International Monetary Economics Note 1


 Grant Logan
 2 years ago
 Views:
Transcription
1 Intenational Monetay Economics Note Let me biefly ecap on the dynamics of cuent accounts in small open economies. Conside the poblem of a epesentative consume in a county that is pefectly integated with wold capital makets and that takes as given a constant wold eal inteest ate >0. The consume is bon at date t =0and lives until t = T with pefeences U(c) ove the consumption vecto c =(c 0,c,,c T ) Fo simplicity, I assume that the consume discounts the futue at a geometic ate and has timesepaable pefeences of the fom U(c) = u (c 0 )+βu(c )+β 2 u(c 2 )+ + β T u(c T ) = β t u(c t ) This consume faces a sequence of flow budget constaints, each of the fom B t+ B t = B t + y t c t i t g t The change in net foeign assets B t+ B t is the county s cuent account balance. If B t+ >B t, the county uns a cuent account suplus in date t while if B t+ <B t,the county uns a cuent account deficit. Govenment expenditue {g t } is a known exogenous sequence. The sum B t +y t is Goss National Poduct (GNP) with Goss Domestic Poduct (GDP) denoted by y t. GDP is detemined by the physical capital stock (labo is not a facto of poduction) accoding to a poduction function y t = F (k t ) Investment is the change in the capital stock net of depeciation, i t = k t+ k t δk t whee δ denotes the depeciation ate. I will assume that δ =0so that physical capital neve depeciates. This implies that i t = k t+ k t The initial capital stock k 0 > 0 is a given paamete of the model. Choosing an investment plan is equivalent to choosing a sequence of capital installations {k t+ }. Intetempoal budget constaint The sequence of flow budget constaints can be integated to give a single intetempoal (o pesent value) budget constaint. This is done by ecusive substitution. The basic idea is to continuously eliminate the futue asset tems, B t+, fom the constaints. Mechanically, B = ()B 0 + y 0 c 0 i 0 g 0 B 2 = ()B + y c i g
2 Substituting B into the second equation gives B 2 =()[( + )B 0 + y 0 c 0 i 0 g 0 ]+y c i g Now wite out an expession fo B 3 B 3 = ()B 2 + y 2 c 2 i 2 g 2 = (){( + )[( + )B 0 + y 0 c 0 i 0 g 0 ]+y c i g } + y 2 c 2 i 2 g 2 Moe geneally, fo any t B t+ =() t+ B 0 + tx ( + ) t s (y s c s i s g s ) s=0 Dividing thoughout by the common facto ( + ) t, evaluating at t = T and eaanging gives the intetempoal budget constaint µ t µ T c t + B T + =()B 0 + Intetempoal optimization The consume s poblem is to choose a consumption vecto c and an investment plan to maximize he utility function subject to the budget constaint, the poduction function, and the definition of investment. The Lagangian fo this poblem is L = = β t u(c t )+λ ( + )B 0 + β t u(c t )+λ ( + )B 0 + (y t i t g t c t ) (F (k t ) (k t+ k t ) g t c t ) µ T B T +# µ T B T +# whee λ denotes a Lagange multiplie. The fist ode conditions that chaacteize this poblem include µ t L = 0 β t u 0 (c t ) λ =0 each t c t µ t µ t+ L = 0 λ + λ F 0 (k t+) =0 each t k t+ (We can also deive the obvious conclusion that B T + =0by noting that thee is a cost to acquiing assets in the last peiod but no offsetting benefit). The optimality conditions can be eaanged to give the familia consumptionsmoothing condition and the equiement that investment take place up to the point whee the maginal poduct of capital equals the given wold eal inteest ate. In this notation, u 0 (c t ) = β( + )u 0 (c t+ ) = F 0 (k t+ ) We can invet the last condition to solve fo the capital stock in tems of. When is constant, k t+ is constant at some k =(F 0 ) () too. With a constant exogenous wold eal inteest ate, capital accumulation is not detemined simultaneously with consumption. 2
3 The consumption function To solve fo consumption, we have to combine the fist ode condition u 0 (c t )=β( + )u 0 (c t+ ) with the budget constaint c t =()B 0 + (I have used the fact that B T + =0). Example. Suppose that β( + ) =so that the discount ate ρ β is equal to the wold eal inteest ate. Then u 0 (c t )=u 0 (c t+ ) implies that c t = c t+ = c each t We still need to solve fo this level c of consumption. Substituting into the budget constaint c =()B 0 + Since c is the same fo all t we can pull it outside of the sum c =()B 0 + Now evaluating the sum on the left hand side gives (fom a standad fomula fo geometic seies, P n i=0 xi = xn+ fo 0 <x<), x = T + = ( + ) (T +) µ So ou consumption function is c = ( + ) (T +) ( + )B 0 + # (Recall that k =(F 0 ) () so that eveything on the ight hand side can be witten in tems of exogenous vaiables). This is a vesion of the pemanent income hypothesis. The 3
