Endogenous timing in a mixed oligopoly consisting of a single public firm and foreign competitors. Abstract
|
|
- Linette Andrews
- 5 years ago
- Views:
Transcription
1 Endogenous tmng n a mxed olgopoly consstng o a sngle publc rm and oregn compettors Yuanzhu Lu Chna Economcs and Management Academy, Central Unversty o Fnance and Economcs Abstract We nvestgate endogenous tmng n a mxed olgopoly consstng o a sngle publc rm and oregn compettors and compare the results wth those n Pal (998) to see the eect o the natonalty o prvate rms on the endogenous role o the publc rm. We nd that the results are the same n two cases: () there are only two tme perods or quantty choce, and () there are more than two tme perods or quantty choce and there are more than two prvate rms; but qute derent when there are more than two tme perods or quantty choce and there are only one or two prvate rms. Ctaton: Lu, Yuanzhu, (7) "Endogenous tmng n a mxed olgopoly consstng o a sngle publc rm and oregn compettors." Economcs Bulletn, Vol., o. pp. -7 Submtted: December 8, 6. Accepted: January 8, 7. URL:
2 . Introducton Endogenous order o moves s an mportant ssue n a pure prvate olgopoly and n a mxed olgopoly as well. In the lterature on mxed olgopoly, Pal (998) analyzed endogenous order o moves n quantty choce n a mxed olgopoly consstng o a sngle publc rm and domestc prvate rms. Matsumura (3) consdered endogenous roles o rms n a mxed duopoly consstng o a state-owned publc rm and a oregn prvate rm. Lu (6) dscussed endogenous tmng n a mxed olgopoly wth both domestc and oregn prvate rms n the lnear demand case. Gven the results n Pal (998), Jacques (4) and Lu (7), the last two o whch slghtly correct Proposton 4. n the rst paper, t s nterestng to nvestgate endogenous tmng n a mxed olgopoly consstng o a sngle publc rm and oregn compettors. What s the eect o the natonalty o prvate rms on the endogenous role o the sngle publc rm? Ths s exactly what we do n ths paper by adoptng the observable delay game o Hamlton and Slutsky (99) n the context o a quantty settng mxed olgopoly where the rms rst choose the tmng o choosng ther quanttes. Usng a general demand uncton, Matsumura (3) dscussed a mxed duopoly case n whch there are only two possble tme perods or quantty choce. The derences between ths paper and Matsumura (3) are: () the number o oregn prvate rms can be more than one; () the number o possble tme perods can be more than two; (3) we use a lnear demand uncton n order to compare the results wth those n Pal (998), Jacques (4) and Lu (7). We nd that the results are the same n two cases: () there are only two tme perods or quantty choce, and () there are more than two tme perods or quantty choce and there are more than two prvate rms; but qute derent when there are more than two tme perods or quantty choce and there are only one or two prvate rms. The organzaton o the paper s as ollows. In Secton, we descrbe the model. Secton 3 presents the results when there are only two possble tme perods or quantty choce. The SPEs are presented n Secton 4 when there are more than two possble tme perods to be chosen. Secton 5 closes the paper.. The model Consder a mxed olgopoly model consstng o one sngle publc rm and ( ) oregn prvate rms, all producng a sngle homogenous product. Let q and q (,,, ) be the quanttes o the publc rm and the oregn prvate rms, respectvely. Let Q= q+ q denote the aggregate quantty. The market prce s determned by the nverse demand uncton p= a Q. To make the results n ths paper drectly comparable to those o Pal (998), Jacques (4) and Lu (7), we make the same assumptons except that the natonalty o the prvate rms s derent. Speccally, the ollowng assumptons are made: () a s sucently large; () All oregn prvate rms have constant and dentcal margnal costs o producton, whch are normalzed to ; (3) The publc rm has a postve, constant margnal cost o producton, c > ; (4) Fxed costs are zero or all rms; (5) The publc rm s objectve s to maxmze domestc socal surplus dened as the sum o consumer
3 surplus and ts prot, whereas each oregn prvate rm s objectve s to maxmze ts own prot. We consder the observable delay game o Hamlton and Slutsky (99) n the context o a quantty settng mxed olgopoly where rms rst announce at whch tme they wll choose ther quanttes and are commtted to ths choce beore they actually choose ther quanttes. There are M possble tme perods or quantty choce and each rm may choose ts quantty n only one o those M perods. The objectve unctons o the publc rm and oregn prvate rm are respectvely gven by SS= a( q+ q ) ( q+ q ) ( a q q ) q cq and π = pq = ( a q q ) q. Our objectve s to solve the SPEs o ths extended quantty settng mxed olgopoly game. We restrct our attenton to symmetrc equlbra n whch all rms o the same type choose to produce n the same perod. Frst, we derve the results or two tme perods (M=). ext, we present the results or more than two tme perods. 3. Results or two tme perods ( M = ) Frst, we prove that the publc rm wll not produce smultaneously wth all oregn prvate rms. Ths s stated n the ollowng proposton. Proposton 3.: All rms producng smultaneously n the same tme perod cannot be sustaned as a SPE outcome. Ths proposton s the same as Proposton 3. n Pal (998) except that the prvate rms n Pal s model are domestc and also the same as Lemma 3. n Lu (6) except that there s no domestc prvate rm n our work. It mples that ths result s robust regardless o the type o prvate rms n the market. Gven Proposton 3. and that we restrct our attenton to symmetrc equlbra, there are two possble equlbra when M=: one nvolves all prvate rms producng smultaneously n perod and the publc rm producng n perod, whle n the other possble equlbrum, the publc rm produces n perod and all prvate rms produce smultaneously n perod. We show that the ormer possble equlbrum s really a SPE or any whle the latter one s a SPE only when. Proposton 3.: I 3, there s a unque SPE, at whch the prvate rms produce n perod and the publc rm produces n perod. I, then there s a second SPE n whch the publc rm produces n perod and all prvate rms produce n perod. One mght wonder why Proposton 3 n Matsumura (3) states there exsts a unque SPE n whch the publc rm produces n perod and all prvate rms produce n perod whle we denty two SPEs or the same mxed duopoly. The reason s that Matsumura restrcts hs attenton to the equlbra whch are not supported by weakly All proos are n the appendx.
