CHAPTER CHAPTER14. Expectations: The Basic Tools. Prepared by: Fernando Quijano and Yvonn Quijano
|
|
- Emery Parrish
- 6 years ago
- Views:
Transcription
1 Expcaions: Th Basic Prpard by: Frnando Quijano and Yvonn Quijano CHAPTER CHAPTER Prnic Hall Businss Publishing Macroconomics, 4/ Olivir Blanchard
2 14-1 Today s Lcur Chapr 14:Expcaions: Th Basic Th disincion bwn nominal and ral inrs ras Prsn discound valus calculaions Adjusing h IS-LM modl o accoun for disincion bwn nominal and ral inrs ras 2006 Prnic Hall Businss Publishing Macroconomics, 4/ Olivir Blanchard 2 of 32
3 14-1 Nominal Vrsus Ral Inrs Ras Chapr 14:Expcaions: Th Basic Inrs Ras xprssd in rms of dollars (or, mor gnrally, in unis of h naional currncy) ar calld nominal inrs ras Inrs ras xprssd in rms of a bask of goods ar calld ral inrs ras Prnic Hall Businss Publishing Macroconomics, 4/ Olivir Blanchard 3 of 32
4 Nominal Vrsus Ral Inrs Ras Chapr 14:Expcaions: Th Basic Figur 14-1 Dfiniion and Drivaion of h Ral Inrs Ra i = nominal inrs ra for yar. r = ral inrs ra for yar. (1+ i ): Lnding on dollar his yar yilds (1+ i ) dollars nx yar. P = pric his yar. P +1 = xpcd pric nx yar Prnic Hall Businss Publishing Macroconomics, 4/ Olivir Blanchard 4 of 32
5 Nominal Vrsus Ral Inrs Ras Chapr 14:Expcaions: Th Basic P W hav: 1 + r = ( 1 + i ) P + 1 W can dfin xpcd inflaion as: Hnc: π + 1 P P Subsiuing back in: P = + 1 ( 1 + r ) = + 1 P 1 P ( 1 + π ) 1 + i 1 + π Prnic Hall Businss Publishing Macroconomics, 4/ Olivir Blanchard 5 of 32
6 Nominal Vrsus Ral Inrs Ras Chapr 14:Expcaions: Th Basic If h nominal inrs ra and h xpcd ra of inflaion ar no oo larg, a simplr xprssion is: r = i + π 1 Th ral inrs ra is (approximaly) qual o h nominal inrs ra minus h xpcd ra of inflaion Prnic Hall Businss Publishing Macroconomics, 4/ Olivir Blanchard 6 of 32
7 Nominal Vrsus Ral Inrs Ras Chapr 14:Expcaions: Th Basic Hr ar som of h implicaions of h rlaion abov: If If if = 0 i = r π π > 0 i > r i r π = i π r 2006 Prnic Hall Businss Publishing Macroconomics, 4/ Olivir Blanchard 7 of 32
8 Nominal and Ral Inrs Ras in h Unid Sas Sinc 1978 Chapr 14:Expcaions: Th Basic Figur 14-2 Nominal and Ral On-Yar T-bill Ras in h Unid Sas sinc 1978 Alhough h nominal inrs ra has dclind considrably sinc h arly 1980s, h ral inrs ra was acually highr in 2001 han in Prnic Hall Businss Publishing Macroconomics, 4/ Olivir Blanchard 8 of 32
9 14-2 Expcd Prsn Discound Valus Chapr 14:Expcaions: Th Basic Figur 14-2 Compuing Prsn Discound Valus Th xpcd prsn discound valu of a squnc of fuur paymns is h valu oday of his xpcd squnc of paymns Prnic Hall Businss Publishing Macroconomics, 4/ Olivir Blanchard 9 of 32
10 Compuing Expcd Prsn Discound Valus Chapr 14:Expcaions: Th Basic (a) On dollar his yar is worh 1+i dollars nx yar. (b) On dollar nx yar is worh 1 his yar 1 + i So, h prsn discound valu of a dollar nx yar is qual o i 2006 Prnic Hall Businss Publishing Macroconomics, 4/ Olivir Blanchard 10 of 32
11 Compuing Expcd Prsn Discound Valus Chapr 14:Expcaions: Th Basic Th word discound coms from h fac ha h valu nx yar is discound, wih (1+i ) bing h discoun facor. (Th 1-yar nominal inrs ra, i, is somims calld h discoun ra Prnic Hall Businss Publishing Macroconomics, 4/ Olivir Blanchard 11 of 32
12 A Gnral Formula Chapr 14:Expcaions: Th Basic Th prsn discound valu of a squnc of paymns, or valu in oday s dollars quals: $ V $ z 1 ( ) $ 1 z i ( i )( i ) $ = z Whn fuur paymns or inrs ras ar uncrain, hn: $ V $ z 1 ( ) $ 1 z i ( i )( i ) $ = z Prsn discound valu, or prsn valu ar anohr way of saying xpcd prsn discound valu Prnic Hall Businss Publishing Macroconomics, 4/ Olivir Blanchard 12 of 32
13 Using Prsn Valus: Exampls Chapr 14:Expcaions: Th Basic $ V $ z 1 ( ) $ 1 z i ( i )( i ) $ = z This formula has hs implicaions: Prsn valu dpnds posiivly on oday s acual paymn and xpcd fuur paymns. Prsn valu dpnds ngaivly on currn and xpcd fuur inrs ras Applicaion: ysrday was in h nws ha xpcaions of (inrs) ra cus by h ECB drov up sock prics Prnic Hall Businss Publishing Macroconomics, 4/ Olivir Blanchard 13 of 32
14 Consan Inrs Ras Chapr 14:Expcaions: Th Basic To focus on h ffcs of h squnc of paymns on h prsn valu, assum ha inrs ras ar xpcd o b consan ovr im, hn: $ V = $ z + 1 ( ) $ 1 z i ( 1 + i) $ z Prnic Hall Businss Publishing Macroconomics, 4/ Olivir Blanchard 14 of 32
15 Consan Inrs Ras and Paymns Chapr 14:Expcaions: Th Basic Whn h squnc of paymns is qual call hm $z, h prsn valu formula simplifis o: $ V = $ z ( 1 + i) ( 1 + i) n 1 Th rms in h xprssion in bracks rprsn a gomric sris. Compuing h sum of h sris, w g: n 1 [ 1/ ( 1 + i) ] $ V = $ z 1 [ 1/ ( 1 + i)] 2006 Prnic Hall Businss Publishing Macroconomics, 4/ Olivir Blanchard 15 of 32
16 Zro Inrs Ras Chapr 14:Expcaions: Th Basic If i = 0, hn 1/(1+i) quals on, and so dos (1/(1+i) n ) for any powr n. For ha rason, h prsn discound valu of a squnc of xpcd paymns is jus h sum of hos xpcd paymns Prnic Hall Businss Publishing Macroconomics, 4/ Olivir Blanchard 16 of 32
