# Solutions to First Midterm

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 rofessor Chrstano Economcs 3, Wnter 2004 Solutons to Frst Mdterm. Multple Choce. 2. (a) v. (b). (c) v. (d) v. (e). (f). (g) v. (a) The goods market s n equlbrum when total demand equals total producton,.e. = Z. n the standard S- model, Z = C d + d + G d = c 0 + c ( T ) + b + G: So usng the equlbrum condton, the equlbrum output as a functon of the exogenous parameters and of the rate of nterest, s: = c c 0 c T + + G b : (b) For a gven nterest rate, the total desred spendng curve s: Z( ) = c 0 + c ( T ) + b + G; so that the vertcal ntercept s c 0 c T + b + G; whle the slope s c : (n the gure, goods market equlbrum s ndcated by (), to remnd ourselves t s determned for a gven nterest rate.) (c) The nancal market s n equlbrum when money demand equals money supply,.e.: M d Solvng the equlbrum condton: M s = M s. = + L L for, = L + L M s ; where all varables on the rght hand sde are parameters but for the level of output. (n the gure, the money market equlbrum nterest rate s ndcated by ( ), to remnd ourselves that t s determned for a gven level of ncome). (d) The demand for money, expressed n terms of the nterest rate s: = L + L M d ; so that the vertcal ntercept s: L + L whle the slope s L.

2 (e). The S curve represents combnatons (; ) such that the goods market s n equlbrum. The S curve has a negatve slope because, as the nterest rate ncreases, desred nvestment decreases and so does goods market equlbrum output (wth the latter change beng larger n absolute value than the former, because of the multpler e ect). The curve represents combnatons (; ) such that nancal markets are n equlbrum. The curve has a postve slope because as ncome ncreases, money demand ncreases and bond demand decreases for a gven nterest rate. But snce money supply and bond supply are xed, equlbrum n nancal markets requres an ncrease n the nterest rate to ncrease bond demand and reduce money demand back to ther ntal equlbrum levels.. Above (below) the S there s excess supply (demand) n the goods market. For a gven ; the nterest rate s hgher (lower) than requred for = Z. Because desred nvestment s decreasng n the nterest rate, desred nvestment s low (hgh), and so > Z ( < Z). The stock of unntended nventory nvestment s postve (negatve).. Above (below) the there s excess supply (demand) n the money market. For a gven ; the nterest rate s hgher (lower) than requred for M s = M d. Because money demand s decreasng n the nterest rate (bonds are more attractve), real money demand s smaller (greater) than money supply, M s < M d. v. f G ncreases by G > 0; the S curve shfts rghtward. The magntude of the rghtward shft s gven by the change n equlbrum n the goods market for a gven nterest rate. n the standard S/ model, ths change s always bgger than the equlbrum change n, snce as ncreases, the equlbrum nterest rate must also ncrease to guarantee market clearng n nancal markets, nducng a decrease n nvestment demand. However, when calculatng the rghtward shft of the S-curve, we are not requrng nancal markets to be n equlbrum: The nterest rate s taken as gven. From the prevous answers: = c c 0 c T + + G b ; so that the rghtward shft s: G c for any value of the nterest rate (parallel shft). v. Dsequlbrum dynamcs nvolves two thngs: whch market varable adjusts and how fast. Output shfts slowly n the goods market and the nterest rate shfts extremely quckly n the nancal market. As a result of these assumptons along the adjustment path (; ) s always on the -curve,.e. nancal markets are always n equlbrum. Because of the expansonary scal shock, the S shfts rghtward by G c to S 0 ; ntersectng the at ( ; ) where < < + G c and > : Because of the slow adjustment n the goods market, the economy does not jump drectly to ( ; ): mmedately after the shock, Z = + G > : There s excess demand n the goods market and hence a decrease n nventores. Frms adjust ther producton upwards accordngly. As they do so, ncome ncreases, and ths n turn ncreases money demand, requrng nterest rate to ncrease at the same tme n order to mantan equlbrum n nancal markets Ths process of output and nterest rate adjustment contnues untl output and nterest rates reach ( ; ) : (Along the adjustment path, the rse n the nterest rate reduces desred nvestment demand, but there remans a (decreasng) excess aggregate desred demand as we are always at (; ) pars below the new S-curve.). 2

3 c 0 c T + + G b ntercept slope=c Z ntercept / L + L ( ) slope=-/l M s ( ) o 45 () Goods Market Money Market M d M S' c G "S-" Dagram S 3. (a) The equlbrum condton n the Keynesan Cross model s Solvng ths equaton for equlbrum yelds The multpler on nvestment s =! = Z c 0 + c T + + G = c c0 c T + + G c [c 0 c T +++G] c [c 0 c T ++G] (b) The equlbrum condton n the Keynesan Cross model wth t > 0 s t >0 = c :! = Z = c 0 + c t >0 T t t >0 + + G Solvng ths equaton for equlbrum yelds t >0 = c ( t ) c0 c T + + G 3

