The safeguard clause, asymmetric information, and endogenous protection.

Size: px
Start display at page:

Download "The safeguard clause, asymmetric information, and endogenous protection."

Transcription

1 T saguard claus, asymmtric inormation, and ndognous protction. ilipp Kolr and Mical O. Moor, Rvisd Marc ABSTRACT: Wn imports surg, govrnmnts otn ac a conlict among political objctivs. Ty sk simultanously to satisy protctionist prssurs troug incrasd taris, induc adjustmnt to orign comptition, and minimiz consumr costs o protction. T WTO s saguard claus can b viwd as a way to rsolv tis political objctivs conlict sinc it allows govrnmnts to or an implicit contract to protctd industris in ordr to induc tm to adjust. In tis papr, w sow tat wit asymmtric inormation about costs, protctd industris bav stratgically wic lads to undradjustmnt. T saguard claus tror cannot optimally rsolv t conlict among domstic political objctivs. Kywords: adjustmnt policy, asymmtric inormation, objctivs conlicts, protctionism, saguard claus. JEL Classiication: F13, L51 Dpartmnt o Economics - Univrsity o Montpllir - Franc - pkol@sc.univ-montp1.r. Dpartmnt o Economics / T Elliott Scool - Gorg Wasington Univrsity - Wasington DC USA - mom@gwu.du. (Corrsponding autor). W would lik to tank an anonymous rr or vry usul commnts on an arlir drat. Any rmaining rrors ar our own. 1

2 1. Introduction. Wnvr a country's pattrn o comparativ advantags sits, som industris incur losss. Economists av long argud tat it is nontlss gnrally optimal to lt t markt play its rol o rsourc allocation sinc r trad usually crats mor aggrgat gains tan losss vn i domstic irms ar orcd itr to lowr costs to rmain conomically viabl or lav t markt Wil r trad s supriority is widly accptd by conomists, slctiv protction masurs rmain among t most crisd tools usd by govrnmnts to rac tir political objctivs. olicy-makrs otn rcogniz opn trad s consumr bnits but l ty cannot ignor t comptitiv prssurs placd upon domstic import-compting industris. Govrnmnts tror av justiid protction by claiming tat domstic industris can rgain intrnational comptitivnss i tmporarily protctd rom orign comptition. On o t prim mans by wic tis tmporary protction may tak plac is t so-calld saguard claus. In tis papr, w analyz t saguard claus and argu tat tis protctionist outcom ariss out o a govrnmnt s attmpt to rsolv a conlict among domstic political objctivs. On on and, t govrnmnt sks to protct prssur groups. On t otr and, it wants to promot ovrall wlar. Ts two objctivs ar otn in conlict, spcially in trad policy. T saguard claus givs a govrnmnt t mans to try to rsolv tis conlict. T saguard s claus us also sows t irarcy tat inluncs trad policy coics --- altoug satisying political prssurs rom import-compting industris is paramount, t cts o protction on domstic conomic icincy and consumrs is not ignord. W sow tat t rsolution o t objctivs conlict troug t saguard mcanism is undrcut wit asymmtric inormation about costs and adjustmnt ort sinc it rsults in undr-adjustmnt o ig-cost industris and tus maks t saguard claus inicint. 2

3 T institutional justiication or t saguard claus can b ound in Articl XIX o t GATT. 1 Undr tis arrangmnt, r-stablisd in t WTO systm, a country may rais taris or a priod o up to our yars to rmdy or prvnt srious injury. Undr t nw WTO Saguard Agrmnt, suc a masur may b xtndd only i tr is vidnc tat t industry is adjusting. 2 Tus, t WTO signatoris av rcognizd tat adjustmnt to orign comptition is particularly important to t unctioning o t saguard mcanism. olitical rality and xprinc owvr sow us tat protctd industris sk gnrally to maintain tir "tmporary" protction. Wil lowr costs incras icincy and nc proits, ty also rais t cancs tat protction will b subsquntly lowrd. Tis raiss t so-calld "ratct ct" problm o trad protction --- bcoming mor proitabl today jopardizs utur protction. Tis problm is urtr xacrbatd bcaus it may b diicult or govrnmnts to monitor accuratly ow muc ort as bn xpndd in adjusting to intrnational comptition. Rsarcrs av also pointd out tat govrnmnts av mixd incntivs wn acing a domstic industry asking or protction. A govrnmnt wos objctiv unction includs rdistributionist goals along wit concrns about conomic icincy will ncountr problms in optimal implmntation o a tari policy. Staigr and Tabllini (1987) or xampl study t trad policy coic o a govrnmnt tat cars about incom rdistribution among workrs and acs an import surg in an import-compting sctor. Staigr and Tabllini point out tat t govrnmnt s concrn about incom rdistribution maks a r trad commitmnt not crdibl. Traditional trad tory prdicts tat i t govrnmnt commits to a r trad rgim, workrs lav t import compting sctor i t wag alls suicintly. Howvr, i workrs in t import compting sctor ully anticipat a utur tari (aimd to improv t incom rdistribution by raising t wag in tis sctor), a r trad commitmnt in t ac o alling import prics is not crdibl 3

4 givn t incom rdistribution concrns o policy makrs. Staigr and Tabllini trby raisd a tim-consistncy conlict or policy-makrs arising out o compting political concrns: conomic bnits rom r trad (along wit optimal allocation o labor among sctors) conlict wit t political rturn rom protction (arising out o incom rdistribution troug taris). Tornll (1991) xamins wtr spciic protctionist tools can b usd to liminat t Staigr and Tabllini tim-inconsistncy problm. Invstmnt-contingnt subsidis grantd atr adjustmnt as takn plac but providd bor t adjustmnt procss troug a bailout mcanism can b tailord to rsolv t tim-inconsistncy problm but would b so costly or t industry tat ty rarly would b cosn. Otr works av ocusd on t political motivation or trad protction and its wlar consquncs. T political gnsis o protction masurs as bn xamind by Hillman (1982) and urtr dvlopd by Cassing and Hillman (1986), van Long and Vousdn (1991), Brainard and Vrdir (1994, 1997), and Grossman and Hlpman (1994) among otrs. 3 A rqunt point o tis litratur is tat political goals (itr maximizing political support or maximizing t canc or rlction) ratr tan conomic concrns may gnrat motivs or protction. Brainard and Vrdir (1997) sow t inctivnss o adjustmnt goals in a dynamic ramwork. rotction coms rom t intrinsic inconsistncy wn policy makr's dcisions ar politically biasd. T domstic industry uss rsourcs to lobby instad o using ts rsourcs to inanc its adjustmnt activitis. Bcaus currnt adjustmnt is not undrtakn, utur potntial protction brings igr gains to t import-compting industry and tus bcoms mor proitabl compard wit utur adjustmnt. Onc initial protction as bn triggrd, undr-adjustmnt may prsist until t industry inally collapss as is as bn sown in t static ramwork o Cassing and Hillman (1986). 4

5 Tis undr-adjustmnt problm is spcially rlvant wit t saguard claus sinc it is xplicitly dsignd to lp industris rspond to incrasd import comptition. 4 In t saguard institutional ramwork, t govrnmnt wic implmnts t protction acs a dilmma --- t govrnmnt must simultanously provid protction rom orign imports and induc t industry to adopt an optimal lvl o adjustmnt. As Jackson (1993, pp ) points out: "[I] adjustmnt truly is t rational or tmporary saguard actions to limit imports, tn it ollows tat it migt b appropriat or t govrnmnt to dmand an ctiv adjustmnt program rom t industry concrnd, and/or to tailor govrnmnt policis (including dirct or tax aids) to ncourag and assist suc adjustmnt." Tus, a saguard policy sould b basd on a contractual rlationsip: t domstic industry tat bnits rom trad protction as obligations to adjustmnt. In tis papr, w analyz a saguard mcanism wit costly adjustmnt wn trad policy dcisions ar motivatd by bot conomic and political cts. W build on Staigr and Tabllini's work and assum tat t govrnmnt knows tat it acs stratgic bavior by t importcompting industry. W also ollow t spirit o Grossman and Hlpman (1994), among otrs, by allowing t govrnmnt to maximiz a wigtd avrag o domstic consumr and producr groups. In our ramwork, i t industry knows tat t govrnmnt uss protction to aciv political objctivs, it will try to manipulat t protction procss in ordr to gt mor protction tan optimal rom t govrnmnt s point o viw. Wit complt inormation, t industry cannot bav stratgically. T govrnmnt sts t saguard tari suc tat t industry's protction-gnratd proit just quals its adjustmnt cost wil t optimal lvl o adjustmnt ort is suc tat t marginal incras o t adjustmnt cost quals t marginal incras o proit. Tis outcom acivs t igst possibl 5