17 Consan Inrs Ras and Paymns, Forvr Chapr 14:Expcaions: Th Basic Assuming ha paymns sar nx yar and go on forvr, hn: $ V = 1 ( ) $ 1 z i ( 1 + i) $ z + = ( + i) 1 1 ( 1 + i) Using h propry of gomric sums, h prsn valu formula abov is: Which simplifis o: 2 $ V 1 1 i ( ( / ( i)) $ = z $ V = + $ z 2006 Prnic Hall Businss Publishing Macroconomics, 4/ Olivir Blanchard 17 of 32 $ z i
18 Nominal Vrsus Ral Inrs Ras, and Prsn Valus Chapr 14:Expcaions: Th Basic $ V $ z 1 ( ) $ 1 z i ( i )( i ) $ = z Rplacing nominal inrs wih ral inrs ras o obain h prsn valu of a squnc of ral paymns, w g: V = z + Which can b simplifid o: 2006 Prnic Hall Businss Publishing Macroconomics, 4/ Olivir Blanchard 18 of z z ( 1 + r ) ( 1 + r )( 1 + r ) $V P + 1 = V Hnc: prsn discound valus in rms of nominal valus using nominal inrs ras o discoun or in ral valus using ral inrs ras gnra h sam ral PDV
19 14-3 Nominal and Ral Inrs Ras, and h IS-LM Modl Chapr 14:Expcaions: Th Basic Whn dciding how much invsmn o undrak, firms car abou ral inrs ras. Thn, h IS rlaion mus rad: Y = C( Y T) + I( Y, r) + G Th inrs ra dircly affcd by monary policy h on ha nrs h LM rlaion is h nominal inrs ra, hn: M P = YL( i) Wih h ral inrs ra: r = i π 2006 Prnic Hall Businss Publishing Macroconomics, 4/ Olivir Blanchard 19 of 32
20 Nominal and Ral Inrs Ras, and h IS-LM Modl Chapr 14:Expcaions: Th Basic Th nominal inrs ra appars in mony dmand In dciding how much mony o hold an individual compars h nominal ra of rurn on mony, which is zro, wih h nominal ra of rurn on bonds, which is h nominal inrs ra Th ral inrs ra appars in h IS curv Th inrs ra affcs invsmn. In dciding abou invsmn firms compar h ral cos of capial goods wih h ral payoffs from ha invsmn 2006 Prnic Hall Businss Publishing Macroconomics, 4/ Olivir Blanchard 20 of 32
21 14-4 Mony Growh, Inflaion, Nominal and Ral Inrs Ras Chapr 14:Expcaions: Th Basic This scion focuss on h following assrions: Highr mony growh lads o lowr nominal inrs ras in h shor run, bu o highr nominal inrs ras in h mdium run. Highr mony growh lads o lowr ral inrs ras in h shor run, bu has no ffc on ral inrs ras in h mdium run Prnic Hall Businss Publishing Macroconomics, 4/ Olivir Blanchard 21 of 32
22 Rvisiing h IS-LM Modl Chapr 14:Expcaions: Th Basic Rducing h IS rlaion, LM rlaion and rlaion bwn h ral and nominal inrs ra givs us: IS LM Y = C( Y T) + I( Y, i π ) + G ( ) M = YL i Th IS curv is sill downward sloping. Th LM curv is upward sloping. Th quilibrium is a h inrscion of h IS curv and h LM curv Prnic Hall Businss Publishing Macroconomics, 4/ Olivir Blanchard 22 of 32
23 Rvisiing h IS-LM Modl Chapr 14:Expcaions: Th Basic Figur 14-4 Equilibrium Oupu and Inrs Ras Th quilibrium lvl of oupu and h quilibrium nominal inrs ra ar givn by h inrscion of h IS curv and h LM curv. Th ral inrs ra quals h nominal inrs ra minus xpcd inflaion Prnic Hall Businss Publishing Macroconomics, 4/ Olivir Blanchard 23 of 32
24 Nominal and Ral Inrs Ras in h Shor Run Chapr 14:Expcaions: Th Basic Figur 14-5 Th Shor-run Effcs of an Incras in Mony Growh An incras in mony growh incrass h ral mony sock in h shor run. This incras in ral mony lads o an incras in oupu and a dcras in boh h nominal and h ral inrs ra as prics ar sicky in h shor run. If r = i π r = i π If π is consan, π = 0 r = i 2006 Prnic Hall Businss Publishing Macroconomics, 4/ Olivir Blanchard 24 of 32
25 Nominal and Ral Inrs Ras in h Mdium Run Chapr 14:Expcaions: Th Basic In h mdium run, Y =, hn: Y n Y = C( Y T) + I( Y, r) + G n n n Th rlaion bwn h nominal inrs ra and h ral inrs ra is: i = r + π In h mdium run, h ral inrs ra quals h naural inrs ra, r n, hn: i = r n + π In h mdium run, xpcd inflaion is qual o acual inflaion, so: i = r n + π Finally, in h mdium run, inflaion is qual o mony growh: i = r + g n m 2006 Prnic Hall Businss Publishing Macroconomics, 4/ Olivir Blanchard 25 of 32
26 Nominal and Ral Inrs Ras in h Mdium Run Chapr 14:Expcaions: Th Basic i = r + g n So, in h mdium run, h nominal inrs ra incrass on for on wih inflaion o bring h ral inrs ra back o is quilibrium lvl. This rsul is known as h Fishr ffc, or h Fishr Hypohsis. For xampl, an incras in nominal mony growh of 10% is vnually rflcd by a 10% incras in h ra of inflaion, a 10% incras in h nominal inrs ra, and no chang in h ral inrs ra. m 2006 Prnic Hall Businss Publishing Macroconomics, 4/ Olivir Blanchard 26 of 32
27 A Monary Expansion: From h Shor Run o h Mdium Run Chapr 14:Expcaions: Th Basic So long as h ral inrs ra is blow h naural ral inrs ra, oupu is highr han h naural lvl of oupu, and unmploymn is blow is naural ra. From h Phillips curv rlaion, w know ha as long as unmploymn is blow h naural ra of unmploymn, inflaion incrass. As inflaion incrass, i bcoms highr han nominal mony growh, lading o ngaiv ral mony growh, h LM curv shifs back In h mdium run, h ral inrs ra incrass back o is iniial valu, bcaus h conomy rurns back o is naural lvl 2006 Prnic Hall Businss Publishing Macroconomics, 4/ Olivir Blanchard 27 of 32