4 main deteminant of consumption is intetempoal wealth (o pemanent income). The maginal popensity to consume out of wealth depends on T As T become lage, ( c = lim ( + )B T ( + ) (T +) 0 + #) = ( + )B 0 + # Thus in the longhoizon limit, consumption is simply popotional to intetempoal wealth. The infinitehoizon model In this case, the consume s pefeences ae odeed by U(c) = u (c 0 )+βu(c )+β 2 u(c 2 )+ = β t u(c t ) which is well defined if 0 <β<and the peiod utility function is eithe i) bounded, o ii) such that consumption does not gow too fast. The natual infinitehoizon budget constaint is µ t µ T c t + lim B T + =()B 0 + T In ode to make this well defined, it is standad pactice to impose a noponzigame constaint of the fom µ T lim B T + 0 T to ensue that the consume cannot ollove debt continuously. This leads to the equiement that the pesent value of consumption satisfy c t ( + )B 0 + (Of couse, if u(c t ) is stictly inceasing in c t this will always hold with equality). The same fist ode conditions can be obtained, namely, u 0 (c t ) = β( + )u 0 (c t+ ) = F 0 (k t+ ) 4
5 Example 2. Now suppose that peiod utility has the isoelastic fom u(c) = c σ σ whee σ>0denotes the constant intetempoal elasticity of substitution of the consume. Then the maginal utility of consumption at date t is u 0 (c t )=c σ t so that the consumption smoothing condition can be witten o c σ t = β( + )c σ t+ c t+ = β σ ( + ) σ c t If β( + ) =we again have that c t+ = c t. Moe geneally, we have c t =[β σ ( + ) σ ] t c 0 so that consumption at any date is a scaled up o down vesion of consumption at date zeo. As befoe, if the consume is elatively patient so that she discounts less than the wold inteest ate she has a gowing consumption path, while if the consume is elatively impatient she has a shinking consumption path. Now combine the fomula c t =[β σ ( + ) σ ] t c 0 with the intetempoal budget constaint c t =()B 0 + to detemine the initial consumption c 0. Obviously, X c 0 β σ ( + ) σ t =()B 0 + But β σ ( + ) σ t = β σ ( + ) = σ β σ ( + ) σ (Assuming that 0 <β σ ( + ) σ < ). Hence c 0 = + v ( + )B 0 + # whee the numbe v is v β σ ( + ) σ v summaizes the influence of σ and of β( + ) 6=. If β( + ) =,wehavethesame consumption function as in Example with v =0. 5
6 Dynamics of the cuent account Let me intoduce some notation which is helpful fo discussing pesent value budget constaints. Fo any vaiable x, let x t denote the pemanent value of x at date t. This is the solution to µ s t x t = µ s t x s Fo a given wold eal inteest ate >0, this is a mapping fom the sequence {x s } to the single numbe x t.specifically, x t = µ s t x s (Using P i=0 zi =( z) fo 0 <z< and eaanging). Hence the pemanent value is a measue of the cental tendency of the sequence {x s } weighted by the discount factos. Now suppose that β( + ) =as in Example. Then as in that example, the consumption function is c 0 = ( + )B 0 + O at any initial date t, c t = ( + )B t + # µ s t (y s i s g s )# (This follows using the changes of vaiable 0 7 t and t 7 s t). In tems of pemanent values, this is just c t = B t +ỹ t ĩ t g t Now ecall the flow budget constaint B t+ B t = B t + y t c t i t g t and eliminate consumption using c t = B t +ỹ t ĩ t g t.thisgives B t+ B t =(y t ỹ t ) (i t ĩ t ) (g t g t ) In this example, the cuent account B t+ B t isthesumoftheetems,eachthediffeence between a vaiable and its pemanent value. If y t is elatively high, so that y t > ỹ t, thee will (ceteis paibus) be a cuent account suplus, B t+ >B t. Similaly, if i t o g t is elatively, high, thee will be a cuent account deficit. Ove time, of couse, the pesent value of cuent accounts must be zeo. Chis Edmond, August
Chapter 3 Savings, Present Value and Ricardian Equivalence
Chapte 3 Savings, Pesent Value and Ricadian Equivalence Chapte Oveview In the pevious chapte we studied the decision of households to supply hous to the labo maket. This decision was a static decision,
More informationQuestions for Review. By buying bonds This period you save s, next period you get s(1+r)
MACROECONOMICS 2006 Week 5 Semina Questions Questions fo Review 1. How do consumes save in the twopeiod model? By buying bonds This peiod you save s, next peiod you get s() 2. What is the slope of a consume
More informationAgenda. Exchange Rates, Business Cycles, and Macroeconomic Policy in the Open Economy, Part 2. The supply of and demand for the dollar
Agenda Exchange Rates, Business Cycles, and Macoeconomic Policy in the Open Economy, Pat 2 How Exchange Rates ae Detemined (again) The ISLM Model fo an Open Economy Macoeconomic Policy in an Open Economy
More informationProblem Set # 9 Solutions
Poblem Set # 9 Solutions Chapte 12 #2 a. The invention of the new highspeed chip inceases investment demand, which shifts the cuve out. That is, at evey inteest ate, fims want to invest moe. The incease
More informationCHAPTER 10 Aggregate Demand I
CHAPTR 10 Aggegate Demand I Questions fo Review 1. The Keynesian coss tells us that fiscal policy has a multiplied effect on income. The eason is that accoding to the consumption function, highe income
More informationThe LCOE is defined as the energy price ($ per unit of energy output) for which the Net Present Value of the investment is zero.