6 consumr surplus consistnt wit a nwly-comptitiv domstic industry. T complt inormation bncmark allows t govrnmnt to comput t wigt assignd to t prssur group in t asymmtric inormation contxt. T wigt is t political sadow pric associatd wit t constraint o non-ngativ domstic industry proits in t complt inormation contxt. I t irm as an unobsrvabl cost structur and adjustmnt ort, t govrnmnt is abl only to obsrv t ralization o t domstic industry s post-protction proits. 5 T industry will us t paramtrs o t govrnmnt protction dcision to maximiz its protction rnt. I t industry as low costs, tn it as an incntiv to misrport its cost structur to obtain a igr tari bcaus it knows tat a ig-cost industry nds t ig protction to inanc its adjustmnt ort. In tis contxt, t protctd industry acts stratgically as a Stacklbrg ladr vis-à-vis t govrnmnt. Bcaus suc stratgic bavior lowrs govrnmnt wlar troug t burdn placd on consumrs, t govrnmnt must try to rvrs t rols in tat gam by using an incntivcompatibl saguard mcanism. Tis protction scm is implmntd by using a govrnmntproposd implicit contract tat stipulats tat protction is maintaind i t protctd industris bcom proitabl. Howvr, t saguard tari ails to ully rsolv t conlicts btwn consumr and producr intrsts sinc sub-optimal adjustmnt will tak plac undr asymmtric inormation. 6 T papr is organizd as ollows. In Sction 2, w introduc t modl, analyz a complt inormation witout domstic industry stratgic bavior, and comput t wigt assignd to t protction rnt o t prssur group in t asymmtric inormation contxt. In Sction 3, w driv t optimal incntiv-compatibl implicit protction contract proposd by t govrnmnt to t domstic industry wn t lattr bavs stratgically in t contxt o 6

7 asymmtric inormation. Concluding rmarks ar containd in Sction Evaluating t political objctivs conlict wit ull inormation. In tis sction, w valuat t political objctivs conlict wit ull inormation. Wn stting t lvl o protction, w assum tat t govrnmnt must considr t impact on two distinct ntitis: consumrs and import-compting irms. T govrnmnt wants to rciv t igst possibl political rturn rom protcting an industry armd by imports but also sks to minimiz t advrs consumr ct gnratd by protction. Ts two objctivs ar antagonistic but tr xists a irarcy btwn tm. In particular, wil w assum tat t govrnmnt considrs t ct o its trad policy dcision on bot groups, t govrnmnt is assumd to oprat wit t undrlying constraint tat t industry must av a minimum lvl o proits. To aciv its goal, t govrnmnt tis political protction cts to wlar cts. A simpl way to bnit rom t political rturn o protction wil minimizing its political cost (givn by t advrs consumr ct) is to transr t rsponsibility o protction to t importcompting industry. By oring an implicit contract to t protctd industry, t govrnmnt asks it to xrt ort to adapt to orign comptition. Our partial quilibrium ramwork ollows t tory o incntivs in rgulation and procurmnt dvlopd by Laont and Tirol (1993). Tr ar two groups o individuals in t domstic conomy. T prrncs o t ownrs o t import-compting irms ar rprsntd by U, wic quals industry (tari-distortd) rnt. T prrncs o domstic consumrs ar summarizd using an aggrgat utility unction dnotd by V. Total domstic utility unction dnotd by W = U + V. T prctly-comptitiv domstic industry producs a omognous product or t 7

8 domstic markt and is composd o idntical irms, ac o wic as a sunk cost and incrasing marginal cost. W assum tat t sunk cost is suicintly ig to prvnt t ntry o nw domstic irms vn in t prsnc o positiv conomic proits. T conomy is small in intrnational markts so tat orign supply is assumd to b ininitly lastic at t world pric. W also assum tat at tis pric t domstic industry as ngativ proits and tus surs rom srious injury, i.., it ulills t rquirmnts or protction undr t WTO saguard systm. Witout any govrnmnt intrvntion, t domstic industry will considr wtr costly adjustmnt to t orign comptition is in its conomic intrsts. For som rang o domstic cost structurs, costly adjustmnt undr r-trad will maks sns; otrwis, t industry will sut down, trby transrring rsourcs to otr uss and also saving any potntial adjustmnt orts. Howvr, in tis modl, w assum tat political considrations prclud t govrnmnt rom allowing t domstic industry to rciv ngativ proits. Tus, t govrnmnt must implicitly dtrmin a nw domstic pric by imposing a tari troug t saguard claus. 7 W lt ( ) Q dnot t total dmand on t domstic markt. T domstic (tariinclusiv) pric is. T domstic industry supply is givn by q ( ) wil q ( ) rprsnts t domstic xcss dmand or imports. T domstic markt claring condition rquirs tat Q( ) = q ( ) + q ( ). T domstic industry's post-protction proit π ( q ), is a unction o t domstic industry cost typ, t domstic supply q ( ), and t lvl o adjustmnt ort. T adjustmnt cost ( ) K is an incrasing and convx unction o t adjustmnt ort. For simplicity, w assum tat π ( q ), and t adjustmnt cost K( ) ar sparabl. 8

9 Domstic industry rnt U arising rom t saguard policy is dind as t dirnc btwn its tari-distortd proit and t adjustmnt cost incurrd during t protction priod to lowr its production costs: T valu o π ( q ) ( ) ( ) U = π q, K (1), quals post-adjustmnt quantity supplid multiplid by t dirnc btwn t marginal cost (qual to domstic pric or ts prct comptitors) and t avrag total cost: [ ] (, ) (, ) (, ) π q = MC q AC q q (2) W mak t ollowing assumptions about t natur o t proit unction: π > 0, π > 0, π > 0, π < 0, π < 0, π 0, π > 0 (3) q qq q Tus, t domstic industry proit is an incrasing and convx unction o its supply q ( ), an incrasing and concav unction o its adjustmnt ort, and a dcrasing and convx unction o its cost paramtr. In addition, igr ort incrass marginal proit. T consumrs utility unction is givn by t sum o consumr surplus and t rdistributd tari rvnu, wr w is t intrnational pric: V = Q z dz + q ( ) ( ) ( ) (4) T govrnmnt maximizs total domstic utility W wic includs bot consumr and irm wlar. Howvr, t govrnmnt also oprats undr a political constraint. Similar to Staigr and Tabllini (1987), t govrnmnt slcts policis so tat proits ar non-ngativ atr protction. Onc implmntd, protction rmains in ordr to kp uncangd t subsqunt import compting industry ownrs' rnt. In tis cas, t industry will xrt an adjustmnt ort i it is compnsatd by a positiv proit rsulting rom t saguard protction. Tus, W is w 9

10 maximizd subjct to: ( q ) K( ) B( ) π, (5) wr ( ) B is a givn valu assignd to t protction rnt by t govrnmnt. Bcaus adjustmnt ort is inancd by import protction and tat ort is obsrvd by t policy-makr during t adjustmnt priod, t industry is bttr o adopting t rquird lvl o ort wn t govrnmnt commits not to xpropriat t rnt o t irm atr ort as takn plac. I t govrnmnt dos not mak tis commitmnt, t adjustmnt program is not individually rational. T industry will only participat in t program i it is bttr o atr its adjustmnt sinc it knows tat t govrnmnt may gain politically in t adjustmnt procss. In otr words, t gam must b positiv-sum --- t govrnmnt gains politically by inducing t industry to adjust but must sar tat gain in ordr to obtain its coopration. In ordr to maximiz t wlar unction W, t govrnmnt will inanc t industry s optimal adjustmnt ort * by raising t markt pric () wit a tari t(), bot o wic ar unctions o t domstic irm s costs. Wit no iddn action or inormation o t industry, t govrnmnt obsrvs t world pric w, t domstic industry cost typ, t proit π ( q ) and t adjustmnt cost ( ) K. T govrnmnt political coic mrgs rom t solution o t program (1):,, ( 1) Max W = Q, s. t. π ( z) dz + π ( q, ) K( ) + ( ) q ( ) ( q, ) K( ) B( ) w (6) T Lagrangian L associatd wit (1) is: 10

11 Max L = Max Q( z) dz + ( w ) q ( ) + ( + λ) [ π( q, ) K( ) ] λ B( ),, λ,, λ 1 (7) wr λ is t Lagrangian multiplir or t non-ngativ proit constraint T govrnmnt s problm can b sn as maximizing a wigtd avrag o domstic intrsts. In particular, i t constraint is binding (i.., irms mak ngativ proits at world prics), tn λ is positiv and t domstic industry proit rcivs a igr wigt tan domstic consumrs. T solution to (1) rsults in t implicit contract in t complt inormation cas (givn by t valus o *, *, t CI ) and must satisy t ollowing (S Appndix 1 or dtails.): π ( q ( ) ) K( ) *, * = * (8) π ( q ( * ), * ) = K ( * ) (9) t CI q = * w = λ (10) q Ts solutions av asy intrprtations. Exprssion (8) mans tat t pric on t domstic markt as to b raisd so tat t rnt o t protctd industry quals zro. Tis rsults in t lowst possibl pric on consumrs consistnt wit non-ngativ industry proit, i.., B() = 0. Exprssion (9) mans tat adjustmnt is cosn optimally rom t industry s viw --- t marginal ct o adjustmnt ort on proit must qual its marginal cost. Exprssion (10) is t complt inormation tari. It will dpnd on t pric ct on domstic xcss dmand and λ, t political sadow cost o t non-ngativ proit constraint. Exprssion (10) can b rarrangd to sow ow λ, t political sadow cost o protction rlcts 11