4 The multpler on nvestment s now t >0 = c ( t ) : Snce 0 < t < ; c ( t ) < c,.e. the nvestment multpler s smaller f t > 0 (and t s decreasng n t ). ntuton: Taxes reduce consumpton and hence demand. f taxes ncrease wth ncome (t > 0), they wll also decrease the e ect of a change n ncome on consumpton and hence demand. Ths wll dampen the multpler e ect of a change n autonomous expendture on equlbrum output. (c) The equlbrum condton n the Keynesan Cross model wth q > 0 (and t = 0) s q>0! = Z = c 0 + c q>0 T + + q + G Solvng ths equaton for equlbrum yelds q>0 = c q c0 c T + + G The multpler on nvestment s now q>0 = c q : Snce q > 0, c q > c (as long as q < c ),.e. the nvestment multpler s larger for q > 0 (and ncreasng n q). ntuton: f nvestment ncreases wth ncome (q > 0), the multpler process s ampl ed. The multpler e ect on equlbrum ncome of an ncrease n autonomous expendtures wll work through not only consumpton but also nvestment. Hence the nvestment multpler s larger for q > 0 (Accelerator E ect). (d) The magntude of the horzontal shft of the S curve s always equal to the product of the correspondng Keynesan Cross-Multpler and the change n autonomous expendture. Ths would be the e ect for a gven nterest rate. Equlbrum changes n output wll however nvolve changes n the nterest rate as nancal markets must also be n equlbrum. f b = 0;nvestment and hence aggregate demand does not depend on the nterest rate. Equlbrum output s solely determned n the goods market: The S curve s vertcal. Even though the equlbrum nterest rate rses n response to > 0 to restore equlbrum n nancal markets at a hgher ; the nvestment multpler s dentcal to the one of the Keynesan Cross model. f nvestment depends negatvely on the nterest rate f b > 0, the equlbrum response of output to wll be smaller than n the case b = 0;because hgher output requres a hgher nterest rate for the nancal markets to clear. (n the gure, ntal equlbrum s drawn at the same (; ) par to smplfy the exposton) 4

5 b= 0 S b=0 S b=0 b>0 b>0 b b>0 = = 0 c b= 0 "S-" Dagram S b>0 S b >0 4. (a) n decdng whether to nvest n a gven project, rms have to decde on what rate of return the project wll generate. Ths n turn depends on how actve the economy s. f rms expect the level of actvty n the economy to be hgh, then they wll expect a hgh rate of return n other words, they form ther expectaton of how hgh economc actvty wll be by lookng at current output. So, the reason q > 0 s that n ths case, a hgher causes rms to revse upward ther assessment of the rate of return on all projects. (b) Each rm has a bunch of potental projects layng around, each wth an expected rate of return. To nvest n a project, they have to convnce someone to gve them the cash. That person has other stu to do wth the cash (ths s measured by ), and so the rm manager won t even make an attempt at a project f ts rate of return s less than. For any rm, the nvestment demand curve s a downward sloped step functon. As you aggregate over the whole economy the steps become ner untl t s just a smooth downward sloped curve. So aggregate nvestment negatvely depends on the nterest rate,.e. b > 0: 5. (a) A decrease n the money supply (or a postve shock to the lqudty demand parameter L) would shft the curve upward. The new equlbrum n the goods and nancal market nvolves a hgher nterest rate ( > ) and lower output ( < ). The drecton of the adjustment 5

6 re ects the assumptons on the dsequlbrum dynamcs. ' "S-" Dagram S (b) A decrease n any component of autonomous expendture would shft the S curve leftward and the new equlbrum would nvolve both a lower nterest rate ( < ) and lower output ( < ). The drecton of the adjustment re ects the assumptons on the dsequlbrum dynamcs. S' "S-" Dagram S 6. n the S- model (a model of the short run), equlbrum output s determned by the demand sde of the economy (how much households, busnesses and governments want to buy). t s assumed that rms do whatever t takes to produce the output that demand requres. Now suppose that a postve technology shocks ncreases productvty n the producton sector. The technology shock does not a ect total demand (t does not appear anywhere n our desred consumpton, nvestment or government consumpton equatons). As productvty ncreases and aggregate demand s una ected, the number of workers shrnks, reducng employment (holdng hours per-worker xed). 7. Desred savng s S t = t C t T t = c0 + ( c)( t T ): As the loss of consumer con dence s unexpected by rms, = 0 ; so that,as a consequence of the fall n c 0 : S = S S 0 = c0 = \$0: As the economy s n equlbrum n perod 0, total demand, whch falls by 0\$ relatve to Z 0 ; s Z = Z 0 0\$ = 0 0\$ = 0\$: So unntended nventory nvestment n perod one s u = Z = 0\$: As the economy s n equlbrum n the perod 0 u = u u0 = u 0 = 0\$. As desred nvestment s unchanged, the change n actual nvestment s a = 0\$: 6