28 From h Shor Run o h Mdium Run Chapr 14:Expcaions: Th Basic Figur 14-6 Th Adjusmn of h Ral and h Nominal Inrs Ra o an Incras in Mony Growh An incras in mony growh lads iniially o a dcras in boh h ral and h nominal inrs ra. Ovr im, h ral inrs ra rurns o is iniial valu. Th nominal inrs ra convrgs o a nw highr valu, qual o h iniial valu plus h incras in mony growh Prnic Hall Businss Publishing Macroconomics, 4/ Olivir Blanchard 28 of 32
29 Evidnc on h Fishr Hypohsis Chapr 14:Expcaions: Th Basic To s if incrass in inflaion lad o on-foron incrass in nominal inrs ras, conomiss look a: Nominal inrs ras and inflaion across counris. Th vidnc of h arly 1990s finds subsanial suppor for h Fishr hypohsis. Swings in inflaion, which should vnually b rflcd in similar swings in h nominal inrs ra. Again, h daa appars o fi h hypohsis qui wll Prnic Hall Businss Publishing Macroconomics, 4/ Olivir Blanchard 29 of 32
30 Evidnc on h Fishr Hypohsis Chapr 14:Expcaions: Th Basic Figur 14-7 Th 3-Monh Trasury Bill Ra and Inflaion sinc 1927 Th incras in inflaion from h arly 1960s o h arly 1980s was associad wih an incras in h nominal inrs ra. Th dcras in inflaion sinc h mid-1980s has bn associad wih a dcras in h nominal inrs ra Prnic Hall Businss Publishing Macroconomics, 4/ Olivir Blanchard 30 of 32
31 Evidnc on h Fishr Hypohsis Chapr 14:Expcaions: Th Basic Figur 14-7 has a las hr inrsing faurs: Th sady incras in inflaion from h arly 1960s o h arly 1980s was associad wih a roughly paralll incras in h nominal inrs ra. Th nominal inrs ra laggd bhind h incras in inflaion in h 1970s, whil h disinflaion of h arly 1980s was associad wih an iniial incras in h nominal inrs ra. Th rlaion during WWII undrscors h imporanc of h mdium-run qualifir in h Fishr hypohsis Prnic Hall Businss Publishing Macroconomics, 4/ Olivir Blanchard 31 of 32
32 Nominal Inrs Ras and Inflaion Across Lain Amrica in h Early 1990s Chapr 14:Expcaions: Th Basic Figur 1 Nominal Inrs Ras and Inflaion: Lain Amrica, Across counris, h rlaion bwn nominal inrs ras and inflaion is pry srong 2006 Prnic Hall Businss Publishing Macroconomics, 4/ Olivir Blanchard 32 of 32
Economics 302 (Sec. 001) Intermediate Macroeconomic Theory and Policy (Spring 2011) 3/28/2012. UW Madison
Economics 302 (Sc. 001) Inrmdia Macroconomic Thory and Policy (Spring 2011) 3/28/2012 Insrucor: Prof. Mnzi Chinn Insrucor: Prof. Mnzi Chinn UW Madison 16 1 Consumpion Th Vry Forsighd dconsumr A vry forsighd
More informationCHAPTER CHAPTER15. Financial Markets and Expectations. Prepared by: Fernando Quijano and Yvonn Quijano
Financial Marks and Prpard by: Frnando Quijano and Yvonn Quijano CHAPTER CHAPTER15 2006 Prnic Hall Businss Publishing Macroconomics, 4/ Olivir Blanchard Bond Prics and Bond Yilds Figur 15-1 U.S. Yild Curvs:
More informationEconomics 302 (Sec. 001) Intermediate Macroeconomic Theory and Policy (Spring 2011) 4/25/2011. UW Madison
conomics 302 (Sc. 001) Inrmdia Macroconomic Thory and Policy (Spring 2011) 4/25/2011 Insrucor: Prof. Mnzi Chinn Insrucor: Prof. Mnzi Chinn UW Madison 21 1 Th Mdium Run ε = P * P Thr ar wo ways in which
More information14.02 Principles of Macroeconomics Fall 2005 Quiz 3 Solutions
4.0 rincipl of Macroconomic Fall 005 Quiz 3 Soluion Shor Quion (30/00 poin la a whhr h following amn ar TRUE or FALSE wih a hor xplanaion (3 or 4 lin. Each quion coun 5/00 poin.. An incra in ax oday alway
More information14.02 Principles of Macroeconomics Problem Set 5 Fall 2005
40 Principls of Macroconomics Problm S 5 Fall 005 Posd: Wdnsday, Novmbr 6, 005 Du: Wdnsday, Novmbr 3, 005 Plas wri your nam AND your TA s nam on your problm s Thanks! Exrcis I Tru/Fals? Explain Dpnding
More informationTHE SHORT-RUN AGGREGATE SUPPLY CURVE WITH A POSITIVE SLOPE. Based on EXPECTATIONS: Lecture. t t t t
THE SHORT-RUN AGGREGATE SUL CURVE WITH A OSITIVE SLOE. Basd on EXECTATIONS: Lcur., 0. In Mankiw:, 0 Ths quaions sa ha oupu dvias from is naural ra whn h pric lvl dvias from h xpcd pric lvl. Th paramr a
More informationMundell-Fleming I: Setup
Mundll-Flming I: Sup In ISLM, w had: E ( ) T I( i π G T C Y ) To his, w now add n xpors, which is a funcion of h xchang ra: ε E P* P ( T ) I( i π ) G T NX ( ) C Y Whr NX is assumd (Marshall Lrnr condiion)
More informationI) Title: Rational Expectations and Adaptive Learning. II) Contents: Introduction to Adaptive Learning
I) Til: Raional Expcaions and Adapiv Larning II) Conns: Inroducion o Adapiv Larning III) Documnaion: - Basdvan, Olivir. (2003). Larning procss and raional xpcaions: an analysis using a small macroconomic
More informationThe Science of Monetary Policy
Th Scinc of Monary Policy. Inroducion o Topics of Sminar. Rviw: IS-LM, AD-AS wih an applicaion o currn monary policy in Japan 3. Monary Policy Sragy: Inrs Ra Ruls and Inflaion Targing (Svnsson EER) 4.