Poject Decision Metics: Levelized Cost of Enegy (LCOE) Let s etun to ou wind powe and natual gas powe plant example fom ealie in this lesson. Suppose that both powe plants wee selling electicity into the
More informationEconomics 326: Input Demands. Ethan Kaplan
Economics 326: Input Demands Ethan Kaplan Octobe 24, 202 Outline. Tems 2. Input Demands Tems Labo Poductivity: Output pe unit of labo. Y (K; L) L What is the labo poductivity of the US? Output is ouhgly
More informationContinuous Compounding and Annualization
Continuous Compounding and Annualization Philip A. Viton Januay 11, 2006 Contents 1 Intoduction 1 2 Continuous Compounding 2 3 Pesent Value with Continuous Compounding 4 4 Annualization 5 5 A Special Poblem
More informationControlling the Money Supply: Bond Purchases in the Open Market
Money Supply By the Bank of Canada and Inteest Rate Detemination Open Opeations and Monetay Tansmission Mechanism The Cental Bank conducts monetay policy Bank of Canada is Canada's cental bank supevises
More informationAMB111F Financial Maths Notes
AMB111F Financial Maths Notes Compound Inteest and Depeciation Compound Inteest: Inteest computed on the cuent amount that inceases at egula intevals. Simple inteest: Inteest computed on the oiginal fixed
More informationPersonal Saving Rate (S Households /Y) SAVING AND INVESTMENT. Federal Surplus or Deficit () Total Private Saving Rate (S Private /Y) 12/18/2009
1 Pesonal Saving Rate (S Households /Y) 2 SAVING AND INVESTMENT 16.0 14.0 12.0 10.0 80 8.0 6.0 4.0 2.0 0.02.04.0 1959 1961 1967 1969 1975 1977 1983 1985 1991 1993 1999 2001 2007 2009 Pivate Saving Rate
More information2 r2 θ = r2 t. (3.59) The equal area law is the statement that the term in parentheses,
3.4. KEPLER S LAWS 145 3.4 Keple s laws You ae familia with the idea that one can solve some mechanics poblems using only consevation of enegy and (linea) momentum. Thus, some of what we see as objects
More informationOpen Economies. Chapter 32. A Macroeconomic Theory of the Open Economy. Basic Assumptions of a Macroeconomic Model of an Open Economy
Chapte 32. A Macoeconomic Theoy of the Open Economy Open Economies An open economy is one that inteacts feely with othe economies aound the wold. slide 0 slide 1 Key Macoeconomic Vaiables in an Open Economy
More informationPower and Sample Size Calculations for the 2Sample ZStatistic
Powe and Sample Size Calculations fo the Sample ZStatistic James H. Steige ovembe 4, 004 Topics fo this Module. Reviewing Results fo the Sample Z (a) Powe and Sample Size in Tems of a oncentality Paamete.
More informationINITIAL MARGIN CALCULATION ON DERIVATIVE MARKETS OPTION VALUATION FORMULAS
INITIAL MARGIN CALCULATION ON DERIVATIVE MARKETS OPTION VALUATION FORMULAS Vesion:.0 Date: June 0 Disclaime This document is solely intended as infomation fo cleaing membes and othes who ae inteested in
More informationIlona V. Tregub, ScD., Professor
Investment Potfolio Fomation fo the Pension Fund of Russia Ilona V. egub, ScD., Pofesso Mathematical Modeling of Economic Pocesses Depatment he Financial Univesity unde the Govenment of the Russian Fedeation
More informationValuation of Floating Rate Bonds 1
Valuation of Floating Rate onds 1 Joge uz Lopez us 316: Deivative Secuities his note explains how to value plain vanilla floating ate bonds. he pupose of this note is to link the concepts that you leaned
More information4a 4ab b 4 2 4 2 5 5 16 40 25. 5.6 10 6 (count number of places from first nonzero digit to
. Simplify: 0 4 ( 8) 0 64 ( 8) 0 ( 8) = (Ode of opeations fom left to ight: Paenthesis, Exponents, Multiplication, Division, Addition Subtaction). Simplify: (a 4) + (a ) (a+) = a 4 + a 0 a = a 7. Evaluate
More informationFinancing Terms in the EOQ Model
Financing Tems in the EOQ Model Habone W. Stuat, J. Columbia Business School New Yok, NY 1007 hws7@columbia.edu August 6, 004 1 Intoduction This note discusses two tems that ae often omitted fom the standad
More informationLINES AND TANGENTS IN POLAR COORDINATES
LINES AND TANGENTS IN POLAR COORDINATES ROGER ALEXANDER DEPARTMENT OF MATHEMATICS 1. Polacoodinate equations fo lines A pola coodinate system in the plane is detemined by a point P, called the pole, and
More informationSTUDENT RESPONSE TO ANNUITY FORMULA DERIVATION
Page 1 STUDENT RESPONSE TO ANNUITY FORMULA DERIVATION C. Alan Blaylock, Hendeson State Univesity ABSTRACT This pape pesents an intuitive appoach to deiving annuity fomulas fo classoom use and attempts