12 t incras o ovrall wlar i t tari was lowrd. It allows us to valuat t acutnss o t political objctivs conlict btwn consumrs and producrs, as masurd by t wigt tat t govrnmnt givs to t domstic industry wn stting its trad policy: ( w *) η ε λ ( w *) = = β (10 ) * * ξ q q q q wr β = ξ = η = ε =,,, (11) q q q q Exprssion (10 ) sows tat λ, t political sadow cost o protction can b brokn into two distinct cts: a pric ct and an lasticity and markt sar ct. First, bot vrsions o (10 ) contain ( w *)/* wic is simply t prcntag drop in t domstic pric i t taris wr rmovd. In otr words, it is t dirct opportunity cost o t pric distortion. T lowr (igr) is t world (tari-distortd) pric, t igr sadow pric o protction. T scond st o lmnts involvs pric lasticitis and markt sar cts. T irst vrsion sows tat t mor lastic import dmand η is, t igr will b t political sadow pric. Convrsly, t lowr t domstic markt sar q /q, t largr λ will b. T scond vrsion sows tat domstic rspons to pric cangs and orign supply cangs ar also important. In particular, a ig valu or domstic pric lasticity ε translats into a ig valu or λ as dos a larg incras in domstic supply as imports all. As sown abov, as long as t govrnmnt can obsrv and t unction π ( q ) can inr ort. Tror, in ordr to minimiz t conomic cost o t protction, t govrnmnt can impos a "minimum proit valu targt" or t domstic industry, π ( q ),, it, *. I t industry dos not xrt t optimal lvl o adjustmnt ort, it as not rspctd t 12

13 implicit contract. T govrnmnt as to pnaliz it at t nd o t protction priod, onc t political rturn as bn arnd, by lowring t tari blow its post-protction commitmnt valu. Howvr, t ability to monitor prctly mans tat t govrnmnt nvr pnalizs bcaus its trat is crdibl. 3. Using t saguard claus undr asymmtric inormation. Wn t govrnmnt is unabl to obsrv domstic production costs, it cannot disntangl t cts o ig domstic production costs and low adjustmnt ort. Low ralizd proits could b t rsult o a ig-cost industry wic ad xrtd optimal adjustmnt ort or it could b a consqunc o a low-cost industry undr-adjusting. Tus, t domstic industry as an incntiv to manipulat t protction scm sinc it knows tat t govrnmnt sks to maximiz its political rturn. T industry may do so by announcing tat it is a ig-cost industry in ordr to obtain a protction lvl xcssiv or its tru costs. Ts acts igligt t principal-agnt rlationsip btwn t govrnmnt and t domstic industry wic can b viwd as a Stacklbrg gam wr t industry is t ladr and t govrnmnt is t ollowr. T purpos o t optimal political coic undr stratgic bavior consists o rvrsing t rols in t gam. By proposing a politically-optimal incntiv-compatibl mcanism to t domstic industry, t govrnmnt rsolvs bot unobsrvabl ort and advrs slction problms arising out o t dsir to implmnt t complt inormation policy in a world o incomplt inormation. T inormation asymmtris man tat t govrnmnt cannot cck t tru lvl o proits. Tror wn t injurd industry asks or protction, t govrnmnt proposs an implicit contract to t domstic industry. T contract spciis t politically optimal markt 13

14 pric (and accordingly t saguard tari) and t lvl o proit tat t domstic industry commits to arn in xcang or t protction. At t bginning o t protction pisod, t proit is subjct to uncrtainty so t protction cannot b dirctly basd on ( ) π.. Instad, t govrnmnt obsrvs a noisy ralizd lvl o proit but dos not know t tru valu o and cannot monitor t lvl o adjustmnt ort,. In otr words, t govrnmnt bass protction on an obsrvabl and vriiabl x-post monitor x subjct to t conditional probability distribution F( x π ) wit dnsity (.). T govrnmnt s xpctations about ar summarizd by a prior cumulativ distribution + G( ) wit dirntiabl dnsity g(), suc tat g() > 0 or all blonging to t st Θ = [ -, ] and suc tat G/g as t monoton azard-rat proprty, i.., is non-dcrasing in. T distribution unction G is common knowldg to all playrs. In ordr to induc t domstic industry to coos t tari dsignd or it and to xrt t optimal lvl o ort, t autority proposs t contract { π ( ), ( )} tat links t typ industry s coic o t domstic markt pric ( ) to t proit π ( ). 3.1 Constraints on t govrnmnt problm wit asymmtric inormation. 3.1.a olitically incntiv-compatibility (IC) constraint. T protction rnt B o t domstic industry o typ wn it rports ~ is: ( ) (12) ~ ~ B, x, q x dx K ( ) = ( ) ( π ) ( ) x By applying t Rvlation rincipl 8, t govrnmnt can rstrict its political coic to incntiv-compatibl mcanisms, i.., mcanisms or wic t industry rports its typ ~ trutully. In tis ramwork, t typ industry will coos a rspons ( ) = i its protction 14

15 rnt B(, ) is at last as ig as its rnt rom lying B ( ~, ). Formally, t mcanism is politically incntiv-compatibl (IC) i: ~ ~ B, B,,,, IC + + ( ) ( ) ( ) [ ] [ ] ( ) (13) Using t wll-known and usul trick o Mirrls (1971), IC can b rwrittn as ollows: ~ B( ) = max x(, q ) ( x ) dx K( ( ) π ) (14) ~ x Exprssion (14) can b usd along wit Libniz s rul and t nvlop torm to obtain: db( ) ~ ~ = x(, q ) π ( x π ) π dx = π x(, q ) π ( x π ) dx (15) d x T optimal adjustmnt lvl () or t industry is givn by: ( ) arg max B( ) (16) Rstricting ourslvs to t irst-ordr-condition approac (s Rogrson, 1985) or a solution to (16) yilds: db( ) ~ = (, ) ( π ) π ( ) = d x x q π x dx K( ) 0 (17) x By rarranging xprssion (17), w gt a mor tractabl xprssion: Substituting (17 ) into (15) yilds: K ( ) ~ = x(, q ) π ( x π ) dx (17 ) π x db d ( ) π = K 0 (18) π Exprssion (18) tus incorporats bot an incntiv-compatibility constraint and t condition tat adjustmnt ort is cosn by t industry to maximiz its own protction rnt. T inquality o (18) mans tat IC protction rnt arising rom t saguard policy must b a 15

16 dcrasing unction o t industry s cost typ. Tis ariss bcaus proit nt o adjustmnt costs is a positiv and ngativ unction o ort and cost typ, rspctivly (π > 0 and π < 0), and adjustmnt costs ris wit ort K > 0. I tis irst-ordr condition is satisid and i π() is non-incrasing in, tn ts conditions ar suicint or t global politically incntiv- compatibility o t govrnmnt political coic mcanism. (S Appndix 2 or IC scond- ordr condition tratmnt). 3.1.b. Non-ngativ proits or all industry cost typs. Wn stting t saguard policy, t domstic govrnmnt as to considr its political objctiv, i.., t political rturn maximization problm wic rquirs tat t domstic industry s protction rnt must b non-ngativ watvr its cost typ. W dnot tis constraint by (R) wic is an individual rationality constraint --- unlss irms aciv at last a sar o t surplus accordd to t govrnmnt troug t politically-optimal protction program, it will not participat in t plan. Formally, w av: Intgrating t IC constraint, w gt: B( ) 0 Θ ( R) (19) ( ) + dk ( ν ) π + B( ) = dν + B( ) (20) d π Sinc w know rom (18) tat ( ) B is a dcrasing unction o t industry cost typ or any IC mcanism, (R) can b rplacd by: ( ) B( ) B + = 0, 0 + (21) tat is, only t igst cost irm will rciv no rnt rom protction. T inormational rnt 16

17 arising out o t incomplt inormation is tus: ( ) + dk ( ν ) π B( ) = dν (20 ) d π 3.2 T govrnmnt s problm undr asymmtric inormation. T privatly-ld inormation will act t industry s protction rnt B and tror cang t govrnmnt coic o a tari. T govrnmnt potntially can us t provision o t rnt to induc t industry to act in a way wic minimizs t political costs o incrasd prics to consumrs. Undr asymmtric inormation, t govrnmnt knows tat t domstic industry will bav stratgically. Tus, t govrnmnt also will tak t IC and t R constraints into account wn maximizing t xpctd valu o t wigtd-avrag national wlar unction (W AI ). Formally: ( 2) + AI Max W g( ) d (.), (.) db( ) dk( ) π st: = d d π B ( IC) + ( ) = 0 ( R) (22) wr W AI is t Lagrangian unction rom t complt inormation problm. Tat is: AI W = V + ( 1 + λ ) U λ B( ) (23) Exprssion (23) maks clar t domstic conlicts acing t govrnmnt. For positiv valus o λ, t producrs rciv a igr wigt tan consumrs. At t sam tim, t inormation asymmtris man tat B() will b gratr tan zro or all but t last icint 17

18 industry typs. But t govrnmnt must b willing to or som positiv rnt to induc good adjustmnt bavior wic will rduc t valu o t govrnmnt s objctiv unction. T govrnmnt, aving a prior bli about t domstic industry cost typ summarizd by t dnsity g(), sks to implmnt its political coic subjct to t political incntivcompatibility and t political rturn constraint. W adopt a control-tortic approac to solv t govrnmnt's problm. 9 In tis approac, t industry's protction rnt B() is t stat variabl and t controls ar, and db()/d). Exprssion (20 ) and t irst-ordr conditions yild (s Appndix 3 or dtails): + π π ( q ( ) ) ( ( )) ( ( ν ), K = K ) dν (24) π π 1+ λ π K g = λ G π ( ) ( ) ( ) ( ) π K K (25) π ( ) * ( ) ( ) w β 1 π = = + G λ K * * η q π g t (26) Ts rsults sow tr typs o distortions du to t stratgic bavior o prssur groups. Exprssion (24) dmonstrats t political rturn distortion. T govrnmnt must incras t protction rnt B o all industris wit lss tan maximum costs ( < + ) i it wants t political rturn constraint (R) not to b violatd. Tis mans tat nsuring a non-ngativ protction rnt to t igst-cost irm will allow otr irms to obtain inormational rnts in addition to protction rnts. T inormational rnt is at its maximum or t lowst-cost industry ( = ) and quals zro or t igst-cost industry ( = + ). Exprssion (25) sows an ort distortion. T trm on t LHS o (24) is t xpctd 18