More informationUNIT #5 EXPONENTIAL AND LOGARITHMIC FUNCTIONS
Answr Ky Nam: Da: UNIT # EXPONENTIAL AND LOGARITHMIC FUNCTIONS Par I Qusions. Th prssion is quivaln o () () 6 6 6. Th ponnial funcion y 6 could rwrin as y () y y 6 () y y (). Th prssion a is quivaln o
More informationThemes. Flexible exchange rates with inflation targeting. Expectations formation under flexible exchange rates
CHAPTER 25 THE OPEN ECONOMY WITH FLEXIBLE EXCHANGE RATES Thms Flxibl xchang ras wih inlaion arging Expcaions ormaion undr lxibl xchang ras Th AS-AD modl wih lxibl xchang ras Macroconomic adjusmn undr lxibl
More informationMidterm Examination (100 pts)
Econ 509 Spring 2012 S.L. Parn Midrm Examinaion (100 ps) Par I. 30 poins 1. Dfin h Law of Diminishing Rurns (5 ps.) Incrasing on inpu, call i inpu x, holding all ohr inpus fixd, on vnuall runs ino h siuaion
More informationSolutions to End-of-Chapter Problems for Chapters 26 & 27 in Textbook
Soluions o End-of-Chapr Problms for Chaprs 26 & 27 in Txbook Chapr 26. Answrs o hs Tru/Fals/Uncrain can b found in h wrin x of Chapr 26. I is lf o h sudn o drmin h soluions. 2. For his qusion kp in mind
More informationChapter 9 Review Questions
Chapr 9 Rviw Qusions. Using h - modl, show ha if marks clar and agns hav raional xpcaions hn mporary shocks canno hav prsisn ffcs on oupu. If marks clar and agns hav raional xpcaions hn mporary produciviy
More informationCharging of capacitor through inductor and resistor
cur 4&: R circui harging of capacior hrough inducor and rsisor us considr a capacior of capacianc is conncd o a D sourc of.m.f. E hrough a rsisr of rsisanc R, an inducor of inducanc and a y K in sris.
More informationLecture 1: Growth and decay of current in RL circuit. Growth of current in LR Circuit. D.K.Pandey
cur : Growh and dcay of currn in circui Growh of currn in Circui us considr an inducor of slf inducanc is conncd o a DC sourc of.m.f. E hrough a rsisr of rsisanc and a ky K in sris. Whn h ky K is swichd
More informationThe Mundell-Fleming Model: Stochastic Dynamics
4 --------------------------------- Th Mundll-Flming Modl: Sochasic Dynamics Th Mundll-Flming modl, which is sill h workhors modl of inrnaional macroconomics, can now b cas in a sochasic framwork. Such
More informationLecture 2: Current in RC circuit D.K.Pandey
Lcur 2: urrn in circui harging of apacior hrough Rsisr L us considr a capacior of capacianc is conncd o a D sourc of.m.f. E hrough a rsisr of rsisanc R and a ky K in sris. Whn h ky K is swichd on, h charging
More informationCSE 245: Computer Aided Circuit Simulation and Verification
CSE 45: Compur Aidd Circui Simulaion and Vrificaion Fall 4, Sp 8 Lcur : Dynamic Linar Sysm Oulin Tim Domain Analysis Sa Equaions RLC Nwork Analysis by Taylor Expansion Impuls Rspons in im domain Frquncy
More informationThe 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 information4.1 The Uniform Distribution Def n: A c.r.v. X has a continuous uniform distribution on [a, b] when its pdf is = 1 a x b
4. Th Uniform Disribuion Df n: A c.r.v. has a coninuous uniform disribuion on [a, b] whn is pdf is f x a x b b a Also, b + a b a µ E and V Ex4. Suppos, h lvl of unblivabiliy a any poin in a Transformrs
More information4. 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 informationH is equal to the surface current J S
Chapr 6 Rflcion and Transmission of Wavs 6.1 Boundary Condiions A h boundary of wo diffrn mdium, lcromagnic fild hav o saisfy physical condiion, which is drmind by Maxwll s quaion. This is h boundary condiion
More informationDouble Slits in Space and Time
Doubl Slis in Sac an Tim Gorg Jons As has bn ror rcnly in h mia, a am l by Grhar Paulus has monsra an inrsing chniqu for ionizing argon aoms by using ulra-shor lasr ulss. Each lasr uls is ffcivly on an
More information1. Inverse Matrix 4[(3 7) (02)] 1[(0 7) (3 2)] Recall that the inverse of A is equal to:
Rfrncs Brnank, B. and I. Mihov (1998). Masuring monary policy, Quarrly Journal of Economics CXIII, 315-34. Blanchard, O. R. Proi (00). An mpirical characrizaion of h dynamic ffcs of changs in govrnmn spnding
More informationB) 25y e. 5. Find the second partial f. 6. Find the second partials (including the mixed partials) of
Sampl Final 00 1. Suppos z = (, y), ( a, b ) = 0, y ( a, b ) = 0, ( a, b ) = 1, ( a, b ) = 1, and y ( a, b ) =. Thn (a, b) is h s is inconclusiv a saddl poin a rlaiv minimum a rlaiv maimum. * (Classiy
More informationBoyce/DiPrima 9 th ed, Ch 2.1: Linear Equations; Method of Integrating Factors
Boc/DiPrima 9 h d, Ch.: Linar Equaions; Mhod of Ingraing Facors Elmnar Diffrnial Equaions and Boundar Valu Problms, 9 h diion, b William E. Boc and Richard C. DiPrima, 009 b John Wil & Sons, Inc. A linar