More informationHour Exam No.1. p 1 v. p = e 0 + v^b. Note that the probe is moving in the direction of the unit vector ^b so the velocity vector is just ~v = v^b and
Hou Exam No. Please attempt all of the following poblems befoe the due date. All poblems count the same even though some ae moe complex than othes. Assume that c units ae used thoughout. Poblem A photon
More informationCoordinate Systems L. M. Kalnins, March 2009
Coodinate Sstems L. M. Kalnins, Mach 2009 Pupose of a Coodinate Sstem The pupose of a coodinate sstem is to uniquel detemine the position of an object o data point in space. B space we ma liteall mean
More informationConverting knowledge Into Practice
Conveting knowledge Into Pactice Boke Nightmae srs Tend Ride By Vladimi Ribakov Ceato of Pips Caie 20 of June 2010 2 0 1 0 C o p y i g h t s V l a d i m i R i b a k o v 1 Disclaime and Risk Wanings Tading
More informationFI3300 Corporate Finance
Leaning Objectives FI00 Copoate Finance Sping Semeste 2010 D. Isabel Tkatch Assistant Pofesso of Finance Calculate the PV and FV in multipeiod multicf timevalueofmoney poblems: Geneal case Pepetuity
More informationUNIT CIRCLE TRIGONOMETRY
UNIT CIRCLE TRIGONOMETRY The Unit Cicle is the cicle centeed at the oigin with adius unit (hence, the unit cicle. The equation of this cicle is + =. A diagam of the unit cicle is shown below: + =   
More informationest using the formula I = Prt, where I is the interest earned, P is the principal, r is the interest rate, and t is the time in years.
9.2 Inteest Objectives 1. Undestand the simple inteest fomula. 2. Use the compound inteest fomula to find futue value. 3. Solve the compound inteest fomula fo diffeent unknowns, such as the pesent value,
More informationSymmetric polynomials and partitions Eugene Mukhin
Symmetic polynomials and patitions Eugene Mukhin. Symmetic polynomials.. Definition. We will conside polynomials in n vaiables x,..., x n and use the shotcut p(x) instead of p(x,..., x n ). A pemutation
More informationChapter 4: Matrix Norms
EE448/58 Vesion.0 John Stensby Chate 4: Matix Noms The analysis of matixbased algoithms often equies use of matix noms. These algoithms need a way to quantify the "size" of a matix o the "distance" between
More informationIntertemporal Macroeconomics
Intetempoal Macoeconomics Genot Doppelhofe* May 2009 Fothcoming in J. McCombie and N. Allington (eds.), Cambidge Essays in Applied Economics, Cambidge UP This chapte eviews models of intetempoal choice
More informationNontrivial lower bounds for the least common multiple of some finite sequences of integers
J. Numbe Theoy, 15 (007), p. 393411. Nontivial lowe bounds fo the least common multiple of some finite sequences of integes Bai FARHI bai.fahi@gmail.com Abstact We pesent hee a method which allows to
More informationDetermining solar characteristics using planetary data
Detemining sola chaacteistics using planetay data Intoduction The Sun is a G type main sequence sta at the cente of the Sola System aound which the planets, including ou Eath, obit. In this inestigation
More informationSkills Needed for Success in Calculus 1
Skills Needed fo Success in Calculus Thee is much appehension fom students taking Calculus. It seems that fo man people, "Calculus" is snonmous with "difficult." Howeve, an teache of Calculus will tell
More informationThe Supply of Loanable Funds: A Comment on the Misconception and Its Implications
JOURNL OF ECONOMICS ND FINNCE EDUCTION Volume 7 Numbe 2 Winte 2008 39 The Supply of Loanable Funds: Comment on the Misconception and Its Implications. Wahhab Khandke and mena Khandke* STRCT Recently FieldsHat
More informationProblem Set 6: Solutions
UNIVESITY OF ALABAMA Depatment of Physics and Astonomy PH 164 / LeClai Fall 28 Poblem Set 6: Solutions 1. Seway 29.55 Potons having a kinetic enegy of 5. MeV ae moving in the positive x diection and ente
More informationTheory and practise of the gindex
Theoy and pactise of the gindex by L. Egghe (*), Univesiteit Hasselt (UHasselt), Campus Diepenbeek, Agoalaan, B3590 Diepenbeek, Belgium Univesiteit Antwepen (UA), Campus Die Eiken, Univesiteitsplein,
More informationFigure 2. So it is very likely that the Babylonians attributed 60 units to each side of the hexagon. Its resulting perimeter would then be 360!
