UNIVERSITY OF NOTTINGHAM. Discussion Papers in Economics STRATEGIC SECOND SOURCING IN A VERTICAL STRUCTURE


 Annis Cross
 1 years ago
 Views:
Transcription
1 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
2 UNVERSTY OF NOTTNGHAM Discussion Ppers in Economics Discussion Pper No. 04/15 STRATEGC SECOND SOURCNG N A VERTCAL STRUCTURE by Arijit Mukherjee Arijit Mukherjee is Lecturer, School of Economics, University of Nottinghm September 004
3 Strtegic second sourcing in verticl structure Arijit Mukherjee * University of Nottinghm nd The Leverhulme Centre for Reserch in Globlistion nd Economic Policy, UK September 004 Abstrct: We show tht monopolist input supplier licenses its technology to crete second source of input supply if second sourcing increses competition in the finl goods mrket. We lso show tht welfre increses under second sourcing. JEL Clssifiction: D43 ; L13 ; O34 Key Words: Entry; Licensing; Downstrem mrket; Second sourcing; Upstrem mrket Correspondence to: Arijit Mukherjee, School of Economics, University of Nottinghm, University Prk, Nottinghm, NG7 RD, UK Emil: Fx: * would like to thnk the prticipnts of the North Americn Summer Meeting of the Econometric Society t the Kellogg School of Mngement, for helpful discussions on n erlier drft. The usul disclimer pplies.
4 Strtegic second sourcing in verticl structure Abstrct: We show tht monopolist input supplier licenses its technology to crete second source of input supply if second sourcing increses competition in the finl goods mrket. We lso show tht welfre increses under second sourcing. JEL Clssifiction: D43 ; L13 ; O34 Key Words: Entry; Licensing; Downstrem mrket; Second sourcing; Upstrem mrket 1. ntroduction f the buyers of product need to ber specific setup costs, the seller cn exproprite the returns to the buyer s specific investment by either incresing price of the product or by reducing qulity of the product. This problem of opportunism in the mrket trnsction reduces profit of the seller nd it cn be resolved if the monopolist seller crtes second source of supply by licensing its technology to competitor. These issues hve been ddressed in Sheprd (1987) nd Frrell nd Gllini (1988). We show tht even if there is no commitment problem bout the future price or qulity of the upstrem product, second sourcing by n upstrem monopolist is profitble if it increses competition in the downstrem mrket. Second sourcing reduces the input price by incresing competition in the upstrem mrket, which my increse competition in the downstrem mrket by ttrcting new firms. The ltter effect increses the demnd for input nd domintes the competition effect in the upstrem mrket. We lso show tht welfre increses under second sourcing. 1
5 Our explntion of second sourcing is consistent with the empiricl evidence. t hs been documented in Sheprd (1987) tht commentry in the trde press nd by industry nlysts ttributes second sourcing to the innovting firm s desire to expnd product demnd in the semiconductor industry. This pper cn lso be relted to works on licensing of innovtion, which shows tht monopolist licenses to the competitor only if the products re imperfect substitutes (see, e.g., FulíOller nd Sndonis, 00). We show tht the upstrem monopolist licenses technology even if the upstrem products re perfect substitutes. The reminder of the pper is orgnized s follows. Section describes the model nd derives the results. Section 3 concludes.. The model nd the results Let us consider n economy with the upstrem nd the downstrem mrkets. Assume tht there is n upstrem monopolist, 1, who hs the technology to produce criticl input for the downstrem firms. The verge cost of input production is constnt nd is ssumed to be, for simplicity. Assume tht there is nother upstrem firm,, 0 who cn produce the input if nd only if it gets the technology of. Assume tht there is n incumbent nd potentil entrnt in the downstrem mrket. We cll these firms s nd D respectively. We consider one downstrem D1 incumbent to show our results in the simplest wy. However, it is needless to sy tht 1 1 our qulittive results hold even if there re n downstrem firms. Assume tht the downstrem firms hve the sme production technology, which requires one unit of 1 To mke second sourcing fesible, it must be profitble for to enter the mrket. To stisfy this in the simplest wy, we ssume wy cost of entry for.
