Perfect competition model (PCM)


 Ross Wilcox
 2 years ago
 Views:
Transcription
1 18/9/21 Consumers: Benefits, WT, nd Demnd roducers: Costs nd Supply Aggregting individul curves erfect competition model (CM) Key ehviourl ssumption Economic gents, whether they e consumers or producers, pursue their selfinterest when mking choices individuls mke choices rtionlly y weighing enefit nd cost of ech possile ction nd choosing ction which mximizes difference, tht is, their privte net enefit. Consumers mke choices (consumption, work, leisure, etc.) to mximize their utility or enefit suject to udget constrint while producers mke decisions (production, investment, dvertising, etc.) to mximize their profits (revenue less costs). Key technicl ssumptions Complete set of mrkets fully ssigned property rights ll goods nd services re privte goods no externlities lrge numer of prticipnts perfect informtion zero trnsction costs well ehved production nd utility functions In the CM, lrge numers of utilitymximizing consumers nd profitmximizing producers meet in the mrket. Consumers nd producers ct s price tkers when mking consumption nd production decisions ecuse the numer of mrket prticipnts is sufficiently lrge so tht no individul prticipnt s ction ffects prices. Thus, prices re treted s exogenous y prticipnts when mking privte decisions. The interction of consumers nd producers in the mrketplce results in the determintion of prices or mrket vlutions of goods nd services. Thus, mrket prices re determined endogenously. The equilirium mrket price (the level t which the price settles down) is the price which clers the mrket (equtes supply nd demnd). The mrket price, in turn, determines the lloction of the good, tht is, how much of the good will e consumed y individul consumers nd produced y individul producers. Let s review how mrkets work, tht is, how consumers nd producers mke their respective choices nd how these choices re ggregted in the mrket, ultimtely determining the mrket vlution or price of good nd hence the lloction of the good. We cn then ssess the mrket s n lloction mechnism. 2 1
2 18/9/21 Consumers: Benefits, WT nd Demnd How do economists mesure the enefits tht ccrue to n individul from consuming good? Economists elieve tht wht people wnt k individul REFERENCES should e the sis of BENEFIT MEASUREMENT How cn we identify n individul s preferences or tstes? One wy is to sk n individul to revel their preferences y sking out their willingness to py (WT) for good. If someone is WT for good, then we cn conclude tht they hve positive preference for tht something. WT concept gives us monetry indictor of preferences Willingness to py WT MWT i or MB i Individul s mrginl willingness to py curve (MWT i ) is locus of individul s MWT!Q pirs. It tells us how much n individul is WT for incrementl units of Q consumption. Individul i is WT 6 for 1 unit, for 2 units, 2 for units nd for units. MWT i is thus flling with consumption level MWT i downwrdsloping. MWT i is lso known s the mrginl enefit of consumption curve (MB i ) MWT i idiosyncrtic Suppose there re I individuls indexed y i so tht MWT i for i = 1,,I. Whenever individuls re heterogeneous (for instnce, if they hve different tstes, vlues or income), then the MWT i for ny two individuls j,k will not e equl MWT j MWT k. MWT i TWT i An individul s totl willingness to py for consumption level (TWT i ( )) is monetry mesure of the enefit (B i ( )) ccruing to the individul from consuming. TWT i is the re under MWT i to the left of the consumption level. TWT i is the sum of the individul s consumer surplus (CS i ), re, nd consumer expenditures (CE i ), re. Individul i s TWT i for one unit of the good cn e derived s follows: CS i (1) = = 1 CE i (1) = = 6 TWT i (1) = B i (1) = CS i (1) + CE i (1) = + = 7 Using the sme methodology, one cn clculte TWT i (2) = + 8 = 12 nd so on. Note tht TWT i is incresing with consumption level. 2
3 18/9/21 Individul consumption decision nd demnd curve An individul pursues his/her selfinterest when mking consumption decisions. Tking price s given, the individul chooses the level of consumption which mximizes their net enefits from consumption: 18 Individul A : = : = Implicitly defines individul A s demnd curve 18 2 = MB A / MWT A 12 Q A = 2 18 = 12 2 Individul A s demnd curve Convention in economics is to plce economic vlue of on verticl xis nd quntity or Q on horizontl xis. When we grph demnd curve in (,Q A ) we re grphing inverse demnd curve. Inverting the demnd curve yields the inverse demnd curve : = = 12 = 2 12 = 18 2 Simplifying, the inverse demnd curve is or or. = 18. Note tht the curve cn lso e leled s Aggregte Demnd Aggregte or mrket demnd for commodity, Q D (), is constructed y ggregting or horizontlly summing the demnd curves of ll consuming individuls in the economy. = = 18 = 18 = 18 = 18 = 12 2 = 6 1 =18 To horizontlly sum individul demnd curves, invert the inverse demnd curves to find the demnd curves nd then dd together. Aggregtion entils summing individul quntities ( ) t ll possile price levels (), tht is, = +. Fix, Vry Q 6