More informationMethodology for Analyzing State Tax Policy By Orphe Pierre Divounguy, PhD, Revised by Andrew J. Kidd, PhD (May 2018)
Mhodology for Analyzing Sa Tax Policy By Orph Pirr Divounguy, PhD, Rvisd by Andrw J. Kidd, PhD (May 2018) Inroducion To analyz how changs o ax policy impacs no only govrnmn rvnus bu also conomic aciviy
More informationPoisson process Markov process
E2200 Quuing hory and lraffic 2nd lcur oion proc Markov proc Vikoria Fodor KTH Laboraory for Communicaion nwork, School of Elcrical Enginring 1 Cour oulin Sochaic proc bhind quuing hory L2-L3 oion proc
More informationElementary Differential Equations and Boundary Value Problems
Elmnar Diffrnial Equaions and Boundar Valu Problms Boc. & DiPrima 9 h Ediion Chapr : Firs Ordr Diffrnial Equaions 00600 คณ ตศาสตร ว ศวกรรม สาขาว ชาว ศวกรรมคอมพ วเตอร ป การศ กษา /55 ผศ.ดร.อร ญญา ผศ.ดร.สมศ
More informationPhysics 160 Lecture 3. R. Johnson April 6, 2015
Physics 6 Lcur 3 R. Johnson April 6, 5 RC Circui (Low-Pass Filr This is h sam RC circui w lookd a arlir h im doma, bu hr w ar rsd h frquncy rspons. So w pu a s wav sad of a sp funcion. whr R C RC Complx
More informationSpring 2006 Process Dynamics, Operations, and Control Lesson 2: Mathematics Review
Spring 6 Procss Dynamics, Opraions, and Conrol.45 Lsson : Mahmaics Rviw. conx and dircion Imagin a sysm ha varis in im; w migh plo is oupu vs. im. A plo migh imply an quaion, and h quaion is usually an
More informationInstitute of Actuaries of India
Insiu of Acuaris of India ubjc CT3 Probabiliy and Mahmaical aisics Novmbr Examinaions INDICATIVE OLUTION Pag of IAI CT3 Novmbr ol. a sampl man = 35 sampl sandard dviaion = 36.6 b for = uppr bound = 35+*36.6
More informationLecture 1: Numerical Integration The Trapezoidal and Simpson s Rule
Lcur : Numrical ngraion Th Trapzoidal and Simpson s Rul A problm Th probabiliy of a normally disribud (man µ and sandard dviaion σ ) vn occurring bwn h valus a and b is B A P( a x b) d () π whr a µ b -
More informationExchange 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 informationTaylor Principle Supplements the Fisher Effect: Empirical Investigation under the US Context
Taylor Principl Supplmns h Fishr Effc: Empirical Invsigaion undr h US Conx Mohammd Saiful ISLAM Mohammad Hasma ALI 2 ABSTRACT This papr rviws h shor- and long-run dynamics of inrs ra and inflaion of h
More informationC From Faraday's Law, the induced voltage is, C The effect of electromagnetic induction in the coil itself is called selfinduction.
Inducors and Inducanc C For inducors, v() is proporional o h ra of chang of i(). Inducanc (con d) C Th proporionaliy consan is h inducanc, L, wih unis of Hnris. 1 Hnry = 1 Wb / A or 1 V sc / A. C L dpnds
More informationChapter 3: Fourier Representation of Signals and LTI Systems. Chih-Wei Liu
Chapr 3: Fourir Rprsnaion of Signals and LTI Sysms Chih-Wi Liu Oulin Inroducion Complx Sinusoids and Frquncy Rspons Fourir Rprsnaions for Four Classs of Signals Discr-im Priodic Signals Fourir Sris Coninuous-im
More informationReview Lecture 5. The source-free R-C/R-L circuit Step response of an RC/RL circuit. The time constant = RC The final capacitor voltage v( )
Rviw Lcur 5 Firs-ordr circui Th sourc-fr R-C/R-L circui Sp rspons of an RC/RL circui v( ) v( ) [ v( 0) v( )] 0 Th i consan = RC Th final capacior volag v() Th iniial capacior volag v( 0 ) Volag/currn-division
More informationXV Exponential and Logarithmic Functions
MATHEMATICS 0-0-RE Dirnial Calculus Marin Huard Winr 08 XV Eponnial and Logarihmic Funcions. Skch h graph o h givn uncions and sa h domain and rang. d) ) ) log. Whn Sarah was born, hr parns placd $000
More informationDiploma 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 informationAR(1) Process. The first-order autoregressive process, AR(1) is. where e t is WN(0, σ 2 )
AR() Procss Th firs-ordr auorgrssiv procss, AR() is whr is WN(0, σ ) Condiional Man and Varianc of AR() Condiional man: Condiional varianc: ) ( ) ( Ω Ω E E ) var( ) ) ( var( ) var( σ Ω Ω Ω Ω E Auocovarianc
More informationMidterm exam 2, April 7, 2009 (solutions)
Univrsiy of Pnnsylvania Dparmn of Mahmaics Mah 26 Honors Calculus II Spring Smsr 29 Prof Grassi, TA Ashr Aul Midrm xam 2, April 7, 29 (soluions) 1 Wri a basis for h spac of pairs (u, v) of smooh funcions
More informationdr 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 informationEXERCISE - 01 CHECK YOUR GRASP
DIFFERENTIAL EQUATION EXERCISE - CHECK YOUR GRASP 7. m hn D() m m, D () m m. hn givn D () m m D D D + m m m m m m + m m m m + ( m ) (m ) (m ) (m + ) m,, Hnc numbr of valus of mn will b. n ( ) + c sinc