1. What ae angles? Last time, we looked at how the Geeks intepeted measument of lengths. Howeve, as fascinated as they wee with geomety, thee was a shape that was much moe enticing than any othe : the
More informationMechanics 1: Work, Power and Kinetic Energy
Mechanics 1: Wok, Powe and Kinetic Eneg We fist intoduce the ideas of wok and powe. The notion of wok can be viewed as the bidge between Newton s second law, and eneg (which we have et to define and discuss).
More information1.4 Phase Line and Bifurcation Diag
Dynamical Systems: Pat 2 2 Bifucation Theoy In pactical applications that involve diffeential equations it vey often happens that the diffeential equation contains paametes and the value of these paametes
More informationAlgebra and Trig. I. A point is a location or position that has no size or dimension.
Algeba and Tig. I 4.1 Angles and Radian Measues A Point A A B Line AB AB A point is a location o position that has no size o dimension. A line extends indefinitely in both diections and contains an infinite
More informationEquity compensation plans New Income Statement impact on guidance Earnings Per Share Questions and answers
Investos/Analysts Confeence: Accounting Wokshop Agenda Equity compensation plans New Income Statement impact on guidance Eanings Pe Shae Questions and answes IAC03 / a / 1 1 Equity compensation plans The
More informationPushing the Limit? Fiscal Policy in the European Monetary Union
Pushing the Limit? Fiscal Policy in the Euopean Monetay Union Betty C. Daniel Depatment of Economics Univesity at Albany Albany, NY 12222 b.daniel@albany.edu Chistos Shiamptanis Depatment of Economics
More informationYIELD TO MATURITY ACCRUED INTEREST QUOTED PRICE INVOICE PRICE
YIELD TO MATURITY ACCRUED INTEREST QUOTED PRICE INVOICE PRICE Septembe 1999 Quoted Rate Teasuy Bills [Called Banke's Discount Rate] d = [ P 1  P 1 P 0 ] * 360 [ N ] d = Bankes discount yield P 1 = face
More informationAN IMPLEMENTATION OF BINARY AND FLOATING POINT CHROMOSOME REPRESENTATION IN GENETIC ALGORITHM
AN IMPLEMENTATION OF BINARY AND FLOATING POINT CHROMOSOME REPRESENTATION IN GENETIC ALGORITHM Main Golub Faculty of Electical Engineeing and Computing, Univesity of Zageb Depatment of Electonics, Micoelectonics,
More informationSoftware Engineering and Development
I T H E A 67 Softwae Engineeing and Development SOFTWARE DEVELOPMENT PROCESS DYNAMICS MODELING AS STATE MACHINE Leonid Lyubchyk, Vasyl Soloshchuk Abstact: Softwae development pocess modeling is gaining
More informationThe Binomial Distribution
The Binomial Distibution A. It would be vey tedious if, evey time we had a slightly diffeent poblem, we had to detemine the pobability distibutions fom scatch. Luckily, thee ae enough similaities between
More informationThe transport performance evaluation system building of logistics enterprises
Jounal of Industial Engineeing and Management JIEM, 213 6(4): 194114 Online ISSN: 213953 Pint ISSN: 2138423 http://dx.doi.og/1.3926/jiem.784 The tanspot pefomance evaluation system building of logistics
More informationQuestions & Answers Chapter 10 Software Reliability Prediction, Allocation and Demonstration Testing
M13914 Questions & Answes Chapte 10 Softwae Reliability Pediction, Allocation and Demonstation Testing 1. Homewok: How to deive the fomula of failue ate estimate. λ = χ α,+ t When the failue times follow
More informationHow Much Should a Firm Borrow. Effect of tax shields. Capital Structure Theory. Capital Structure & Corporate Taxes
How Much Should a Fim Boow Chapte 19 Capital Stuctue & Copoate Taxes Financial Risk  Risk to shaeholdes esulting fom the use of debt. Financial Leveage  Incease in the vaiability of shaeholde etuns that
More informationFirstmark Credit Union Commercial Loan Department
Fistmak Cedit Union Commecial Loan Depatment Thank you fo consideing Fistmak Cedit Union as a tusted souce to meet the needs of you business. Fistmak Cedit Union offes a wide aay of business loans and
More informationGauss Law. Physics 231 Lecture 21
Gauss Law Physics 31 Lectue 1 lectic Field Lines The numbe of field lines, also known as lines of foce, ae elated to stength of the electic field Moe appopiately it is the numbe of field lines cossing
More informationChannel selection in ecommerce age: A strategic analysis of coop advertising models
Jounal of Industial Engineeing and Management JIEM, 013 6(1):89103 Online ISSN: 0130953 Pint ISSN: 013843 http://dx.doi.og/10.396/jiem.664 Channel selection in ecommece age: A stategic analysis of
More informationVector Calculus: Are you ready? Vectors in 2D and 3D Space: Review
Vecto Calculus: Ae you eady? Vectos in D and 3D Space: Review Pupose: Make cetain that you can define, and use in context, vecto tems, concepts and fomulas listed below: Section 7.7. find the vecto defined
More informationEpisode 401: Newton s law of universal gravitation
Episode 401: Newton s law of univesal gavitation This episode intoduces Newton s law of univesal gavitation fo point masses, and fo spheical masses, and gets students pactising calculations of the foce
More informationConcept and Experiences on using a Wikibased System for Softwarerelated Seminar Papers
Concept and Expeiences on using a Wikibased System fo Softwaeelated Semina Papes Dominik Fanke and Stefan Kowalewski RWTH Aachen Univesity, 52074 Aachen, Gemany, {fanke, kowalewski}@embedded.wthaachen.de,
More informationMagnetic Field and Magnetic Forces. Young and Freedman Chapter 27
Magnetic Field and Magnetic Foces Young and Feedman Chapte 27 Intoduction Reiew  electic fields 1) A chage (o collection of chages) poduces an electic field in the space aound it. 2) The electic field
More informationThings to Remember. r Complete all of the sections on the Retirement Benefit Options form that apply to your request.