4 domnated strateges. We can check that or a mxed duopoly case (=), the addtonal SPE dented n Proposton 3. s ndeed supported by a weakly domnated strategy. Comparng the results o ths secton wth those n Pal (998), we nd that the endogenous order o moves s actually the same. It seems that the natonalty o prvate rms does not aect the endogenous tmng. However, ths s not completely true when there are more than two tme perods or quantty choce. 4. Man Results or more than two perods ( M > ) Proposton 4.: I M >, then () when 3, there s a unque SPE, at whch all prvate rms produce smultaneously n perod and the publc rm produces n a subsequent perod. () when =, there s a second SPE, at whch the publc rm produces n any perod except the last one and the two prvate rms produce n the subsequent perod. (3) when =, there are two SPEs. In one SPE, the prvate rm produces n perod and the publc rm produces n the last perod; n the other SPE, the publc rm produces n any perod except the last one and the prvate rm produces n a subsequent perod. Comparng the results o ths secton wth those n Pal (998), Jacques (4) and Lu (7), we nd that the endogenous order o moves s actually the same when 3 but qute derent when. When =, we stll have the same SPE as n Pal (998), but we also have a second SPE at whch the publc rm produces n any perod except the last one and the two prvate rms produce n the subsequent perod. When =, we stll have two SPEs but they are totally derent rom Jacques (4) and Lu (7). The reason s smple. That s because the publc rm preers to be a leader when prvate rms are oregn whle t preers to be a ollower when competng wth domestc prvate rms. 5. Concludng Remarks In ths paper, we nvestgate endogenous tmng n a mxed olgopoly consstng o one sngle publc rm and ( ) oregn prvate rms by consderng the observable delay game o Hamlton and Slutsky (99) n the context o a quantty settng mxed olgopoly. We nd that the results are the same when there are only two tme perods or quantty choce and when there are more than two tme perods or quantty choce and there are more than two prvate rms but qute derent when there are more than two tme perods or quantty choce and there are one or two prvate rms. Ths derence s the result o the publc rm s derent desred role when competng wth prvate rms o derent natonalty. Reerences Hamlton, J. and S. Slutsky (99) Endogenous Tmng n Duopoly Games: Stackelberg or Cournot Equlbra Games and Economc Behavor, Jacques, A. (4) Endogenous Tmng n a Mxed Olgopoly: a Forgotten Equlbrum Economcs Letters 83,
5 Lu, Y. (6) Endogenous Tmng n a Mxed Olgopoly wth Foregn Prvate Compettors: the Lnear Demand Case Journal o Economcs 88, Lu, Y. (7) Endogenous Tmng n a Mxed Olgopoly: another Forgotten Equlbrum Economcs Letters, orthcomng. Matsumura, T. (3) Stackelberg Mxed Duopoly wth a Foregn Compettor Bulletn o Economc Research 55, Pal, D. (998) Endogenous Tmng n a Mxed Olgopoly Economcs Letters 6, Appendx In the ollowng proos, we let q, Q and p respectvely denote the publc rm s quantty, the total quantty and the prce n equlbrum or any gven tmng, and q denote a oregn prvate rm s quantty or any gven tmng n whch all oregn prvate rms produce n the same perod. When we consder whether a oregn prvate rm has the ncentve to devate rom any gven tmng, we always choose oregn prvate rm to be the deector. I oregn prvate rm devates, we let q denote the deector s quantty, and q (, 3,, ) denote the quantty o those oregn prvate rms who do not deect. I all rms produce smultaneously n perod t (=, ), then every rm s payo maxmzaton problem gves us the ollowng rst-order condtons: SS = a ( q + q ) + q c= a q c= π q, (A) = a q qk q =, or,,..., q k=, k =. (A) Solvng these equatons gves us q = a c and q = c /( + ). It ollows that Q = a c /( + ), p = c /( + ), SS = a / ac+ ( + + ) c / ( + ), and π = c /( + ). Proo o Proposton 3. We can show that ether the publc rm or a oregn prvate rm has the ncentve to devate all rms produce smultaneously n the same perod, that s, devate rom the ollowng two cases. Case.: All rms produce smultaneously n perod. Consder oregn prvate rm devatng to be a ollower. Then n perod, t wll choose q to maxmze π= a q q q q and the rst order condton (A.) ( ) mples q = a q q. It ollows that p= a q q and thus n perod, oregn prvate rm s (,..., ) prot uncton s π = q a q q 4
6 and the publc rm s objectve uncton s SS= a a+ q+ q a q q a q q a q q cq The rst order condtons mply q = a 4c ( + ) and q = 4 c /( + ) (,..., ). It ollows that q = c /(+ ) Q = a c /(+ ), p = c /( + ), and π = 4 c /( + ) > c /( + ). Thereore, oregn prvate rm has the ncentve to devate. Case.: All rms produce smultaneously n perod. Consder the publc rm devatng to be a leader. Then n perod, (A.) mples q = a q +. It ollows that n perod, the publc rms objectve uncton s ( ) ( ) SS= a( a+ q) ( + ) ( a+ q) ( + ) ( a q) ( + ) cq. The rst order condton mples q a ( ) c ( ) = ( + ) /( + ), ( ) q c π = + /( + ), c ( ) [ ] ( ) = + +. It ollows that SS = a / ac+ + c / (+ ) > a / ac+ + + c / ( + ). Thereore, the publc rm has the ncentve to devate. Proo o Proposton 3. () We prove that the possble equlbrum n whch all prvate rms produce smultaneously n perod and the publc rm produces n perod s really a SPE or any by showng that no rm has the ncentve to devate. Frst we obtan the equlbrum quanttes, prce and each rm s payo n ths possble equlbrum. In perod, (A.) mples q = a c. It ollows that p= c q and n perod, oregn prvate rm s prot uncton s π c q q. The rst order condtons mply q = c /( + ). It ollows that ( ) SS = a / ac+ + + c / ( + ), and π = c /( + ). Clearly the publc rm has no ncentve to devate snce the socal surplus would be the same t devated to produce smultaneously wth all the oregn prvate rms n perod. ow consder oregn prvate rm devatng to produce n perod. (A.) and (A.) ( ) mply q = a c and q = c q. In perod, oregn prvate rm s (,..., ) prot uncton s π = q c q and the rst order condtons mply q = c /. It ollows that q = c /( ), p = c /( ), and π = c c + (equal and only / 4 /( ) to devate. = ). So no oregn prvate rm wants 5