4 18/9/21 Aggregte Demnd = = = TWT, B, CE, CS Aggregte or totl willingness to py, TWT, is the re under the ggregte demnd curve to the left of the quntity demnded. Suppose tht = 12 so tht Q = 6 units re demnded. TWT for 6 units of the good is the sum of ggregte consumer surplus (CS), re, nd ggregte consumer expenditures (CE), re. TWT for Q units of the good cn e derived s follows: CS(6) = = 18 CE(6) = = 72 TWT(6) = + = = 9 Individul A Individul B Aggregte Demnd (Q A ) 6 6 (Q B ) Q A Q B Q B 7 roducers: Costs nd Supply roduction costs include ll costs incurred to produce good cpitl equipment costs, lour costs, cost of mteril inputs, etc. roduction costs re privte costs incurred y n individul producer. MC i = /2 C i Firm i MC i c 2 The locus of incrementl production costq pirs is the firm s mrginl cost of production curve, MC i. It is mrginl cost function ecuse it descries the firm s cost of producing incrementl units of the good. Individul firm s MC i idiosyncrtic MC i sed on firm s production processes nd technologies so will generlly e different eg., cost differences cn derive from different vintges of cpitl equipment. Firm i s cost of producing the 1 th unit is 2. Height of verticl line t 1 units is C pi (1 th unit), tht is, the incrementl or mrginl cost of producing the 1 th unit. The incrementl cost of producing the 2 th unit is. MC i is upwrdsloping ecuse the incrementl cost of producing is incresing. Firm i s cost of producing units is the re under MC i to the left of. The firm s cost of producing 1 units is C pi (1) = 1 (re ) nd the cost of producing units is 6 (res + + c). Note tht C pi is incresing t n incresing rte. 8
5 18/9/21 roduction decision nd supply curve An individul firm pursues its selfinterest when mking production decisions. Tking price s given, the firm chooses level of output to mximize profit, where profit is the difference etween totl revenue, R i, or lterntively production enefit, B i, nd production cost, C pi. =rg = Firm i MC i p or S() : = Implicitly defines firm i s supply curve : = Revenue, Costs nd roducer Surplus R i ( ) = * = + C i ( ) = = 2 = 2 Firm i s inverse supply curve Firm i s supply curve = = + = is lso known s producer surplus 9 Aggregte or Mrket Supply The ggregte or mrket supply of commodity is constructed y ggregting or horizontlly summing the supply curves of ll the producing firms in the economy. = 2 2 = = 2 = 1 1 = = 1 1 = 2 = 1 2 Inverse ggregte supply curve Aggregte supply curve Aggregtion of production entils summing individul producers quntities ( ) t ll possile price levels (), tht is, = + 1
6 18/9/21 Aggregte or Mrket Supply R, C, S When = 12, 6 units re supplied. Industry revenue, R, is re A + B. Industry production cost, C, is re B. Industry surplus is re A, the difference etween industry revenue nd production cost. We cn compute the vlues for our exmple s follows: R(6) = A + B = 72 C (6) = B = 6 S(6) = B(6) = A B = 6 Firm 1 Firm 2 Aggregte Supply 18 MC 1 18 MC 2 18 Q S () or MC A B Q Q 2 Q 11 6
Math Review 1. , where α (alpha) is a constant between 0 and 1, is one specific functional form for the general production function.
Mth Review Vribles, Constnts nd Functions A vrible is mthemticl bbrevition for concept For emple in economics, the vrible Y usully represents the level of output of firm or the GDP of n economy, while
More informationBasic Analysis of Autarky and Free Trade Models
Bsic Anlysis of Autrky nd Free Trde Models AUTARKY Autrky condition in prticulr commodity mrket refers to sitution in which country does not engge in ny trde in tht commodity with other countries. Consequently
More informationEcon 4721 Money and Banking Problem Set 2 Answer Key
Econ 472 Money nd Bnking Problem Set 2 Answer Key Problem (35 points) Consider n overlpping genertions model in which consumers live for two periods. The number of people born in ech genertion grows in
More informationExperiment 6: Friction
Experiment 6: Friction In previous lbs we studied Newton s lws in n idel setting, tht is, one where friction nd ir resistnce were ignored. However, from our everydy experience with motion, we know tht
More informationChapter 5: Elasticity. measures how strongly people respond to changes in prices and changes in income.