7 8. The equlbrum nterest rate s found by equatng money demand and money supply: M s = 00\$ = M d = \$00 (:05 ), so that = :05 or = 5%: Assumng that there are no assets other than money and bonds, wealth s nvested n ether of the two that s: W = M d + B d. From ths, and the fact that the equlbrum level of nomnal money s 00\$; the equlbrum demand for bonds s 900\$: 7

### Chapter 4 Financial Markets

Chapter 4 Fnancal Markets ECON2123 (Sprng 2012) 14 & 15.3.2012 (Tutoral 5) The demand for money Assumptons: There are only two assets n the fnancal market: money and bonds Prce s fxed and s gven, that

### Problem Set 3. a) We are asked how people will react, if the interest rate i on bonds is negative.

Queston roblem Set 3 a) We are asked how people wll react, f the nterest rate on bonds s negatve. When

### Answer: A). There is a flatter IS curve in the high MPC economy. Original LM LM after increase in M. IS curve for low MPC economy

4.02 Quz Solutons Fall 2004 Multple-Choce Questons (30/00 ponts) Please, crcle the correct answer for each of the followng 0 multple-choce questons. For each queston, only one of the answers s correct.

### IS-LM Model 1 C' dy = di

- odel Solow Assumptons - demand rrelevant n long run; assumes economy s operatng at potental GDP; concerned wth growth - Assumptons - supply s rrelevant n short run; assumes economy s operatng below potental

### CHAPTER 18 INFLATION, UNEMPLOYMENT AND AGGREGATE SUPPLY. Themes of the chapter. Nominal rigidities, expectational errors and employment fluctuations

CHAPTER 18 INFLATION, UNEMPLOYMENT AND AGGREGATE SUPPLY Themes of the chapter Nomnal rgdtes, expectatonal errors and employment fluctuatons The short-run trade-off between nflaton and unemployment The

### Exchange Rates in the Short Run

Exchange Rates n the Short Run What determnes exchange rates n the short-run?» Exchange rates are prced lke fnancal assets» Asset prces change quckly, often by more than contemporaneous changes n underlyng

### A) 3.1 B) 3.3 C) 3.5 D) 3.7 E) 3.9 Solution.

ACTS 408 Instructor: Natala A. Humphreys SOLUTION TO HOMEWOR 4 Secton 7: Annutes whose payments follow a geometrc progresson. Secton 8: Annutes whose payments follow an arthmetc progresson. Problem Suppose

### Addendum to: Importing Skill-Biased Technology

Addendum to: Importng Skll-Based Technology Arel Bursten UCLA and NBER Javer Cravno UCLA August 202 Jonathan Vogel Columba and NBER Abstract Ths Addendum derves the results dscussed n secton 3.3 of our

### Week 6 Market Failure due to Externalities

Week 6 Market Falure due to Externaltes 1. Externaltes n externalty exsts when the acton of one agent unavodably affects the welfare of another agent. The affected agent may be a consumer, gvng rse to

### 7.5. Present Value of an Annuity. Investigate

7.5 Present Value of an Annuty Owen and Anna are approachng retrement and are puttng ther fnances n order. They have worked hard and nvested ther earnngs so that they now have a large amount of money on

### The example below solves a system in the unknowns α and β:

The Fnd Functon The functon Fnd returns a soluton to a system of equatons gven by a solve block. You can use Fnd to solve a lnear system, as wth lsolve, or to solve nonlnear systems. The example below

### Compound Interest: Further Topics and Applications. Chapter 9

9-2 Compound Interest: Further Topcs and Applcatons Chapter 9 9-3 Learnng Objectves After letng ths chapter, you wll be able to:? Calculate the nterest rate and term n ound nterest applcatons? Gven a nomnal

### 9 Arithmetic and Geometric Sequence

AAU - Busness Mathematcs I Lecture #5, Aprl 4, 010 9 Arthmetc and Geometrc Sequence Fnte sequence: 1, 5, 9, 13, 17 Fnte seres: 1 + 5 + 9 + 13 +17 Infnte sequence: 1,, 4, 8, 16,... Infnte seres: 1 + + 4

### Nasdaq Iceland Bond Indices 01 April 2015

Nasdaq Iceland Bond Indces 01 Aprl 2015 -Fxed duraton Indces Introducton Nasdaq Iceland (the Exchange) began calculatng ts current bond ndces n the begnnng of 2005. They were a response to recent changes

### b) The mean of the fitted (predicted) values of Y is equal to the mean of the Y values: c) The residuals of the regression line sum up to zero: = ei

Mathematcal Propertes of the Least Squares Regresson The least squares regresson lne obeys certan mathematcal propertes whch are useful to know n practce. The followng propertes can be establshed algebracally:

### An Alternative Way to Measure Private Equity Performance

An Alternatve Way to Measure Prvate Equty Performance Peter Todd Parlux Investment Technology LLC Summary Internal Rate of Return (IRR) s probably the most common way to measure the performance of prvate

### 10. (# 45, May 2001). At time t = 0, 1 is deposited into each of Fund X and Fund Y. Fund X accumulates at a force of interest