6 the input to produce one unit of the finl goods. For simplicity, we consider tht the finl product requires only the criticl input produced by the upstrem firm(s). Assume tht the inverse mrket demnd function for the finl product is P = q 1 q, (1) where nd re outputs of nd D respectively nd q1 q D1 P is price of the finl good. Assume tht the firms in the upstrem nd the downstrem mrkets choose outputs to mximize their profits. n cse of competition in the upstrem nd/or in the downstrem mrkets, the respective firms compete like Cournot duopolists with homogeneous products. So, we consider n economy with successive Cournot oligopolists like Sheprd (1987). Therefore, the upstrem firm(s) chooses output(s) nd the input price, w, is determined from the input demnd function. Further, like Sheprd (1987) nd Frrell nd Gllini (1988), we ssume wy verticl restrints nd verticl integrtion between the upstrem nd the downstrem firms. 3 We lso ssume tht the ntitrust uthority prevents collusion in the finl goods mrket, which will be justified lso by our nlysis. We consider the following gme. At stge 1, 1 decides whether to license to or not. n cse of licensing, it gives tkeitorleveit offer to, which either ccepts or rejects the offer. At stge, the domestic entrnt D decides whether to enter or not. At stge 3, ( nd ) produces (produce simultneously) if there is 1 1 no licensing (licensing) t stge 1. At stge 4, (D nd ) produces (produce D 1 1 D One my, e.g., refer to Abiru (1988), Slinger (1988) nd Abiru et l. (1998) for other works with successive Cournot oligopolists. 3 Hrt nd Tirole (1990) rgued tht verticl integrtion would not occur for significnt cost of integrtion. 3
7 simultneously) if D does not enter (enters) t stge nd the profits re relized. We solve the gme through bckwrd induction..1 No licensing Let us consider the sitution where does not license its technology to. n this 1 sitution, we hve two possibilities: (i) where D enters the downstrem mrket nd (ii) where D does not enter the downstrem mrket. f enters then, given the input price, both nd D produce D D1 ( w). 3 So, the demnd for input is q ( w) =. () 3 1 produces to mximize the following expression: Mx( q ) q. (3) 1 q Optiml input supply nd the input price re respectively 3 nd. Profit of 1 is 6 nd profits of D nd D re respectively 1 nd E. So, if 1 is monopolist in the upstrem mrket, D enters provided > E. f < E, is monopolist in the downstrem mrket nd the input demnd D 1 is So, 1 q ( w) =. (4) produces to mximize the following expression: 4
8 Mx 1 1 ( q ) 1 q q. (5) Optiml input supply nd the input price re respectively 4 nd. Profits of 1 nd D 1 re respectively 8 nd. 16. Licensing to crete second sourcing Now ssume tht licenses its technology to. To show our results in the simplest 1 wy, following Ktz nd Shpiro (1985), Mrjit (1990), Mukherjee (001) nd others, we ssume tht, under licensing, 1 chrges n upfront fixedfee 4 for its technology, nd ccepts the offer if it is not worse off under licensing thn no licensing. So, under licensing, both nd produce the input t zero verge cost of production. 1 We normlize the pyoff of under no licensing to 0. Agin we hve to consider two situtions: (i) where D enters the downstrem mrket nd (ii) where D does not enter the downstrem mrket. f D enters, the input demnd is given by (). The i th firm, i = 1,, in the upstrem mrket produces to mximize the following expression: 3 i 3 j i Mx q q q q i ( ), i j. (6) 4 Noninfringing imittion or inventing round the licensed technology by the licensee or lck of informtion needed for roylty provision might be the reson for licensing contrct with upfront fixedfee only (see, e.g., Ktz nd Shpiro, 1985 nd Rockett, 1990). 5
9 Both nd produce 1. Totl input supply nd the input price re respectively 9 4 nd. Therefore, optiml profits of both nd re nd optiml Profits of nd D re respectively D1 4 nd E So, D enters provided 4 4 > E 81. f 4 < 81 E then is monopolist nd the demnd for input is given by (4). D 1 The i th firm, i = 1,, in the upstrem mrket produces to mximize the following expression: Mx( q q ) q, q i i j i i j. (7) Both nd produce 1. Totl input supply nd the input price re respectively 6 3 nd. Profits of both 1 nd re 3 18 nd profit of D 1 is. 9.3 ncentive for second sourcing We hve seen tht D enters the mrket under no licensing nd licensing in the upstrem mrket if > E nd 4 > E 81 respectively, where 4 >. 81 Proposition 1: (i) f either E < or E > 4 81, second sourcing is mot profitble. 4 (ii) Second sourcing is profitble if E (, ). 81 6