7 () We prove that the possble equlbrum n whch the publc rm produces n perod and all prvate rms produce smultaneously n perod s a SPE only when. The equlbrum quanttes, prce and each rm s payo n ths possble equlbrum have been obtaned n the proo o proposton 3. (case.), q ( ) a c ( ) q = ( + ) c/(+ ), ( ) π = + /( + ), SS a / ac ( ) c /[ ( ) ] = + +, c = Clearly, the publc rm has no ncentve to devate. ow consder oregn prvate rm devates to produce n perod. (A.) (,..., ) mply ( ) q ( a q q ) q = a q q. In perod, oregn prvate rm s prot uncton s / / π = and the publc rm s objectve uncton s ( ) ( ) SS a q a q q cq a+ q + q a+ q + q a q q = + ( ). q = a c 3 and q = c ( 3 ). It The rst order condtons mply ( ) ollows that q = c ( 3 ) (,..., ), p c ( 3 ) 3 π = c ( ) whch s lower than ( ) c /( ) / 3 hgher when 3. =, and + + when = or but Proo o Proposton 4.: Frstly, clearly, smultaneous play cannot be sustaned as a SPE outcome. Secondly, prvate rms producng n perod t(>) whle the publc rm producng as a ollower cannot be sustaned as a SPE outcome. To prove ths, we lst domestc socal surplus n three derent cases: () when the publc rm produces smultaneously wth all prvate rms, SS = a / ac+ ( + + ) c / ( + ) ; () when the publc rm produces as a leader o all prvate rms, SS = a / ac+ ( + ) c / ( + ) ; (3) when the publc rm produces as a ollower o all prvate rms, SS = a / ac+ ( + + ) c / ( + ). So the publc rm preers to be a leader. I prvate rms produce n perod t(>), the publc rm wll choose to produce n perod. Thrdly, prvate rms produce n perod and the publc rm produces n perod t ( t< T ), then we can show a oregn prvate rm has the ncentve to devate to be a ollower o the publc rm when = but no ncentve to do so when. We can also show a oregn prvate rm has no ncentve to devate to produce n perod s ( s< t ) when t 3. 3 I prvate rms produce n perod and the publc rm produces Straghtorward calculaton yelds the deector s prot s π ( = 4 c / 9 ) π = /( + ) when 3 3 c, equal when =, but hgher when =. Straghtorward calculaton yelds the deector s prot s π ( = c / 4 ) π = /( + ) when c, equal when =., whch s lower than, whch s lower than 6
8 n perod T, then clearly no rm has the ncentve to devate. So ar we have proved that prvate rms want to be leaders o the publc rm, they have to produce n perod. When they do so, the publc rm producng n any subsequent perod when can be sustaned as SPE, whle the publc rm has to choose to produce n the last perod when =. Fourthly, by Proposton 3., the publc rm producng as a leader o all prvate rms cannot be sustaned as SPE when 3. Fthly, the publc rm produces n perod t(<t) and prvate rms produce n a subsequent perod, then clearly the publc rm has no ncentve to devate, and we can show that a prvate rm has no ncentve to devate to be a leader o the publc rm when t>, that a prvate rm has the ncentve to devate to be a leader o the other prvate rm when = except that prvate rms produce n the subsequent perod, and that a prvate rm has no ncentve to devate =. 7
Online Appendix. t=1 (p t w)q t. Then the first order condition shows that
Artcle forthcomng to ; manuscrpt no (Please, provde the manuscrpt number!) 1 Onlne Appendx Appendx E: Proofs Proof of Proposton 1 Frst we derve the equlbrum when the manufacturer does not vertcally ntegrate
More informationConstant Best-Response Functions: Interpreting Cournot
Internatonal Journal of Busness and Economcs, 009, Vol. 8, No., -6 Constant Best-Response Functons: Interpretng Cournot Zvan Forshner Department of Economcs, Unversty of Hafa, Israel Oz Shy * Research
More information3.2. Cournot Model Cournot Model
Matlde Machado Assumptons: All frms produce an homogenous product The market prce s therefore the result of the total supply (same prce for all frms) Frms decde smultaneously how much to produce Quantty
More informationEnvironmental taxation: Privatization with Different Public Firm s Objective Functions
Appl. Math. Inf. Sc. 0 No. 5 657-66 (06) 657 Appled Mathematcs & Informaton Scences An Internatonal Journal http://dx.do.org/0.8576/ams/00503 Envronmental taxaton: Prvatzaton wth Dfferent Publc Frm s Objectve
More informationHila Etzion. Min-Seok Pang
RESERCH RTICLE COPLEENTRY ONLINE SERVICES IN COPETITIVE RKETS: INTINING PROFITILITY IN THE PRESENCE OF NETWORK EFFECTS Hla Etzon Department of Technology and Operatons, Stephen. Ross School of usness,
More informationWelfare Analysis of Cournot and Bertrand Competition With(out) Investment in R & D
MPRA Munch Personal RePEc Archve Welfare Analyss of Cournot and Bertrand Competton Wth(out) Investment n R & D Jean-Baptste Tondj Unversty of Ottawa 25 March 2016 Onlne at https://mpra.ub.un-muenchen.de/75806/
More informationA Simple Research of Divisor Graphs
The 29th Workshop on Combnatoral Mathematcs and Computaton Theory A Smple Research o Dvsor Graphs Yu-png Tsao General Educaton Center Chna Unversty o Technology Tape Tawan yp-tsao@cuteedutw Tape Tawan
More informationCS286r Assign One. Answer Key
CS286r Assgn One Answer Key 1 Game theory 1.1 1.1.1 Let off-equlbrum strateges also be that people contnue to play n Nash equlbrum. Devatng from any Nash equlbrum s a weakly domnated strategy. That s,
More informationThe oligopolistic markets
ernando Branco 006-007 all Quarter Sesson 5 Part II The olgopolstc markets There are a few supplers. Outputs are homogenous or dfferentated. Strategc nteractons are very mportant: Supplers react to each
More informationPrice competition with capacity constraints. Consumers are rationed at the low-price firm. But who are the rationed ones?
