International Monetary Economics Note 1

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "International Monetary Economics Note 1"

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 time-sepaable 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 consumption-smoothing 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 long-hoizon limit, consumption is simply popotional to intetempoal wealth. The infinite-hoizon 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 infinite-hoizon 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 no-ponzi-game constaint of the fom µ T lim B T + 0 T to ensue that the consume cannot oll-ove 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

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 information

Questions for Review. By buying bonds This period you save s, next period you get s(1+r)

Questions 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 two-peiod model? By buying bonds This peiod you save s, next peiod you get s() 2. What is the slope of a consume

More information

Agenda. 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 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 IS-LM Model fo an Open Economy Macoeconomic Policy in an Open Economy

More information

Problem Set # 9 Solutions

Problem Set # 9 Solutions Poblem Set # 9 Solutions Chapte 12 #2 a. The invention of the new high-speed chip inceases investment demand, which shifts the cuve out. That is, at evey inteest ate, fims want to invest moe. The incease

More information

CHAPTER 10 Aggregate Demand I

CHAPTER 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 information

The LCOE is defined as the energy price ($ per unit of energy output) for which the Net Present Value of the investment is zero.

The 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 information

Economics 326: Input Demands. Ethan Kaplan

Economics 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 information

Continuous Compounding and Annualization

Continuous 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 information

Controlling the Money Supply: Bond Purchases in the Open Market

Controlling 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 information

AMB111F Financial Maths Notes

AMB111F 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 information

Personal Saving Rate (S Households /Y) SAVING AND INVESTMENT. Federal Surplus or Deficit (-) Total Private Saving Rate (S Private /Y) 12/18/2009

Personal 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 0.0-2.0-4.0 1959 1961 1967 1969 1975 1977 1983 1985 1991 1993 1999 2001 2007 2009 Pivate Saving Rate

More information

2 r2 θ = r2 t. (3.59) The equal area law is the statement that the term in parentheses,

2 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 information

Open Economies. Chapter 32. A Macroeconomic Theory of the Open Economy. Basic Assumptions of a Macroeconomic Model of an Open Economy

Open 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 information

Power and Sample Size Calculations for the 2-Sample Z-Statistic

Power and Sample Size Calculations for the 2-Sample Z-Statistic Powe and Sample Size Calculations fo the -Sample Z-Statistic 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 information

INITIAL MARGIN CALCULATION ON DERIVATIVE MARKETS OPTION VALUATION FORMULAS

INITIAL 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 information

Ilona V. Tregub, ScD., Professor

Ilona 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 information

Valuation of Floating Rate Bonds 1

Valuation 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 information

4a 4ab b 4 2 4 2 5 5 16 40 25. 5.6 10 6 (count number of places from first non-zero digit to

4a 4ab b 4 2 4 2 5 5 16 40 25. 5.6 10 6 (count number of places from first non-zero 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 information

Financing Terms in the EOQ Model

Financing 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 information

LINES AND TANGENTS IN POLAR COORDINATES

LINES AND TANGENTS IN POLAR COORDINATES LINES AND TANGENTS IN POLAR COORDINATES ROGER ALEXANDER DEPARTMENT OF MATHEMATICS 1. Pola-coodinate equations fo lines A pola coodinate system in the plane is detemined by a point P, called the pole, and

More information

STUDENT RESPONSE TO ANNUITY FORMULA DERIVATION

STUDENT 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 information

Hour 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

Hour 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 information

Coordinate Systems L. M. Kalnins, March 2009

Coordinate 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 information

Converting knowledge Into Practice

Converting 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 information

FI3300 Corporate Finance

FI3300 Corporate Finance Leaning Objectives FI00 Copoate Finance Sping Semeste 2010 D. Isabel Tkatch Assistant Pofesso of Finance Calculate the PV and FV in multi-peiod multi-cf time-value-of-money poblems: Geneal case Pepetuity

More information

UNIT CIRCLE TRIGONOMETRY

UNIT 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 information

est 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.

est 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 information

Symmetric polynomials and partitions Eugene Mukhin

Symmetric 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 information

Chapter 4: Matrix Norms

Chapter 4: Matrix Norms EE448/58 Vesion.0 John Stensby Chate 4: Matix Noms The analysis of matix-based algoithms often equies use of matix noms. These algoithms need a way to quantify the "size" of a matix o the "distance" between

More information

Intertemporal Macroeconomics

Intertemporal 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 information

Nontrivial lower bounds for the least common multiple of some finite sequences of integers

Nontrivial lower bounds for the least common multiple of some finite sequences of integers J. Numbe Theoy, 15 (007), p. 393-411. 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 information

Determining solar characteristics using planetary data

Determining 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 information

Skills Needed for Success in Calculus 1

Skills 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 information

The Supply of Loanable Funds: A Comment on the Misconception and Its Implications

The 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 Fields-Hat

More information

Problem Set 6: Solutions

Problem Set 6: Solutions UNIVESITY OF ALABAMA Depatment of Physics and Astonomy PH 16-4 / 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 information

Theory and practise of the g-index

Theory and practise of the g-index Theoy and pactise of the g-index by L. Egghe (*), Univesiteit Hasselt (UHasselt), Campus Diepenbeek, Agoalaan, B-3590 Diepenbeek, Belgium Univesiteit Antwepen (UA), Campus Die Eiken, Univesiteitsplein,

More information

Figure 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!