10 Proof: (i) f > E, totl profit in the upstrem mrket under second sourcing is 4 nd it is lower thn the profit of 1 when it is monopolist, which is. 7 6 f 4 E >, totl profit in the upstrem mrket under second sourcing is 81 9 nd it is lower thn the profit of 1 when it is monopolist, which is. 8 4 (ii) f E (, ), totl profit in the upstrem mrket under second sourcing is 81 4 nd it is greter thn the profit of 1 when it is monopolist, which is 7 8. Q.E.D. f second sourcing in the upstrem mrket does not induce entry in the downstrem mrket, it cretes competition in the upstrem mrket while the input demnd function remins unchnged. This competition effect reduces totl profit in the upstrem mrket nd mkes second sourcing unprofitble. However, second sourcing reduces the input price by creting competition in the upstrem mrket nd my induce entry in the downstrem mrket. f second sourcing increses competition in the downstrem mrket, it increses the demnd for input, for given input price. We show tht the effect of higher input demnd domintes the competition effect in the upstrem mrket nd mkes second sourcing profitble..4 Welfre implictions of second sourcing 4 We hve seen tht second sourcing occurs for E (, ). n this sitution, 81 welfre under monopoly in the upstrem mrket nd second sourcing re respectively 7
11 7 3 nd 56 E 16. (8) Comprison of the welfre vlues in (8) gives the following proposition. 4 Proposition : Suppose, E (, ). Second sourcing increses welfre 81 compred to monopoly in the upstrem mrket. t is strightforwrd to see tht collusion in the downstrem mrket reduces welfre if there is no second sourcing. Proposition 1 implies tht if the upstrem monopolist nticiptes collusion in the downstrem mrket, second sourcing does not occur. Then, it follows from Proposition tht collusion in the product mrket further reduces welfre by preventing second sourcing, which my encourge the ntitrust uthority to prevent collusion in the product mrket s ssumed in our nlysis. 3. Conclusion We show tht monopolist input supplier hs the incentive to license its technology to crete second source of input supply if second sourcing increses competition in the downstrem mrket. So, unlike pervious work on second sourcing by the monopolist input supplier, we show tht even if the upstrem firm does not fce ny commitment problem bout the future price or qulity of its product, second sourcing it still profitble. We lso find tht second sourcing increse welfre compred to monopoly in the upstrem mrket. 8
12 References Abiru, M., 1988, Verticl integrtion, vrible proportions nd successive oligopolies, Journl of ndustril Economics, : Abiru, M., B. Nht, S. Rychudhuri nd M. Wterson, 1998, Equilibrium structures in verticl oligopoly, Journl of Economic Behvior nd Orgniztion, 37: Frrell, J. nd N. Gllini, 1988, Secondsourcing s commitment: monopoly incentives to ttrct competition, The Qurterly Journl of Economics, 103: FuliOller, R. nd J. Sndonis, 00, Welfre reducing licensing, Gmes nd Economic Behvior, 41: Hrt, O. nd J. Tirole, 1990, Verticl integrtion nd mrket foreclosure, Brookings Ppers on Economic Activity, nd Ktz, M. nd C. Shpiro, 1985, On the licensing of innovtion, Rnd Journl of Economics, 16: Mrjit, S., 1990, On noncoopertive theory of technology trnsfer, Economics Letters, 33: Mukherjee, A., 001, Technology trnsfer with commitment, Economic Theory, 17: Rockett, K., 1990, The qulity of licensed technology, nterntionl Journl of ndustril Orgniztion, 8: Slinger, M. A., 1988, Verticl mergers nd mrket foreclosure, The Qurterly Journl of Economics, 103: Sheprd, A., 1987, Licensing to enhnce the demnd for new product, Rnd Journl of Economics, 18:
Nash Equilibrium A game consists of a set of players a set of strategies for each player A mapping from set of strategies to a set of payoffs, one
Nsh Euilibrium A gme consists of set of plyers set of strtegies for ech plyer A mpping from set of strtegies to set of pyoffs, one for ech plyer N.E.: A Set of strtegies form NE if, for plyer i, the strtegy
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 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 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 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 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 informationThe Relative Advantages of Flexible versus Designated Manufacturing Technologies
The Reltive Advntges of Flexible versus Designted Mnufcturing Technologies George Normn Cummings Professor of Entrepreneurship nd Business Economics Tufts University Medford MA 055 USA emil: george.normn@tufts.edu
More informationHomework #6: Answers. a. If both goods are produced, what must be their prices?
