con.kob-u.ac.jp) 1 and Chiharu Kobayashi (ckobayas@mail.doshisha.ac.jp) Abstract Thr ar larg dviations in accss to tlcommunications

More information

Addition of angular momentum

Addition of angular momentum Addition of angular momntum April, 07 Oftn w nd to combin diffrnt sourcs of angular momntum to charactriz th total angular momntum of a systm, or to divid th total angular momntum into parts to valuat

More information

ES 330 Electronics II Homework # 9 (Fall 2017 Due Monday, December 4, 2017)

ES 330 Electronics II Homework # 9 (Fall 2017 Due Monday, December 4, 2017) Pag1 Na OLUTON E 330 Elctronics Howork # 9 (Fall 017 Du Monday, Dcbr 4, 017) Probl 1 (14 points) Dsign a MO diffrntial aplifir illsuratd in th schatic blow to oprat at O = 0.5 olt with a transconductanc

More information

PROBLEM SET Problem 1.

PROBLEM SET Problem 1. PROLEM SET 1 PROFESSOR PETER JOHNSTONE 1. Problm 1. 1.1. Th catgory Mat L. OK, I m not amiliar with th trminology o partially orr sts, so lt s go ovr that irst. Dinition 1.1. partial orr is a binary rlation

More information

CS 491 G Combinatorial Optimization

CS 491 G Combinatorial Optimization CS 49 G Cobinatorial Optiization Lctur Nots Junhui Jia. Maiu Flow Probls Now lt us iscuss or tails on aiu low probls. Thor. A asibl low is aiu i an only i thr is no -augnting path. Proo: Lt P = A asibl

More information

5.80 Small-Molecule Spectroscopy and Dynamics

5.80 Small-Molecule Spectroscopy and Dynamics MIT OpnCoursWar http://ocw.mit.du 5.80 Small-Molcul Spctroscopy and Dynamics Fall 008 For information about citing ths matrials or our Trms of Us, visit: http://ocw.mit.du/trms. Lctur # 3 Supplmnt Contnts

More information