1 Exam FM questons 1. (# 12, May 2001). Bruce and Robbe each open up new bank accounts at tme 0. Bruce deposts 100 nto hs bank account, and Robbe deposts 50 nto hs. Each account earns an annual e ectve

### Gibbs Free Energy and Chemical Equilibrium (or how to predict chemical reactions without doing experiments)

Gbbs Free Energy and Chemcal Equlbrum (or how to predct chemcal reactons wthout dong experments) OCN 623 Chemcal Oceanography Readng: Frst half of Chapter 3, Snoeynk and Jenkns (1980) Introducton We want

### Interest Rate Futures

Interest Rate Futures Chapter 6 6.1 Day Count Conventons n the U.S. (Page 129) Treasury Bonds: Corporate Bonds: Money Market Instruments: Actual/Actual (n perod) 30/360 Actual/360 The day count conventon

### Chapter 15 Debt and Taxes

hapter 15 Debt and Taxes 15-1. Pelamed Pharmaceutcals has EBIT of \$325 mllon n 2006. In addton, Pelamed has nterest expenses of \$125 mllon and a corporate tax rate of 40%. a. What s Pelamed s 2006 net

### Simple Interest Loans (Section 5.1) :

Chapter 5 Fnance The frst part of ths revew wll explan the dfferent nterest and nvestment equatons you learned n secton 5.1 through 5.4 of your textbook and go through several examples. The second part

### 0.02t if 0 t 3 δ t = 0.045 if 3 < t

1 Exam FM questons 1. (# 12, May 2001). Bruce and Robbe each open up new bank accounts at tme 0. Bruce deposts 100 nto hs bank account, and Robbe deposts 50 nto hs. Each account earns an annual effectve

### Section 5.4 Annuities, Present Value, and Amortization

Secton 5.4 Annutes, Present Value, and Amortzaton Present Value In Secton 5.2, we saw that the present value of A dollars at nterest rate per perod for n perods s the amount that must be deposted today

### 1. Math 210 Finite Mathematics

1. ath 210 Fnte athematcs Chapter 5.2 and 5.3 Annutes ortgages Amortzaton Professor Rchard Blecksmth Dept. of athematcal Scences Northern Illnos Unversty ath 210 Webste: http://math.nu.edu/courses/math210

Newtonan modellng In ths actvty you wll see how Newton s Laws of Moton are used to connect the moton of an object wth the forces actng on t. You wll practse applyng Newton s three laws n some real contexts.

### Entry Games in Exogenous Sunk Costs Industries (Sutton, Chapter 2)

Entry Games n Exogenous Sunk Costs Industres (Sutton, Chapter 2) Structure-Conduct-erformance aradgm: Models one-way chan of causaton Concentraton to erformance, treatng Conduct as a Black Box ew Industral

### Capital asset pricing model, arbitrage pricing theory and portfolio management

Captal asset prcng model, arbtrage prcng theory and portfolo management Vnod Kothar The captal asset prcng model (CAPM) s great n terms of ts understandng of rsk decomposton of rsk nto securty-specfc rsk

### 2 The TTL Inverter. (i) An input transistor, T 1, which performs a current steering function, can be thought of as a back-to-back diode arrangement.

The TTL Inverter.1 Crcut Structure The crcut dagram of the Transstor Transstor Logc nverter s shown n Fg..1. Ths crcut overcomes the lmtatons of the sngle transstor nverter crcut. Some of the notable features

### Thursday, December 10, 2009 Noon - 1:50 pm Faraday 143

1. ath 210 Fnte athematcs Chapter 5.2 and 4.3 Annutes ortgages Amortzaton Professor Rchard Blecksmth Dept. of athematcal Scences Northern Illnos Unversty ath 210 Webste: http://math.nu.edu/courses/math210

### ( ) Homework Solutions Physics 8B Spring 09 Chpt. 32 5,18,25,27,36,42,51,57,61,76

Homework Solutons Physcs 8B Sprng 09 Chpt. 32 5,8,25,27,3,42,5,57,,7 32.5. Model: Assume deal connectng wres and an deal battery for whch V bat = E. Please refer to Fgure EX32.5. We wll choose a clockwse

### Homework Solutions Physics 8B Spring 2012 Chpt. 32 5,18,25,27,36,42,51,57,61,76

Homework Solutons Physcs 8B Sprng 202 Chpt. 32 5,8,25,27,3,42,5,57,,7 32.5. Model: Assume deal connectng wres and an deal battery for whch V bat =. Please refer to Fgure EX32.5. We wll choose a clockwse

### Halliday/Resnick/Walker 7e Chapter 25 Capacitance

HRW 7e hapter 5 Page o 0 Hallday/Resnck/Walker 7e hapter 5 apactance. (a) The capactance o the system s q 70 p 35. pf. 0 (b) The capactance s ndependent o q; t s stll 3.5 pf. (c) The potental derence becomes

### Kiel Institute for World Economics Duesternbrooker Weg 120 24105 Kiel (Germany) Kiel Working Paper No. 1120

Kel Insttute for World Economcs Duesternbrooker Weg 45 Kel (Germany) Kel Workng Paper No. Path Dependences n enture Captal Markets by Andrea Schertler July The responsblty for the contents of the workng

### Solution: Let i = 10% and d = 5%. By definition, the respective forces of interest on funds A and B are. i 1 + it. S A (t) = d (1 dt) 2 1. = d 1 dt.