Text questions, hpter 7, problems 12. Homework #6: Answers 1. Suppose there is only one technique tht cn be used in clothing production. To produce one unit of clothing requires four lborhours nd one
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 informationThis paper considers two independent firms that invest in resources such as capacity or inventory based on
MANAGEMENT SCIENCE Vol. 5, No., December 006, pp. 93 99 issn 005909 eissn 56550 06 5 93 informs doi 0.87/mnsc.060.0574 006 INFORMS Strtegic Investments, Trding, nd Pricing Under Forecst Updting Jiri
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 informationIn this section make precise the idea of a matrix inverse and develop a method to find the inverse of a given square matrix when it exists.
Mth 52 Sec S060/S0602 Notes Mtrices IV 5 Inverse Mtrices 5 Introduction In our erlier work on mtrix multipliction, we sw the ide of the inverse of mtrix Tht is, for squre mtrix A, there my exist mtrix
More informationTests for One Poisson Mean
Chpter 412 Tests for One Poisson Men Introduction The Poisson probbility lw gives the probbility distribution of the number of events occurring in specified intervl of time or spce. The Poisson distribution
More informationCollege Admissions with Entrance Exams: Centralized versus Decentralized
Is E. Hflir Rustmdjn Hkimov Dorothe Kübler Morimitsu Kurino College Admissions with Entrnce Exms: Centrlized versus Decentrlized Discussion Pper SP II 2014 208 October 2014 (WZB Berlin Socil Science Center
More informationThe Effect of M&A on Wage: Evidence from Financial Institution in Taiwan, ROC
Li nd Lee, Interntionl Journl of Applied Economics, 8(2), September 2011, 8693 86 The Effect of M&A on Wge: Evidence from Finncil Institution in Tiwn, ROC YuCheng Li nd KunChin Lee* Shih Chien University
More informationChapter 6 Solving equations
Chpter 6 Solving equtions Defining n eqution 6.1 Up to now we hve looked minly t epressions. An epression is n incomplete sttement nd hs no equl sign. Now we wnt to look t equtions. An eqution hs n = sign
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 informationON THE FRAMESTEWART ALGORITHM FOR THE TOWER OF HANOI
ON THE FRAMESTEWART ALGORITHM FOR THE TOWER OF HANOI MICHAEL RAND 1. Introduction The Tower of Hnoi puzzle ws creted over century go by the number theorist Edourd Lucs [, 4], nd it nd its vrints hve chllenged
More informationStrategic Sourcing in the Presence of Uncertain Supply and Retail Competition
Vol. 2, No. 10, October 2014, pp. 174 1760 ISSN 1059147 EISSN 1975956 14 210 174 DOI 10.1111/poms.1207 201 Production nd Opertions Mngement Society Strtegic Sourcing in the Presence of Uncertin Supply
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 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 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 informationThe ISLM Model. Underlying model due to John Maynard Keynes Model representation due to John Hicks Used to make predictions about
The SLM Model Underlying model due to John Mynrd Keynes Model representtion due to John Hicks Used to mke predictions bout nterest rtes Aggregte spending ( ggregte output) mportnt ssumption: price is
More informationUniform convergence and its consequences
Uniform convergence nd its consequences The following issue is centrl in mthemtics: On some domin D, we hve sequence of functions {f n }. This mens tht we relly hve n uncountble set of ordinry sequences,
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 informationNOTES AND CORRESPONDENCE. Uncertainties of Derived Dewpoint Temperature and Relative Humidity
MAY 4 NOTES AND CORRESPONDENCE 81 NOTES AND CORRESPONDENCE Uncertinties of Derived Dewpoint Temperture nd Reltive Humidity X. LIN AND K. G. HUBBARD High Plins Regionl Climte Center, School of Nturl Resource
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 information11. Fourier series. sin mx cos nx dx = 0 for any m, n, sin 2 mx dx = π.
