Cost sharing: efficiency and implementation
|
|
- Isaac Holt
- 5 years ago
- Views:
Transcription
1 Journal of Mathematcal Economcs Cost sharng: effcency and mlementaton Todd R. Kalan, Davd Wettsten ) Deartment of Economcs, Ben-Guron UnÕersty of the egeõ, P.O.B. 653, Beer-SheÕa 84105, Israel Receved 7 July 1997; receved n revsed form 7 Setember 1998; acceted 15 December 1998 Abstract We study envronments where a roducton rocess s jontly shared by a fnte grou of agents. The socal decson nvolves the determnaton of nut contrbuton and outut dstrbuton. We defne a comettve soluton when there s decreasng-returns-to-scale whch leads to a Pareto otmal outcome. Snce there s a fnte number of agents, the comettve soluton s rone to manulaton. We construct a mechansm for whch the set of ash equlbra concdes wth the set of comettve soluton outcomes. We defne a margnal-cost-rcng equlbrum MCPE. soluton for envronments wth ncreasng returns to scale. These solutons are Pareto otmal under certan condtons. We construct another mechansm that realzes the MCPE. q 1999 Elsever Scence S.A. All rghts reserved. JEL classfcaton: D51; D61; D78 Keywords: Cost sharng; Margnal-cost-rcng equlbrum; Increasng returns to scale 1. Introducton The sharng of costs s revalent n many facets of economc actvty. Large enterrses allocate overhead costs among varous deartments. Members of a unversty share the cost of a software ste lcense. The artes watchng a ay-er-vew boxng match share the fee. ) Corresondng author. E-mal: wettstn@bgumal.bgu.ac.l r99r$ - see front matter q 1999 Elsever Scence S.A. All rghts reserved. PII: S
2 Issues of cost sharng surface exlctly as well as mlctly. The roblem arses exlctly whenever a grou of ndvduals jontly uses a common resource or undertakes a jont roject for an excellent survey, see Young, A cost-sharng method arses mlctly n any rvate-ownersh comettve economy. In such an economy, an ndvdual s share of the roducton costs of a frm s the amount he ays for goods urchased mnus the rofts he earns from shares owned n that frm. The roertes of the cost-sharng method are of major concern. Does t lead to effcent outcomes? Is the outcome unque? Can t be manulated by the ndvduals nvolved? Mouln and Shenker rovde the seral cost-sharng method and have demonstrated ts aeal as far as manulablty and unqueness are concerned. Mouln and Shenker and Mouln and Watts analyze more tradtonal methods such as average cost sharng. Both seral and average cost sharng do not guarantee Pareto otmalty. Our contrbuton s to resent two mechansms that wll generate Pareto otmal outcomes for several classes of envronments. We start by observng that n a neoclasscal economy, the mlct cost sharng mentoned above mles effcency. A cost-sharng method that attemts to relcate a neoclasscal economy by creatng a fcttous frm would have two shortcomngs: manulaton may exst wth a fnte number of ndvduals and convexty of the technology s requred. Both manulaton and non-convexty may lead to an undesrable outcome, whle non-convexty may also lead to nonexstence of equlbra. We suggest two cost-allocaton mechansms that obtan effcent outcomes by mtatng mlct cost sharng and addressng both roblems. The manulaton ssue s resolved n art by elmnatng the market ower ossessed by the ndvduals. To address the nonexstence ssue, we resort to margnal-cost-rcng equlbra that exst for a large class of non-convex envronments see Brown, The aer roceeds as follows. In Secton 2, we resent the comettve soluton. In Secton 3, the comettve soluton s mlemented and the resultng mechansm s comared to other cost-sharng methods. In Secton 4, we address the roblems created by ncreasng returns to scale. Fnally, n Secton 5, we conclude the aer and menton further drectons of research. 2. Allocaton of costs the comettve soluton The large varety of cost-allocaton roblems makes t ntractable to resent a general method to allocate costs effcently. In ths secton, we defne the class of envronments that we analyze n ths aer. Then, we ntroduce the comettve soluton concet for ths class. We show that for a subclass the comettve soluton yelds effcent allocatons only when gnorng ossble manulaton by ndvduals.
