PROFIT RATIO AND MARKET STRUCTURE

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "PROFIT RATIO AND MARKET STRUCTURE"

Transcription

1 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 of performance. The most popular one, however, has been the usng of proft rates to measure the concentraton and barrers to entry. In general, ths type of studes tend to confrm the expectaton that, other thngs beng equal, profts wll tend to be hgher n ndustres n whch structural condtons depart substantally from those of the compettve model. But these studes has not always been clearly based on a well-defned theoretcal model. So when a theoretcal model s spelled out t becomes obvous that some nterndustry relatonshps of ths sort are meanngless because of the certan omtted varables. A prme example s the omsson of the ndustry prce elastcty of demand. Ths means that the former studes have all assumed that the prce elastcty of demand across ndustres wthn the cross-secton are the same. Ths s defntely wrong because n fact these s few chances for the prce elastcty of even two ndustres to be the same. In ths paper, a explct theoretcal model wth varable η whch represents the prce elastcty of demand s gven out. Ths supposed to be able to examne the relatonshp between two dfferent ndustres wth dfferent prce elastcty of demand. However, t s too complcated. Here my suggest s: Snce the prce elastcty wthn one ndustry s always more steady than that of dfferent ndustres, why can't we use tme-

2 seres data to analyss a sngle ndustry? Maybe the results that ths ntra-ndustry study wll yeld s more meanngful. The Basc Model: Consder an ndustry wth n frms producng a homogenous product. We can wrte down the proft equaton for the th frm as: = pq c( q ) F (1) Where Π s proft, p s prce, q s output, c s varable cost and F s fxed cost, assumng that for the moment the same cost condtons for each frm. The nverse market demand functon s: p = f ( q) = f ( q1 + q q n ) () Now assumng proft-maxmzng behavor and neglectng the problem of potental entry at present, we get: Where d p q f q = + ( ) c '( q ) = 0 (3) d j q = 1+ = 1+ β j Multplyng (3) by q and summng over the n frms, we have: pq q q f q q + c q q '( )( 1+ β ) ' ( ) = 0 (4) Or we can rewrte t as :

3 pq pq c ' ( q ) q t q f '( q) q = ( ) ( 1 + µ ) (5) q pq Where n n / = 1 = 1 µ = β q q (see ader, 197, pp.71~7). If we assume the frms have constant margnal cost equal to average varable cost, then the left sde of the equaton s the rato of proft plus fxed cost (Π+F) to revenue( ). On the rght sde the frst term s the Hrschmann-Herfndahl ndex of concentraton ( H ),so the equaton can be rewrte as: + F H = ( 1 + µ ) (6) η Where η s the prce elastcty of demand. We therefore have the predcton that the proft-revenue rato s related postvely to the Hrschmann-herfndahl ndex of concentraton and nversely to the prce elastcty of demand. The problem wth testng ths predcton s the that t s always hard to measure the prce elastcty of a ndustry. So here a good approach s to change the focus of analyss away from explanng nter-ndustry dfferences to explanng ntra-ndustry changes over tme. Thus, assumng that all prce elastcty wthn a sngle ndustry durng a certan perod s constant. It s also reasonable to assume that µ s constant. Now for perod t we have:

4 t + Ft t Ht = ( 1 + µ ) (7) η For perod t' we have: t' + Ft t ' ' Ht ' = ( 1 + µ ) (8) η Take the rato of equaton (7) and (8), we get: + F ( ) t + F ( ) t' = Ht Ht' (9) We assume that the fxed cost s constant durng the perod of tme, so though the magantude of F wll nfluence the absolute rato of HHI, t won't change the relatve rato. So here fxed cost s possbly to be omtted. Thus we get the new equaton: ( ) t Ht = ( ) Ht' t ' (10) Appled to a sngle ndustry: Industry Select and Data arrangement From the above mentoned analyss we know that the most reasonable ndustry for ths model s an ndustry wth a sgnfcant change n the concentraton rato durng a perod of years. Thanks for professor Looms, he gave me some advce on the selectng of the telecommuncaton ndustry as the objectve and also help me by gvng me the quarterly revenue and concentraton rato data of the ndustry through year 1984 to year However, the proft data have really taken me some tme.

5 (1) Concentraton rato Our model defnes the Hrschmann-Herfndahl measure as the relevant one, but unfortunately, the HHI of the telecommuncaton ndustry s not publshed. I am grateful to professor Looms for gvng me the revenue of the major companes also the whole ndustry durng these years so I can roughly calculate out the market share of each company then the HHI of the whole ndustry. However, because I ddn t take some trval companes nto account, we should note that ths method of estmaton wll a lttle understate the true level of HHI. But, anyway, ths won t do much matter. () evenue Fortunately, as mentoned above, I got both the revenue of each company and the total revenue of the whole ndustry drectly from the quarterly toll revenue reported to shareholders. (3) Proft Wthn the three varables n the equaton, defntely proft s the one that I have done much more effort. At frst I want to use equaton (9) to do the analyss because by usng ths method the results should be more precse. In order to do ths, the sum of proft and fxed cost must be fnd out. The frst way I have thought about s to fnd drectly the proft and the fxed cost of the ndustry then sum them up. But I can t fnd anythng about the fxed cost. Even the proft I can only fnd a sngle company s wthn a sngle year. It s mpossbly complcated for me to sum them all out. Then I want to try another way, to measure the sum of proft and fxed cost as gross output mnus raw materals purchases and wages and salares. However,ths s also tested to be too complex. At last,i have to change equaton (9) to equaton (10). Ths only need us to fnd the proft, revenue and the