Chapter 9 Revew problems 9.1 Interest rate measurement Example 9.1. Fund A accumulates at a smple nterest rate of 10%. Fund B accumulates at a smple dscount rate of 5%. Fnd the pont n tme at whch the forces

### The circuit shown on Figure 1 is called the common emitter amplifier circuit. The important subsystems of this circuit are:

polar Juncton Transstor rcuts Voltage and Power Amplfer rcuts ommon mtter Amplfer The crcut shown on Fgure 1 s called the common emtter amplfer crcut. The mportant subsystems of ths crcut are: 1. The basng

### Multiple discount and forward curves

Multple dscount and forward curves TopQuants presentaton 21 ovember 2012 Ton Broekhuzen, Head Market Rsk and Basel coordnator, IBC Ths presentaton reflects personal vews and not necessarly the vews of

### Number of Levels Cumulative Annual operating Income per year construction costs costs (\$) (\$) (\$) 1 600,000 35,000 100,000 2 2,200,000 60,000 350,000

Problem Set 5 Solutons 1 MIT s consderng buldng a new car park near Kendall Square. o unversty funds are avalable (overhead rates are under pressure and the new faclty would have to pay for tself from

### Formula of Total Probability, Bayes Rule, and Applications

1 Formula of Total Probablty, Bayes Rule, and Applcatons Recall that for any event A, the par of events A and A has an ntersecton that s empty, whereas the unon A A represents the total populaton of nterest.

### c is the consumption of commodity i by consumer j

Blanchard, O. and F. Gavazz 2003. Macroeconomc Effects of Regulaton and Deregulaton n Goods and Labour markets, Quarterly Journal of Economcs: 879-906 Man message: lberalsng roduct markets may be renforced

### Institute of Informatics, Faculty of Business and Management, Brno University of Technology,Czech Republic

Lagrange Multplers as Quanttatve Indcators n Economcs Ivan Mezník Insttute of Informatcs, Faculty of Busness and Management, Brno Unversty of TechnologCzech Republc Abstract The quanttatve role of Lagrange

### Lecture 3: Annuity. Study annuities whose payments form a geometric progression or a arithmetic progression.

Lecture 3: Annuty Goals: Learn contnuous annuty and perpetuty. Study annutes whose payments form a geometrc progresson or a arthmetc progresson. Dscuss yeld rates. Introduce Amortzaton Suggested Textbook

### ANALYZING THE RELATIONSHIPS BETWEEN QUALITY, TIME, AND COST IN PROJECT MANAGEMENT DECISION MAKING

ANALYZING THE RELATIONSHIPS BETWEEN QUALITY, TIME, AND COST IN PROJECT MANAGEMENT DECISION MAKING Matthew J. Lberatore, Department of Management and Operatons, Vllanova Unversty, Vllanova, PA 19085, 610-519-4390,

### PSYCHOLOGICAL RESEARCH (PYC 304-C) Lecture 12

14 The Ch-squared dstrbuton PSYCHOLOGICAL RESEARCH (PYC 304-C) Lecture 1 If a normal varable X, havng mean µ and varance σ, s standardsed, the new varable Z has a mean 0 and varance 1. When ths standardsed

### SPEE Recommended Evaluation Practice #6 Definition of Decline Curve Parameters Background:

SPEE Recommended Evaluaton Practce #6 efnton of eclne Curve Parameters Background: The producton hstores of ol and gas wells can be analyzed to estmate reserves and future ol and gas producton rates and

### EXAMPLE PROBLEMS SOLVED USING THE SHARP EL-733A CALCULATOR

EXAMPLE PROBLEMS SOLVED USING THE SHARP EL-733A CALCULATOR 8S CHAPTER 8 EXAMPLES EXAMPLE 8.4A THE INVESTMENT NEEDED TO REACH A PARTICULAR FUTURE VALUE What amount must you nvest now at 4% compoune monthly

### 3. Present value of Annuity Problems

Mathematcs of Fnance The formulae 1. A = P(1 +.n) smple nterest 2. A = P(1 + ) n compound nterest formula 3. A = P(1-.n) deprecaton straght lne 4. A = P(1 ) n compound decrease dmshng balance 5. P = -

### Luby s Alg. for Maximal Independent Sets using Pairwise Independence

Lecture Notes for Randomzed Algorthms Luby s Alg. for Maxmal Independent Sets usng Parwse Independence Last Updated by Erc Vgoda on February, 006 8. Maxmal Independent Sets For a graph G = (V, E), an ndependent

### Texas Instruments 30X IIS Calculator

Texas Instruments 30X IIS Calculator Keystrokes for the TI-30X IIS are shown for a few topcs n whch keystrokes are unque. Start by readng the Quk Start secton. Then, before begnnng a specfc unt of the

### Lesson 2 Chapter Two Three Phase Uncontrolled Rectifier

Lesson 2 Chapter Two Three Phase Uncontrolled Rectfer. Operatng prncple of three phase half wave uncontrolled rectfer The half wave uncontrolled converter s the smplest of all three phase rectfer topologes.