Retiement Benefit 1 Things to Remembe Complete all of the sections on the Retiement Benefit fom that apply to you equest. If this is an initial equest, and not a change in a cuent distibution, emembe to
More information1240 ev nm 2.5 ev. (4) r 2 or mv 2 = ke2
Chapte 5 Example The helium atom has 2 electonic enegy levels: E 3p = 23.1 ev and E 2s = 20.6 ev whee the gound state is E = 0. If an electon makes a tansition fom 3p to 2s, what is the wavelength of the
More informationA Capacitated Commodity Trading Model with Market Power
A Capacitated Commodity Tading Model with Maket Powe Victo MatínezdeAlbéniz Josep Maia Vendell Simón IESE Business School, Univesity of Navaa, Av. Peason 1, 08034 Bacelona, Spain VAlbeniz@iese.edu JMVendell@iese.edu
More informationUnit Vectors. the unit vector rˆ. Thus, in the case at hand, 5.00 rˆ, means 5.00 m/s at 36.0.
Unit Vectos What is pobabl the most common mistake involving unit vectos is simpl leaving thei hats off. While leaving the hat off a unit vecto is a nast communication eo in its own ight, it also leads
More informationAn Introduction to Omega
An Intoduction to Omega Con Keating and William F. Shadwick These distibutions have the same mean and vaiance. Ae you indiffeent to thei iskewad chaacteistics? The Finance Development Cente 2002 1 Fom
More informationBasic Financial Mathematics
Financial Engineeing and Computations Basic Financial Mathematics Dai, TianShy Outline Time Value of Money Annuities Amotization Yields Bonds Time Value of Money PV + n = FV (1 + FV: futue value = PV
More informationCONCEPT OF TIME AND VALUE OFMONEY. Simple and Compound interest
CONCEPT OF TIME AND VALUE OFMONEY Simple and Compound inteest What is the futue value of shs 10,000 invested today to ean an inteest of 12% pe annum inteest payable fo 10 yeas and is compounded; a. Annually
More informationSemipartial (Part) and Partial Correlation
Semipatial (Pat) and Patial Coelation his discussion boows heavily fom Applied Multiple egession/coelation Analysis fo the Behavioal Sciences, by Jacob and Paticia Cohen (975 edition; thee is also an updated
More informationGESTÃO FINANCEIRA II PROBLEM SET 1  SOLUTIONS
GESTÃO FINANCEIRA II PROBLEM SET 1  SOLUTIONS (FROM BERK AND DEMARZO S CORPORATE FINANCE ) LICENCIATURA UNDERGRADUATE COURSE 1 ST SEMESTER 20102011 Chapte 1 The Copoation 113. What is the diffeence
More informationGRADE 5 TEXAS. Multiplication and Division WORKSHEETS
GRADE 5 TEXAS Multiplication and Division WORKSHEETS Multidigit multiplication Multiplying lage numbes is a pocess of multiple steps. Fist, you multiply: 542 6 =,252 2 You have now used up all you ones.
More informationFXA 2008. Candidates should be able to : Describe how a mass creates a gravitational field in the space around it.