6 HHI, I have menton above how to fnd revenue and the HHI, so the only varable left s proft. As aforesad, t s also too complex to fnd all years total proft, so I wll just use three years proft data, that s year 1984,1990 and Data Partcpaton and the esult (1) evenue Data: for year 1984: (dollar amounts show n mllons) Frst quarter: AT&T 8,684 MCI 475 SPINT 30 WOLDCOM 0 OTHE 405 TOTAL 9,866 Second quarter: AT&T 9,169 MCI 485 SPINT 317 WOPLDCOM 0 OTHE 43 TOTAL 10,394 Thrd quarter: AT&T 9,097 MCI 478 SPINT 307 WOLDCOM 0 OTHE 44 TOTAL 10,34 Forth quarter: AT&T 9,7 MCI 51 SPINT 30 WOLDCOM 0 OTHE 46 TOTAL 10,574 So AT&T yearly total: 36, MCI yearly total: 1,959 SPINT yearly total: 1,46 Industry yearly total: 41,158 for year 1990: Industry yearly total: 56,98

7 for year 1996: Industry yearly total: 94,331 () Concentraton Data: Usng the revenue data, we can calculate out the concentraton rato: for year 1984: HHI=7, for year 1990: HHI=4, for year 1996: HHI=3,34.5 (3) Proft Data: I get the proft data from the annual report: for year 1984: ndustry total proft: 10,80.5 for year 1990: ndustry total proft: 1,487.7 for year 1996: ndustry total proft: 14,51.5 Substtute these data nto equaton (10), we can test the theory that as the rato of proft to revenue declnes, so wll the concentraton rato. Concluson: Untl recently, the analyss of frms performance wth respect to the market structure has generally been based on an ndustry-by-ndustry descrptve approach. A recent study by Mller analyzed the mpact of the dstrbuton of ndustry shares among successve groups of frms top four, next four, and so forth whch he descrbed as the margnal concentraton, ntroducng an ntra-ndustry study.

8 However, n ths paper, the spelled out model s able to both support the analyss of an nter-ndustry study and also the analyss of an ntra-ndustry study. Especally, we should say, t s more effcent for us to do an ntra-ndustry study. ths s because: (1) The prce elastcty s more steady wthn the same ndustry than n dfferent ndustres. () The product wthn the same ndustry s lkely to be homogenous. So we don t have to consder the product dfferentaton. In general, n the analyzng of the performance and market structure, our statstcal results speak rather drectly themselves. HHI appears to be sgnfcantly assocated wth ntra-ndustry proft rato to the total revenue. Data won t be attached. eferences: (1) prce-cost margns and ndustry structure Norman. Collns and Lee E. Preston the revew of economcs and statstcs 71~86. () Ban s concentraton and rates of return revsed Brozen Y. journal of law and economcs 14,351~369. (3) profts, varablty of profts and frm sze Samuels J.M. and Smyth D.J. economca 35,17~139. (4) concentraton and prce-cost margns n food manufacturng ndustres Collns N.. and L. E. Preston journal of ndustral economcs (July 1996),6~4.

9 (5) concentraton ratos n manufacturng ndustry U.S. Congress Washngton: U.S. government Prntng offce,196. (6) prce-cost structure and behavor of proft margns Sato K. Yale economc essays, fall 1961,361~418.

Chapter 7: Answers to Questions and Problems

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

More information

Can Auto Liability Insurance Purchases Signal Risk Attitude?

Can Auto Liability Insurance Purchases Signal Risk Attitude? Internatonal Journal of Busness and Economcs, 2011, Vol. 10, No. 2, 159-164 Can Auto Lablty Insurance Purchases Sgnal Rsk Atttude? Chu-Shu L Department of Internatonal Busness, Asa Unversty, Tawan Sheng-Chang

More information

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

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

More information

The Analysis of Outliers in Statistical Data

The Analysis of Outliers in Statistical Data THALES Project No. xxxx The Analyss of Outlers n Statstcal Data Research Team Chrysses Caron, Assocate Professor (P.I.) Vaslk Karot, Doctoral canddate Polychrons Economou, Chrstna Perrakou, Postgraduate

More information

Inequality and The Accounting Period. Quentin Wodon and Shlomo Yitzhaki. World Bank and Hebrew University. September 2001.

Inequality and The Accounting Period. Quentin Wodon and Shlomo Yitzhaki. World Bank and Hebrew University. September 2001. Inequalty and The Accountng Perod Quentn Wodon and Shlomo Ytzha World Ban and Hebrew Unversty September Abstract Income nequalty typcally declnes wth the length of tme taen nto account for measurement.

More information

PSYCHOLOGICAL RESEARCH (PYC 304-C) Lecture 12

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

More information

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

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

More information

An Alternative Way to Measure Private Equity Performance

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

More information

Study on CET4 Marks in China s Graded English Teaching

Study on CET4 Marks in China s Graded English Teaching Study on CET4 Marks n Chna s Graded Englsh Teachng CHE We College of Foregn Studes, Shandong Insttute of Busness and Technology, P.R.Chna, 264005 Abstract: Ths paper deploys Logt model, and decomposes

More information

Calculation of Sampling Weights

Calculation of Sampling Weights Perre Foy Statstcs Canada 4 Calculaton of Samplng Weghts 4.1 OVERVIEW The basc sample desgn used n TIMSS Populatons 1 and 2 was a two-stage stratfed cluster desgn. 1 The frst stage conssted of a sample

More information

Recurrence. 1 Definitions and main statements

Recurrence. 1 Definitions and main statements Recurrence 1 Defntons and man statements Let X n, n = 0, 1, 2,... be a MC wth the state space S = (1, 2,...), transton probabltes p j = P {X n+1 = j X n = }, and the transton matrx P = (p j ),j S def.