### Chapter 14 Traditional Models of Imperfect Competition

Chapter 14 Tradtonal Models of Imperfect Competton Now we wll relax some assumptons of perfect competton; the assumptons about the number (and sze) of frms n the ndustry, homogenety of products, and freedom

### The OC Curve of Attribute Acceptance Plans

The OC Curve of Attrbute Acceptance Plans The Operatng Characterstc (OC) curve descrbes the probablty of acceptng a lot as a functon of the lot s qualty. Fgure 1 shows a typcal OC Curve. 10 8 6 4 1 3 4

### Chapter 11 Practice Problems Answers

Chapter 11 Practce Problems Answers 1. Would you be more wllng to lend to a frend f she put all of her lfe savngs nto her busness than you would f she had not done so? Why? Ths problem s ntended to make

### n + d + q = 24 and.05n +.1d +.25q = 2 { n + d + q = 24 (3) n + 2d + 5q = 40 (2)

MATH 16T Exam 1 : Part I (In-Class) Solutons 1. (0 pts) A pggy bank contans 4 cons, all of whch are nckels (5 ), dmes (10 ) or quarters (5 ). The pggy bank also contans a con of each denomnaton. The total

### Section B9: Zener Diodes

Secton B9: Zener Dodes When we frst talked about practcal dodes, t was mentoned that a parameter assocated wth the dode n the reverse bas regon was the breakdown voltage, BR, also known as the peak-nverse

### FINANCIAL MATHEMATICS. A Practical Guide for Actuaries. and other Business Professionals

FINANCIAL MATHEMATICS A Practcal Gude for Actuares and other Busness Professonals Second Edton CHRIS RUCKMAN, FSA, MAAA JOE FRANCIS, FSA, MAAA, CFA Study Notes Prepared by Kevn Shand, FSA, FCIA Assstant

### II. PROBABILITY OF AN EVENT

II. PROBABILITY OF AN EVENT As ndcated above, probablty s a quantfcaton, or a mathematcal model, of a random experment. Ths quantfcaton s a measure of the lkelhood that a gven event wll occur when the

### Chapter 4 ECONOMIC DISPATCH AND UNIT COMMITMENT

Chapter 4 ECOOMIC DISATCH AD UIT COMMITMET ITRODUCTIO A power system has several power plants. Each power plant has several generatng unts. At any pont of tme, the total load n the system s met by the

### Rate Monotonic (RM) Disadvantages of cyclic. TDDB47 Real Time Systems. Lecture 2: RM & EDF. Priority-based scheduling. States of a process

Dsadvantages of cyclc TDDB47 Real Tme Systems Manual scheduler constructon Cannot deal wth any runtme changes What happens f we add a task to the set? Real-Tme Systems Laboratory Department of Computer

### Solution of Algebraic and Transcendental Equations

CHAPTER Soluton of Algerac and Transcendental Equatons. INTRODUCTION One of the most common prolem encountered n engneerng analyss s that gven a functon f (, fnd the values of for whch f ( = 0. The soluton

### Thus, if the two coffee shops collude, then they will produce a level of output q m

Introductory Mcroeconomcs (ES10001) Exercse 9: Suggested Solutons 1. There are two coffee shops on campus facng an aggregate demand functon for cups of coffee of q d = 00 0 p. The coffee s dentcal and

### Chapter 15: Debt and Taxes

Chapter 15: Debt and Taxes-1 Chapter 15: Debt and Taxes I. Basc Ideas 1. Corporate Taxes => nterest expense s tax deductble => as debt ncreases, corporate taxes fall => ncentve to fund the frm wth debt

### Chapter 7: Answers to Questions and Problems

19. Based on the nformaton contaned n Table 7-3 of the text, the food and apparel ndustres are most compettve and therefore probably represent the best match for the expertse of these managers. Chapter

### Lecture 3: Force of Interest, Real Interest Rate, Annuity

Lecture 3: Force of Interest, Real Interest Rate, Annuty Goals: Study contnuous compoundng and force of nterest Dscuss real nterest rate Learn annuty-mmedate, and ts present value Study annuty-due, and

### Notes on Engineering Economic Analysis

College of Engneerng and Computer Scence Mechancal Engneerng Department Mechancal Engneerng 483 lternatve Energy Engneerng II Sprng 200 umber: 7724 Instructor: Larry Caretto otes on Engneerng Economc nalyss