Prce competton wth capacty constrants Consumers are ratoned at the low-prce frm. But who are the ratoned ones? As before: two frms; homogeneous goods. Effcent ratonng If p < p and q < D(p ), then the resdual
More informationOn endogenous Stackelberg leadership: The case of horizontally differentiated duopoly and asymmetric net work compatibility effects
On endogenous Stackelberg leadershp: The case of horzontally dfferentated duopoly and asymmetrc net work compatblty effects Tsuyosh TOSHIMITSU School of Economcs,Kwanse Gakun Unversty Abstract Introducng
More informationOPTIMISATION. Introduction Single Variable Unconstrained Optimisation Multivariable Unconstrained Optimisation Linear Programming
OPTIMIATION Introducton ngle Varable Unconstraned Optmsaton Multvarable Unconstraned Optmsaton Lnear Programmng Chapter Optmsaton /. Introducton In an engneerng analss, sometmes etremtes, ether mnmum or
More informationMergers among leaders and mergers among followers. Abstract
Mergers among leaders and mergers among followers John S. Heywood Unversty of Wsconsn - Mlwaukee Matthew McGnty Unversty of Wsconsn-Mlwaukee Abstract We are the frst to confrm that suffcent cost convexty
More informationA Cournot-Stackelberg Advertising Duopoly Derived From A Cobb-Douglas Utility Function
MDEF Workshop 01, Urbno, 0- September A Cournot-Stackelberg Advertsng Duopoly Derved From A Cobb-Douglas Utlty Functon Alna Ghrvu * and Tönu Puu** *Faculty of Economc Studes and Busness Admnstraton, Babeş-
More informationVolume 31, Issue 1. The Stackelberg equilibrium as a consistent conjectural equilibrium
Volume 3, Issue The Stackelberg equlbrum as a consstent conjectural equlbrum Ludovc A. Julen LEG, Unversté de Bourgogne Olver Musy EconomX, Unversté Pars Ouest-Nanterre La Défense Aurélen W. Sad Informaton
More informationLecture Notes, January 11, 2010
Economcs 200B UCSD Wnter 2010 Lecture otes, January 11, 2010 Partal equlbrum comparatve statcs Partal equlbrum: Market for one good only wth supply and demand as a functon of prce. Prce s defned as the
More informationConjectures in Cournot Duopoly under Cost Uncertainty
Conjectures n Cournot Duopoly under Cost Uncertanty Suyeol Ryu and Iltae Km * Ths paper presents a Cournot duopoly model based on a condton when frms are facng cost uncertanty under rsk neutralty and rsk
More informationChapter 3 Differentiation and Integration
MEE07 Computer Modelng Technques n Engneerng Chapter Derentaton and Integraton Reerence: An Introducton to Numercal Computatons, nd edton, S. yakowtz and F. zdarovsky, Mawell/Macmllan, 990. Derentaton
More informationTit-For-Tat Equilibria in Discounted Repeated Games with. Private Monitoring
1 Tt-For-Tat Equlbra n Dscounted Repeated Games wth Prvate Montorng Htosh Matsushma 1 Department of Economcs, Unversty of Tokyo 2 Aprl 24, 2007 Abstract We nvestgate nfntely repeated games wth mperfect
More informationCournot Equilibrium with N firms
Recap Last class (September 8, Thursday) Examples of games wth contnuous acton sets Tragedy of the commons Duopoly models: ournot o class on Sept. 13 due to areer Far Today (September 15, Thursday) Duopoly
More informationPerfect Competition and the Nash Bargaining Solution
Perfect Competton and the Nash Barganng Soluton Renhard John Department of Economcs Unversty of Bonn Adenauerallee 24-42 53113 Bonn, Germany emal: rohn@un-bonn.de May 2005 Abstract For a lnear exchange
More information3.1 Expectation of Functions of Several Random Variables. )' be a k-dimensional discrete or continuous random vector, with joint PMF p (, E X E X1 E X
Statstcs 1: Probablty Theory II 37 3 EPECTATION OF SEVERAL RANDOM VARIABLES As n Probablty Theory I, the nterest n most stuatons les not on the actual dstrbuton of a random vector, but rather on a number
More informationThe Second Anti-Mathima on Game Theory
The Second Ant-Mathma on Game Theory Ath. Kehagas December 1 2006 1 Introducton In ths note we wll examne the noton of game equlbrum for three types of games 1. 2-player 2-acton zero-sum games 2. 2-player
More informationUniversity of California, Davis Date: June 22, 2009 Department of Agricultural and Resource Economics. PRELIMINARY EXAMINATION FOR THE Ph.D.