More information

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

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

More information

Analysis of Premium Liabilities for Australian Lines of Business

Analysis of Premium Liabilities for Australian Lines of Business Summary of Analyss of Premum Labltes for Australan Lnes of Busness Emly Tao Honours Research Paper, The Unversty of Melbourne Emly Tao Acknowledgements I am grateful to the Australan Prudental Regulaton

More information

DEFINING %COMPLETE IN MICROSOFT PROJECT

DEFINING %COMPLETE IN MICROSOFT PROJECT CelersSystems DEFINING %COMPLETE IN MICROSOFT PROJECT PREPARED BY James E Aksel, PMP, PMI-SP, MVP For Addtonal Informaton about Earned Value Management Systems and reportng, please contact: CelersSystems,

More information

1 Example 1: Axis-aligned rectangles

1 Example 1: Axis-aligned rectangles COS 511: Theoretcal Machne Learnng Lecturer: Rob Schapre Lecture # 6 Scrbe: Aaron Schld February 21, 2013 Last class, we dscussed an analogue for Occam s Razor for nfnte hypothess spaces that, n conjuncton

More information

Module 2 LOSSLESS IMAGE COMPRESSION SYSTEMS. Version 2 ECE IIT, Kharagpur

Module 2 LOSSLESS IMAGE COMPRESSION SYSTEMS. Version 2 ECE IIT, Kharagpur Module LOSSLESS IMAGE COMPRESSION SYSTEMS Lesson 3 Lossless Compresson: Huffman Codng Instructonal Objectves At the end of ths lesson, the students should be able to:. Defne and measure source entropy..

More information

benefit is 2, paid if the policyholder dies within the year, and probability of death within the year is ).

benefit is 2, paid if the policyholder dies within the year, and probability of death within the year is ). REVIEW OF RISK MANAGEMENT CONCEPTS LOSS DISTRIBUTIONS AND INSURANCE Loss and nsurance: When someone s subject to the rsk of ncurrng a fnancal loss, the loss s generally modeled usng a random varable or

More information

The Journal of Applied Business Research January/February 2010 Volume 26, Number 1

The Journal of Applied Business Research January/February 2010 Volume 26, Number 1 Product Dversfcaton In Compettve R&D-Intensve Frms: An Emprcal Study Of The Computer Software Industry C. Catherne Chang, Elon Unversty, USA ABSTRACT Ths paper studes the effect of dversfcaton nto dfferent

More information

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

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

More information

HOUSEHOLDS DEBT BURDEN: AN ANALYSIS BASED ON MICROECONOMIC DATA*

HOUSEHOLDS DEBT BURDEN: AN ANALYSIS BASED ON MICROECONOMIC DATA* HOUSEHOLDS DEBT BURDEN: AN ANALYSIS BASED ON MICROECONOMIC DATA* Luísa Farnha** 1. INTRODUCTION The rapd growth n Portuguese households ndebtedness n the past few years ncreased the concerns that debt

More information

STAMP DUTY ON SHARES AND ITS EFFECT ON SHARE PRICES

STAMP DUTY ON SHARES AND ITS EFFECT ON SHARE PRICES STAMP UTY ON SHARES AN ITS EFFECT ON SHARE PRICES Steve Bond Mke Hawkns Alexander Klemm THE INSTITUTE FOR FISCAL STUIES WP04/11 STAMP UTY ON SHARES AN ITS EFFECT ON SHARE PRICES Steve Bond (IFS and Unversty

More information

IS-LM Model 1 C' dy = di

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

More information

Experiment 8 Two Types of Pendulum

Experiment 8 Two Types of Pendulum Experment 8 Two Types of Pendulum Preparaton For ths week's quz revew past experments and read about pendulums and harmonc moton Prncples Any object that swngs back and forth can be consdered a pendulum

More information

1. Measuring association using correlation and regression

1. Measuring association using correlation and regression How to measure assocaton I: Correlaton. 1. Measurng assocaton usng correlaton and regresson We often would lke to know how one varable, such as a mother's weght, s related to another varable, such as a

More information

SIMPLE LINEAR CORRELATION

SIMPLE LINEAR CORRELATION SIMPLE LINEAR CORRELATION Smple lnear correlaton s a measure of the degree to whch two varables vary together, or a measure of the ntensty of the assocaton between two varables. Correlaton often s abused.

More information

2.4 Bivariate distributions

2.4 Bivariate distributions page 28 2.4 Bvarate dstrbutons 2.4.1 Defntons Let X and Y be dscrete r.v.s defned on the same probablty space (S, F, P). Instead of treatng them separately, t s often necessary to thnk of them actng together

More information

Exhaustive Regression. An Exploration of Regression-Based Data Mining Techniques Using Super Computation

Exhaustive Regression. An Exploration of Regression-Based Data Mining Techniques Using Super Computation Exhaustve Regresson An Exploraton of Regresson-Based Data Mnng Technques Usng Super Computaton Antony Daves, Ph.D. Assocate Professor of Economcs Duquesne Unversty Pttsburgh, PA 58 Research Fellow The

More information

The OC Curve of Attribute Acceptance Plans

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

More information

CS 2750 Machine Learning. Lecture 3. Density estimation. CS 2750 Machine Learning. Announcements

CS 2750 Machine Learning. Lecture 3. Density estimation. CS 2750 Machine Learning. Announcements Lecture 3 Densty estmaton Mlos Hauskrecht mlos@cs.ptt.edu 5329 Sennott Square Next lecture: Matlab tutoral Announcements Rules for attendng the class: Regstered for credt Regstered for audt (only f there

More information

Addendum to: Importing Skill-Biased Technology

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

More information

The impact of hard discount control mechanism on the discount volatility of UK closed-end funds

The impact of hard discount control mechanism on the discount volatility of UK closed-end funds Investment Management and Fnancal Innovatons, Volume 10, Issue 3, 2013 Ahmed F. Salhn (Egypt) The mpact of hard dscount control mechansm on the dscount volatlty of UK closed-end funds Abstract The mpact

More information

Production. 2. Y is closed A set is closed if it contains its boundary. We need this for the solution existence in the profit maximization problem.