### Texas Instruments 30Xa Calculator

Teas Instruments 30Xa Calculator Keystrokes for the TI-30Xa are shown for a few topcs n whch keystrokes are unque. Start by readng the Quk Start secton. Then, before begnnng a specfc unt of the tet, check

### Productivity Growth: Theory and Measurement

Productvty Growth: Theory and Measurement Davd T. Owyong INTRODUCTION Productvty growth has receved greater attenton from economsts and polcy makers n Asa n the 1990s. Ths s partly due to the work of Alwyn

### Passive Filters. References: Barbow (pp 265-275), Hayes & Horowitz (pp 32-60), Rizzoni (Chap. 6)

Passve Flters eferences: Barbow (pp 6575), Hayes & Horowtz (pp 360), zzon (Chap. 6) Frequencyselectve or flter crcuts pass to the output only those nput sgnals that are n a desred range of frequences (called

### The Magnetic Field. Concepts and Principles. Moving Charges. Permanent Magnets

. The Magnetc Feld Concepts and Prncples Movng Charges All charged partcles create electrc felds, and these felds can be detected by other charged partcles resultng n electrc force. However, a completely

### 9.1 The Cumulative Sum Control Chart

Learnng Objectves 9.1 The Cumulatve Sum Control Chart 9.1.1 Basc Prncples: Cusum Control Chart for Montorng the Process Mean If s the target for the process mean, then the cumulatve sum control chart s

### Section 5.3 Annuities, Future Value, and Sinking Funds

Secton 5.3 Annutes, Future Value, and Snkng Funds Ordnary Annutes A sequence of equal payments made at equal perods of tme s called an annuty. The tme between payments s the payment perod, and the tme

### Trade Adjustment and Productivity in Large Crises. Online Appendix May 2013. Appendix A: Derivation of Equations for Productivity

Trade Adjustment Productvty n Large Crses Gta Gopnath Department of Economcs Harvard Unversty NBER Brent Neman Booth School of Busness Unversty of Chcago NBER Onlne Appendx May 2013 Appendx A: Dervaton

### Graph Theory and Cayley s Formula

Graph Theory and Cayley s Formula Chad Casarotto August 10, 2006 Contents 1 Introducton 1 2 Bascs and Defntons 1 Cayley s Formula 4 4 Prüfer Encodng A Forest of Trees 7 1 Introducton In ths paper, I wll

### Time Value of Money Module

Tme Value of Money Module O BJECTIVES After readng ths Module, you wll be able to: Understand smple nterest and compound nterest. 2 Compute and use the future value of a sngle sum. 3 Compute and use the

### greatest common divisor

4. GCD 1 The greatest common dvsor of two ntegers a and b (not both zero) s the largest nteger whch s a common factor of both a and b. We denote ths number by gcd(a, b), or smply (a, b) when there s no

### Time Value of Money. Types of Interest. Compounding and Discounting Single Sums. Page 1. Ch. 6 - The Time Value of Money. The Time Value of Money

Ch. 6 - The Tme Value of Money Tme Value of Money The Interest Rate Smple Interest Compound Interest Amortzng a Loan FIN21- Ahmed Y, Dasht TIME VALUE OF MONEY OR DISCOUNTED CASH FLOW ANALYSIS Very Important

### On the Role of Consumer Expectations in Markets with Network Effects

No 13 On the Role of Consumer Expectatons n Markets wth Network Effects Irna Suleymanova, Chrstan Wey November 2010 (frst verson: July 2010) IMPRINT DICE DISCUSSION PAPER Publshed by Henrch Hene Unverstät

### EE201 Circuit Theory I 2015 Spring. Dr. Yılmaz KALKAN

EE201 Crcut Theory I 2015 Sprng Dr. Yılmaz KALKAN 1. Basc Concepts (Chapter 1 of Nlsson - 3 Hrs.) Introducton, Current and Voltage, Power and Energy 2. Basc Laws (Chapter 2&3 of Nlsson - 6 Hrs.) Voltage

### Hedging Interest-Rate Risk with Duration

FIXED-INCOME SECURITIES Chapter 5 Hedgng Interest-Rate Rsk wth Duraton Outlne Prcng and Hedgng Prcng certan cash-flows Interest rate rsk Hedgng prncples Duraton-Based Hedgng Technques Defnton of duraton

### Quasi-Hyperbolic Discounting and Social Security Systems

Quas-Hyperbolc Dscountng and Socal Securty Systems Mordecha E. Schwarz a and Eytan Sheshnsk b May 22, 26 Abstract Hyperbolc countng has become a common assumpton for modelng bounded ratonalty wth respect

### Depreciation of Business R&D Capital

Deprecaton of Busness R&D Captal U.S. Bureau of Economc Analyss Abstract R&D deprecaton rates are crtcal to calculatng the rates of return to R&D nvestments and captal servce costs, whch are mportant for

### U.C. Berkeley CS270: Algorithms Lecture 4 Professor Vazirani and Professor Rao Jan 27,2011 Lecturer: Umesh Vazirani Last revised February 10, 2012