Chpter 5: Elsticity Elsticity responsiveness mesures how strongly people respond to chnges in prices nd chnges in income. Exmples of questions tht elsticity helps nswer Wht hppens to ttendnce t your museum
More informationFirm Objectives. The Theory of the Firm II. Cost Minimization Mathematical Approach. First order conditions. Cost Minimization Graphical Approach
Pro. Jy Bhttchry Spring 200 The Theory o the Firm II st lecture we covered: production unctions Tody: Cost minimiztion Firm s supply under cost minimiztion Short vs. long run cost curves Firm Ojectives
More informationUse Geometry Expressions to create a more complex locus of points. Find evidence for equivalence using Geometry Expressions.
Lerning Objectives Loci nd Conics Lesson 3: The Ellipse Level: Preclculus Time required: 120 minutes In this lesson, students will generlize their knowledge of the circle to the ellipse. The prmetric nd
More informationHomework #4: Answers. 1. Draw the array of world outputs that free trade allows by making use of each country s transformation schedule.
Text questions, Chpter 5, problems 15: Homework #4: Answers 1. Drw the rry of world outputs tht free trde llows by mking use of ech country s trnsformtion schedule.. Drw it. This digrm is constructed
More informationLecture 15  Curve Fitting Techniques
Lecture 15  Curve Fitting Techniques Topics curve fitting motivtion liner regression Curve fitting  motivtion For root finding, we used given function to identify where it crossed zero where does fx
More informationReasoning to Solve Equations and Inequalities
Lesson4 Resoning to Solve Equtions nd Inequlities In erlier work in this unit, you modeled situtions with severl vriles nd equtions. For exmple, suppose you were given usiness plns for concert showing
More informationOperations with Polynomials
38 Chpter P Prerequisites P.4 Opertions with Polynomils Wht you should lern: Write polynomils in stndrd form nd identify the leding coefficients nd degrees of polynomils Add nd subtrct polynomils Multiply
More informationWeek 7  Perfect Competition and Monopoly
Week 7  Perfect Competition nd Monopoly Our im here is to compre the industrywide response to chnges in demnd nd costs by monopolized industry nd by perfectly competitive one. We distinguish between
More informationEQUATIONS OF LINES AND PLANES
EQUATIONS OF LINES AND PLANES MATH 195, SECTION 59 (VIPUL NAIK) Corresponding mteril in the ook: Section 12.5. Wht students should definitely get: Prmetric eqution of line given in pointdirection nd twopoint
More informationGraphs on Logarithmic and Semilogarithmic Paper
0CH_PHClter_TMSETE_ 3//00 :3 PM Pge Grphs on Logrithmic nd Semilogrithmic Pper OBJECTIVES When ou hve completed this chpter, ou should be ble to: Mke grphs on logrithmic nd semilogrithmic pper. Grph empiricl
More informationVectors 2. 1. Recap of vectors
Vectors 2. Recp of vectors Vectors re directed line segments  they cn be represented in component form or by direction nd mgnitude. We cn use trigonometry nd Pythgors theorem to switch between the forms
More informationRational Functions. Rational functions are the ratio of two polynomial functions. Qx bx b x bx b. x x x. ( x) ( ) ( ) ( ) and
Rtionl Functions Rtionl unctions re the rtio o two polynomil unctions. They cn be written in expnded orm s ( ( P x x + x + + x+ Qx bx b x bx b n n 1 n n 1 1 0 m m 1 m + m 1 + + m + 0 Exmples o rtionl unctions
More informationDouble Integrals over General Regions
Double Integrls over Generl egions. Let be the region in the plne bounded b the lines, x, nd x. Evlute the double integrl x dx d. Solution. We cn either slice the region verticll or horizontll. ( x x Slicing
More informationAppendix D: Completing the Square and the Quadratic Formula. In Appendix A, two special cases of expanding brackets were considered:
Appendi D: Completing the Squre nd the Qudrtic Formul Fctoring qudrtic epressions such s: + 6 + 8 ws one of the topics introduced in Appendi C. Fctoring qudrtic epressions is useful skill tht cn help you
More informationMath 135 Circles and Completing the Square Examples
Mth 135 Circles nd Completing the Squre Exmples A perfect squre is number such tht = b 2 for some rel number b. Some exmples of perfect squres re 4 = 2 2, 16 = 4 2, 169 = 13 2. We wish to hve method for
More informationMATH 150 HOMEWORK 4 SOLUTIONS
MATH 150 HOMEWORK 4 SOLUTIONS Section 1.8 Show tht the product of two of the numbers 65 1000 8 2001 + 3 177, 79 1212 9 2399 + 2 2001, nd 24 4493 5 8192 + 7 1777 is nonnegtive. Is your proof constructive
More informationP.3 Polynomials and Factoring. P.3 an 1. Polynomial STUDY TIP. Example 1 Writing Polynomials in Standard Form. What you should learn
33337_0P03.qp 2/27/06 24 9:3 AM Chpter P Pge 24 Prerequisites P.3 Polynomils nd Fctoring Wht you should lern Polynomils An lgeric epression is collection of vriles nd rel numers. The most common type of
More informationExample 27.1 Draw a Venn diagram to show the relationship between counting numbers, whole numbers, integers, and rational numbers.