Production. 2. Y is closed A set is closed if it contains its boundary. We need this for the solution existence in the profit maximization problem. Producer Theory Producton ASSUMPTION 2.1 Propertes of the Producton Set The producton set Y satsfes the followng propertes 1. Y s non-empty If Y s empty, we have nothng to talk about 2. Y s closed A set

More information

The covariance is the two variable analog to the variance. The formula for the covariance between two variables is

The covariance is the two variable analog to the variance. The formula for the covariance between two variables is Regresson Lectures So far we have talked only about statstcs that descrbe one varable. What we are gong to be dscussng for much of the remander of the course s relatonshps between two or more varables.

More information

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

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

More information

Structural Estimation of Variety Gains from Trade Integration in a Heterogeneous Firms Framework

Structural Estimation of Variety Gains from Trade Integration in a Heterogeneous Firms Framework Journal of Economcs and Econometrcs Vol. 55, No.2, 202 pp. 78-93 SSN 2032-9652 E-SSN 2032-9660 Structural Estmaton of Varety Gans from Trade ntegraton n a Heterogeneous Frms Framework VCTOR RVAS ABSTRACT

More information

Forecasting the Direction and Strength of Stock Market Movement

Forecasting the Direction and Strength of Stock Market Movement Forecastng the Drecton and Strength of Stock Market Movement Jngwe Chen Mng Chen Nan Ye cjngwe@stanford.edu mchen5@stanford.edu nanye@stanford.edu Abstract - Stock market s one of the most complcated systems

More information

The Probability of Informed Trading and the Performance of Stock in an Order-Driven Market

The Probability of Informed Trading and the Performance of Stock in an Order-Driven Market Asa-Pacfc Journal of Fnancal Studes (2007) v36 n6 pp871-896 The Probablty of Informed Tradng and the Performance of Stock n an Order-Drven Market Ta Ma * Natonal Sun Yat-Sen Unversty, Tawan Mng-hua Hseh

More information

Depreciation of Business R&D Capital

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

More information

Communication Networks II Contents

Communication Networks II Contents 8 / 1 -- Communcaton Networs II (Görg) -- www.comnets.un-bremen.de Communcaton Networs II Contents 1 Fundamentals of probablty theory 2 Traffc n communcaton networs 3 Stochastc & Marovan Processes (SP

More information

WORKING PAPERS. The Impact of Technological Change and Lifestyles on the Energy Demand of Households

WORKING PAPERS. The Impact of Technological Change and Lifestyles on the Energy Demand of Households ÖSTERREICHISCHES INSTITUT FÜR WIRTSCHAFTSFORSCHUNG WORKING PAPERS The Impact of Technologcal Change and Lfestyles on the Energy Demand of Households A Combnaton of Aggregate and Indvdual Household Analyss

More information

ADVERSE SELECTION IN INSURANCE MARKETS: POLICYHOLDER EVIDENCE FROM THE U.K. ANNUITY MARKET

ADVERSE SELECTION IN INSURANCE MARKETS: POLICYHOLDER EVIDENCE FROM THE U.K. ANNUITY MARKET ADVERSE SELECTION IN INSURANCE MARKETS: POLICYHOLDER EVIDENCE FROM THE U.K. ANNUITY MARKET Amy Fnkelsten Harvard Unversty and NBER James Poterba MIT and NBER Revsed May 2003 ABSTRACT In ths paper, we nvestgate

More information

FORCED CONVECTION HEAT TRANSFER IN A DOUBLE PIPE HEAT EXCHANGER

FORCED CONVECTION HEAT TRANSFER IN A DOUBLE PIPE HEAT EXCHANGER FORCED CONVECION HEA RANSFER IN A DOUBLE PIPE HEA EXCHANGER Dr. J. Mchael Doster Department of Nuclear Engneerng Box 7909 North Carolna State Unversty Ralegh, NC 27695-7909 Introducton he convectve heat

More information

The Current Employment Statistics (CES) survey,

The Current Employment Statistics (CES) survey, Busness Brths and Deaths Impact of busness brths and deaths n the payroll survey The CES probablty-based sample redesgn accounts for most busness brth employment through the mputaton of busness deaths,

More information

Week 6 Market Failure due to Externalities

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

More information

Risk-based Fatigue Estimate of Deep Water Risers -- Course Project for EM388F: Fracture Mechanics, Spring 2008

Risk-based Fatigue Estimate of Deep Water Risers -- Course Project for EM388F: Fracture Mechanics, Spring 2008 Rsk-based Fatgue Estmate of Deep Water Rsers -- Course Project for EM388F: Fracture Mechancs, Sprng 2008 Chen Sh Department of Cvl, Archtectural, and Envronmental Engneerng The Unversty of Texas at Austn

More information

Power-of-Two Policies for Single- Warehouse Multi-Retailer Inventory Systems with Order Frequency Discounts

Power-of-Two Policies for Single- Warehouse Multi-Retailer Inventory Systems with Order Frequency Discounts Power-of-wo Polces for Sngle- Warehouse Mult-Retaler Inventory Systems wth Order Frequency Dscounts José A. Ventura Pennsylvana State Unversty (USA) Yale. Herer echnon Israel Insttute of echnology (Israel)