19 marginal political rturn o t adjustmnt program, i.., t incras in domstic proit du to ort, valuatd at t industry wigt in t govrnmnt s problm ( 1+ λ ). T RHS is t xpctd incrasd cost o t inormational rnt as ort riss. (Rcall tat µ ( ) = λ G ( ) is t co-stat variabl associatd wit t stat quation IC in t Hamiltonian.) Tus, t govrnmnt inducs t industry to incras its adjustmnt ort until t xpctd marginal proit quals t conomic cost o t inormational rnt. Tis yilds an optimal lvl o ort only or t low cost industry. For tat industry, t lvl o adjustmnt ort is t sam as in t symmtric inormation stup. For all otr industris, t lvl o adjustmnt ort is lowr tan wit symmtric inormation. T coic o protction undr asymmtric inormation tror yilds lowr ort or t ig-cost industris. Tis act rlcts t trad-o acd by t govrnmnt btwn assisting t adjustmnt ort (incrasing t political rturn) and rducing t domstic industris' inormational rnt (dcrasing t conomic cost). On on and, t govrnmnt is orcd to lav rnts to t industry to induc it to adopt an optimal adjustmnt ort. On t otr and, it wants to rduc t bnits tat ar costly or consumrs troug ig domstic prics. Ts rsults allow us to giv t ollowing proposition: roposition 1: Undr stratgic industry bavior, t political coic o trad protction troug t saguard claus ntails a trad-o btwn maximizing political rturn and minimizing conomic costs. Tis trad-o cts a sub-optimal lvl o adjustmnt ort: lss icint industris undr-adjust wil only t most icint adjusts optimally. T saguard claus tror is conomically irrational. 19

20 T ct o asymmtric inormation on t lvl o t tari compard to complt inormation is ambiguous and dpnds on t cts o rducd imports on t proit trad-o btwn ort and cost typ. In particular, xprssions (10) and (26) sows tat t dirnc btwn t complt and incomplt inormation lvl o taris quals: 1 G( ) K g( ) ( π / π ) q T sign o (26) dpnds on t valu o ( π π / ) q (27), wic is ow canging domstic xcss dmand or imports q acts t marginal rat o substitution btwn ort and cost typ or a constant lvl o proits. I ( π π / ) q > 0, tn or a givn lvl o proits, a li about costs will rsult in lowr adjustmnt ort. Howvr, wil t tari will b igr, t ( ) + dk ( ν ) π inormational rnt, B( ) = dν, will also b adjustd downward. d π Tis yilds t ollowing proposition: roposition 2: I a rduction in imports rducs (incrass) t trad-o btwn ort and cost typ, an incomplt inormation saguard tari will b igr (lowr) tan t complt inormation tari. T govrnmnt consquntly adjusts t inormational rnt downward (upward). Stratgic bavior tus rducs (incrass) consumr wlar at t cost o sub-optimal adjustmnt ort o inicint industris. Wn t domstic industry adopts stratgic bavior, t autority dos not tak into account t ral protction rnt but considrs a "virtual protction rnt" wic includs t 20

21 inormational part o t protction rnt. T conjunction o asymmtric inormation and dirnt industry cost structurs rsults in a ngativ inormational xtrnality --- t prsnc o ig-cost industris causs t low-cost industris to bav stratgically. In ordr to intrnaliz tat inormational xtrnality gnratd by t prsnc o ig-cost industris, t autority distorts t symmtric inormation saguard policy o ig-cost industris and inducs tm to adopt a sub-optimal lvl o adjustmnt ort. 4. Concluding rmarks. In tis papr, w av sd som ligt on govrnmnt us o t saguard claus. W av modld t saguard claus as a dvic usd by govrnmnts to rsolv political objctivs conlicts arising rom t tnsion btwn maintaining non-ngativ domstic industry proits and t impact on consumrs o igr taris. W av don so in a modl wr t domstic irm incurs costs as it adjusts to orign comptition. T govrnmnt s policy is politically constraind by a rquirmnt tat domstic irms arn non-ngativ proits. W ound tat i t govrnmnt can monitor ort and costs prctly, t govrnmnt can or a tari in xcang or an adjustmnt ort optimal or t domstic industry s spciic cost structur. Complt inormation and t lack o stratgic bavior by t domstic industry allows t govrnmnt to or only noug protction to insur tat t industry will adjust but tat simultanously minimizs consumr costs. Ts consumr costs will b rlativly small wn domstic production xpands rlativly mor tan t domstic consumption contracts. W also av studid ow a govrnmnt migt try to implmnt a protction plan wn t problm o t objctivs conlict is urtr complicatd by asymmtric inormation. W av assumd tat t govrnmnt is imprctly inormd about t domstic industry's aturs. 21

22 Spciically, t govrnmnt is abl to cck t domstic industry s proit lvl at t nd o t protction priod but is unabl to disntangl t cts o dirnt irm cost typs rom irm ort to incras icincy. W sowd tat in suc an nvironmnt, t domstic industry acts stratgically so tat a (constraind) optimal protction rul must b drivd wic is incntiv-compatibl. T rsulting incntiv mcanism consists o a mnu o implicit contracts proposd by t govrnmnt to t domstic industry wn t saguard policy is rqustd. T implicit contract wic implmnts t politically-optimal tari coic (i.., t coic tat rsolvs t political objctivs conlicts among dirnt domstic intrsts), rsults in a ig-cost industry rmaining inicint. T only industry wic would adopt t optimal lvl o adjustmnt, ironically, as t lowst-cost. 10 Tis rsarc rinorcs t argumnt tat t WTO saguard mcanism as wak oundations in pur conomic considrations. T basic contradiction containd in t saguard cod (protcting in ordr to lp adjustmnt) and our rsults suggst tat r trad would b a mor icint adjustmnt program. Witout govrnmnt intrvntion, domstic irms tmslvs would mak t dcision wtr adjustmnt or xit would mak mor sns. Evn toug Articl XIX o t GATT rquirs adjustmnt plans to b part o a saguard mcanism, t rsults prsntd r cast doubt on govrnmnts ability to induc domstic industris to adjust to orign comptition. Wil politicians migt lgitimat saguard mcanisms by appals to adjustmnt, suc programs likly would b implmntd inicintly. Rrncs: Baldwin Robrt E., "T olitical Economy o Trad olicy", Journal o Economic rspctivs 3 (1989): Brainard, S. Lal and Tirry Vrdir, "Lobbying and Adjustmnt in Dclining Industris" 22

23 Europan Economic Rviw 38 (1994): Brainard, S. Lal and Tirry Vrdir, "T olitical Economy o Dclining Industris: Snscnt Industry Collaps Rvisitd" Journal o Intrnational Economics, 42 (1997): Cassing, Jams H. and Ayr L. Hillman, "Siting Comparativ Advantag and Snscnt Industry Collaps" Amrican Economic Rviw, 76 (1986): Dinopoulos, Elias, Tracy Lwis, and David Sappington, Optimal Industrial Targting wit Unknown Larning-by-doing. Journal o Intrnational Economics, 38 (1995): Fnstra, Robrt C. and Tracy Lwis, Distributing t Gains rom Trad wit Incomplt Inormation, Economics and olitics, 3 (1991): Grossman, Gn and Elanan Hlpman, rotction or Sal, Amrican Economic Rviw; 84 (1994): Hillman, Ayr L., "Dclining Industris and olitical-support rotctionist Motivs" Amrican Economic Rviw, 72 (1982): Hillman, Ayr L., T olitical Economy o rotction, Cur, Switzrland:. Harwood Acadmic ublisrs, Jackson, Jon H., "Saguard and Adjustmnt olicis," in Robrt M. Strn, (d.), T Multilatral Trading Systm: Analysis and Options or Cang, Ann Arbor: Univrsity o Micigan rss, Laont, Jan-Jacqus and Jan Tirol, A Tory o Incntivs in rocurmnt and Rgulation, Cambridg, MA: MIT rss, 1993,. Mirrls, Jams, "An xploration in t tory o optimum incom taxation", Rviw o Economic Studis, 38 (1971), Moor, Mical O., "Nw Dvlopmnts in t olitical Economy o rotction," in Colin Cartr, Alx McCalla and Jrry Sarpls (ds.), Imprct Comptition and olitical Economy, Bouldr, CO: Wstviw rss, Moor, Mical O. and Stvn Suranovic, "A Wlar Comparison Btwn VERs and Taris 23