2 Rtionl Numbers Integers such s 5 were importnt when solving the eqution x+5 = 0. In similr wy, frctions re importnt for solving equtions like 2x = 1. Wht bout equtions like 2x + 1 = 0? Equtions of this
More informationPolynomial Functions. Polynomial functions in one variable can be written in expanded form as ( )
Polynomil Functions Polynomil functions in one vrible cn be written in expnded form s n n 1 n 2 2 f x = x + x + x + + x + x+ n n 1 n 2 2 1 0 Exmples of polynomils in expnded form re nd 3 8 7 4 = 5 4 +
More information9.3. The Scalar Product. Introduction. Prerequisites. Learning Outcomes
The Sclr Product 9.3 Introduction There re two kinds of multipliction involving vectors. The first is known s the sclr product or dot product. This is soclled becuse when the sclr product of two vectors
More informationSquare Roots Teacher Notes
Henri Picciotto Squre Roots Techer Notes This unit is intended to help students develop n understnding of squre roots from visul / geometric point of view, nd lso to develop their numer sense round this
More informationLecture 3 Gaussian Probability Distribution
Lecture 3 Gussin Probbility Distribution Introduction l Gussin probbility distribution is perhps the most used distribution in ll of science. u lso clled bell shped curve or norml distribution l Unlike
More information2 DIODE CLIPPING and CLAMPING CIRCUITS
2 DIODE CLIPPING nd CLAMPING CIRCUITS 2.1 Ojectives Understnding the operting principle of diode clipping circuit Understnding the operting principle of clmping circuit Understnding the wveform chnge of
More informationExample A rectangular box without lid is to be made from a square cardboard of sides 18 cm by cutting equal squares from each corner and then folding
1 Exmple A rectngulr box without lid is to be mde from squre crdbord of sides 18 cm by cutting equl squres from ech corner nd then folding up the sides. 1 Exmple A rectngulr box without lid is to be mde
More informationA.7.1 Trigonometric interpretation of dot product... 324. A.7.2 Geometric interpretation of dot product... 324
A P P E N D I X A Vectors CONTENTS A.1 Scling vector................................................ 321 A.2 Unit or Direction vectors...................................... 321 A.3 Vector ddition.................................................
More informationAssuming all values are initially zero, what are the values of A and B after executing this Verilog code inside an always block? C=1; A <= C; B = C;
B26 Appendix B The Bsics of Logic Design Check Yourself ALU n [Arthritic Logic Unit or (rre) Arithmetic Logic Unit] A rndomnumer genertor supplied s stndrd with ll computer systems Stn KellyBootle,
More information15.6. The mean value and the rootmeansquare value of a function. Introduction. Prerequisites. Learning Outcomes. Learning Style
The men vlue nd the rootmensqure vlue of function 5.6 Introduction Currents nd voltges often vry with time nd engineers my wish to know the verge vlue of such current or voltge over some prticulr time
More informationWarmup for Differential Calculus
Summer Assignment Wrmup for Differentil Clculus Who should complete this pcket? Students who hve completed Functions or Honors Functions nd will be tking Differentil Clculus in the fll of 015. Due Dte:
More information4 Geometry: Shapes. 4.1 Circumference and area of a circle. FM Functional Maths AU (AO2) Assessing Understanding PS (AO3) Problem Solving HOMEWORK 4A
Geometry: Shpes. Circumference nd re of circle HOMEWORK D C 3 5 6 7 8 9 0 3 U Find the circumference of ech of the following circles, round off your nswers to dp. Dimeter 3 cm Rdius c Rdius 8 m d Dimeter
More informationMatrix Inverse and Condition
Mtrix Inverse nd Condition Berlin Chen Deprtment of Computer Science & Informtion Engineering Ntionl Tiwn Norml University Reference: 1. Applied Numericl Methods with MATLAB for Engineers, Chpter 11 &
More informationRotating DC Motors Part II
Rotting Motors rt II II.1 Motor Equivlent Circuit The next step in our consiertion of motors is to evelop n equivlent circuit which cn be use to better unerstn motor opertion. The rmtures in rel motors
More informationModule 2. Analysis of Statically Indeterminate Structures by the Matrix Force Method. Version 2 CE IIT, Kharagpur
Module Anlysis of Stticlly Indeterminte Structures by the Mtrix Force Method Version CE IIT, Khrgpur esson 9 The Force Method of Anlysis: Bems (Continued) Version CE IIT, Khrgpur Instructionl Objectives
More informationMechanics Cycle 1 Chapter 5. Chapter 5
Chpter 5 Contct orces: ree Body Digrms nd Idel Ropes Pushes nd Pulls in 1D, nd Newton s Second Lw Neglecting riction ree Body Digrms Tension Along Idel Ropes (i.e., Mssless Ropes) Newton s Third Lw Bodies
More informationLabor Productivity and Comparative Advantage: The Ricardian Model of International Trade
Lbor Productivity nd omrtive Advntge: The Ricrdin Model of Interntionl Trde Model of trde with simle (unrelistic) ssumtions. Among them: erfect cometition; one reresenttive consumer; no trnsction costs,
More informationBinary Representation of Numbers Autar Kaw
Binry Representtion of Numbers Autr Kw After reding this chpter, you should be ble to: 1. convert bse rel number to its binry representtion,. convert binry number to n equivlent bse number. In everydy
More information1. In the Bohr model, compare the magnitudes of the electron s kinetic and potential energies in orbit. What does this imply?