More information

8.5 UNITARY AND HERMITIAN MATRICES. The conjugate transpose of a complex matrix A, denoted by A*, is given by

8.5 UNITARY AND HERMITIAN MATRICES. The conjugate transpose of a complex matrix A, denoted by A*, is given by 6 CHAPTER 8 COMPLEX VECTOR SPACES 5. Fnd the kernel of the lnear transformaton gven n Exercse 5. In Exercses 55 and 56, fnd the mage of v, for the ndcated composton, where and are gven by the followng

More information

Corporate Giving, Competition and the Economic Cycle

Corporate Giving, Competition and the Economic Cycle School of Economcs and Management TECHNICAL UNIVERSITY OF LISBON Department of Economcs Carlos Pestana Barros & Ncolas Peypoch Ana S. Branca, Joaqum Pna, Margarda Catalão-Lopes Corporate Gvng, Competton

More information

Marginal Benefit Incidence Analysis Using a Single Cross-section of Data. Mohamed Ihsan Ajwad and Quentin Wodon 1. World Bank.

Marginal Benefit Incidence Analysis Using a Single Cross-section of Data. Mohamed Ihsan Ajwad and Quentin Wodon 1. World Bank. Margnal Beneft Incdence Analyss Usng a Sngle Cross-secton of Data Mohamed Ihsan Ajwad and uentn Wodon World Bank August 200 Abstract In a recent paper, Lanjouw and Ravallon proposed an attractve and smple

More information

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

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.

More information

On the Optimal Control of a Cascade of Hydro-Electric Power Stations

On the Optimal Control of a Cascade of Hydro-Electric Power Stations On the Optmal Control of a Cascade of Hydro-Electrc Power Statons M.C.M. Guedes a, A.F. Rbero a, G.V. Smrnov b and S. Vlela c a Department of Mathematcs, School of Scences, Unversty of Porto, Portugal;

More information

Understanding the Impact of Marketing Actions in Traditional Channels on the Internet: Evidence from a Large Scale Field Experiment

Understanding the Impact of Marketing Actions in Traditional Channels on the Internet: Evidence from a Large Scale Field Experiment A research and educaton ntatve at the MT Sloan School of Management Understandng the mpact of Marketng Actons n Tradtonal Channels on the nternet: Evdence from a Large Scale Feld Experment Paper 216 Erc

More information

The Analysis of Covariance. ERSH 8310 Keppel and Wickens Chapter 15

The Analysis of Covariance. ERSH 8310 Keppel and Wickens Chapter 15 The Analyss of Covarance ERSH 830 Keppel and Wckens Chapter 5 Today s Class Intal Consderatons Covarance and Lnear Regresson The Lnear Regresson Equaton TheAnalyss of Covarance Assumptons Underlyng the

More information

High Correlation between Net Promoter Score and the Development of Consumers' Willingness to Pay (Empirical Evidence from European Mobile Markets)

High Correlation between Net Promoter Score and the Development of Consumers' Willingness to Pay (Empirical Evidence from European Mobile Markets) Hgh Correlaton between et Promoter Score and the Development of Consumers' Wllngness to Pay (Emprcal Evdence from European Moble Marets Ths paper shows that the correlaton between the et Promoter Score

More information

IMPACT ANALYSIS OF A CELLULAR PHONE

IMPACT ANALYSIS OF A CELLULAR PHONE 4 th ASA & μeta Internatonal Conference IMPACT AALYSIS OF A CELLULAR PHOE We Lu, 2 Hongy L Bejng FEAonlne Engneerng Co.,Ltd. Bejng, Chna ABSTRACT Drop test smulaton plays an mportant role n nvestgatng

More information

greatest common divisor

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

More information

Oligopoly Theory Made Simple

Oligopoly Theory Made Simple Olgopoly Theory Made Smple Huw Dxon Chapter 6, Surfng Economcs, pp 5-60. Olgopoly made smple Chapter 6. Olgopoly Theory Made Smple 6. Introducton. Olgopoly theory les at the heart of ndustral organsaton

More information

Macro Factors and Volatility of Treasury Bond Returns

Macro Factors and Volatility of Treasury Bond Returns Macro Factors and Volatlty of Treasury Bond Returns Jngzh Huang Department of Fnance Smeal Colleage of Busness Pennsylvana State Unversty Unversty Park, PA 16802, U.S.A. Le Lu School of Fnance Shangha

More information

Offshoring and Immigrant Employment: Firm-level theory and evidence

Offshoring and Immigrant Employment: Firm-level theory and evidence Offshorng and Immgrant Employment: Frm-level theory and evdence Gorgo Barba Navarett () Guseppe Bertola () Alessandro Sembenell () December 2008 Abstract: In an Italan dataset wth frm-level nformaton on

More information

The Application of Fractional Brownian Motion in Option Pricing

The Application of Fractional Brownian Motion in Option Pricing Vol. 0, No. (05), pp. 73-8 http://dx.do.org/0.457/jmue.05.0..6 The Applcaton of Fractonal Brownan Moton n Opton Prcng Qng-xn Zhou School of Basc Scence,arbn Unversty of Commerce,arbn zhouqngxn98@6.com

More information

PRIVATE SCHOOL CHOICE: THE EFFECTS OF RELIGIOUS AFFILIATION AND PARTICIPATION

PRIVATE SCHOOL CHOICE: THE EFFECTS OF RELIGIOUS AFFILIATION AND PARTICIPATION PRIVATE SCHOOL CHOICE: THE EFFECTS OF RELIIOUS AFFILIATION AND PARTICIPATION Danny Cohen-Zada Department of Economcs, Ben-uron Unversty, Beer-Sheva 84105, Israel Wllam Sander Department of Economcs, DePaul