. Fourier series Summry of the bsic ides The following is quick summry of the introductory tretment of Fourier series in MATH. We consider function f with period π, tht is, stisfying f(x + π) = f(x) for
More informationBertrand with complements
Microeconomics, 2 nd Edition David Besanko and Ron Braeutigam Chapter 13: Market Structure and Competition Prepared by Katharine Rockett Dieter Balkenborg Todd Kaplan Miguel Fonseca Bertrand with complements
More informationEconomics Letters 65 (1999) 9 15. macroeconomists. a b, Ruth A. Judson, Ann L. Owen. Received 11 December 1998; accepted 12 May 1999
Economics Letters 65 (1999) 9 15 Estimting dynmic pnel dt models: guide for q mcroeconomists b, * Ruth A. Judson, Ann L. Owen Federl Reserve Bord of Governors, 0th & C Sts., N.W. Wshington, D.C. 0551,
More informationRedistributing the Gains from Trade through Nonlinear. Lumpsum Transfers
Redistributing the Gins from Trde through Nonliner Lumpsum Trnsfers Ysukzu Ichino Fculty of Economics, Konn University April 21, 214 Abstrct I exmine lumpsum trnsfer rules to redistribute the gins from
More informationInnovative and applied research on big data platforms of smart heritage
Innovtive nd pplied reserch on big dt pltforms of smrt heritge J. Qiu, J. Li, H. Sun * qiujie@thid.cn lijijun@thid.cn sunhuijio@thid.cn KEY WORDS: Smrt heritge, Big dt, Explntion ABSTRACT: Big dt hs huge
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 informationAnswer, Key Homework 8 David McIntyre 1
Answer, Key Homework 8 Dvid McIntyre 1 This printout should hve 17 questions, check tht it is complete. Multiplechoice questions my continue on the net column or pge: find ll choices before mking your
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 informationPerfect competition model (PCM)
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,
More informationSection 4.3. By the Mean Value Theorem, for every i = 1, 2, 3,..., n, there exists a point c i in the interval [x i 1, x i ] such that
Difference Equtions to Differentil Equtions Section 4.3 The Fundmentl Theorem of Clculus We re now redy to mke the longpromised connection between differentition nd integrtion, between res nd tngent lines.
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 informationAVERAGE COST BASED ACCESS PRICING AND THE NON DISCRIMINATION PRINCIPLE: A LEVEL PLAYINGFIELD?
AVERAGE COST BASED ACCESS PRICING AND THE NON DISCRIMINATION PRINCIPLE: A LEVEL PLAYINGIELD? KENNETH JELL nd ØYSTEIN OROS Norwegin School of Economics nd Business Administrtion We re grteful to Kåre P.
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 informationPreApproval Application
PreApprovl Appliction In tody s rel estte mrket, PreApproved mortgge provides you the buyer with powerful tool in the home purchse process! Once you hve received your PreApprovl, you cn shop for your
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 informationDoes Trade Increase Employment? A Developing Country Perspective
Does Trde Increse Employment? A Developing Country Perspective By Sugt Mrjit City University of Hong Kong nd Center for Studies in Socil Sciences, Indi Hmid Beldi University of Texs t Sn Antonio 005 Address
More informationQuantity Oriented Resource Allocation Strategy on Multiple Resources Projects under Stochastic Conditions
Interntionl Conference on Industril Engineering nd Systems Mngement IESM 2009 My 1315 MONTRÉAL  CANADA Quntity Oriented Resource Alloction Strtegy on Multiple Resources Projects under Stochstic Conditions
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 informationSocial efficiency of entry with market leaders
UNIVERSITY OF NOTTINGHAM Discussion Papers in Economics Discussion Paper No. 10/07 Social efficiency of entry with market leaders Arijit Mukherjee August 2010 2010 DP 10/07 Social efficiency of entry with
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 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 informationQUESTIONNAIRE. 1. Your Name: 2. Agegroup: Below 25 years 2635 years. 3. Gender : Male Female. 4. Education : H.S.C or Below H.S.C.