Figure 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 information

Mechanics 1: Work, Power and Kinetic Energy

Mechanics 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 information

1.4 Phase Line and Bifurcation Diag

1.4 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 information

Algebra and Trig. I. A point is a location or position that has no size or dimension.

Algebra 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 information

Equity compensation plans New Income Statement impact on guidance Earnings Per Share Questions and answers

Equity 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 information

Pushing the Limit? Fiscal Policy in the European Monetary Union

Pushing 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 information

YIELD TO MATURITY ACCRUED INTEREST QUOTED PRICE INVOICE PRICE

YIELD 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 information

AN IMPLEMENTATION OF BINARY AND FLOATING POINT CHROMOSOME REPRESENTATION IN GENETIC ALGORITHM

AN 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 information

Software Engineering and Development

Software 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 information

The Binomial Distribution

The 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 information

The transport performance evaluation system building of logistics enterprises

The transport performance evaluation system building of logistics enterprises Jounal of Industial Engineeing and Management JIEM, 213 6(4): 194-114 Online ISSN: 213-953 Pint ISSN: 213-8423 http://dx.doi.og/1.3926/jiem.784 The tanspot pefomance evaluation system building of logistics

More information

Questions & Answers Chapter 10 Software Reliability Prediction, Allocation and Demonstration Testing

Questions & 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 information

How Much Should a Firm Borrow. Effect of tax shields. Capital Structure Theory. Capital Structure & Corporate Taxes

How 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 information

Firstmark Credit Union Commercial Loan Department

Firstmark 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 information

Gauss Law. Physics 231 Lecture 2-1

Gauss Law. Physics 231 Lecture 2-1 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 information

Channel selection in e-commerce age: A strategic analysis of co-op advertising models

Channel selection in e-commerce age: A strategic analysis of co-op advertising models Jounal of Industial Engineeing and Management JIEM, 013 6(1):89-103 Online ISSN: 013-0953 Pint ISSN: 013-843 http://dx.doi.og/10.396/jiem.664 Channel selection in e-commece age: A stategic analysis of

More information

Vector Calculus: Are you ready? Vectors in 2D and 3D Space: Review

Vector 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 information

Episode 401: Newton s law of universal gravitation

Episode 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 information

Concept and Experiences on using a Wiki-based System for Software-related Seminar Papers

Concept and Experiences on using a Wiki-based System for Software-related Seminar Papers Concept and Expeiences on using a Wiki-based System fo Softwae-elated Semina Papes Dominik Fanke and Stefan Kowalewski RWTH Aachen Univesity, 52074 Aachen, Gemany, {fanke, kowalewski}@embedded.wth-aachen.de,

More information

Magnetic Field and Magnetic Forces. Young and Freedman Chapter 27

Magnetic 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 information

Things to Remember. r Complete all of the sections on the Retirement Benefit Options form that apply to your request.

Things 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 information

1240 ev nm 2.5 ev. (4) r 2 or mv 2 = ke2

1240 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 information

A Capacitated Commodity Trading Model with Market Power

A Capacitated Commodity Trading Model with Market Power A Capacitated Commodity Tading Model with Maket Powe Victo Matínez-de-Albéniz Josep Maia Vendell Simón IESE Business School, Univesity of Navaa, Av. Peason 1, 08034 Bacelona, Spain VAlbeniz@iese.edu JMVendell@iese.edu

More information

Unit Vectors. the unit vector rˆ. Thus, in the case at hand, 5.00 rˆ, means 5.00 m/s at 36.0.

Unit 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 information

An Introduction to Omega

An 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 isk-ewad chaacteistics? The Finance Development Cente 2002 1 Fom

More information

Basic Financial Mathematics

Basic Financial Mathematics Financial Engineeing and Computations Basic Financial Mathematics Dai, Tian-Shy Outline Time Value of Money Annuities Amotization Yields Bonds Time Value of Money PV + n = FV (1 + FV: futue value = PV

More information

CONCEPT OF TIME AND VALUE OFMONEY. Simple and Compound interest

CONCEPT 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 information

Semipartial (Part) and Partial Correlation

Semipartial (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 information

GESTÃO FINANCEIRA II PROBLEM SET 1 - SOLUTIONS

GESTÃO 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 2010-2011 Chapte 1 The Copoation 1-13. What is the diffeence

More information

GRADE 5 TEXAS. Multiplication and Division WORKSHEETS

GRADE 5 TEXAS. Multiplication and Division WORKSHEETS GRADE 5 TEXAS Multiplication and Division WORKSHEETS Multi-digit 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 information

FXA 2008. Candidates should be able to : Describe how a mass creates a gravitational field in the space around it.