More information+ 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 informationOn the Derivatives of Bessel and Modified Bessel Functions with Respect to the Order and the Argument
Inrnaional Rsarch Journal of Applid Basic Scincs 03 Aailabl onlin a wwwirjabscom ISSN 5-838X / Vol 4 (): 47-433 Scinc Eplorr Publicaions On h Driais of Bssl Modifid Bssl Funcions wih Rspc o h Ordr h Argumn
More informationDecomposing the relationship between international bond markets
Dcomposing h rlaionship bwn inrnaional bond marks Andrw Clar and Ilias Lkkos 1 1. Inroducion Th corrlaions bwn major ass classs ar of concrn and inrs o monary auhoriis and financial rgulaors alik h ponial
More informationChapter 5 The Laplace Transform. x(t) input y(t) output Dynamic System
EE 422G No: Chapr 5 Inrucor: Chung Chapr 5 Th Laplac Tranform 5- Inroducion () Sym analyi inpu oupu Dynamic Sym Linar Dynamic ym: A procor which proc h inpu ignal o produc h oupu dy ( n) ( n dy ( n) +
More informationTransfer function and the Laplace transformation
Lab No PH-35 Porland Sa Univriy A. La Roa Tranfr funcion and h Laplac ranformaion. INTRODUTION. THE LAPLAE TRANSFORMATION L 3. TRANSFER FUNTIONS 4. ELETRIAL SYSTEMS Analyi of h hr baic paiv lmn R, and
More information2.1. Differential Equations and Solutions #3, 4, 17, 20, 24, 35
MATH 5 PS # Summr 00.. Diffrnial Equaions and Soluions PS.# Show ha ()C #, 4, 7, 0, 4, 5 ( / ) is a gnral soluion of h diffrnial quaion. Us a compur or calculaor o skch h soluions for h givn valus of h
More informationMonetary Policy and Exchange Rate Overshooting in Iran
Inrnaional Economic Sudis Vol. 44, No. 1, Spring & Summr 2014 pp. 67-74 Rcivd: 15-10-2013 Accpd: 12-05-2014 Monary Policy and Exchang Ra Ovrshooing in Iran Hosin Sharifi-Rnani * Dparmn of Economics, Khorasgan
More informationOn the Speed of Heat Wave. Mihály Makai
On h Spd of Ha Wa Mihály Maai maai@ra.bm.hu Conns Formulaion of h problm: infini spd? Local hrmal qulibrium (LTE hypohsis Balanc quaion Phnomnological balanc Spd of ha wa Applicaion in plasma ranspor 1.
More informationApplied Statistics and Probability for Engineers, 6 th edition October 17, 2016
Applid Saisics and robabiliy for Enginrs, 6 h diion Ocobr 7, 6 CHATER Scion - -. a d. 679.. b. d. 88 c d d d. 987 d. 98 f d.. Thn, = ln. =. g d.. Thn, = ln.9 =.. -7. a., by symmry. b.. d...6. 7.. c...
More informationSOLUTIONS. 1. Consider two continuous random variables X and Y with joint p.d.f. f ( x, y ) = = = 15. Stepanov Dalpiaz
STAT UIUC Pracic Problms #7 SOLUTIONS Spanov Dalpiaz Th following ar a numbr of pracic problms ha ma b hlpful for compling h homwor, and will lil b vr usful for suding for ams.. Considr wo coninuous random
More informationChapter 4 Longitudinal static stability and control Effect of acceleration (Lecture 15)
Chapr 4 Longiudinal saic sabiliy and conrol Effc of acclraion (Lcur 15) Kywords : Elvaor rquird in pull-up; sick-fixd manuvr poin; sick forc gradin in pull-up; manuvr poin sick-fr; ovrall limis on c.g.
More informationCopyright 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Chapr Rviw 0 6. ( a a ln a. This will qual a if an onl if ln a, or a. + k an (ln + c. Thrfor, a an valu of, whr h wo curvs inrsc, h wo angn lins will b prpnicular. 6. (a Sinc h lin passs hrough h origin
More informationMicroscopic Flow Characteristics Time Headway - Distribution
CE57: Traffic Flow Thory Spring 20 Wk 2 Modling Hadway Disribuion Microscopic Flow Characrisics Tim Hadway - Disribuion Tim Hadway Dfiniion Tim Hadway vrsus Gap Ahmd Abdl-Rahim Civil Enginring Dparmn,
More informationWave Equation (2 Week)
Rfrnc Wav quaion ( Wk 6.5 Tim-armonic filds 7. Ovrviw 7. Plan Wavs in Losslss Mdia 7.3 Plan Wavs in Loss Mdia 7.5 Flow of lcromagnic Powr and h Poning Vcor 7.6 Normal Incidnc of Plan Wavs a Plan Boundaris
More informationChapter 5 Fiscal and monetary policy interaction II: The role of expectations, inflationary and fiscal regimes
Chapr 5 Fiscal and monary policy inracion II: Th rol of xpcaions inflaionary and fiscal rgims 5. Inroducion In Chapr w considrd on of h basic approachs o h macroconomic policy namly h principl of a susainabl
More informationChapter 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 informationPhys463.nb Conductivity. Another equivalent definition of the Fermi velocity is
39 Anohr quival dfiniion of h Fri vlociy is pf vf (6.4) If h rgy is a quadraic funcion of k H k L, hs wo dfiniions ar idical. If is NOT a quadraic funcion of k (which could happ as will b discussd in h
More information3. The Rational Expectations Revolution
Poliicas macroconomicas, handou, Migul Lbr d Frias (mlbrdfrias@gmail.com) 3. Th Raional Expcaions Rvoluion Indx: 3. Th Raional Expcaions Rvoluion... 3. Inroducion...3 3.2 Th workr misprcpion modl...4 3.2.