Assignment 3: Bohr s model nd lser fundmentls 1. In the Bohr model, compre the mgnitudes of the electron s kinetic nd potentil energies in orit. Wht does this imply? When n electron moves in n orit, the
More informationVersion 001 CIRCUITS holland (1290) 1
Version CRCUTS hollnd (9) This printout should hve questions Multiplechoice questions my continue on the next column or pge find ll choices efore nswering AP M 99 MC points The power dissipted in wire
More informationVolumes of solids of revolution
Volumes of solids of revolution We sometimes need to clculte the volume of solid which cn be obtined by rotting curve bout the xxis. There is strightforwrd technique which enbles this to be done, using
More informationSection 74 Translation of Axes
62 7 ADDITIONAL TOPICS IN ANALYTIC GEOMETRY Section 74 Trnsltion of Aes Trnsltion of Aes Stndrd Equtions of Trnslted Conics Grphing Equtions of the Form A 2 C 2 D E F 0 Finding Equtions of Conics In the
More information2. Transaction Cost Economics
3 2. Trnsction Cost Economics Trnsctions Trnsctions Cn Cn Be Be Internl Internl or or Externl Externl n n Orgniztion Orgniztion Trnsctions Trnsctions occur occur whenever whenever good good or or service
More informationHomework 3 Solutions
CS 341: Foundtions of Computer Science II Prof. Mrvin Nkym Homework 3 Solutions 1. Give NFAs with the specified numer of sttes recognizing ech of the following lnguges. In ll cses, the lphet is Σ = {,1}.
More informationSmall Business Networking
Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd processes. Introducing technology
More informationSmall Business Networking
Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd business. Introducing technology
More informationLINEAR TRANSFORMATIONS AND THEIR REPRESENTING MATRICES
LINEAR TRANSFORMATIONS AND THEIR REPRESENTING MATRICES DAVID WEBB CONTENTS Liner trnsformtions 2 The representing mtrix of liner trnsformtion 3 3 An ppliction: reflections in the plne 6 4 The lgebr of
More informationSmall Business Networking
Why Network is n Essentil Productivity Tool for Any Smll Business TechAdvisory.org SME Reports sponsored by Effective technology is essentil for smll businesses looking to increse their productivity. Computer
More informationUNIVERSITY OF NOTTINGHAM. Discussion Papers in Economics STRATEGIC SECOND SOURCING IN A VERTICAL STRUCTURE
UNVERSTY OF NOTTNGHAM Discussion Ppers in Economics Discussion Pper No. 04/15 STRATEGC SECOND SOURCNG N A VERTCAL STRUCTURE By Arijit Mukherjee September 004 DP 04/15 SSN 10438 UNVERSTY OF NOTTNGHAM Discussion
More information1. Find the zeros Find roots. Set function = 0, factor or use quadratic equation if quadratic, graph to find zeros on calculator
AP Clculus Finl Review Sheet When you see the words. This is wht you think of doing. Find the zeros Find roots. Set function =, fctor or use qudrtic eqution if qudrtic, grph to find zeros on clcultor.