Unversty of Calforna, Davs Date: June 22, 29 Department of Agrcultural and Resource Economcs Department of Economcs Tme: 5 hours Mcroeconomcs Readng Tme: 2 mnutes PRELIMIARY EXAMIATIO FOR THE Ph.D. DEGREE
More informationEconomics 101. Lecture 4 - Equilibrium and Efficiency
Economcs 0 Lecture 4 - Equlbrum and Effcency Intro As dscussed n the prevous lecture, we wll now move from an envronment where we looed at consumers mang decsons n solaton to analyzng economes full of
More informationPRICING VS SLOT POLICIES WHEN AIRPORT PROFITS MATTER
Workng Paper 009- PRICING VS SLOT POLICIES WHEN AIRPORT PROFITS MATTER Leonardo J. Basso Department o Cvl Engneerng, Unversdad de Chle Caslla 8-3, Santago, Chle Ph. 56-978 4380, Fax 56-689 406 lbasso@ng.uchle.cl
More informationRyan (2009)- regulating a concentrated industry (cement) Firms play Cournot in the stage. Make lumpy investment decisions
1 Motvaton Next we consder dynamc games where the choce varables are contnuous and/or dscrete. Example 1: Ryan (2009)- regulatng a concentrated ndustry (cement) Frms play Cournot n the stage Make lumpy
More informationk t+1 + c t A t k t, t=0
Macro II (UC3M, MA/PhD Econ) Professor: Matthas Kredler Fnal Exam 6 May 208 You have 50 mnutes to complete the exam There are 80 ponts n total The exam has 4 pages If somethng n the queston s unclear,
More informationCOS 521: Advanced Algorithms Game Theory and Linear Programming
COS 521: Advanced Algorthms Game Theory and Lnear Programmng Moses Charkar February 27, 2013 In these notes, we ntroduce some basc concepts n game theory and lnear programmng (LP). We show a connecton
More informationInner Product. Euclidean Space. Orthonormal Basis. Orthogonal
Inner Product Defnton 1 () A Eucldean space s a fnte-dmensonal vector space over the reals R, wth an nner product,. Defnton 2 (Inner Product) An nner product, on a real vector space X s a symmetrc, blnear,
More informationWelfare Properties of General Equilibrium. What can be said about optimality properties of resource allocation implied by general equilibrium?
APPLIED WELFARE ECONOMICS AND POLICY ANALYSIS Welfare Propertes of General Equlbrum What can be sad about optmalty propertes of resource allocaton mpled by general equlbrum? Any crteron used to compare
More informationFirms Costs, Profits, Entries, and Innovation under Optimal Privatization Policy
MPRA Munch Personal RePEc Archve Frms Costs, Profts, Entres, and Innovaton under Optmal Prvatzaton Polcy Junch Haraguch and Toshhro Matsumura 22 August 2017 Onlne at https://mpra.ub.un-muenchen.de/80927/
More informationInvestment Secrecy and Competitive R&D
BE J. Econ. nal. Polcy 2016; aop Letter dt Sengupta* Investment Secrecy and Compettve R&D DOI 10.1515/beeap-2016-0047 bstract: Secrecy about nvestment n research and development (R&D) can promote greater
More informationUniversity of Washington Department of Chemistry Chemistry 452/456 Summer Quarter 2014
Lecture 16 8/4/14 Unversty o Washngton Department o Chemstry Chemstry 452/456 Summer Quarter 214. Real Vapors and Fugacty Henry s Law accounts or the propertes o extremely dlute soluton. s shown n Fgure
More informationIn the figure below, the point d indicates the location of the consumer that is under competition. Transportation costs are given by td.
UC Berkeley Economcs 11 Sprng 006 Prof. Joseph Farrell / GSI: Jenny Shanefelter Problem Set # - Suggested Solutons. 1.. In ths problem, we are extendng the usual Hotellng lne so that now t runs from [-a,
More informationPricing and Resource Allocation Game Theoretic Models
Prcng and Resource Allocaton Game Theoretc Models Zhy Huang Changbn Lu Q Zhang Computer and Informaton Scence December 8, 2009 Z. Huang, C. Lu, and Q. Zhang (CIS) Game Theoretc Models December 8, 2009
More information(1 ) (1 ) 0 (1 ) (1 ) 0
Appendx A Appendx A contans proofs for resubmsson "Contractng Informaton Securty n the Presence of Double oral Hazard" Proof of Lemma 1: Assume that, to the contrary, BS efforts are achevable under a blateral
More informationPROBLEM SET 7 GENERAL EQUILIBRIUM
PROBLEM SET 7 GENERAL EQUILIBRIUM Queston a Defnton: An Arrow-Debreu Compettve Equlbrum s a vector of prces {p t } and allocatons {c t, c 2 t } whch satsfes ( Gven {p t }, c t maxmzes βt ln c t subject
More informationQuantity Precommitment and Cournot and Bertrand Models with Complementary Goods
Quantty Precommtment and Cournot and Bertrand Models wth Complementary Goods Kazuhro Ohnsh 1 Insttute for Basc Economc Scence, Osaka, Japan Abstract Ths paper nestgates Cournot and Bertrand duopoly models
More informationMarket structure and Innovation
Market structure and Innovaton Ths presentaton s based on the paper Market structure and Innovaton authored by Glenn C. Loury, publshed n The Quarterly Journal of Economcs, Vol. 93, No.3 ( Aug 1979) I.