More information

On some special nonlevel annuities and yield rates for annuities

On some special nonlevel annuities and yield rates for annuities On some specal nonlevel annutes and yeld rates for annutes 1 Annutes wth payments n geometrc progresson 2 Annutes wth payments n Arthmetc Progresson 1 Annutes wth payments n geometrc progresson 2 Annutes

More information

x f(x) 1 0.25 1 0.75 x 1 0 1 1 0.04 0.01 0.20 1 0.12 0.03 0.60

x f(x) 1 0.25 1 0.75 x 1 0 1 1 0.04 0.01 0.20 1 0.12 0.03 0.60 BIVARIATE DISTRIBUTIONS Let be a varable that assumes the values { 1,,..., n }. Then, a functon that epresses the relatve frequenc of these values s called a unvarate frequenc functon. It must be true

More information

DO LOSS FIRMS MANAGE EARNINGS AROUND SEASONED EQUITY OFFERINGS?

DO LOSS FIRMS MANAGE EARNINGS AROUND SEASONED EQUITY OFFERINGS? DO LOSS FIRMS MANAGE EARNINGS AROUND SEASONED EQUITY OFFERINGS? Fernando Comran, Unversty of San Francsco, School of Management, 2130 Fulton Street, CA 94117, Unted States, fcomran@usfca.edu Tatana Fedyk,

More information

ADVERSE SELECTION IN INSURANCE MARKETS: POLICYHOLDER EVIDENCE FROM THE U.K. ANNUITY MARKET *

ADVERSE SELECTION IN INSURANCE MARKETS: POLICYHOLDER EVIDENCE FROM THE U.K. ANNUITY MARKET * ADVERSE SELECTION IN INSURANCE MARKETS: POLICYHOLDER EVIDENCE FROM THE U.K. ANNUITY MARKET * Amy Fnkelsten Harvard Unversty and NBER James Poterba MIT and NBER * We are grateful to Jeffrey Brown, Perre-Andre

More information

A Model of Private Equity Fund Compensation

A Model of Private Equity Fund Compensation A Model of Prvate Equty Fund Compensaton Wonho Wlson Cho Andrew Metrck Ayako Yasuda KAIST Yale School of Management Unversty of Calforna at Davs June 26, 2011 Abstract: Ths paper analyzes the economcs

More information

Short-run and Long-run structural international tourism demand modeling based on Dynamic AIDS model -An empirical research in Japan-

Short-run and Long-run structural international tourism demand modeling based on Dynamic AIDS model -An empirical research in Japan- hort-run and ong-run structural nternatonal toursm demand modelng based on Dynamc AID model -An emprcal research n Japan- Atsush KOIKE a, Dasuke YOHINO b a Graduate chool of Engneerng, Kobe Unversty, Kobe,

More information

MERGERS AND ACQUISITIONS IN THE SPANISH BANKING INDUSTRY: SOME EMPIRICAL EVIDENCE

MERGERS AND ACQUISITIONS IN THE SPANISH BANKING INDUSTRY: SOME EMPIRICAL EVIDENCE MERGERS AN ACQUISITIONS IN THE SPANISH BANKING INUSTRY: SOME EMPIRICA EVIENCE Ignaco Fuentes and Teresa Sastre Banco de España Banco de España Servco de Estudos ocumento de Trabajo n.º 9924 MERGERS AN

More information

An Evaluation of the Extended Logistic, Simple Logistic, and Gompertz Models for Forecasting Short Lifecycle Products and Services

An Evaluation of the Extended Logistic, Simple Logistic, and Gompertz Models for Forecasting Short Lifecycle Products and Services An Evaluaton of the Extended Logstc, Smple Logstc, and Gompertz Models for Forecastng Short Lfecycle Products and Servces Charles V. Trappey a,1, Hsn-yng Wu b a Professor (Management Scence), Natonal Chao

More information

The timing ability of hybrid funds of funds

The timing ability of hybrid funds of funds The tmng ablty of hybrd funds of funds Javer Rodríguez* Graduate School of Busness Admnstraton Unversty of Puerto Rco PO 23332 San Juan, PR 00931 Abstract Hybrd mutual funds are funds that nvest n a combnaton

More information

Estimating Total Claim Size in the Auto Insurance Industry: a Comparison between Tweedie and Zero-Adjusted Inverse Gaussian Distribution

Estimating Total Claim Size in the Auto Insurance Industry: a Comparison between Tweedie and Zero-Adjusted Inverse Gaussian Distribution Avalable onlne at http:// BAR, Curtba, v. 8, n. 1, art. 3, pp. 37-47, Jan./Mar. 2011 Estmatng Total Clam Sze n the Auto Insurance Industry: a Comparson between Tweede and Zero-Adjusted Inverse Gaussan

More information

Whose Private Benefits of Control. Owners or Managers?