Candidates should be able to : Descibe how a mass ceates a gavitational field in the space aound it. Define gavitational field stength as foce pe unit mass. Define and use the peiod of an object descibing
More informationContingent capital with repeated interconversion between debt and equity
Contingent capital with epeated inteconvesion between debt and equity Zhaojun Yang 1, Zhiming Zhao School of Finance and Statistics, Hunan Univesity, Changsha 410079, China Abstact We develop a new type
More informationDefinitions and terminology
I love the Case & Fai textbook but it is out of date with how monetay policy woks today. Please use this handout to supplement the chapte on monetay policy. The textbook assumes that the Fedeal Reseve
More informationTrading Volume and Serial Correlation in Stock Returns in Pakistan. Abstract
Tading Volume and Seial Coelation in Stock Retuns in Pakistan Khalid Mustafa Assistant Pofesso Depatment of Economics, Univesity of Kaachi email: khalidku@yahoo.com and Mohammed Nishat Pofesso and Chaiman,
More informationChapter 30: Magnetic Fields Due to Currents
d Chapte 3: Magnetic Field Due to Cuent A moving electic chage ceate a magnetic field. One of the moe pactical way of geneating a lage magnetic field (.11 T) i to ue a lage cuent flowing though a wie.
More informationFinancial Planning and Riskreturn profiles
Financial Planning and Risketun pofiles Stefan Gaf, Alexande Kling und Jochen Russ Pepint Seies: 201016 Fakultät fü Mathematik und Witschaftswissenschaften UNIERSITÄT ULM Financial Planning and Risketun
More informationData Center Demand Response: Avoiding the Coincident Peak via Workload Shifting and Local Generation
(213) 1 28 Data Cente Demand Response: Avoiding the Coincident Peak via Wokload Shifting and Local Geneation Zhenhua Liu 1, Adam Wieman 1, Yuan Chen 2, Benjamin Razon 1, Niangjun Chen 1 1 Califonia Institute
More informationVoltage ( = Electric Potential )
V1 of 9 Voltage ( = lectic Potential ) An electic chage altes the space aound it. Thoughout the space aound evey chage is a vecto thing called the electic field. Also filling the space aound evey chage
More informationPhysics 235 Chapter 5. Chapter 5 Gravitation
Chapte 5 Gavitation In this Chapte we will eview the popeties of the gavitational foce. The gavitational foce has been discussed in geat detail in you intoductoy physics couses, and we will pimaily focus
More informationRevision Guide for Chapter 11
Revision Guide fo Chapte 11 Contents Student s Checklist Revision Notes Momentum... 4 Newton's laws of motion... 4 Gavitational field... 5 Gavitational potential... 6 Motion in a cicle... 7 Summay Diagams
More informationLife Insurance Purchasing to Reach a Bequest. Erhan Bayraktar Department of Mathematics, University of Michigan Ann Arbor, Michigan, USA, 48109
Life Insuance Puchasing to Reach a Bequest Ehan Bayakta Depatment of Mathematics, Univesity of Michigan Ann Abo, Michigan, USA, 48109 S. David Pomislow Depatment of Mathematics, Yok Univesity Toonto, Ontaio,
More information2. SCALARS, VECTORS, TENSORS, AND DYADS
2. SCALARS, VECTORS, TENSORS, AND DYADS This section is a eview of the popeties of scalas, vectos, and tensos. We also intoduce the concept of a dyad, which is useful in MHD. A scala is a quantity that
More informationAn Analysis of Manufacturer Benefits under Vendor Managed Systems
An Analysis of Manufactue Benefits unde Vendo Managed Systems Seçil Savaşaneil Depatment of Industial Engineeing, Middle East Technical Univesity, 06531, Ankaa, TURKEY secil@ie.metu.edu.t Nesim Ekip 1
More informationSaturated and weakly saturated hypergraphs
Satuated and weakly satuated hypegaphs Algebaic Methods in Combinatoics, Lectues 67 Satuated hypegaphs Recall the following Definition. A family A P([n]) is said to be an antichain if we neve have A B
More informationExperimentation under Uninsurable Idiosyncratic Risk: An Application to Entrepreneurial Survival
Expeimentation unde Uninsuable Idiosyncatic Risk: An Application to Entepeneuial Suvival Jianjun Miao and Neng Wang May 28, 2007 Abstact We popose an analytically tactable continuoustime model of expeimentation
More informationThe PersonalTax Advantages of Equity
The PesonalTax Advantages of Equity Richad C. Geen and Buton Hollifield Gaduate School of Industial Administation Canegie Mellon Univesity Decembe 23, 999 Discussions with Piee Collin Dufesne, Bob Dammon,
More informationProgramming Assignment #1
Due: Nov 3 (11:59pm). Pogamming Assignment #1 CMSC 351 Fall 2014 Rules 1) You may only use C/C++, Java. 2) You pogam should use the standad input/output. Fo example C/C++ uses should use scanf/pintf/cin/cout
More informationOptimal Peer Selection in a FreeMarket PeerResource Economy
Optimal Pee Selection in a FeeMaket PeeResouce Economy Micah Adle, Rakesh Kuma, Keith Ross, Dan Rubenstein, David Tune and David D Yao Dept of Compute Science Univesity of Massachusetts Amhest, MA; Email:
More informationSpirotechnics! September 7, 2011. Amanda Zeringue, Michael Spannuth and Amanda Zeringue Dierential Geometry Project
Spiotechnics! Septembe 7, 2011 Amanda Zeingue, Michael Spannuth and Amanda Zeingue Dieential Geomety Poject 1 The Beginning The geneal consensus of ou goup began with one thought: Spiogaphs ae awesome.