U.C. Berkeley CS270: Algorthms Lecture 4 Professor Vazran and Professor Rao Jan 27,2011 Lecturer: Umesh Vazran Last revsed February 10, 2012 Lecture 4 1 The multplcatve weghts update method The multplcatve

### In our example i = r/12 =.0825/12 At the end of the first month after your payment is received your amount owed is. P (1 + i) A

Amortzed loans: Suppose you borrow P dollars, e.g., P = 100, 000 for a house wth a 30 year mortgage wth an nterest rate of 8.25% (compounded monthly). In ths type of loan you make equal payments of A dollars

### A Master Time Value of Money Formula. Floyd Vest

A Master Tme Value of Money Formula Floyd Vest For Fnancal Functons on a calculator or computer, Master Tme Value of Money (TVM) Formulas are usually used for the Compound Interest Formula and for Annutes.

### Implementation of Deutsch's Algorithm Using Mathcad

Implementaton of Deutsch's Algorthm Usng Mathcad Frank Roux The followng s a Mathcad mplementaton of Davd Deutsch's quantum computer prototype as presented on pages - n "Machnes, Logc and Quantum Physcs"

### Marginal Returns to Education For Teachers

The Onlne Journal of New Horzons n Educaton Volume 4, Issue 3 MargnalReturnstoEducatonForTeachers RamleeIsmal,MarnahAwang ABSTRACT FacultyofManagementand Economcs UnverstPenddkanSultan Idrs ramlee@fpe.ups.edu.my

### Information Acquisition and Transparency in Global Games

Informaton Acquston and Transparency n Global Games Mchal Szkup y and Isabel Trevno New York Unversty Abstract We ntroduce costly nformaton acquston nto the standard global games model. In our setup agents

### Mathematics of Finance

CHAPTER 5 Mathematcs of Fnance 5.1 Smple and Compound Interest 5.2 Future Value of an Annuty 5.3 Present Value of an Annuty; Amortzaton Revew Exercses Extended Applcaton: Tme, Money, and Polynomals Buyng

### Comparing Class Level Chain Drift for Different Elementary Aggregate Formulae Using Locally Collected CPI Data

Comparng Class Level Chan Drft for Dfferent Elementary Aggregate Formulae Usng Gareth Clews 1, Anselma Dobson-McKttrck 2 and Joseph Wnton Summary The Consumer Prces Index (CPI) s a measure of consumer

### Mathematics of Finance

Mathematcs of Fnance 5 C H A P T E R CHAPTER OUTLINE 5.1 Smple Interest and Dscount 5.2 Compound Interest 5.3 Annutes, Future Value, and Snkng Funds 5.4 Annutes, Present Value, and Amortzaton CASE STUDY

### PROFIT RATIO AND MARKET STRUCTURE

POFIT ATIO AND MAKET STUCTUE By Yong Yun Introducton: Industral economsts followng from Mason and Ban have run nnumerable tests of the relaton between varous market structural varables and varous dmensons

### Finite Math Chapter 10: Study Guide and Solution to Problems

Fnte Math Chapter 10: Study Gude and Soluton to Problems Basc Formulas and Concepts 10.1 Interest Basc Concepts Interest A fee a bank pays you for money you depost nto a savngs account. Prncpal P The amount

### 17 Capital tax competition

17 Captal tax competton 17.1 Introducton Governments would lke to tax a varety of transactons that ncreasngly appear to be moble across jursdctonal boundares. Ths creates one obvous problem: tax base flght.

### 6. EIGENVALUES AND EIGENVECTORS 3 = 3 2

EIGENVALUES AND EIGENVECTORS The Characterstc Polynomal If A s a square matrx and v s a non-zero vector such that Av v we say that v s an egenvector of A and s the correspondng egenvalue Av v Example :

### ANALYSIS OF FINANCIAL FLOWS

ANALYSIS OF FINANCIAL FLOWS AND INVESTMENTS II 4 Annutes Only rarely wll one encounter an nvestment or loan where the underlyng fnancal arrangement s as smple as the lump sum, sngle cash flow problems

### EXPLORATION 2.5A Exploring the motion diagram of a dropped object

-5 Acceleraton Let s turn now to moton that s not at constant elocty. An example s the moton of an object you release from rest from some dstance aboe the floor. EXPLORATION.5A Explorng the moton dagram

### Bond futures. Bond futures contracts are futures contracts that allow investor to buy in the

Bond futures INRODUCION Bond futures contracts are futures contracts that allow nvestor to buy n the future a theoretcal government notonal bond at a gven prce at a specfc date n a gven quantty. Compared

### DETERMINATION THERMODYNAMIC PROPERTIES OF WATER AND STEAM

DETERMINATION THERMODYNAMIC PROPERTIES OF WATER AND STEAM S. Sngr, J. Spal Afflaton Abstract Ths work presents functons of thermodynamc parameters developed n MATLAB. There are functons to determne: saturaton