QUESTIONNAIRE A. PERSONAL DETAILS: 1. Your Nme: 2. Agegroup: Below 25 yers 2635 yers 3645 yers Over 45 yers 3. Gender : Mle Femle 4. Eduction : H.S.C or Below H.S.C. Grdution PostGrdution Any other
More informationOptimal Execution of OpenMarket Stock Repurchase Programs
Optiml Eecution of OpenMrket Stock Repurchse Progrms Jcob Oded This Drft: December 15, 005 Abstrct We provide theoreticl investigtion of the eecution of openmrket stock repurchse progrms. Our model suggests
More informationSolutions to Section 1
Solutions to Section Exercise. Show tht nd. This follows from the fct tht mx{, } nd mx{, } Exercise. Show tht = { if 0 if < 0 Tht is, the bsolute vlue function is piecewise defined function. Grph this
More informationUnleashing the Power of Cloud
Unleshing the Power of Cloud A Joint White Pper by FusionLyer nd NetIQ Copyright 2015 FusionLyer, Inc. All rights reserved. No prt of this publiction my be reproduced, stored in retrievl system, or trnsmitted,
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 informationResearch Article Competition with Online and Offline Demands considering Logistics Costs Based on the Hotelling Model
Mthemticl Problems in Engineering Volume 4, Article ID 678, pges http://dx.doi.org/.55/4/678 Reserch Article Competition with Online nd Offline Demnds considering Logistics Costs Bsed on the Hotelling
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 informationOn the Meaning of Regression Coefficients for Categorical and Continuous Variables: Model I and Model II; Effect Coding and Dummy Coding
Dt_nlysisclm On the Mening of Regression for tegoricl nd ontinuous Vribles: I nd II; Effect oding nd Dummy oding R Grdner Deprtment of Psychology This describes the simple cse where there is one ctegoricl
More informationCurve Sketching. 96 Chapter 5 Curve Sketching
96 Chpter 5 Curve Sketching 5 Curve Sketching A B A B A Figure 51 Some locl mximum points (A) nd minimum points (B) If (x, f(x)) is point where f(x) reches locl mximum or minimum, nd if the derivtive of
More informationApplication of Analytical Hierarchy Process (AHP) Technique To Evaluate and Selecting Suppliers in an Effective Supply Chain
Appliction of Anlyticl Hierrchy Process (AHP) Technique To Evlute nd Selecting Suppliers in n Effective Supply Chin Shhroodi 1*, Kmbiz, Industril Mngement Deprtment, Islmic Azd University (Rsht Brnch),
More informationVoIP for the Small Business
Reducing your telecommunictions costs VoIP (Voice over Internet Protocol) offers low cost lterntive to expensive trditionl phone services nd is rpidly becoming the communictions system of choice for smll
More informationAn OffCenter Coaxial Cable
1 Problem An OffCenter Coxil Cble Kirk T. McDonld Joseph Henry Lbortories, Princeton University, Princeton, NJ 08544 Nov. 21, 1999 A coxil trnsmission line hs inner conductor of rdius nd outer conductor
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 informationAddition and subtraction of rational expressions
Lecture 5. Addition nd subtrction of rtionl expressions Two rtionl expressions in generl hve different denomintors, therefore if you wnt to dd or subtrct them you need to equte the denomintors first. The
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 informationData quality issues for accounting information systems implementation: Systems, stakeholders, and organizational factors
Journl of Technology Reserch Dt qulity issues for ccounting informtion systems implementtion: Systems, stkeholders, nd orgniztionl fctors ABSTRACT Hongjing Xu Butler University Qulity informtion is one
More information4: RIEMANN SUMS, RIEMANN INTEGRALS, FUNDAMENTAL THEOREM OF CALCULUS
4: RIEMA SUMS, RIEMA ITEGRALS, FUDAMETAL THEOREM OF CALCULUS STEVE HEILMA Contents 1. Review 1 2. Riemnn Sums 2 3. Riemnn Integrl 3 4. Fundmentl Theorem of Clculus 7 5. Appendix: ottion 10 1. Review Theorem
More informationClearPeaks Customer Care Guide. Business as Usual (BaU) Services Peace of mind for your BI Investment