3 We consder a class of cost allocaton roblems 1 where there s a fnte number of ndvduals, greater than 2, that consume two goods, x and y, and X X have access to technology c: R R, where c y. q q s the cost of roducng y unts of good y. The references of each ndvdual can be reresented by a utlty functon u x, y. where utlty s strctly ncreasng, dfferentable,. concave and satsfes the Inada condtons lm u x, y s lm u x, y. x 0 1 y 0 2 s `, lm... u x, y s lm x ` 1 y `u2 x, y s 0. The ndvduals are endowed wth strctly ostve amounts w of good x and none of good y. An allocaton s gven by a 2 q 2-tule x, y., x, y. s1 where the frst comonents denote the ndvduals consumton levels and the last two comonents the roducton levels. The allocaton s feasble f: Ýx qx F Ý s1 s1 Ý y Fy s1 c y. Fx. w A feasble allocaton s Pareto otmal f there does not exst a feasble allocaton whch makes no ndvdual worse off and at least one ndvdual strctly better off. We wll say the cost-allocaton roblem belongs to class D I. f the cost functon s dfferentable and convex concave., wth c 0. s0. In the frst case, we are n the decreasng-returns-to-scale scenaro, whereas n the second case, roducton s characterzed by ncreasng returns to scale. In order to defne a comettve soluton, we need to create a frm that owns the technology and endow ndvduals wth strctly ostve ownersh shares a.a X X. X X X comettve soluton s a feasble allocaton x, y, x, y. s1 and a rce X for good y n terms of good x. such that gven the rce, the frm s maxmzng ts rofts and the ndvduals are maxmzng ther utlty subject to ther budget constrants: x X, y X. solves max X y yx x, y s.t. c y. Fx 1 These roblems encomass both tradtonal cost sharng when ndvduals demand oututs and the mechansm determnes nuts. and surlus sharng when ndvduals suly nuts and the mechansm determnes oututs.. Our mechansm can be nterreted as a hybrd constructon snce t determnes both nuts and oututs.
4 X x, y X. solves max u x, y x, y s.t. x q X y Fw qa where denotes the rofts of the frm. When the comettve soluton exsts ths s guaranteed only n class D., the standard arguments leadng to the Frst Welfare Theorem show that the comettve soluton yelds a Pareto otmal allocaton. Prooston 1. All comettõe solutons for a gõen cost allocaton roblem are Pareto otmal. Restrctng attenton to the class D of cost-allocaton roblems, the comettve soluton exsts and generates an allocaton wth an mlct sharng of costs. The cost of roducton mlctly mosed on ndvdual s the dfference between s exendtures on y and s share n the roft. The secfc allocaton realzed deends uon the ownersh structure and may not ossess an axomatc characterzaton lke several cost allocaton methods ut forward n the lterature. It s, however, Pareto otmal. Ths may seem to be a vable method to reach an effcent cost allocaton, but strategc behavor by the ndvduals may undermne the effcency. An ndvdual, by msreresentng hs references, may be able to secure an outcome referable to the comettve cost allocaton acheved wth hs true reference. Several aers have addressed the ncentves roblem nherent n the Walrasan aradgm for ure exchange economes Hurwcz, 1979; Schmedler, 1980; Postlewate and Wettsten, and for roducton economes Hong, In Secton 3, we offer a contnuous and feasble mechansm that would realze the comettve soluton to the cost allocaton roblem. All the ash equlbra of ths mechansm yeld Pareto otmal outcomes. ( ) 3. Realzaton of the comettve soluton mechansm A Mechansm A conssts of an n-tule of strategy sets and an outcome functon mang strateges nto allocatons. The strategy sace of ndvdual s S s 2 R =R =R=R wth a generc element denoted by, c, t, r. qq qq. The frst comonent s a rce for commodty y submtted by ndvdual, the second s a net consumton bundle, the thrd s an nut level nto the roducton rocess, and the fourth s a number used n averagng out the ossbly conflctng demands of all the ndvduals. We wll now outlne the way mechansm A oerates nformally, before we formally descrbe t. The mechansm constructs an average rce based on the announced rces and an average roducton lan based on the announced roducton lans. The requred amount of nut, secfed n the roducton lan, s collected from the ndvduals and used n roducton. Indvdual budget sets are