24 Undr t GATT," Canadian Journal o Economics, 26 (1993): Myrson, Rogr B., "Incntiv Compatibility and t Bargaining roblm", Economtrica, 47 (1979): Nlson Douglas, "Endognous Tari Tory: A Critical Survy", Amrican Journal o olitical Scinc, 32 (1988): Rodrik Dani,, "olitical Economy o Trad olicy" in Gn M. Grossman and Knnt Rogo (ds.), Handbook o Intrnational Economics, Vol.3, Amstrdam: Elsvir Scinc ublisrs, Rogrson, William, "T First Ordr Approac to rincipal-agnt roblms", Economtrica, 53 (1985): Staigr Robrt W. and Guido Tabllini, "Discrtionary Trad olicy and Excssiv rotction", Amrican Economic Rviw, 77 (1987): Tornll, Aaron, 1991, "On t Inctivnss o Mad-to-Masur rotctionist rograms", in Elanan Hlpman and Assa Razin, (ds.), Intrnational Trad And Trad olicy, Cambridg, MA: MIT rss. Uruguay Round Agrmnt on Saguards ttp:// Marc Van Long, Ngo and Nil Vousdn, "rotctionist Rspons and Dclining Industris" Journal o Intrnational Economics, 30 (1991):

25 Appndix 1: Saguard tari wit symmtric inormation: T domstic govrnmnt maximizs t sum o consumr surplus, domstic proit nt o adjustmnt costs, and tari rvnu: Max W, s. t. π = Q ( z) dz + π ( q, ) K( ) + ( ) q ( ) ( q, ) K( ) B( ) ( λ) w (A1a) W can rwrit (A1a) as ollows: Max ( ) ( ) ( ( ) ( )) ( ) ( ) ( ) L Max = Q z dz + 1+ λ π q, K + w q λ B,, λ,, λ Consumr surplus will b igst wil maintaining non-ngativ domstic proits wn ( ) B = 0. First-ordr conditions yild: L = 0 K ( ) π q ( ) * = *, * ( ) L = 0 K( * ) = π * q ( ) *, * λ ( ) ( q, ) L q ( ) ( λ) π = 0 w = q 1+ [ ] Bcaus π (, ) (, ) (, ) q = MC q AC q q w can rwrit (A1d) as: ( ) q ( 1 λ) (, ) q MC q w = + q q q (A1b) (A1c) (A1d) (A1) Bcaus ac irm is a pric-takr, w av: MC q (, ) q Substituting (A1) into (A1) yilds t optimal complt inormation tari: q = 1 (A1) 25

26 26 t q q CI w = = λ (A1g) Dividing by t optimal domstic pric * and rarranging yilds t valu o t political sadow pric on t domstic proit constraint: ξ ε β η λ = = * *) ( * *) ( w w (A1) Wit: β ξ η ε = = = = q q q q q q q q,,,

27 Appndix 2: Scond-ordr conditions or incntiv-compatibility wit asymmtric inormation: ( ) Lt ( ) =, π ( ), q ( ) b t ort ndd to arn a proit π ( ) wn t supply is q ( ) and assum tat: > 0, > 0, < 0, < 0, < 0, π q π q Assum tat t industry is lying about its cost typ. In tis cas, its ort will b: ( ) ~ ~ ~ (, ) =, π ( ), q ( ) wr ~ is t dgr o t li. In tis cas, t rnt rom lying is: Trut-tlling implis: B ~ ( ) B ~~ ( ) ( ( )) ~ ~ ~ ~ (, ) π ( ), π ( ), ( ) B = K q (A2a) ~, = 0 ~,, < 0 wic is quivalnt to: B ~, = 0 ~,, > 0 (A2b) ( ) B ( ) ~ ~ ~, ~, ~, bcaus db ~ ( ) = 0 = B ~~ ( ) + B ~ ( ) ~, > 0: Lt us sow tat B ~ ( ) ~ ~ ~ ~ (, ) & ( ), ( ), ( ) d ~ ~ ( ( )) ~ (, π ( ), q ( )) B ~ = π K π q (A2c) d ~ B ( ) K d π ~, = + d dq d dπ K d + dq d π q π q (A2d) W av B ~ ( ) ~, > 0 i dq ( ) > 0. T domstic supply as to b a incrasing unction o t cost typ d wn t adjustmnt program taks plac or t scond-ordr conditions to b satisid. Tis will b t cas i t tari is an incrasing unction o t cost typ. 27

28 ( ) ( ) Appndix 3: Saguard tari wit asymmtric inormation T govrnmnt s problm wit asymmtric inormation will b: + Max E ( W) = Max ,..,. ( ) ( ) ( ) ( ) ( ) ( ) ( ) Q( z) dz ( 1 λ) π( q, ) K( ) w q λ B g d subjct to: db d ( ) π = K 0 (IC) π + + ( ) = ( ) > [ ] B 0 and B 0 or, (R) T Lagrangian associatd wit t maximization problm is: Qz L= + µ ( ) dz+ ( 1+ λ) ( π( q, ) K( ) ) + ( ) q ( ) λ B( ) g( ) π π ( ) K + µ &( ) B( ) w d µ + + ( ) B( ) (A3a) wr ( ) µ is t co-stat variabl associatd wit t stat quation (IC). Lt H b t Hamiltonian associatd wit t Lagrangian L. (,,, µ, ) H B By rwriting L, w obtain: Q z dz q K = 1 + ( w ) q ( ) λ B( ) ( ) ( ) + ( + λ) π(, ) ( ) dk( ) π g( ) + µ ( ) d π (A3b) ( ) + + [ (,,,, ) &( ) ( )] ( ) ( ) L = H B µ + µ B d µ B (A3c) Lt γ ( ) = ( ), ( ) b t control vctor. A ncssary condition or L to b a maximum is tat t cang in L vaniss: 28

29 + H H dl = d γ + + µ & B µ γ T cang in t valu o L vanis i: + + ( ) db( ) d ( ) db( ) H H = 0 = = 0 = 0 B, µ & ( ), µ ( + ) B( + ), µ ( ) bcaus t trminal valu B( ) is r. Tis yilds t ncssary conditions or optimality: ( ) H ( ) ( λ) π q, π = q q ( ) µ ( ) ( ) + w + + g K ( ) + ' 1 = 0 ( ) π H ( ) π = µ π π K K λ ( π q K ) g( ) + π + 1+, = 0 ( ) ( ) ( ) ( ) H = µ & ( ) = λ g( ) B( ) Using t transvrsality condition, ( ) Tis yilds: µ = 0, w gt µ ( ) = λ G( ) π 1+ λ ( π ) ( ) = ( ) q, K g λ G π ( ) ( ) ( ) + π K K π (A3d) * * w K = λ β 1 + π η q π G( ) g( ) (A3) 29

30 Endnots 1 Similar saguard clauss can b ound in prrntial trading agrmnts suc as NAFTA and Mrcosur. 2 Articl VII o t Uruguay Round Agrmnt on Saguards (1994). 3 S Baldwin (1989), Bagwati (1988), Hillman (1989), Moor (1990), Nlson (1988), and Rodrik (1995) or survys o t ndognous protction litratur and industry rspons to import comptition. 4 Tis is in contrast to otr masurs suc as antidumping and countrvailing duty masurs wic, at last in principl, ar not dsignd to protct domstic industris rom siting comparativ advantag but instad insulat tm rom allgd "unair" trad practics. 5 S Dinopoulos, t al. (1995) or optimal policy wn a irm s larning-by-doing abilitis ar unobsrvabl. 6 Fnstra and Lwis (1991) analyz taris in a pur xcang conomy wn domstic agnts av privat inormation about tir ndowmnts. Ty ind tat i t govrnmnt is constraind by nsuring arto gains rom trad, a non-linar tari structur will rsult. 7 W ignor t compnsation rquird undr t saguard claus as rquird undr Articl XIX o t GATT. S Moor and Suranovic (1993) or a modl wit GATT-consistnt saguard compnsation scms. 8 S Myrson (1979). 9 In tis program, w tak t lvl o ort as t control variabl. Indd, t control variabl is π ( ) but i w assum tat π ( ) = y( ) z( q ) wr t unctions y(.) and z(.)ar obsrvabl, t two approacs ar quivalnt bcaus π(.) can b immdiatly dducd rom t valu o (.) 10 Wil t discussion ocusd on ort to rduc costs dirctly, a rr as pointd out tat it could also b altrd to analyz incntivs or canging a wol rang o conomic activitis acting costs witin an import-compting irm. Ts migt includ work practics, adoption o nw tcnologis, workr training, tc. 30

Oligopoly Equilibria à la Stackelberg. in Pure Exchange Economies

Oligopoly Equilibria à la Stackelberg. in Pure Exchange Economies Oligopoly Equilibria à la Stacklbrg in Pur Excang Economis L.A. JLIEN & F. TRICO EconomiX, nivrsité Paris X-Nantrr Burau K6 00, avnu d la Républiqu 900 Nantrr Cédx Incomplt and prliminary vrsion 5-06-07

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

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

+ 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

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

3-2-1 ANN Architecture

3-2-1 ANN Architecture ARTIFICIAL NEURAL NETWORKS (ANNs) Profssor Tom Fomby Dpartmnt of Economics Soutrn Mtodist Univrsity Marc 008 Artificial Nural Ntworks (raftr ANNs) can b usd for itr prdiction or classification problms.

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

HAZARD MORAL MODELS WITH THREE STATES OF NATURE

HAZARD MORAL MODELS WITH THREE STATES OF NATURE Quantitativ thods Inquirs HAZARD ORA ODES ITH THREE STATES OF NATRE Danila ARINESC PhD Associat Prossor nivrsity o Economic Studis ucharst Romania E-mail: danila.marinscu@csi.as.ro Dumitru IRON PhD Prossor

More information

Environmental Policy and Time Consistency: Emission Taxes and Emissions Trading

Environmental Policy and Time Consistency: Emission Taxes and Emissions Trading Environmntal Policy and Tim Consistncy: Emission Taxs and Emissions Trading Ptr W. Knndy 1 and Bnoît Laplant 2 1 Dpartmnt of Economics, Univrsity of Victoria, Victoria, British Columbia V8W 2Y2, Canada.