More informationSection 54 Trigonometric Functions
5 Trigonometric Functions Section 5 Trigonometric Functions Definition of the Trigonometric Functions Clcultor Evlution of Trigonometric Functions Definition of the Trigonometric Functions Alternte Form
More informationSmall Businesses Decisions to Offer Health Insurance to Employees
Smll Businesses Decisions to Offer Helth Insurnce to Employees Ctherine McLughlin nd Adm Swinurn, June 2014 Employersponsored helth insurnce (ESI) is the dominnt source of coverge for nonelderly dults
More informationand thus, they are similar. If k = 3 then the Jordan form of both matrices is
Homework ssignment 11 Section 7. pp. 24925 Exercise 1. Let N 1 nd N 2 be nilpotent mtrices over the field F. Prove tht N 1 nd N 2 re similr if nd only if they hve the sme miniml polynomil. Solution: If
More informationMath 314, Homework Assignment 1. 1. Prove that two nonvertical lines are perpendicular if and only if the product of their slopes is 1.
Mth 4, Homework Assignment. Prove tht two nonverticl lines re perpendiculr if nd only if the product of their slopes is. Proof. Let l nd l e nonverticl lines in R of slopes m nd m, respectively. Suppose
More information. At first sight a! b seems an unwieldy formula but use of the following mnemonic will possibly help. a 1 a 2 a 3 a 1 a 2
7 CHAPTER THREE. Cross Product Given two vectors = (,, nd = (,, in R, the cross product of nd written! is defined to e: " = (!,!,! Note! clled cross is VECTOR (unlike which is sclr. Exmple (,, " (4,5,6
More informationApplications to Physics and Engineering
Section 7.5 Applictions to Physics nd Engineering Applictions to Physics nd Engineering Work The term work is used in everydy lnguge to men the totl mount of effort required to perform tsk. In physics
More informationThe Chain Rule. rf dx. t t lim " (x) dt " (0) dx. df dt = df. dt dt. f (r) = rf v (1) df dx
The Chin Rule The Chin Rule In this section, we generlize the chin rule to functions of more thn one vrible. In prticulr, we will show tht the product in the singlevrible chin rule extends to n inner
More informationAll pay auctions with certain and uncertain prizes a comment
CENTER FOR RESEARC IN ECONOMICS AND MANAGEMENT CREAM Publiction No. 12015 All py uctions with certin nd uncertin prizes comment Christin Riis All py uctions with certin nd uncertin prizes comment Christin
More informationEnterprise Risk Management Software Buyer s Guide
Enterprise Risk Mngement Softwre Buyer s Guide 1. Wht is Enterprise Risk Mngement? 2. Gols of n ERM Progrm 3. Why Implement ERM 4. Steps to Implementing Successful ERM Progrm 5. Key Performnce Indictors
More informationMathematics. Vectors. hsn.uk.net. Higher. Contents. Vectors 128 HSN23100
hsn.uk.net Higher Mthemtics UNIT 3 OUTCOME 1 Vectors Contents Vectors 18 1 Vectors nd Sclrs 18 Components 18 3 Mgnitude 130 4 Equl Vectors 131 5 Addition nd Subtrction of Vectors 13 6 Multipliction by
More informationPlotting and Graphing
Plotting nd Grphing Much of the dt nd informtion used by engineers is presented in the form of grphs. The vlues to be plotted cn come from theoreticl or empiricl (observed) reltionships, or from mesured
More informationDlNBVRGH + Sickness Absence Monitoring Report. Executive of the Council. Purpose of report
DlNBVRGH + + THE CITY OF EDINBURGH COUNCIL Sickness Absence Monitoring Report Executive of the Council 8fh My 4 I.I...3 Purpose of report This report quntifies the mount of working time lost s result of
More informationThe remaining two sides of the right triangle are called the legs of the right triangle.
10 MODULE 6. RADICAL EXPRESSIONS 6 Pythgoren Theorem The Pythgoren Theorem An ngle tht mesures 90 degrees is lled right ngle. If one of the ngles of tringle is right ngle, then the tringle is lled right
More informationCS99S Laboratory 2 Preparation Copyright W. J. Dally 2001 October 1, 2001
CS99S Lortory 2 Preprtion Copyright W. J. Dlly 2 Octoer, 2 Ojectives:. Understnd the principle of sttic CMOS gte circuits 2. Build simple logic gtes from MOS trnsistors 3. Evlute these gtes to oserve logic
More informationSmall Business Cloud Services
Smll Business Cloud Services Summry. We re thick in the midst of historic sechnge in computing. Like the emergence of personl computers, grphicl user interfces, nd mobile devices, the cloud is lredy profoundly
More informationOr more simply put, when adding or subtracting quantities, their uncertainties add.