ClerPeks Customer Cre Guide Business s Usul (BU) Services Pece of mind for your BI Investment ClerPeks Customer Cre Business s Usul Services Tble of Contents 1. Overview...3 Benefits of Choosing ClerPeks
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 informationSection 2.3. Motion Along a Curve. The Calculus of Functions of Several Variables
The Clculus of Functions of Severl Vribles Section 2.3 Motion Along Curve Velocity ccelertion Consider prticle moving in spce so tht its position t time t is given by x(t. We think of x(t s moving long
More informationLecture 3 Basic Probability and Statistics
Lecture 3 Bsic Probbility nd Sttistics The im of this lecture is to provide n extremely speedy introduction to the probbility nd sttistics which will be needed for the rest of this lecture course. The
More informationpork.org Pork Industry Productivity Analysis National Pork Board Research Grant Report Dr. Kenneth J. Stalder, Iowa State University
pork.org 8004567675 Complete REPORT Pork Industry Productivity Anlysis Ntionl Pork Bord Reserch Grnt Report Dr. Kenneth J. Stlder, Iow Stte University Industry Summry The swine industry, like ny industry,
More informationHillsborough Township Public Schools Mathematics Department Computer Programming 1
Essentil Unit 1 Introduction to Progrmming Pcing: 15 dys Common Unit Test Wht re the ethicl implictions for ming in tody s world? There re ethicl responsibilities to consider when writing computer s. Citizenship,
More informationPHYS 110A  HW #7 Solutions by David Pace Any referenced equations are from Griffiths
PHYS 110A  HW #7 Solutions by Dvid Pce Any referenced equtions re from Griffiths [1.] Problem 4.11 from Griffiths A cylinder of length L nd rdius hs permnent polriztion prllel to its xis. Find the bound
More informationMATLAB: Mfiles; Numerical Integration Last revised : March, 2003
MATLAB: Mfiles; Numericl Integrtion Lst revised : Mrch, 00 Introduction to Mfiles In this tutoril we lern the bsics of working with Mfiles in MATLAB, so clled becuse they must use.m for their filenme
More informationUnit 29: Inference for TwoWay Tables
Unit 29: Inference for TwoWy Tbles Prerequisites Unit 13, TwoWy Tbles is prerequisite for this unit. In ddition, students need some bckground in significnce tests, which ws introduced in Unit 25. Additionl
More informationIntegration. 148 Chapter 7 Integration
48 Chpter 7 Integrtion 7 Integrtion t ech, by supposing tht during ech tenth of second the object is going t constnt speed Since the object initilly hs speed, we gin suppose it mintins this speed, but
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 informationComparison of Factors toward the Changes of Composite Stock Price Index in LQ 45 and Jakarta Islamic Index. (Case Study in Indonesian Stock Exchange)
DOI: 10.7763/IPEDR. 2013. V65. 15 Comprison of Fctors towrd the Chnges of Composite Stock Price Index in LQ 45 nd Jkrt Islmic Index (Cse Study in Indonesin Stock Exchnge) Lely Fer Trini 1, Etty Puji Lestri
More information10.5 Graphing Quadratic Functions
0.5 Grphing Qudrtic Functions Now tht we cn solve qudrtic equtions, we wnt to lern how to grph the function ssocited with the qudrtic eqution. We cll this the qudrtic function. Grphs of Qudrtic Functions
More informationIntegration by Substitution
Integrtion by Substitution Dr. Philippe B. Lvl Kennesw Stte University August, 8 Abstrct This hndout contins mteril on very importnt integrtion method clled integrtion by substitution. Substitution is
More informationQuality Evaluation of Entrepreneur Education on Graduate Students Based on AHPfuzzy Comprehensive Evaluation Approach ZhongXiaojun 1, WangYunfeng 2
Interntionl Journl of Engineering Reserch & Science (IJOER) ISSN [23956992] [Vol2, Issue1, Jnury 2016] Qulity Evlution of Entrepreneur Eduction on Grdute Students Bsed on AHPfuzzy Comprehensive Evlution