More informationChapter 12 Introduction To The Laplace Transform
Chapr Inroducion To Th aplac Tranorm Diniion o h aplac Tranorm - Th Sp & Impul uncion aplac Tranorm o pciic uncion 5 Opraional Tranorm Applying h aplac Tranorm 7 Invr Tranorm o Raional uncion 8 Pol and
More informationwhereby we can express the phase by any one of the formulas cos ( 3 whereby we can express the phase by any one of the formulas
Third In-Class Exam Soluions Mah 6, Profssor David Lvrmor Tusday, 5 April 07 [0] Th vrical displacmn of an unforcd mass on a spring is givn by h 5 3 cos 3 sin a [] Is his sysm undampd, undr dampd, criically
More informationA THREE COMPARTMENT MATHEMATICAL MODEL OF LIVER
A THREE COPARTENT ATHEATICAL ODEL OF LIVER V. An N. Ch. Paabhi Ramacharyulu Faculy of ahmaics, R D collgs, Hanamonda, Warangal, India Dparmn of ahmaics, Naional Insiu of Tchnology, Warangal, India E-ail:
More informationVoltage v(z) ~ E(z)D. We can actually get to this wave behavior by using circuit theory, w/o going into details of the EM fields!
Considr a pair of wirs idal wirs ngh >, say, infinily long olag along a cabl can vary! D olag v( E(D W can acually g o his wav bhavior by using circui hory, w/o going ino dails of h EM filds! Thr
More information5. An object moving along an x-coordinate axis with its scale measured in meters has a velocity of 6t
AP CALCULUS FINAL UNIT WORKSHEETS ACCELERATION, VELOCTIY AND POSITION In problms -, drmin h posiion funcion, (), from h givn informaion.. v (), () = 5. v ()5, () = b g. a (), v() =, () = -. a (), v() =
More informationChapter 17 Handout: Autocorrelation (Serial Correlation)
Chapr 7 Handou: Auocorrlaion (Srial Corrlaion Prviw Rviw o Rgrssion Modl o Sandard Ordinary Las Squars Prmiss o Esimaion Procdurs Embddd wihin h Ordinary Las Squars (OLS Esimaion Procdur o Covarianc and
More informationMeasuring the NAIRU: Evidence from the European Union, USA and Japan
Inrnaional Rsarch Journal of Financ and Economics ISSN 10- Issu 1 (00) EuroJournals Publishing, Inc. 00 hp://www.urojournals.com/financ.hm Masuring h : Evidnc from h Europan Union, USA and Japan Gorg Sphanids
More information10. If p and q are the lengths of the perpendiculars from the origin on the tangent and the normal to the curve
0. If p and q ar h lnghs of h prpndiculars from h origin on h angn and h normal o h curv + Mahmaics y = a, hn 4p + q = a a (C) a (D) 5a 6. Wha is h diffrnial quaion of h family of circls having hir cnrs
More information22/ 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 informationDecline Curves. Exponential decline (constant fractional decline) Harmonic decline, and Hyperbolic decline.
Dlin Curvs Dlin Curvs ha lo flow ra vs. im ar h mos ommon ools for forasing roduion and monioring wll rforman in h fild. Ths urvs uikly show by grahi mans whih wlls or filds ar roduing as xd or undr roduing.
More informationGerhard Illing Script: Money - Theory and Practise
Grhard Illing Scrip: Mony - hory and Pracis Spring 212 Par 2-2 Inracion bwn Monary and Fiscal Policy: Aciv and Passiv Monary Rgims Up o now, w lookd a a vry sylizd horical modl, rying o undrsand mchanisms
More informationDemand Shocks, Credibility and Macroeconomic Dynamics
Dmand Shocks, Crdibiliy and Macroconomic Dynamics José García-Solans* and Carmn Marín-Marínz** Univrsidad d Murcia Jun 2013 Absrac: In his papr w build and simula an opn macroconomic modl o invsiga h dynamic
More informationLaPlace Transform in Circuit Analysis
LaPlac Tranform in Circui Analyi Obciv: Calcula h Laplac ranform of common funcion uing h dfiniion and h Laplac ranform abl Laplac-ranform a circui, including componn wih non-zro iniial condiion. Analyz
More informationUniversity of Kansas, Department of Economics Economics 911: Applied Macroeconomics. Problem Set 2: Multivariate Time Series Analysis
Univrsiy of Kansas, Dparmn of Economics Economics 9: Applid Macroconomics Problm S : Mulivaria Tim Sris Analysis Unlss sad ohrwis, assum ha shocks (.g. g and µ) ar whi nois in h following qusions.. Considr
More informationPredicting Growth Components Unemployment, Housing Prices and Consumption Using Both Government and Corporate Yield Curves
Inrnaional Journal of Economics and Financ; Vol. 10, No. 6; 2018 ISSN 1916-971X E-ISSN 1916-9728 Publishd by Canadian Cnr of Scinc and Educaion Prdicing Growh Componns Unmploymn, Housing Prics and Consumpion
More informationChapter 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 informationCPSC 211 Data Structures & Implementations (c) Texas A&M University [ 259] B-Trees
CPSC 211 Daa Srucurs & Implmnaions (c) Txas A&M Univrsiy [ 259] B-Trs Th AVL r and rd-black r allowd som variaion in h lnghs of h diffrn roo-o-laf pahs. An alrnaiv ida is o mak sur ha all roo-o-laf pahs
More information5.80 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 informationGeneral Article Application of differential equation in L-R and C-R circuit analysis by classical method. Abstract
Applicaion of Diffrnial... Gnral Aricl Applicaion of diffrnial uaion in - and C- circui analysis by classical mhod. ajndra Prasad gmi curr, Dparmn of Mahmaics, P.N. Campus, Pokhara Email: rajndraprasadrgmi@yahoo.com
More information4. (5a + b) 7 & x 1 = (3x 1)log 10 4 = log (M1) [4] d = 3 [4] T 2 = 5 + = 16 or or 16.