Whose Private Benefits of Control. Owners or Managers? Whose Prvate Benefts of Control Owners or Managers? Joon Ho Hwang Fnance Department Kelley School of Busness Indana Unversty 1309 East Tenth Street Bloomngton, IN 47405 johwang@ndana.edu August, 2004 ABSTRACT

More information

Two Faces of Intra-Industry Information Transfers: Evidence from Management Earnings and Revenue Forecasts

Two Faces of Intra-Industry Information Transfers: Evidence from Management Earnings and Revenue Forecasts Two Faces of Intra-Industry Informaton Transfers: Evdence from Management Earnngs and Revenue Forecasts Yongtae Km Leavey School of Busness Santa Clara Unversty Santa Clara, CA 95053-0380 TEL: (408) 554-4667,

More information

INDONESIA S MANUFACTURED EXPORTS: A CONSTANT MARKET SHARES ANALYSIS

INDONESIA S MANUFACTURED EXPORTS: A CONSTANT MARKET SHARES ANALYSIS Wawan Juswanto dan Pu Mulyant INDONESIA S MANUFACTURED EXPORTS: A CONSTANT MARKET SHARES ANALYSIS By: Wawan Juswanto 1 and Pu Mulyant 2 Abstract Manufactured exports are beleved to be one of the engnes

More information

Efficiency Test on Taiwan s Life Insurance Industry- Using X-Efficiency Approach

Efficiency Test on Taiwan s Life Insurance Industry- Using X-Efficiency Approach Informaton and Management Scences Volume 18, Number 1, pp. 37-48, 2007 Effcency Test on Tawan s Lfe Insurance Industry- Usng X-Effcency Approach James C. Hao Tamkang Unversty R.O.C. Abstract Usng twenty-three

More information

Human Capital and Regional Economic Growth in Slovenia

Human Capital and Regional Economic Growth in Slovenia Human Captal and Regonal Economc Growth n Slovena Matjaž Novak and Štefan Bojnec Unversty of Prmorska Slovena Ths artcle presents the emprcal results concernng the economc growth n Slovena at the aggregate

More information

CIRCUIT ELEMENTS AND CIRCUIT ANALYSIS

CIRCUIT ELEMENTS AND CIRCUIT ANALYSIS EECS 4 SPING 00 Lecture 9 Copyrght egents of Unversty of Calforna CICUIT ELEMENTS AND CICUIT ANALYSIS Lecture 5 revew: Termnology: Nodes and branches Introduce the mplct reference (common) node defnes

More information

THE DISTRIBUTION OF LOAN PORTFOLIO VALUE * Oldrich Alfons Vasicek

THE DISTRIBUTION OF LOAN PORTFOLIO VALUE * Oldrich Alfons Vasicek HE DISRIBUION OF LOAN PORFOLIO VALUE * Oldrch Alfons Vascek he amount of captal necessary to support a portfolo of debt securtes depends on the probablty dstrbuton of the portfolo loss. Consder a portfolo

More information

IDENTIFICATION AND CORRECTION OF A COMMON ERROR IN GENERAL ANNUITY CALCULATIONS

IDENTIFICATION AND CORRECTION OF A COMMON ERROR IN GENERAL ANNUITY CALCULATIONS IDENTIFICATION AND CORRECTION OF A COMMON ERROR IN GENERAL ANNUITY CALCULATIONS Chrs Deeley* Last revsed: September 22, 200 * Chrs Deeley s a Senor Lecturer n the School of Accountng, Charles Sturt Unversty,

More information

Modelling the Cocaine and Heroin Markets in the Era of Globalization and Drug Reduction Policies Claudia Costa Storti and Paul De Grauwe

Modelling the Cocaine and Heroin Markets in the Era of Globalization and Drug Reduction Policies Claudia Costa Storti and Paul De Grauwe Modellng the Cocane and Heron Markets n the Era of Globalzaton and Drug Reducton Polces Clauda Costa Stort and Paul De Grauwe Modellng the Cocane and Heron Markets n the Era of Globalzaton and Drug Reducton

More information

MEASURING OPERATION EFFICIENCY OF THAI HOTELS INDUSTRY: EVIDENCE FROM META-FRONTIER ANALYSIS. Abstract

MEASURING OPERATION EFFICIENCY OF THAI HOTELS INDUSTRY: EVIDENCE FROM META-FRONTIER ANALYSIS. Abstract Internatonal Conference On Appled Economcs ICOAE 2011 315 MEASURING OPERATION EFFICIENCY OF THAI HOTELS INDUSTRY: EVIDENCE FROM METAFRONTIER ANALYSIS PHANIN KHRUEATHAI 1, AKARAPONG UNTONG 2, MINGSARN KAOSAARD

More information

LOOP ANALYSIS. The second systematic technique to determine all currents and voltages in a circuit

LOOP ANALYSIS. The second systematic technique to determine all currents and voltages in a circuit LOOP ANALYSS The second systematic technique to determine all currents and voltages in a circuit T S DUAL TO NODE ANALYSS - T FRST DETERMNES ALL CURRENTS N A CRCUT AND THEN T USES OHM S LAW TO COMPUTE

More information

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.

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

More information

Editing and Imputing Administrative Tax Return Data. Charlotte Gaughan Office for National Statistics UK

Editing and Imputing Administrative Tax Return Data. Charlotte Gaughan Office for National Statistics UK Edtng and Imputng Admnstratve Tax Return Data Charlotte Gaughan Offce for Natonal Statstcs UK Overvew Introducton Lmtatons Data Lnkng Data Cleanng Imputaton Methods Concluson and Future Work Introducton

More information

AN EMPIRICAL INVESTIGATION OF IPO UNDERPRICING IN CHINA

AN EMPIRICAL INVESTIGATION OF IPO UNDERPRICING IN CHINA AN EMPIRICAL INVESTIGATION OF IPO UNDERPRICING IN CHINA Lu T Senor Fellow/Executve Manager Research Center Shangha Stock Exchange Summary Chna enjoys the hghest level of ntal returns of ntal publc offerngs

More information

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

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

More information

Determining the Intensity of Buy and Sell Limit Order Submissions: A Look at the Market Preopening Period

Determining the Intensity of Buy and Sell Limit Order Submissions: A Look at the Market Preopening Period Determnng the Intensty of Buy and Sell Lmt Order Submssons: A Look at the Market Preopenng Perod Mke Bowe Stuart Hyde Ike Johnson Abstract Usng a unque dataset we examne the behavor of market partcpants