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 informationJaERM SoftwareasaSolution Package
JERM SoftwresSolution Pckge Enterprise Risk Mngement ( ERM ) Public listed compnies nd orgnistions providing finncil services re required by Monetry Authority of Singpore ( MAS ) nd/or Singpore Stock
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 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 informationIntroduction to Mathematical Reasoning, Saylor 111
Frction versus rtionl number. Wht s the difference? It s not n esy question. In fct, the difference is somewht like the difference between set of words on one hnd nd sentence on the other. A symbol is
More informationAN ANALYTICAL HIERARCHY PROCESS METHODOLOGY TO EVALUATE IT SOLUTIONS FOR ORGANIZATIONS
AN ANALYTICAL HIERARCHY PROCESS METHODOLOGY TO EVALUATE IT SOLUTIONS FOR ORGANIZATIONS Spiros Vsilkos (), Chrysostomos D. Stylios (),(b), John Groflkis (c) () Dept. of Telemtics Center, Computer 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 informationGFI MilArchiver 6 vs C2C Archive One Policy Mnger GFI Softwre www.gfi.com GFI MilArchiver 6 vs C2C Archive One Policy Mnger GFI MilArchiver 6 C2C Archive One Policy Mnger Who we re Generl fetures Supports
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 informationInternet Channel Entry: Retail Coverage and Entry Cost Advantage
Internet Chnnel Entry: Retil Coverge nd Entry Cost Advntge June Cheng Fculty of Business The Hong Kong Polytechnic University Hung Hom, Kowloon, Hong Kong fzcheng@inet.polyu.edu.hk Brrie R. Nult Hskyne
More informationAntiderivatives/Indefinite Integrals of Basic Functions
Antiderivtives/Indefinite Integrls of Bsic Functions Power Rule: x n+ x n n + + C, dx = ln x + C, if n if n = In prticulr, this mens tht dx = ln x + C x nd x 0 dx = dx = dx = x + C Integrl of Constnt:
More informationBiostatistics 103: Qualitative Data Tests of Independence
Singpore Med J 2003 Vol 44(10) : 498503 B s i c S t t i s t i c s F o r D o c t o r s Biosttistics 103: Qulittive Dt Tests of Independence Y H Chn Prmetric & nonprmetric tests (1) re used when the outcome
More informationMultiple Testing in a TwoStage Adaptive Design With Combination Tests Controlling FDR
This rticle ws downloded by: [New Jersey Institute of Technology] On: 28 Februry 204, At: 08:46 Publisher: Tylor & Frncis Inform Ltd Registered in nglnd nd Wles Registered Number: 072954 Registered office:
More informationHealth insurance exchanges What to expect in 2014
Helth insurnce exchnges Wht to expect in 2014 33096CAEENABC 02/13 The bsics of exchnges As prt of the Affordble Cre Act (ACA or helth cre reform lw), strting in 2014 ALL Americns must hve minimum mount
More informationFAULT TREES AND RELIABILITY BLOCK DIAGRAMS. Harry G. Kwatny. Department of Mechanical Engineering & Mechanics Drexel University
SYSTEM FAULT AND Hrry G. Kwtny Deprtment of Mechnicl Engineering & Mechnics Drexel University OUTLINE SYSTEM RBD Definition RBDs nd Fult Trees System Structure Structure Functions Pths nd Cutsets Reliility
More informationWorksheet 24: Optimization
Worksheet 4: Optimiztion Russell Buehler b.r@berkeley.edu 1. Let P 100I I +I+4. For wht vlues of I is P mximum? P 100I I + I + 4 Tking the derivtive, www.xkcd.com P (I + I + 4)(100) 100I(I + 1) (I + I
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 informationENHANCING CUSTOMER EXPERIENCE THROUGH BUSINESS PROCESS IMPROVEMENT: AN APPLICATION OF THE ENHANCED CUSTOMER EXPERIENCE FRAMEWORK (ECEF)
ENHNCING CUSTOMER EXPERIENCE THROUGH BUSINESS PROCESS IMPROVEMENT: N PPLICTION OF THE ENHNCED CUSTOMER EXPERIENCE FRMEWORK (ECEF) G.J. Both 1, P.S. Kruger 2 & M. de Vries 3 Deprtment of Industril nd Systems
More informationVoIP for the Small Business
VoIP for the Smll Business Reducing your telecommunictions costs Reserch firm IDC 1 hs estimted tht VoIP system cn reduce telephonyrelted expenses by 30%. Voice over Internet Protocol (VoIP) hs become
More information