. 7 7 7... 7 7 (n )0 7 (M) 0(n ) 00 n (A) S ((7) 0(0)) (M) (7 00) 8897 (A). (5a b) 7 7... (5a)... (M) 7 5 5 (a b ) 5 5 a b (M)(A) So th cofficint is 75 (A) (C) [] S (7 7) (M) () 8897 (A) (C) [] 5. x.55
More informationAn Indian Journal FULL PAPER. Trade Science Inc. A stage-structured model of a single-species with density-dependent and birth pulses ABSTRACT
[Typ x] [Typ x] [Typ x] ISSN : 974-7435 Volum 1 Issu 24 BioTchnology 214 An Indian Journal FULL PAPE BTAIJ, 1(24), 214 [15197-1521] A sag-srucurd modl of a singl-spcis wih dnsiy-dpndn and birh pulss LI
More informationSurvey Expectations, Rationality and the Dynamics of Euro Area Inflation
Survy Expcaions, Raionaliy and h Dynamics of Euro Ara Inflaion M. Forslls* and G. Knny Rvisd: Dcmbr 2005 Absrac This papr uss survy daa in ordr o analys and assss h mpirical propris of consumrs inflaion
More information9. Simple Rules for Monetary Policy
9. Smpl Ruls for Monar Polc John B. Talor, Ma 0, 03 Woodford, AR 00 ovrvw papr Purpos s o consdr o wha xn hs prscrpon rsmbls h sor of polc ha conomc hor would rcommnd Bu frs, l s rvw how hs sor of polc
More informationEXCHANGE RATE REGIME AND HOUSEHOLD S CHOICE OF DEBT
EXCHANGE RATE REGIME AND HOUSEHOLD S CHOICE OF DEBT Summary This papr looks a h impac of h xchang ra rgim and h houshold s choic of db. On of h characrisics of conomic ransiion in asrn Europan counris
More informationIntroduction to Fourier Transform
EE354 Signals and Sysms Inroducion o Fourir ransform Yao Wang Polychnic Univrsiy Som slids includd ar xracd from lcur prsnaions prpard y McClllan and Schafr Licns Info for SPFirs Slids his work rlasd undr
More informationThe Variance-Covariance Matrix
Th Varanc-Covaranc Marx Our bggs a so-ar has bn ng a lnar uncon o a s o daa by mnmzng h las squars drncs rom h o h daa wh mnsarch. Whn analyzng non-lnar daa you hav o us a program l Malab as many yps o
More informationResponse of LTI Systems to Complex Exponentials
3 Fourir sris coiuous-im Rspos of LI Sysms o Complx Expoials Ouli Cosidr a LI sysm wih h ui impuls rspos Suppos h ipu sigal is a complx xpoial s x s is a complx umbr, xz zis a complx umbr h or h h w will
More informationChapter 10. The singular integral Introducing S(n) and J(n)
Chaptr Th singular intgral Our aim in this chaptr is to rplac th functions S (n) and J (n) by mor convnint xprssions; ths will b calld th singular sris S(n) and th singular intgral J(n). This will b don
More informationThe transition:transversion rate ratio vs. the T-ratio.
PhyloMah Lcur 8 by Dan Vandrpool March, 00 opics of Discussion ransiion:ransvrsion ra raio Kappa vs. ransiion:ransvrsion raio raio alculaing h xpcd numbr of subsiuions using marix algbra Why h nral im
More informationInvestigating Neutrality and Lack of Neutrality of Money in Iranian Economy
AENSI Journals Advancs in Environmnal Biology Journal hom pag: hp://www.ansiwb.com/ab.hml Invsigaing Nuraliy and Lack of Nuraliy of Mony in Iranian Economy Abolghasm Esnaashari Amiri Dparmn of Economics,
More information10. The Discrete-Time Fourier Transform (DTFT)
Th Discrt-Tim Fourir Transform (DTFT Dfinition of th discrt-tim Fourir transform Th Fourir rprsntation of signals plays an important rol in both continuous and discrt signal procssing In this sction w
More informationA Condition for Stability in an SIR Age Structured Disease Model with Decreasing Survival Rate
A Condiion for abiliy in an I Ag rucurd Disas Modl wih Dcrasing urvival a A.K. upriana, Edy owono Dparmn of Mahmaics, Univrsias Padjadjaran, km Bandung-umng 45363, Indonsia fax: 6--7794696, mail: asupria@yahoo.com.au;
More information2. Laser physics - basics
. Lasr physics - basics Spontanous and stimulatd procsss Einstin A and B cofficints Rat quation analysis Gain saturation What is a lasr? LASER: Light Amplification by Stimulatd Emission of Radiation "light"
More informationSECTION 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 informationA 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 informationWITHOUT NEGLECTING THE ECONOMIC GROWTH: MONETARY POLICY, CREDIBILITY, AND INFLATION TARGETING IN AN IS-MP MODEL
WITHOUT NEGLECTING THE ECONOMIC GROWTH: MONETARY POLICY, CREDIBILITY, AND INFLATION TARGETING IN AN IS-MP MODEL Hldr Frrira d Mndonça Gabril Caldas Mons TD. Msrado m Economia Aplicada FEA/UFJF 03/009 Juiz
More informationANSWERS TO EVEN NUMBERED EXERCISES IN CHAPTER 11
8 Jun ANSWERS TO EVEN NUMBERED EXERCISES IN CHAPTER SECTION : INCENTIVE COMPATABILITY Exrcis - Educaional Signaling A yp consulan has a marginal produc of m( ) = whr Θ = {,, 3} Typs ar uniformly disribud
More information