More information

Statistical Methods to Develop Rating Models

Statistical Methods to Develop Rating Models Statstcal Methods to Develop Ratng Models [Evelyn Hayden and Danel Porath, Österrechsche Natonalbank and Unversty of Appled Scences at Manz] Source: The Basel II Rsk Parameters Estmaton, Valdaton, and

More information

MEASURING ECONOMIC DIVERSIFICATION IN HAWAII

MEASURING ECONOMIC DIVERSIFICATION IN HAWAII MEASURING ECONOMIC DIVERSIFICATION IN HAWAII December 2011 It s wdely held that a dversfed economy s less senstve to the ups and downs assocated wth any partcular ndustry because rsk s spread more evenly

More information

THE RELATIONSHIP BETWEEN FINANCING POLICY AND FINANCIAL PERFORMANCE IN THE BRAZILIAN TEXTILE INDUSTRY

THE RELATIONSHIP BETWEEN FINANCING POLICY AND FINANCIAL PERFORMANCE IN THE BRAZILIAN TEXTILE INDUSTRY THE RELATIONSHIP BETWEEN FINANCING POLICY AND FINANCIAL PERFORMANCE IN THE BRAZILIAN TEXTILE INDUSTRY Davd Ferrera Lopes Santos UNESP Unv. Estadual Paulsta Rod. Paulo Donato Castellane, s/n Jabotcabal-SP

More information

The Choice of Direct Dealing or Electronic Brokerage in Foreign Exchange Trading

The Choice of Direct Dealing or Electronic Brokerage in Foreign Exchange Trading The Choce of Drect Dealng or Electronc Brokerage n Foregn Exchange Tradng Mchael Melvn & Ln Wen Arzona State Unversty Introducton Electronc Brokerage n Foregn Exchange Start from a base of zero n 1992

More information

Estimating Total Claim Size in the Auto Insurance Industry: a Comparison between Tweedie and Zero-Adjusted Inverse Gaussian Distribution

Estimating Total Claim Size in the Auto Insurance Industry: a Comparison between Tweedie and Zero-Adjusted Inverse Gaussian Distribution Estmatng otal Clam Sze n the Auto Insurance Industry: a Comparson between weede and Zero-Adjusted Inverse Gaussan Dstrbuton Autora: Adrana Bruscato Bortoluzzo, Italo De Paula Franca, Marco Antono Leonel

More information

1. Fundamentals of probability theory 2. Emergence of communication traffic 3. Stochastic & Markovian Processes (SP & MP)

1. Fundamentals of probability theory 2. Emergence of communication traffic 3. Stochastic & Markovian Processes (SP & MP) 6.3 / -- Communcaton Networks II (Görg) SS20 -- www.comnets.un-bremen.de Communcaton Networks II Contents. Fundamentals of probablty theory 2. Emergence of communcaton traffc 3. Stochastc & Markovan Processes

More information

Estimation of price elasticities of demand for alcohol in the United Kingdom

Estimation of price elasticities of demand for alcohol in the United Kingdom Knowledge, Analyss, and Intellgence (KAI) Estmaton of prce elastctes of demand for alcohol n the Unted Kngdom João Sousa December 2014 HMRC Workng Paper 16 Estmaton of prce elastctes of demand for alcohol

More information

Multiple discount and forward curves

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

More information

How Large are the Gains from Economic Integration? Theory and Evidence from U.S. Agriculture, 1880-2002

How Large are the Gains from Economic Integration? Theory and Evidence from U.S. Agriculture, 1880-2002 How Large are the Gans from Economc Integraton? Theory and Evdence from U.S. Agrculture, 1880-2002 Arnaud Costnot MIT and NBER Dave Donaldson MIT, NBER and CIFAR PRELIMINARY AND INCOMPLETE August 15, 2011

More information

The Willingness to Pay for Job Amenities: Evidence from Mothers' Return to Work

The Willingness to Pay for Job Amenities: Evidence from Mothers' Return to Work ILRRevew Volume 65 Number 2 Artcle 10 2012 The Wllngness to Pay for Job Amentes: Evdence from Mothers' Return to Chrstna Felfe Unversty of St. Gallen, chrstna.felfe@unsg.ch The Wllngness to Pay for Job

More information

THE DETERMINANTS OF THE TUNISIAN BANKING INDUSTRY PROFITABILITY: PANEL EVIDENCE

THE DETERMINANTS OF THE TUNISIAN BANKING INDUSTRY PROFITABILITY: PANEL EVIDENCE THE DETERMINANTS OF THE TUNISIAN BANKING INDUSTRY PROFITABILITY: PANEL EVIDENCE Samy Ben Naceur ERF Research Fellow Department of Fnance Unversté Lbre de Tuns Avenue Khéreddne Pacha, 002 Tuns Emal : sbennaceur@eudoramal.com

More information

The Mathematical Derivation of Least Squares

The Mathematical Derivation of Least Squares Pscholog 885 Prof. Federco The Mathematcal Dervaton of Least Squares Back when the powers that e forced ou to learn matr algera and calculus, I et ou all asked ourself the age-old queston: When the hell

More information

THE IMPLIED VOLATILITY OF ETF AND INDEX OPTIONS

THE IMPLIED VOLATILITY OF ETF AND INDEX OPTIONS The Internatonal Journal of Busness and Fnance Research Volume 5 Number 4 2011 THE IMPLIED VOLATILITY OF ETF AND INDEX OPTIONS Stoyu I. Ivanov, San Jose State Unversty Jeff Whtworth, Unversty of Houston-Clear

More information