5 constructed based on the average rce and the rofts generated from the roducton lan. The consumton bundles requested are rojected onto these budget sets. The resultng bundles may not be feasble n the aggregate, but aggregate feasblty s reached by scalng down the bundles. We assume the ndvduals are comletely nformed as regards the technology, references and endowments. We also assume the desgner knows the ndvduals ntal endowments, but we do not assume that the desgner knows the technology. 2 otce that the frm s a fcttous entty, whch s created n order to defne the outcome functon. It s thus controlled by the desgner and has no strategc role. We show that mechansm A has ash equlbra that are all comettve solutons, thereby, yeldng an effcent soluton to the roblem of cost allocaton. In order to resent more clearly the formal descrton of the mechansm, we wll roceed n several stes even though the mechansm tself s a one-stage game. Ste 1: An average rce s constructed as follows. Defne: X t t 2 Ý Ý a s < y < ; as a X t,t / a b s a)0 a 1 s s Ý b s1 as0 s1 The constructon of mles that f all ndvduals other than ndvdual announce the same rce q, the average rce constructed wll be q and furthermore, ndvdual s announcement wll have no effect on the rce reached. Ste 2: The roducton lan x, y. used by the mechansm s determned by: y1 ž ½ 55 ž ½ ½ 55/ / s1 s1 s1 s1. Ý ½ Ý Ý Ý x, y s mn w,max 0, t,c mn w,max 0, t The aearance of the cost functon n the roducton lan does not mly that the desgner needs to know the technology. The oeraton of the mechansm 2 Knowledge of ntal endowments can be relaxed at the cost of a more comlcated mechansm that would handle destructon and wthholdng of ntal endowments as n the work of Hong Furthermore, note that each ndvdual needs only to know the set of references and endowments that exst n the entre socety and not the secfc reference or endowment for any artcular other. ndvdual.
6 reveals the value of c at a sngle ont the roducton ont yelded by the choces of the ndvduals. Ste 3: ndvdual budget sets are constructed elements are net trades., based on the average rce and the roducton lan: z qz Fa y yx. 1 2 ~ Ý 1 s1 B s z, z gr z qw F w yx ; z qw G0 z Fy ; z G0 ß 2 2 Let Õ be the closest ont n B to c. In order to nsure the fnal allocaton s feasble, the followng set J s constructed: rpr F1 for s1..., ~ Ý Ý Ý 1 2 ß Js rgr qq r r Õ qw F w ; r r Õ Fy s1 s1 s1 Let rsmax ˆ r g J r. The bundles allocated to the ndvduals by the mechansm are: g srpr ˆ Õ qw ; g srpr ˆ Õ for s1,..., The mechansm n addton to the ndvduals utlty functons consttutes a well defned game. We analyze the ash equlbra of games resultng from our mechansm A. Several other soluton concets lke subgame erfect equlbra Moore and Reullo, 1988; Abreu and Sen, 1990 and more recently Varan, 1994., equlbra n undomnated strateges Palfrey and Srvastava, and vrtual equlbra Matsushma, 1988 and Abreu and Sen, have been used to analyze mechansms n the lterature. Mechansms relyng on these soluton concets may requre more strngent nformatonal assumtons or larger strategy saces. ext, we wll show that all ash equlbra generated by our mechansm gve rse to Pareto otmal allocatons. Prooston 2. For any cost allocaton roblem n D, the ash equlbra of the mechansm constructed aboõe yeld a comettõe soluton that s Pareto otmal. X X X X X X X Proof. Denote, x, y, r, rˆ and x, y s1 as the values and allocatons generated at the ash equlbrum ont. We show ths s a comettve soluton va the followng lemmata. X Lemma 1. IndÕdual can get arbtrarly close to any ont u n B.