More information1 The Sidrauski model
The Sdrausk model There are many ways to brng money nto the macroeconomc debate. Among the fundamental ssues n economcs the treatment of money s probably the LESS satsfactory and there s very lttle agreement
More information= s j Ui U j. i, j, then s F(U) with s Ui F(U) G(U) F(V ) G(V )
1 Lecture 2 Recap Last tme we talked about presheaves and sheaves. Preshea: F on a topologcal space X, wth groups (resp. rngs, sets, etc.) F(U) or each open set U X, wth restrcton homs ρ UV : F(U) F(V
More informationNorm Bounds for a Transformed Activity Level. Vector in Sraffian Systems: A Dual Exercise
ppled Mathematcal Scences, Vol. 4, 200, no. 60, 2955-296 Norm Bounds for a ransformed ctvty Level Vector n Sraffan Systems: Dual Exercse Nkolaos Rodousaks Department of Publc dmnstraton, Panteon Unversty
More informationEcon107 Applied Econometrics Topic 3: Classical Model (Studenmund, Chapter 4)
I. Classcal Assumptons Econ7 Appled Econometrcs Topc 3: Classcal Model (Studenmund, Chapter 4) We have defned OLS and studed some algebrac propertes of OLS. In ths topc we wll study statstcal propertes
More informationComputing a Cournot Equilibrium in Integers
Computng a Cournot Equlbrum n Integers Mchael J. Todd December 6, 2013 Abstract We gve an effcent algorthm for computng a Cournot equlbrum when the producers are confned to ntegers, the nverse demand functon
More informationTHE CHINESE REMAINDER THEOREM. We should thank the Chinese for their wonderful remainder theorem. Glenn Stevens
THE CHINESE REMAINDER THEOREM KEITH CONRAD We should thank the Chnese for ther wonderful remander theorem. Glenn Stevens 1. Introducton The Chnese remander theorem says we can unquely solve any par of
More informationMixed Taxation and Production Efficiency
Floran Scheuer 2/23/2016 Mxed Taxaton and Producton Effcency 1 Overvew 1. Unform commodty taxaton under non-lnear ncome taxaton Atknson-Stgltz (JPubE 1976) Theorem Applcaton to captal taxaton 2. Unform
More informationGame Theory. Lecture Notes By Y. Narahari. Department of Computer Science and Automation Indian Institute of Science Bangalore, India February 2008
Game Theory Lecture Notes By Y. Narahar Department of Computer Scence and Automaton Indan Insttute of Scence Bangalore, Inda February 2008 Chapter 10: Two Person Zero Sum Games Note: Ths s a only a draft
More informationWelfare Comparisons with a Consumer-Friendly Upstream Firm: Centralized vs. Decentralized Bargaining
Open Journal of Socal Scences 07 5 8-97 http://www.scrp.org/ournal/ss ISSN Onlne: 37-5960 ISSN Prnt: 37-595 Welfare Comparsons wth a Consumer-Frendly Upstream Frm: Centralzed vs. Decentralzed Barganng
More informationGeneral Tips on How to Do Well in Physics Exams. 1. Establish a good habit in keeping track of your steps. For example, when you use the equation
General Tps on How to Do Well n Physcs Exams 1. Establsh a good habt n keepng track o your steps. For example when you use the equaton 1 1 1 + = d d to solve or d o you should rst rewrte t as 1 1 1 = d
More informationCS : Algorithms and Uncertainty Lecture 17 Date: October 26, 2016
CS 29-128: Algorthms and Uncertanty Lecture 17 Date: October 26, 2016 Instructor: Nkhl Bansal Scrbe: Mchael Denns 1 Introducton In ths lecture we wll be lookng nto the secretary problem, and an nterestng
More informationMeasuring the Impact of Increased Product Substitution on Pricing and Capacity Decisions under Linear Demand Models
Measurng the Impact o Increased Product Substtuton on Prcng and Capacty Decsons under Lnear Demand Models Betul Lus Unversty o Massachusetts 160 Governors Drve, Amherst, MA 01003 Tel.: (413) 545-150 Fax:
More informationPartial collusion with asymmetric cross-price effects Luca Savorelli Quaderni - Working Papers DSE N 715
Partal colluson wth asymmetrc cross-prce effects Luca Savorell Quadern - Workng Papers DSE N 715 Partal colluson wth asymmetrc cross-prce e ects Luca Savorell y October 8, 2010 Abstract Asymmetres n cross-prce
More informationAbsorbing Markov Chain Models to Determine Optimum Process Target Levels in Production Systems with Rework and Scrapping
Archve o SID Journal o Industral Engneerng 6(00) -6 Absorbng Markov Chan Models to Determne Optmum Process Target evels n Producton Systems wth Rework and Scrappng Mohammad Saber Fallah Nezhad a, Seyed
More informationHow Strong Are Weak Patents? Joseph Farrell and Carl Shapiro. Supplementary Material Licensing Probabilistic Patents to Cournot Oligopolists *
How Strong Are Weak Patents? Joseph Farrell and Carl Shapro Supplementary Materal Lcensng Probablstc Patents to Cournot Olgopolsts * September 007 We study here the specal case n whch downstream competton
More informationVickrey Auction VCG Combinatorial Auctions. Mechanism Design. Algorithms and Data Structures. Winter 2016
Mechansm Desgn Algorthms and Data Structures Wnter 2016 1 / 39 Vckrey Aucton Vckrey-Clarke-Groves Mechansms Sngle-Mnded Combnatoral Auctons 2 / 39 Mechansm Desgn (wth Money) Set A of outcomes to choose
More informationWork is the change in energy of a system (neglecting heat transfer). To examine what could
Work Work s the change n energy o a system (neglectng heat transer). To eamne what could cause work, let s look at the dmensons o energy: L ML E M L F L so T T dmensonally energy s equal to a orce tmes
More informationAndreas C. Drichoutis Agriculural University of Athens. Abstract
Heteroskedastcty, the sngle crossng property and ordered response models Andreas C. Drchouts Agrculural Unversty of Athens Panagots Lazards Agrculural Unversty of Athens Rodolfo M. Nayga, Jr. Texas AMUnversty
More information,, MRTS is the marginal rate of technical substitution
Mscellaneous Notes on roducton Economcs ompled by eter F Orazem September 9, 00 I Implcatons of conve soquants Two nput case, along an soquant 0 along an soquant Slope of the soquant,, MRTS s the margnal
More informationLet p z be the price of z and p 1 and p 2 be the prices of the goods making up y. In general there is no problem in grouping goods.
Economcs 90 Prce Theory ON THE QUESTION OF SEPARABILITY What we would lke to be able to do s estmate demand curves by segmentng consumers purchases nto groups. In one applcaton, we aggregate purchases
More informationIntroduction. 1. The Model
H23, Q5 Introducton In the feld of polluton regulaton the problems stemmng from the asymmetry of nformaton between the regulator and the pollutng frms have been thoroughly studed. The semnal works by Wetzman
More informationThe optimal delay of the second test is therefore approximately 210 hours earlier than =2.