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

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

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

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

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

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

Hospital Readmission Reduction Strategies Using a Penalty-Incentive Model

Hospital Readmission Reduction Strategies Using a Penalty-Incentive Model Procdings of th 2016 Industrial and Systms Enginring Rsarch Confrnc H. Yang, Z. Kong, and MD Sardr, ds. Hospital Radmission Rduction Stratgis Using a Pnalty-Incntiv Modl Michll M. Alvarado Txas A&M Univrsity

More information

Supplementary Materials

Supplementary Materials 6 Supplmntary Matrials APPENDIX A PHYSICAL INTERPRETATION OF FUEL-RATE-SPEED FUNCTION A truck running on a road with grad/slop θ positiv if moving up and ngativ if moving down facs thr rsistancs: arodynamic

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

Trigonometric functions

Trigonometric functions Robrto s Nots on Diffrntial Calculus Captr 5: Drivativs of transcndntal functions Sction 5 Drivativs of Trigonomtric functions Wat you nd to know alrady: Basic trigonomtric limits, t dfinition of drivativ,

More information

University of Washington Department of Chemistry Chemistry 453 Winter Quarter 2014 Lecture 20: Transition State Theory. ERD: 25.14

University of Washington Department of Chemistry Chemistry 453 Winter Quarter 2014 Lecture 20: Transition State Theory. ERD: 25.14 Univrsity of Wasinton Dpartmnt of Cmistry Cmistry 453 Wintr Quartr 04 Lctur 0: Transition Stat Tory. ERD: 5.4. Transition Stat Tory Transition Stat Tory (TST) or ctivatd Complx Tory (CT) is a raction mcanism

More information

Online Supplement: Advance Selling in a Supply Chain under Uncertain Supply and Demand

Online Supplement: Advance Selling in a Supply Chain under Uncertain Supply and Demand Onlin Supplmnt Avanc Slling in a Supply Cain unr Uncrtain Supply an Dman. Proos o Analytical sults Proo o Lmma. Using a = minl 0 ; x g; w can rwrit () as ollows (x ; w ; x ; w ) = a +(m0 w )a +( +" x w

More information

The Ramsey Model. Reading: Firms. Households. Behavior of Households and Firms. Romer, Chapter 2-A;

The Ramsey Model. Reading: Firms. Households. Behavior of Households and Firms. Romer, Chapter 2-A; Th Ramsy Modl Rading: Romr, Chaptr 2-A; Dvlopd by Ramsy (1928), latr dvlopd furthr by Cass (1965) and Koopmans (1965). Similar to th Solow modl: labor and knowldg grow at xognous rats. Important diffrnc:

More information

SECTION where P (cos θ, sin θ) and Q(cos θ, sin θ) are polynomials in cos θ and sin θ, provided Q is never equal to zero.

SECTION where P (cos θ, sin θ) and Q(cos θ, sin θ) are polynomials in cos θ and sin θ, provided Q is never equal to zero. SETION 6. 57 6. Evaluation of Dfinit Intgrals Exampl 6.6 W hav usd dfinit intgrals to valuat contour intgrals. It may com as a surpris to larn that contour intgrals and rsidus can b usd to valuat crtain

More information

MEASURING ECONOMIC IMPACT OF A DISASTER WITHOUT DOUBLE COUNTING: A THEORETICAL ANALYSIS

MEASURING ECONOMIC IMPACT OF A DISASTER WITHOUT DOUBLE COUNTING: A THEORETICAL ANALYSIS MEASURING ECONOMIC IMPACT OF A DISASTER WITHOUT DOUBLE COUNTING: A THEORETICAL ANALYSIS ABSTRACT : H. Tatano and K. Nakano Profssor, Disastr Prvntion Rsarch Institut, Kyoto Univrsity, Uji. Japan Ph.D Candidat,

More information

There is an arbitrary overall complex phase that could be added to A, but since this makes no difference we set it to zero and choose A real.

There is an arbitrary overall complex phase that could be added to A, but since this makes no difference we set it to zero and choose A real. Midtrm #, Physics 37A, Spring 07. Writ your rsponss blow or on xtra pags. Show your work, and tak car to xplain what you ar doing; partial crdit will b givn for incomplt answrs that dmonstrat som concptual

More information

dy 1. If fx ( ) is continuous at x = 3, then 13. If y x ) for x 0, then f (g(x)) = g (f (x)) when x = a. ½ b. ½ c. 1 b. 4x a. 3 b. 3 c.

dy 1. If fx ( ) is continuous at x = 3, then 13. If y x ) for x 0, then f (g(x)) = g (f (x)) when x = a. ½ b. ½ c. 1 b. 4x a. 3 b. 3 c. AP CALCULUS BC SUMMER ASSIGNMENT DO NOT SHOW YOUR WORK ON THIS! Complt ts problms during t last two wks of August. SHOW ALL WORK. Know ow to do ALL of ts problms, so do tm wll. Itms markd wit a * dnot

More information

Fourier Transforms and the Wave Equation. Key Mathematics: More Fourier transform theory, especially as applied to solving the wave equation.

Fourier Transforms and the Wave Equation. Key Mathematics: More Fourier transform theory, especially as applied to solving the wave equation. Lur 7 Fourir Transforms and th Wav Euation Ovrviw and Motivation: W first discuss a fw faturs of th Fourir transform (FT), and thn w solv th initial-valu problm for th wav uation using th Fourir transform

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

Appendices * for. R&D Policies, Endogenous Growth and Scale Effects

Appendices * for. R&D Policies, Endogenous Growth and Scale Effects Appndics * for R&D Policis, Endognous Growth and Scal Effcts by Fuat Snr (Union Collg) Working Papr Fbruary 2007 * Not to b considrd for publication. To b mad availabl on th author s wb sit and also upon

More information

Physics 43 HW #9 Chapter 40 Key

Physics 43 HW #9 Chapter 40 Key Pysics 43 HW #9 Captr 4 Ky Captr 4 1 Aftr many ours of dilignt rsarc, you obtain t following data on t potolctric ffct for a crtain matrial: Wavlngt of Ligt (nm) Stopping Potntial (V) 36 3 4 14 31 a) Plot

More information

Equilibria in a Capacity-Constrained Di erentiated Duopoly

Equilibria in a Capacity-Constrained Di erentiated Duopoly Equilibria in a Capacity-Constraind Di rntiatd Duopoly Maxim Sinitsyn McGill Univrsity Prliminary and incomplt. Abstract In this papr I analyz th modl of pric-stting duopoly with capacity-constraind rms

More information

Chapter 8 Employment, unemployment and wages

Chapter 8 Employment, unemployment and wages Chaptr 8 Employmnt, unmploymnt and ags Th birth o Fordism (5/1/1914): ags r mor than doubld orking hours r rducd Consquncs: incras in th quu o job applicants rduction o turnovr (rom 50000 to 5000 quits,

More information

Data Assimilation 1. Alan O Neill National Centre for Earth Observation UK

Data Assimilation 1. Alan O Neill National Centre for Earth Observation UK Data Assimilation 1 Alan O Nill National Cntr for Earth Obsrvation UK Plan Motivation & basic idas Univariat (scalar) data assimilation Multivariat (vctor) data assimilation 3d-Variational Mthod (& optimal

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

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

Exponential Functions

Exponential Functions Eponntial Functions Dinition: An Eponntial Function is an unction tat as t orm a, wr a > 0. T numbr a is calld t bas. Eampl: Lt i.. at intgrs. It is clar wat t unction mans or som valus o. 0 0,,, 8,,.,.

More information

Estimation of apparent fraction defective: A mathematical approach

Estimation of apparent fraction defective: A mathematical approach Availabl onlin at www.plagiarsarchlibrary.com Plagia Rsarch Library Advancs in Applid Scinc Rsarch, 011, (): 84-89 ISSN: 0976-8610 CODEN (USA): AASRFC Estimation of apparnt fraction dfctiv: A mathmatical

More information

(Upside-Down o Direct Rotation) β - Numbers

(Upside-Down o Direct Rotation) β - Numbers Amrican Journal of Mathmatics and Statistics 014, 4(): 58-64 DOI: 10593/jajms0140400 (Upsid-Down o Dirct Rotation) β - Numbrs Ammar Sddiq Mahmood 1, Shukriyah Sabir Ali,* 1 Dpartmnt of Mathmatics, Collg

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

Thinking outside the (Edgeworth) Box

Thinking outside the (Edgeworth) Box Tinking outsid t (dgwort) ox by Jon G. Rily Dartmnt of conomics UCL 0 Novmbr 008 To dvlo an undrstanding of Walrasian quilibrium allocations, conomists tyically start wit t two rson, two-commodity xcang

More information

Cramér-Rao Inequality: Let f(x; θ) be a probability density function with continuous parameter

Cramér-Rao Inequality: Let f(x; θ) be a probability density function with continuous parameter WHEN THE CRAMÉR-RAO INEQUALITY PROVIDES NO INFORMATION STEVEN J. MILLER Abstract. W invstigat a on-paramtr family of probability dnsitis (rlatd to th Parto distribution, which dscribs many natural phnomna)

More information

Full Waveform Inversion Using an Energy-Based Objective Function with Efficient Calculation of the Gradient