Propgtion of Uncertint through Mthemticl Opertions Since the untit of interest in n eperiment is rrel otined mesuring tht untit directl, we must understnd how error propgtes when mthemticl opertions re
More informationSmall Business Networking
Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd business. Introducing technology
More informationPROBLEMS 13  APPLICATIONS OF DERIVATIVES Page 1
PROBLEMS  APPLICATIONS OF DERIVATIVES Pge ( ) Wter seeps out of conicl filter t the constnt rte of 5 cc / sec. When the height of wter level in the cone is 5 cm, find the rte t which the height decreses.
More informationINTRODUCTION THE LABOR MARKET LABOR SUPPLY INCOME VS. LEISURE THE SUPPLY OF LABOR
INTRODUCTION Chapter 15 THE LBOR MRKET This chapter covers why there are differences in wages: How do people decide how much time to spend working? What determines the wage rate an employer is willing
More informationSPH simulation of fluidstructure interaction problems
Diprtimento di ingegneri idrulic e mientle SPH simultion of fluidstructure interction prolems C. Antoci, M. Gllti, S. Siill Reserch project Prolem: deformtion of plte due to the ction of fluid (lrge displcement
More informationPhysics 43 Homework Set 9 Chapter 40 Key
Physics 43 Homework Set 9 Chpter 4 Key. The wve function for n electron tht is confined to x nm is. Find the normliztion constnt. b. Wht is the probbility of finding the electron in. nmwide region t x
More informationSCHOOL OF ENGINEERING & BUILT ENVIRONMENT. Mathematics. Basic Algebra
SCHOOL OF ENGINEERING & BUILT ENVIRONMENT Mthemtics Bsic Alger. Opertions nd Epressions. Common Mistkes. Division of Algeric Epressions. Eponentil Functions nd Logrithms. Opertions nd their Inverses. Mnipulting
More informationA Note on Complement of Trapezoidal Fuzzy Numbers Using the αcut Method
Interntionl Journl of Applictions of Fuzzy Sets nd Artificil Intelligence ISSN  Vol.  A Note on Complement of Trpezoidl Fuzzy Numers Using the αcut Method D. Stephen Dingr K. Jivgn PG nd Reserch Deprtment
More informationTreatment Spring Late Summer Fall 0.10 5.56 3.85 0.61 6.97 3.01 1.91 3.01 2.13 2.99 5.33 2.50 1.06 3.53 6.10 Mean = 1.33 Mean = 4.88 Mean = 3.
The nlysis of vrince (ANOVA) Although the ttest is one of the most commonly used sttisticl hypothesis tests, it hs limittions. The mjor limittion is tht the ttest cn be used to compre the mens of only
More informationRotational Equilibrium: A Question of Balance
Prt of the IEEE Techer InService Progrm  Lesson Focus Demonstrte the concept of rottionl equilirium. Lesson Synopsis The Rottionl Equilirium ctivity encourges students to explore the sic concepts of
More informationAnswer, Key Homework 10 David McIntyre 1
Answer, Key Homework 10 Dvid McIntyre 1 This printout should hve 22 questions, check tht it is complete. Multiplechoice questions my continue on the next column or pge: find ll choices efore mking your
More informationNQF Level: 2 US No: 7480
NQF Level: 2 US No: 7480 Assessment Guide Primry Agriculture Rtionl nd irrtionl numers nd numer systems Assessor:.......................................... Workplce / Compny:.................................
More informationSPECIAL PRODUCTS AND FACTORIZATION
MODULE  Specil Products nd Fctoriztion 4 SPECIAL PRODUCTS AND FACTORIZATION In n erlier lesson you hve lernt multipliction of lgebric epressions, prticulrly polynomils. In the study of lgebr, we come
More informationSmall Business Networking
Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd processes. Introducing technology
More informationSmall Business Networking
Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd processes. Introducing technology
More informationPROF. BOYAN KOSTADINOV NEW YORK CITY COLLEGE OF TECHNOLOGY, CUNY
MAT 0630 INTERNET RESOURCES, REVIEW OF CONCEPTS AND COMMON MISTAKES PROF. BOYAN KOSTADINOV NEW YORK CITY COLLEGE OF TECHNOLOGY, CUNY Contents 1. ACT Compss Prctice Tests 1 2. Common Mistkes 2 3. Distributive
More informationIIMK/WPS/121/FIN/2013/07. Abhilash S. Nair 1
IIMK/WPS/2/FIN/203/07 EXISTENCE OF CAPITAL MARKET EQUILIBRIUM IN THE PRESENCE OF HERDING AND FEEDBACK TRADING Abhilsh S. Nir Assistnt Professor, Indin Institute of Mngement Kozhikode, IIMK Cmpus PO, Kozhikode
More informationArithmetic Sequences
Arithmetic equeces A simple wy to geerte sequece is to strt with umber, d dd to it fixed costt d, over d over gi. This type of sequece is clled rithmetic sequece. Defiitio: A rithmetic sequece is sequece
More informationIntroduction 1 From need to demand Solutions 1 a
Introduction 1 From need to demnd Solutions 1 Need Existence need Sfety need Socil need Esteem need Selfctuliztion need Exmples Clothing, medicl cre, wrmth, sexulity Protection ginst threts, stility Belonging
More information, and the number of electrons is 19. e e 1.60 10 C. The negatively charged electrons move in the direction opposite to the conventional current flow.