THE IEC 61508 FORMULAS 223 The optmal delay of the second test s therefore approxmately 210 hours earler than =2. 8.4 The IEC 61508 Formulas IEC 61508-6 provdes approxmaton formulas for the PF for smple
More informationChapter 5. Solution of System of Linear Equations. Module No. 6. Solution of Inconsistent and Ill Conditioned Systems
Numercal Analyss by Dr. Anta Pal Assstant Professor Department of Mathematcs Natonal Insttute of Technology Durgapur Durgapur-713209 emal: anta.bue@gmal.com 1 . Chapter 5 Soluton of System of Lnear Equatons
More informationJoint Ventures and Technology Adoption
Jont Ventures and Technology Adopton Kazuhko Mkam School o Economcs, Unversty o Hyogo Kezo Mzuno School o Busness Admnstraton, Kwanse Gakun Unversty March 08 Abstract Ths paper examnes rms ncentves or
More informationMore metrics on cartesian products
More metrcs on cartesan products If (X, d ) are metrc spaces for 1 n, then n Secton II4 of the lecture notes we defned three metrcs on X whose underlyng topologes are the product topology The purpose of
More informationCollusion in Capacity Under Irreversible Investment
Colluson n Capacty Under Irreversble Investment Thomas Fagart November 2017 Stellenbosch Unversty Centre for Competton Law and Economcs Workng Paper Seres WPS01/2017 Workng Paper Seres Edtor: Roan Mnne
More informationEE 330 Lecture 24. Small Signal Analysis Small Signal Analysis of BJT Amplifier
EE 0 Lecture 4 Small Sgnal Analss Small Sgnal Analss o BJT Ampler Eam Frda March 9 Eam Frda Aprl Revew Sesson or Eam : 6:00 p.m. on Thursda March 8 n Room Sweene 6 Revew rom Last Lecture Comparson o Gans
More informationVolume 29, Issue 4. Incomplete third-degree price discrimination, and market partition problem. Yann Braouezec ESILV
Volume 29, Issue 4 Incomplete thrd-degree prce dscrmnaton, and market partton problem Yann Braouezec ESILV Abstract We ntroduce n ths paper the "ncomplete" thrd-degree prce dscrmnaton, whch s the stuaton
More informationBasically, if you have a dummy dependent variable you will be estimating a probability.
ECON 497: Lecture Notes 13 Page 1 of 1 Metropoltan State Unversty ECON 497: Research and Forecastng Lecture Notes 13 Dummy Dependent Varable Technques Studenmund Chapter 13 Bascally, f you have a dummy
More informationInformation Acquisition in Global Games of Regime Change
Informaton Acquston n Global Games of Regme Change Mchal Szkup and Isabel Trevno y Abstract We study costly nformaton acquston n global games of regme change (that s, coordnaton games where payo s are
More informationOnline Appendix: Reciprocity with Many Goods
T D T A : O A Kyle Bagwell Stanford Unversty and NBER Robert W. Stager Dartmouth College and NBER March 2016 Abstract Ths onlne Appendx extends to a many-good settng the man features of recprocty emphaszed
More informationGame Theory Approach to Competitive Economic Dynamics
Scuola d Dottorato n Economa Dottorato d Rcerca n Matematca per le Applcazon Economco-Fnanzare XXV cclo Game Theory Approach to Compettve Economc Dynamcs Thess submtted n partal fulfllment of the requrements
More informationDesigning of Combined Continuous Lot By Lot Acceptance Sampling Plan
Internatonal Journal o Scentc Research Engneerng & Technology (IJSRET), ISSN 78 02 709 Desgnng o Combned Contnuous Lot By Lot Acceptance Samplng Plan S. Subhalakshm 1 Dr. S. Muthulakshm 2 1 Research Scholar,
More informationThe lower and upper bounds on Perron root of nonnegative irreducible matrices
Journal of Computatonal Appled Mathematcs 217 (2008) 259 267 wwwelsevercom/locate/cam The lower upper bounds on Perron root of nonnegatve rreducble matrces Guang-Xn Huang a,, Feng Yn b,keguo a a College
More informationThe Mixed Strategy Nash Equilibrium of the Television News Scheduling Game
The Mxed Strategy Nash Equlbrum of the Televson News Schedulng Game Jean Gabszewcz Dder Laussel Mchel Le Breton July 007 Abstract We characterze the unque mxed-strategy equlbrum of an extenson of the "televson
More informationprinceton univ. F 17 cos 521: Advanced Algorithm Design Lecture 7: LP Duality Lecturer: Matt Weinberg
prnceton unv. F 17 cos 521: Advanced Algorthm Desgn Lecture 7: LP Dualty Lecturer: Matt Wenberg Scrbe: LP Dualty s an extremely useful tool for analyzng structural propertes of lnear programs. Whle there
More informationR&D investment, asymmetric costs, and research joint ventures
R&D nvestment, asymmetrc costs, and research jont ventures Alejandro Montecnos Thomas Gresk July 6, 207 Abstract Ths paper nvestgates how an ntal asymmetry n producton costs affects the welfare dfferences
More information(A1) and bˆ represents the expected price conditional on b. being one of the winning bids. Rewrite expression (A1) as follows:.