Full Waveform Inversion Using an Energy-Based Objective Function with Efficient Calculation of the Gradient Full Wavform Invrsion Using an Enrgy-Basd Objctiv Function with Efficint Calculation of th Gradint Itm yp Confrnc Papr Authors Choi, Yun Sok; Alkhalifah, ariq Ali Citation Choi Y, Alkhalifah (217) Full

More information

Network Congestion Games

Network Congestion Games Ntwork Congstion Gams Assistant Profssor Tas A&M Univrsity Collg Station, TX TX Dallas Collg Station Austin Houston Bst rout dpnds on othrs Ntwork Congstion Gams Travl tim incrass with congstion Highway

More information

Types of Transfer Functions. Types of Transfer Functions. Types of Transfer Functions. Ideal Filters. Ideal Filters

Types of Transfer Functions. Types of Transfer Functions. Types of Transfer Functions. Ideal Filters. Ideal Filters Typs of Transfr Typs of Transfr x[n] X( LTI h[n] H( y[n] Y( y [ n] h[ k] x[ n k] k Y ( H ( X ( Th tim-domain classification of an LTI digital transfr function is basd on th lngth of its impuls rspons h[n]:

More information

Market power, Growth and Unemployment

Market power, Growth and Unemployment Markt powr, Growth and Unmploymnt Pitro F Prtto Dpartmnt of Economics, Duk Univrsity Jun 13, 2011 Abstract I prsnt a modl whr firms and workrs st wags abov th markt-claring lvl Unmploymnt is thus gnratd

More information

u x v x dx u x v x v x u x dx d u x v x u x v x dx u x v x dx Integration by Parts Formula

u x v x dx u x v x v x u x dx d u x v x u x v x dx u x v x dx Integration by Parts Formula 7. Intgration by Parts Each drivativ formula givs ris to a corrsponding intgral formula, as w v sn many tims. Th drivativ product rul yilds a vry usful intgration tchniqu calld intgration by parts. Starting

More information

MCB137: Physical Biology of the Cell Spring 2017 Homework 6: Ligand binding and the MWC model of allostery (Due 3/23/17)

MCB137: Physical Biology of the Cell Spring 2017 Homework 6: Ligand binding and the MWC model of allostery (Due 3/23/17) MCB37: Physical Biology of th Cll Spring 207 Homwork 6: Ligand binding and th MWC modl of allostry (Du 3/23/7) Hrnan G. Garcia March 2, 207 Simpl rprssion In class, w drivd a mathmatical modl of how simpl

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

Determination of Vibrational and Electronic Parameters From an Electronic Spectrum of I 2 and a Birge-Sponer Plot

Determination of Vibrational and Electronic Parameters From an Electronic Spectrum of I 2 and a Birge-Sponer Plot 5 J. Phys. Chm G Dtrmination of Vibrational and Elctronic Paramtrs From an Elctronic Spctrum of I 2 and a Birg-Sponr Plot 1 15 2 25 3 35 4 45 Dpartmnt of Chmistry, Gustavus Adolphus Collg. 8 Wst Collg

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

Accident Prevention and Damage Reduction in an Extended Liability Scheme

Accident Prevention and Damage Reduction in an Extended Liability Scheme Thortical Economics Lttrs 05 5 46-55 Publishd Onlin April 05 in cis http://wwwscirporg/journal/tl http://dxdoiorg/0436/tl05509 Accidnt Prvntion and Damag duction in an Extndd Liability chm Atsuo Tomori

More information

Section 11.6: Directional Derivatives and the Gradient Vector

Section 11.6: Directional Derivatives and the Gradient Vector Sction.6: Dirctional Drivativs and th Gradint Vctor Practic HW rom Stwart Ttbook not to hand in p. 778 # -4 p. 799 # 4-5 7 9 9 35 37 odd Th Dirctional Drivativ Rcall that a b Slop o th tangnt lin to th

More information

Case Study 1 PHA 5127 Fall 2006 Revised 9/19/06

Case Study 1 PHA 5127 Fall 2006 Revised 9/19/06 Cas Study Qustion. A 3 yar old, 5 kg patint was brougt in for surgry and was givn a /kg iv bolus injction of a muscl rlaxant. T plasma concntrations wr masurd post injction and notd in t tabl blow: Tim

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

Homotopy perturbation technique

Homotopy perturbation technique Comput. Mthods Appl. Mch. Engrg. 178 (1999) 257±262 www.lsvir.com/locat/cma Homotopy prturbation tchniqu Ji-Huan H 1 Shanghai Univrsity, Shanghai Institut of Applid Mathmatics and Mchanics, Shanghai 272,

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

MAT 270 Test 3 Review (Spring 2012) Test on April 11 in PSA 21 Section 3.7 Implicit Derivative

MAT 270 Test 3 Review (Spring 2012) Test on April 11 in PSA 21 Section 3.7 Implicit Derivative MAT 7 Tst Rviw (Spring ) Tst on April in PSA Sction.7 Implicit Drivativ Rmmbr: Equation of t tangnt lin troug t point ( ab, ) aving slop m is y b m( a ). dy Find t drivativ y d. y y. y y y. y 4. y sin(

More information

4037 ADDITIONAL MATHEMATICS

4037 ADDITIONAL MATHEMATICS CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Ordinary Lvl MARK SCHEME for th Octobr/Novmbr 0 sris 40 ADDITIONAL MATHEMATICS 40/ Papr, maimum raw mark 80 This mark schm is publishd as an aid to tachrs and candidats,

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

Trade Liberalization, Foreign Aid, and Welfare under Unemployment and Cross-border Pollution

Trade Liberalization, Foreign Aid, and Welfare under Unemployment and Cross-border Pollution Trad Libraliation, Forign Aid, and Wlfar undr Unmploymnt and Cross-bordr Pollution Nikos Tsakiris, Panos Hatipanayotou and Michal S. Michal August 2007 (Prliminary Draft) Abstract W construct a two-country

More information

Derivation of Electron-Electron Interaction Terms in the Multi-Electron Hamiltonian

Derivation of Electron-Electron Interaction Terms in the Multi-Electron Hamiltonian Drivation of Elctron-Elctron Intraction Trms in th Multi-Elctron Hamiltonian Erica Smith Octobr 1, 010 1 Introduction Th Hamiltonian for a multi-lctron atom with n lctrons is drivd by Itoh (1965) by accounting

More information

Aim To manage files and directories using Linux commands. 1. file Examines the type of the given file or directory

Aim To manage files and directories using Linux commands. 1. file Examines the type of the given file or directory m E x. N o. 3 F I L E M A N A G E M E N T Aim To manag ils and dirctoris using Linux commands. I. F i l M a n a g m n t 1. il Examins th typ o th givn il or dirctory i l i l n a m > ( o r ) < d i r c t

More information

u r du = ur+1 r + 1 du = ln u + C u sin u du = cos u + C cos u du = sin u + C sec u tan u du = sec u + C e u du = e u + C

u r du = ur+1 r + 1 du = ln u + C u sin u du = cos u + C cos u du = sin u + C sec u tan u du = sec u + C e u du = e u + C Tchniqus of Intgration c Donald Kridr and Dwight Lahr In this sction w ar going to introduc th first approachs to valuating an indfinit intgral whos intgrand dos not hav an immdiat antidrivativ. W bgin

More information

COMPUTER GENERATED HOLOGRAMS Optical Sciences 627 W.J. Dallas (Monday, April 04, 2005, 8:35 AM) PART I: CHAPTER TWO COMB MATH.

COMPUTER GENERATED HOLOGRAMS Optical Sciences 627 W.J. Dallas (Monday, April 04, 2005, 8:35 AM) PART I: CHAPTER TWO COMB MATH. C:\Dallas\0_Courss\03A_OpSci_67\0 Cgh_Book\0_athmaticalPrliminaris\0_0 Combath.doc of 8 COPUTER GENERATED HOLOGRAS Optical Scincs 67 W.J. Dallas (onday, April 04, 005, 8:35 A) PART I: CHAPTER TWO COB ATH

More information

Forces. Quantum ElectroDynamics. α = = We have now:

Forces. Quantum ElectroDynamics. α = = We have now: W hav now: Forcs Considrd th gnral proprtis of forcs mdiatd by xchang (Yukawa potntial); Examind consrvation laws which ar obyd by (som) forcs. W will nxt look at thr forcs in mor dtail: Elctromagntic

More information

CPSC 665 : An Algorithmist s Toolkit Lecture 4 : 21 Jan Linear Programming

CPSC 665 : An Algorithmist s Toolkit Lecture 4 : 21 Jan Linear Programming CPSC 665 : An Algorithmist s Toolkit Lctur 4 : 21 Jan 2015 Lcturr: Sushant Sachdva Linar Programming Scrib: Rasmus Kyng 1. Introduction An optimization problm rquirs us to find th minimum or maximum) of

More information

That is, we start with a general matrix: And end with a simpler matrix:

That is, we start with a general matrix: And end with a simpler matrix: DIAGON ALIZATION OF THE STR ESS TEN SOR INTRO DUCTIO N By th us of Cauchy s thorm w ar abl to rduc th numbr of strss componnts in th strss tnsor to only nin valus. An additional simplification of th strss

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

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

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

A Welfare Analysis of the U.S. Ethanol Subsidy

A Welfare Analysis of the U.S. Ethanol Subsidy A Wlar Analysis o th U.S. Ethanol Subsidy Xiaodong Du, Drmot J. Hays, and Mindy Bakr Working apr 08-W 480 Novmbr 2008 (Rvisd) ntr or Agricultural and Rural Dvlopmnt Iowa Stat Univrsity Ams, Iowa 50011-1070

More information

Chapter 13 GMM for Linear Factor Models in Discount Factor form. GMM on the pricing errors gives a crosssectional

Chapter 13 GMM for Linear Factor Models in Discount Factor form. GMM on the pricing errors gives a crosssectional Chaptr 13 GMM for Linar Factor Modls in Discount Factor form GMM on th pricing rrors givs a crosssctional rgrssion h cas of xcss rturns Hors rac sting for charactristic sting for pricd factors: lambdas

More information

Direct Approach for Discrete Systems One-Dimensional Elements

Direct Approach for Discrete Systems One-Dimensional Elements CONTINUUM & FINITE ELEMENT METHOD Dirct Approach or Discrt Systms On-Dimnsional Elmnts Pro. Song Jin Par Mchanical Enginring, POSTECH Dirct Approach or Discrt Systms Dirct approach has th ollowing aturs:

More information

Exam 1. It is important that you clearly show your work and mark the final answer clearly, closed book, closed notes, no calculator.