More informationLiquidity and Insurance for the Unemployed
Liquidity and Insuance fo the Unemployed Robet Shime Univesity of Chicago and NBER shime@uchicago.edu Iván Wening MIT, NBER and UTDT iwening@mit.edu Fist Daft: July 15, 2003 This Vesion: Septembe 22, 2005
More informationCRRC1 Method #1: Standard Practice for Measuring Solar Reflectance of a Flat, Opaque, and Heterogeneous Surface Using a Portable Solar Reflectometer
CRRC Method #: Standad Pactice fo Measuing Sola Reflectance of a Flat, Opaque, and Heteogeneous Suface Using a Potable Sola Reflectomete Scope This standad pactice coves a technique fo estimating the
More informationJapan s trading losses reach JPY20 trillion
IEEJ: Mach 2014. All Rights Reseved. Japan s tading losses each JPY20 tillion Enegy accounts fo moe than half of the tading losses YANAGISAWA Akia Senio Economist Enegy Demand, Supply and Foecast Goup
More informationModel Question Paper Mathematics Class XII
Model Question Pape Mathematics Class XII Time Allowed : 3 hous Maks: 100 Ma: Geneal Instuctions (i) The question pape consists of thee pats A, B and C. Each question of each pat is compulsoy. (ii) Pat
More informationPhysics 505 Homework No. 5 Solutions S51. 1. Angular momentum uncertainty relations. A system is in the lm eigenstate of L 2, L z.
Physics 55 Homewok No. 5 s S5. Angula momentum uncetainty elations. A system is in the lm eigenstate of L 2, L z. a Show that the expectation values of L ± = L x ± il y, L x, and L y all vanish. ψ lm
More information81 Newton s Law of Universal Gravitation
81 Newton s Law of Univesal Gavitation One of the most famous stoies of all time is the stoy of Isaac Newton sitting unde an apple tee and being hit on the head by a falling apple. It was this event,
More informationLecture 16: Color and Intensity. and he made him a coat of many colours. Genesis 37:3
Lectue 16: Colo and Intensity and he made him a coat of many colous. Genesis 37:3 1. Intoduction To display a pictue using Compute Gaphics, we need to compute the colo and intensity of the light at each
More informationPAN STABILITY TESTING OF DC CIRCUITS USING VARIATIONAL METHODS XVIII  SPETO  1995. pod patronatem. Summary
PCE SEMINIUM Z PODSTW ELEKTOTECHNIKI I TEOII OBWODÓW 8  TH SEMIN ON FUNDMENTLS OF ELECTOTECHNICS ND CICUIT THEOY ZDENĚK BIOLEK SPŠE OŽNO P.., CZECH EPUBLIC DLIBO BIOLEK MILITY CDEMY, BNO, CZECH EPUBLIC
More informationTECHNICAL DATA. JIS (Japanese Industrial Standard) Screw Thread. Specifications
JIS (Japanese Industial Standad) Scew Thead Specifications TECNICAL DATA Note: Although these specifications ae based on JIS they also apply to and DIN s. Some comments added by Mayland Metics Coutesy
More informationImmigration Restrictions and Labor Market Skills Preliminary and Incomplete
Immigation Restictions and Labo Maket Skills Peliminay and Incomplete John Kennan Univesity of WisconsinMadison and NBER Apil 2014 Abstact Diffeences in income levels acoss counties ae geneally attibuted
More informationHow do investments in heat pumps affect household energy consumption?
Discussion Papes Statistics Noway Reseach depatment No. 737 Apil 203 Bente Halvosen and Bodil Meethe Lasen How do investments in heat pumps affect household enegy consumption? Discussion Papes No. 737,
More informationWeek 34: Permutations and Combinations
Week 34: Pemutations and Combinations Febuay 24, 2016 1 Two Counting Pinciples Addition Pinciple Let S 1, S 2,, S m be disjoint subsets of a finite set S If S S 1 S 2 S m, then S S 1 + S 2 + + S m Multiplication
More information2. TRIGONOMETRIC FUNCTIONS OF GENERAL ANGLES
. TRIGONOMETRIC FUNCTIONS OF GENERAL ANGLES In ode to etend the definitions of the si tigonometic functions to geneal angles, we shall make use of the following ideas: In a Catesian coodinate sstem, an
More informationDefinitions. Optimization of online direct marketing efforts. Test 1: Two Email campaigns. Raw Results. Xavier Drèze André Bonfrer. Lucid.
Definitions Optimization of online diect maketing effots Xavie Dèze Andé Bonfe Lucid Easily undestood; intelligible. Mentally sound; sane o ational. Tanslucent o tanspaent. Limpid Chaacteized by tanspaent
More informationVoltage ( = Electric Potential )
V1 Voltage ( = Electic Potential ) An electic chage altes the space aound it. Thoughout the space aound evey chage is a vecto thing called the electic field. Also filling the space aound evey chage is
More information