Aendx: Proo o Prooston : Bdder s (lnear) exected utlty rom dng s: S Q U (A) where Q reresents the roalty that she wns the aucton wth and reresents the exected rce condtonal on eng one o the wnnng ds Rewrte
More informationFolk Theorem in Stotchastic Games with Private State and Private Monitoring Preliminary: Please do not circulate without permission
Folk Theorem n Stotchastc Games wth Prvate State and Prvate Montorng Prelmnary: Please do not crculate wthout permsson Takuo Sugaya Stanford Graduate School of Busness December 9, 202 Abstract We show
More informationFE REVIEW OPERATIONAL AMPLIFIERS (OP-AMPS)
FE EIEW OPEATIONAL AMPLIFIES (OPAMPS) 1 The Opamp An opamp has two nputs and one output. Note the opamp below. The termnal labeled wth the () sgn s the nvertng nput and the nput labeled wth the () sgn
More informationMicroeconomics: Auctions
Mcroeconomcs: Auctons Frédérc Robert-coud ovember 8, Abstract We rst characterze the PBE n a smple rst prce and second prce sealed bd aucton wth prvate values. The key result s that the expected revenue
More informationa b a In case b 0, a being divisible by b is the same as to say that
Secton 6.2 Dvsblty among the ntegers An nteger a ε s dvsble by b ε f there s an nteger c ε such that a = bc. Note that s dvsble by any nteger b, snce = b. On the other hand, a s dvsble by only f a = :
More informationCHAPTER 5 NUMERICAL EVALUATION OF DYNAMIC RESPONSE
CHAPTER 5 NUMERICAL EVALUATION OF DYNAMIC RESPONSE Analytcal soluton s usually not possble when exctaton vares arbtrarly wth tme or f the system s nonlnear. Such problems can be solved by numercal tmesteppng
More informationLecture 3. Ax x i a i. i i
18.409 The Behavor of Algorthms n Practce 2/14/2 Lecturer: Dan Spelman Lecture 3 Scrbe: Arvnd Sankar 1 Largest sngular value In order to bound the condton number, we need an upper bound on the largest
More information2.3 Nilpotent endomorphisms
s a block dagonal matrx, wth A Mat dm U (C) In fact, we can assume that B = B 1 B k, wth B an ordered bass of U, and that A = [f U ] B, where f U : U U s the restrcton of f to U 40 23 Nlpotent endomorphsms
More informationRobust Implementation: The Role of Large Type Spaces
Robust Implementaton: The Role of Large Type Spaces Drk Bergemann y Stephen Morrs z Frst Verson: March 2003 Ths Verson: Aprl 2004 Abstract We analyze the problem of fully mplementng a socal choce functon
More informationDiscontinuous Extraction of a Nonrenewable Resource
Dscontnuous Extracton of a Nonrenewable Resource Erc Iksoon Im 1 Professor of Economcs Department of Economcs, Unversty of Hawa at Hlo, Hlo, Hawa Uayant hakravorty Professor of Economcs Department of Economcs,
More informationUniqueness of Nash Equilibrium in Private Provision of Public Goods: Extension. Nobuo Akai *
Unqueness of Nash Equlbrum n Prvate Provson of Publc Goods: Extenson Nobuo Aka * nsttute of Economc Research Kobe Unversty of Commerce Abstract Ths note proves unqueness of Nash equlbrum n prvate provson
More informationBOUNDEDNESS OF THE RIESZ TRANSFORM WITH MATRIX A 2 WEIGHTS
BOUNDEDNESS OF THE IESZ TANSFOM WITH MATIX A WEIGHTS Introducton Let L = L ( n, be the functon space wth norm (ˆ f L = f(x C dx d < For a d d matrx valued functon W : wth W (x postve sem-defnte for all
More informationGames and Market Imperfections
Games and Market Imperfectons Q: The mxed complementarty (MCP) framework s effectve for modelng perfect markets, but can t handle mperfect markets? A: At least part of the tme A partcular type of game/market
More informationChapter 6. Operational Amplifier. inputs can be defined as the average of the sum of the two signals.
6 Operatonal mpler Chapter 6 Operatonal mpler CC Symbol: nput nput Output EE () Non-nvertng termnal, () nvertng termnal nput mpedance : Few mega (ery hgh), Output mpedance : Less than (ery low) Derental
More informationCopyright (C) 2008 David K. Levine This document is an open textbook; you can redistribute it and/or modify it under the terms of the Creative
Copyrght (C) 008 Davd K. Levne Ths document s an open textbook; you can redstrbute t and/or modfy t under the terms of the Creatve Commons Attrbuton Lcense. Compettve Equlbrum wth Pure Exchange n traders
More informationEuropean Regional Science Association 36th European Congress ETH Zurich, Switzerland August 1996
European Regonal Scence Assocaton 36th European Congress ETH Zurch, Swtzerland 6-3 August 996 Se-l Mun and Mn-xue Wang raduate School of nformaton Scences Tohoku Unversty Katahra Cho-me, Aoba-ku, Senda
More informationPoisson brackets and canonical transformations
rof O B Wrght Mechancs Notes osson brackets and canoncal transformatons osson Brackets Consder an arbtrary functon f f ( qp t) df f f f q p q p t But q p p where ( qp ) pq q df f f f p q q p t In order
More informationThe Value of Demand Postponement under Demand Uncertainty
Recent Researches n Appled Mathematcs, Smulaton and Modellng The Value of emand Postponement under emand Uncertanty Rawee Suwandechocha Abstract Resource or capacty nvestment has a hgh mpact on the frm
More informationf(x,y) = (4(x 2 4)x,2y) = 0 H(x,y) =
Problem Set 3: Unconstraned mzaton n R N. () Fnd all crtcal ponts of f(x,y) (x 4) +y and show whch are ma and whch are mnma. () Fnd all crtcal ponts of f(x,y) (y x ) x and show whch are ma and whch are
More informatione - c o m p a n i o n
OPERATIONS RESEARCH http://dxdoorg/0287/opre007ec e - c o m p a n o n ONLY AVAILABLE IN ELECTRONIC FORM 202 INFORMS Electronc Companon Generalzed Quantty Competton for Multple Products and Loss of Effcency
More informationGlobal Sensitivity. Tuesday 20 th February, 2018
Global Senstvty Tuesday 2 th February, 28 ) Local Senstvty Most senstvty analyses [] are based on local estmates of senstvty, typcally by expandng the response n a Taylor seres about some specfc values
More informationExample: (13320, 22140) =? Solution #1: The divisors of are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 41,
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 confuson
More informationYong Joon Ryang. 1. Introduction Consider the multicommodity transportation problem with convex quadratic cost function. 1 2 (x x0 ) T Q(x x 0 )
Kangweon-Kyungk Math. Jour. 4 1996), No. 1, pp. 7 16 AN ITERATIVE ROW-ACTION METHOD FOR MULTICOMMODITY TRANSPORTATION PROBLEMS Yong Joon Ryang Abstract. The optmzaton problems wth quadratc constrants often
More information