Prolem 1. f current of 80.0 ma exists in metl wire, how mny electrons flow pst given cross section of the wire in 10.0 min? Sketch the directions of the current nd the electrons motion. Solution: The chrge
More informationAlgebra Review. How well do you remember your algebra?
Algebr Review How well do you remember your lgebr? 1 The Order of Opertions Wht do we men when we write + 4? If we multiply we get 6 nd dding 4 gives 10. But, if we dd + 4 = 7 first, then multiply by then
More informationDerivatives and Rates of Change
Section 2.1 Derivtives nd Rtes of Cnge 2010 Kiryl Tsiscnk Derivtives nd Rtes of Cnge Te Tngent Problem EXAMPLE: Grp te prbol y = x 2 nd te tngent line t te point P(1,1). Solution: We ve: DEFINITION: Te
More informationHelicopter Theme and Variations
Helicopter Theme nd Vritions Or, Some Experimentl Designs Employing Pper Helicopters Some possible explntory vribles re: Who drops the helicopter The length of the rotor bldes The height from which the
More informationLec 2: Gates and Logic
Lec 2: Gtes nd Logic Kvit Bl CS 34, Fll 28 Computer Science Cornell University Announcements Clss newsgroup creted Posted on wepge Use it for prtner finding First ssignment is to find prtners Due this
More informationGuide to Reading Your Morgan Stanley Smith Barney Statement
Guide to Reding Your Morgn Stnley Smith Brney Sttement Your Morgn Stnley Smith Brney ( MSSB ) ccount sttement is vluble nd, powerful resource tht provides you with the informtion you need to prtner with
More informationCOMPARISON OF SOME METHODS TO FIT A MULTIPLICATIVE TARIFF STRUCTURE TO OBSERVED RISK DATA BY B. AJNE. Skandza, Stockholm ABSTRACT
COMPARISON OF SOME METHODS TO FIT A MULTIPLICATIVE TARIFF STRUCTURE TO OBSERVED RISK DATA BY B. AJNE Skndz, Stockholm ABSTRACT Three methods for fitting multiplictive models to observed, crossclssified
More informationMA 15800 Lesson 16 Notes Summer 2016 Properties of Logarithms. Remember: A logarithm is an exponent! It behaves like an exponent!
MA 5800 Lesson 6 otes Summer 06 Rememer: A logrithm is n eponent! It ehves like n eponent! In the lst lesson, we discussed four properties of logrithms. ) log 0 ) log ) log log 4) This lesson covers more
More informationExponential and Logarithmic Functions
Nme Chpter Eponentil nd Logrithmic Functions Section. Eponentil Functions nd Their Grphs Objective: In this lesson ou lerned how to recognize, evlute, nd grph eponentil functions. Importnt Vocbulr Define
More informationCUBICFOOT VOLUME OF A LOG
CUBICFOOT VOLUME OF A LOG Wys to clculte cuic foot volume ) xylometer: tu of wter sumerge tree or log in wter nd find volume of wter displced. ) grphic: exmple: log length = 4 feet, ech section feet in
More information6.5  Areas of Surfaces of Revolution and the Theorems of Pappus
Lecture_06_05.n 1 6.5  Ares of Surfces of Revolution n the Theorems of Pppus Introuction Suppose we rotte some curve out line to otin surfce, we cn use efinite integrl to clculte the re of the surfce.
More informationAnswer, Key Homework 4 David McIntyre Mar 25,
Answer, Key Homework 4 Dvid McIntyre 45123 Mr 25, 2004 1 his printout should hve 18 questions. Multiplechoice questions my continue on the next column or pe find ll choices before mkin your selection.
More informationMathematics Higher Level
Mthemtics Higher Level Higher Mthemtics Exmintion Section : The Exmintion Mthemtics Higher Level. Structure of the exmintion pper The Higher Mthemtics Exmintion is divided into two ppers s detiled below:
More informationVendor Rating for Service Desk Selection
Vendor Presented By DATE Using the scores of 0, 1, 2, or 3, plese rte the vendor's presenttion on how well they demonstrted the functionl requirements in the res below. Also consider how efficient nd functionl
More information