FXA 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 information

Contingent capital with repeated interconversion between debt and equity

Contingent 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 information

Definitions and terminology

Definitions 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 information

Trading Volume and Serial Correlation in Stock Returns in Pakistan. Abstract

Trading 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 e-mail: khalidku@yahoo.com and Mohammed Nishat Pofesso and Chaiman,

More information

Chapter 30: Magnetic Fields Due to Currents

Chapter 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 (.1-1 T) i to ue a lage cuent flowing though a wie.

More information

Financial Planning and Risk-return profiles

Financial Planning and Risk-return profiles Financial Planning and Risk-etun pofiles Stefan Gaf, Alexande Kling und Jochen Russ Pepint Seies: 2010-16 Fakultät fü Mathematik und Witschaftswissenschaften UNIERSITÄT ULM Financial Planning and Risk-etun

More information

Data Center Demand Response: Avoiding the Coincident Peak via Workload Shifting and Local Generation

Data 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 information

Voltage ( = Electric Potential )

Voltage ( = Electric Potential ) V-1 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 information

Physics 235 Chapter 5. Chapter 5 Gravitation

Physics 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 information

Revision Guide for Chapter 11

Revision 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 information

Life Insurance Purchasing to Reach a Bequest. Erhan Bayraktar Department of Mathematics, University of Michigan Ann Arbor, Michigan, USA, 48109

Life 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 information

2. SCALARS, VECTORS, TENSORS, AND DYADS

2. 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 information

An Analysis of Manufacturer Benefits under Vendor Managed Systems

An 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 information

Saturated and weakly saturated hypergraphs

Saturated and weakly saturated hypergraphs Satuated and weakly satuated hypegaphs Algebaic Methods in Combinatoics, Lectues 6-7 Satuated hypegaphs Recall the following Definition. A family A P([n]) is said to be an antichain if we neve have A B

More information

Experimentation under Uninsurable Idiosyncratic Risk: An Application to Entrepreneurial Survival

Experimentation 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 continuous-time model of expeimentation

More information

The Personal-Tax Advantages of Equity

The Personal-Tax Advantages of Equity The Pesonal-Tax 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 information

Programming Assignment #1

Programming 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 information

Optimal Peer Selection in a Free-Market Peer-Resource Economy

Optimal Peer Selection in a Free-Market Peer-Resource Economy Optimal Pee Selection in a Fee-Maket Pee-Resouce 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 information

Spirotechnics! September 7, 2011. Amanda Zeringue, Michael Spannuth and Amanda Zeringue Dierential Geometry Project

Spirotechnics! 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 information

Liquidity and Insurance for the Unemployed

Liquidity 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 information

CRRC-1 Method #1: Standard Practice for Measuring Solar Reflectance of a Flat, Opaque, and Heterogeneous Surface Using a Portable Solar Reflectometer

CRRC-1 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 information

Japan s trading losses reach JPY20 trillion

Japan 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 information

Model Question Paper Mathematics Class XII

Model 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 information

Physics 505 Homework No. 5 Solutions S5-1. 1. Angular momentum uncertainty relations. A system is in the lm eigenstate of L 2, L z.

Physics 505 Homework No. 5 Solutions S5-1. 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 information

8-1 Newton s Law of Universal Gravitation

8-1 Newton s Law of Universal Gravitation 8-1 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 information

Lecture 16: Color and Intensity. and he made him a coat of many colours. Genesis 37:3

Lecture 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 information

PAN STABILITY TESTING OF DC CIRCUITS USING VARIATIONAL METHODS XVIII - SPETO - 1995. pod patronatem. Summary

PAN 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 information

TECHNICAL DATA. JIS (Japanese Industrial Standard) Screw Thread. Specifications

TECHNICAL 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 information

Immigration Restrictions and Labor Market Skills Preliminary and Incomplete

Immigration Restrictions and Labor Market Skills Preliminary and Incomplete Immigation Restictions and Labo Maket Skills Peliminay and Incomplete John Kennan Univesity of Wisconsin-Madison and NBER Apil 2014 Abstact Diffeences in income levels acoss counties ae geneally attibuted

More information

How do investments in heat pumps affect household energy consumption?

How 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 information

Week 3-4: Permutations and Combinations

Week 3-4: Permutations and Combinations Week 3-4: 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 information

2. TRIGONOMETRIC FUNCTIONS OF GENERAL ANGLES

2. 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 information

Definitions. Optimization of online direct marketing efforts. Test 1: Two Email campaigns. Raw Results. Xavier Drèze André Bonfrer. Lucid.

Definitions. 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 information

Voltage ( = Electric Potential )

Voltage ( = Electric Potential ) V-1 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