Exam 1. It is important that you clearly show your work and mark the final answer clearly, closed book, closed notes, no calculator. Exam N a m : _ S O L U T I O N P U I D : I n s t r u c t i o n s : It is important that you clarly show your work and mark th final answr clarly, closd book, closd nots, no calculator. T i m : h o u r

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

The Matrix Exponential

The Matrix Exponential Th Matrix Exponntial (with xrciss) by Dan Klain Vrsion 28928 Corrctions and commnts ar wlcom Th Matrix Exponntial For ach n n complx matrix A, dfin th xponntial of A to b th matrix () A A k I + A + k!

More information

Propositional Logic. Combinatorial Problem Solving (CPS) Albert Oliveras Enric Rodríguez-Carbonell. May 17, 2018

Propositional Logic. Combinatorial Problem Solving (CPS) Albert Oliveras Enric Rodríguez-Carbonell. May 17, 2018 Propositional Logic Combinatorial Problm Solving (CPS) Albrt Olivras Enric Rodríguz-Carbonll May 17, 2018 Ovrviw of th sssion Dfinition of Propositional Logic Gnral Concpts in Logic Rduction to SAT CNFs

More information

The Matrix Exponential

The Matrix Exponential Th Matrix Exponntial (with xrciss) by D. Klain Vrsion 207.0.05 Corrctions and commnts ar wlcom. Th Matrix Exponntial For ach n n complx matrix A, dfin th xponntial of A to b th matrix A A k I + A + k!

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

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

is an appropriate single phase forced convection heat transfer coefficient (e.g. Weisman), and h

is an appropriate single phase forced convection heat transfer coefficient (e.g. Weisman), and h For t BWR oprating paramtrs givn blow, comput and plot: a) T clad surfac tmpratur assuming t Jns-Lotts Corrlation b) T clad surfac tmpratur assuming t Tom Corrlation c) T clad surfac tmpratur assuming

More information

Lecture 18 - Semiconductors - continued

Lecture 18 - Semiconductors - continued Lctur 18 - Smiconductors - continud Lctur 18: Smiconductors - continud (Kittl C. 8) + a - Donors and accptors Outlin Mor on concntrations of lctrons and ols in Smiconductors Control of conductivity by

More information

Sundials and Linear Algebra

Sundials and Linear Algebra Sundials and Linar Algbra M. Scot Swan July 2, 25 Most txts on crating sundials ar dirctd towards thos who ar solly intrstd in making and using sundials and usually assums minimal mathmatical background.

More information

Abstract Interpretation. Lecture 5. Profs. Aiken, Barrett & Dill CS 357 Lecture 5 1

Abstract Interpretation. Lecture 5. Profs. Aiken, Barrett & Dill CS 357 Lecture 5 1 Abstract Intrprtation 1 History On brakthrough papr Cousot & Cousot 77 (?) Inspird by Dataflow analysis Dnotational smantics Enthusiastically mbracd by th community At last th functional community... At

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

INTEGRATION BY PARTS

INTEGRATION BY PARTS Mathmatics Rvision Guids Intgration by Parts Pag of 7 MK HOME TUITION Mathmatics Rvision Guids Lvl: AS / A Lvl AQA : C Edcl: C OCR: C OCR MEI: C INTEGRATION BY PARTS Vrsion : Dat: --5 Eampls - 6 ar copyrightd

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

Characteristics of Gliding Arc Discharge Plasma

Characteristics of Gliding Arc Discharge Plasma Caractristics of Gliding Arc Discarg Plasma Lin Li( ), Wu Bin(, Yang Ci(, Wu Cngkang ( Institut of Mcanics, Cins Acadmy of Scincs, Bijing 8, Cina E-mail: linli@imc.ac.cn Abstract A gliding arc discarg

More information

LINEAR DELAY DIFFERENTIAL EQUATION WITH A POSITIVE AND A NEGATIVE TERM

LINEAR DELAY DIFFERENTIAL EQUATION WITH A POSITIVE AND A NEGATIVE TERM Elctronic Journal of Diffrntial Equations, Vol. 2003(2003), No. 92, pp. 1 6. ISSN: 1072-6691. URL: http://jd.math.swt.du or http://jd.math.unt.du ftp jd.math.swt.du (login: ftp) LINEAR DELAY DIFFERENTIAL

More information

Principles of Humidity Dalton s law

Principles of Humidity Dalton s law Principls of Humidity Dalton s law Air is a mixtur of diffrnt gass. Th main gas componnts ar: Gas componnt volum [%] wight [%] Nitrogn N 2 78,03 75,47 Oxygn O 2 20,99 23,20 Argon Ar 0,93 1,28 Carbon dioxid

More information

Function Spaces. a x 3. (Letting x = 1 =)) a(0) + b + c (1) = 0. Row reducing the matrix. b 1. e 4 3. e 9. >: (x = 1 =)) a(0) + b + c (1) = 0

Function Spaces. a x 3. (Letting x = 1 =)) a(0) + b + c (1) = 0. Row reducing the matrix. b 1. e 4 3. e 9. >: (x = 1 =)) a(0) + b + c (1) = 0 unction Spacs Prrquisit: Sction 4.7, Coordinatization n this sction, w apply th tchniqus of Chaptr 4 to vctor spacs whos lmnts ar functions. Th vctor spacs P n and P ar familiar xampls of such spacs. Othr

More information

Quasi-Classical States of the Simple Harmonic Oscillator

Quasi-Classical States of the Simple Harmonic Oscillator Quasi-Classical Stats of th Simpl Harmonic Oscillator (Draft Vrsion) Introduction: Why Look for Eignstats of th Annihilation Oprator? Excpt for th ground stat, th corrspondnc btwn th quantum nrgy ignstats

More information

Chapter Taylor Theorem Revisited

Chapter Taylor Theorem Revisited Captr 0.07 Taylor Torm Rvisitd Atr radig tis captr, you sould b abl to. udrstad t basics o Taylor s torm,. writ trascdtal ad trigoomtric uctios as Taylor s polyomial,. us Taylor s torm to id t valus o

More information

Types of Transfer Functions. Types of Transfer Functions. Ideal Filters. Ideal Filters. Ideal Filters

Types of Transfer Functions. Types of Transfer Functions. Ideal Filters. Ideal Filters. Ideal Filters Typs of Transfr Typs of Transfr Th tim-domain classification of an LTI digital transfr function squnc is basd on th lngth of its impuls rspons: - Finit impuls rspons (FIR) transfr function - Infinit impuls

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

Outlines: Graphs Part-4. Applications of Depth-First Search. Directed Acyclic Graph (DAG) Generic scheduling problem.

Outlines: Graphs Part-4. Applications of Depth-First Search. Directed Acyclic Graph (DAG) Generic scheduling problem. Outlins: Graps Part-4 Applications o DFS Elmntary Grap Aloritms Topoloical Sort o Dirctd Acyclic Grap Stronly Connctd Componnts PART-4 1 2 Applications o Dpt-First Sarc Topoloical Sort: Usin dpt-irst sarc

More information

A NEW SIGNATURE PROTOCOL BASED ON RSA AND ELGAMAL SCHEME

A NEW SIGNATURE PROTOCOL BASED ON RSA AND ELGAMAL SCHEME A NEW SIGNATURE PROTOCOL BASED ON RSA AND ELGAMAL SCHEME ABSTRACT J Ettanfoui and O Kadir Laboratory of Matmatics, Cryptograpy and Mcanics, Fstm, Univrsity Hassan II of Casablanca, Morocco In tis papr,

More information

Optimal Investment Planning of Bulk Energy Storage Systems

Optimal Investment Planning of Bulk Energy Storage Systems sustainability Articl Optimal Invstmnt Planning of Bulk Enrgy Storag Systms Dina Kastiva *,, Ilias Dimoulkas and Mikal Amlin Royal Institut of Tcnology (KTH), Tknikringn 33, 114 28 Stockolm, Swdn; iliasd@kt.s

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

Derangements and Applications

Derangements and Applications 2 3 47 6 23 Journal of Intgr Squncs, Vol. 6 (2003), Articl 03..2 Drangmnts and Applications Mhdi Hassani Dpartmnt of Mathmatics Institut for Advancd Studis in Basic Scincs Zanjan, Iran mhassani@iasbs.ac.ir

More information