7 Proof. Announcng the net trade leadng to u as c and a large enough r wll generate an outcome arbtrarly close to u. The large r nullfes the effect of all the other terms n the constructon, and the calculaton of the fnal bundles allocated to the ndvduals wll leave ndvdual arbtrarly close to u.b X Lemma 2. IndÕdual can generate a B ( ) that contans net trades leadng to strctly ostõe consumton bundles for hmself gõen any choce of strateges by the other ndõduals. X Proof. Snce w )0 and )0 ndvdual can, by sendng n an arorate t, force a roducton lan that has x and y strctly ostve and yelds a ostve ncome level for consumer even f rofts are always negatve, t s ossble to choose a small enough roducton level to guarantee ostve ncome.. Ths X mles that B. contans net trades that lead to strctly ostve consumton bundles for ndvdual.b X Lemma 3. The equlbrum allocaton must be strctly nteror x, y X. s1 g 2 R. qq. Proof. Assume by way of contradcton, there exsts an ndvdual for whom X X. 2 x, y f R qq. By Lemma 2, ndvdual can, by sendng n a ossbly X dfferent t, obtan a B. that contans net trades leadng to strctly ostve consumton bundles. Any one of those consumton bundles s strctly referred X to x, y X.. By Lemma 1 and contnuty of references, there exsts an obtanable consumton that s referred to the equlbrum consumton. Ths contradcts that ndvdual was layng a ash equlbrum strategy. Hence, the equlbrum outcome entals a strctly nteror allocaton.b Lemma 4. The roducton lan ( x, y ) maxmzes rofts under rce. X X X Proof. Assume, by way of contradcton, there s a roducton lan x, y. that X X yelds hgher rofts. Any ont of the form l x q 1yl. x, l y q 1yl. y. wth 0-l-1 yelds hgher rofts by convexty of the cost functon. By Lemma 3, there exsts a l close enough to 1, where such a ont s feasble. By Lemma 2, any ndvdual could obtan ths ont by alterng the t message. Thus, ndvdual X exands the B. set, and by Lemma 1 and contnuty of references can obtan a referred outcome, n contradcton to the orgnal outcome beng an equlbrum outcome.b Lemma 5. The consumton lan ( x X, y X ) maxmzes ndõdual s utlty subject X X X to the budget constrant wth rce and roducton lan ( x, y ).
8 Proof. Assume, by way of contradcton, there s a consumton lan x, y. that X satsfes ndvdual s budget constrant and s strctly better than x, y X..By X X X Lemma 3, only the frst constrant n B. can be bndng at the ont x, y.. X By ths fact, there exsts a l close enough to 1 such that l x q 1 y l x, X X l y q 1yl. y. belongs to B.. By convexty of references, ths ont s X referred to x, y X.. By Lemma 1 and contnuty of references, ths contradcts that ndvdual s layng a ash equlbrum strategy.b By Lemmata 4 and 5, any equlbrum s a comettve soluton and by Prooston 1, ths soluton yelds a Pareto otmal allocaton.b The result of Prooston 2 may be vacuously satsfed f the mechansm suggested does not ossess any ash equlbra. We show that ths s not the case. Gven our assumtons, a comettve soluton always exsts. Prooston 3 shows that any comettve soluton s a ash equlbrum. Hence, the mechansm ossesses a ash equlbrum. Prooston 3. For any cost-allocaton roblem n D, the set of comettõe solutons s contaned n the set of ash equlbra outcomes of mechansm A. X X X. X X X Proof. Let A s x, y, x, y. s1 and rce consttute a comettve X X X. X soluton. A set of strateges realzng t s: s ; c s x yw, y ; t sx r; r s1 for all. Ths -tule of strateges yelds the average rce X and the consumton roducton allocaton A X. We now show that these strateges form a ash equlbrum, snce they are best resonses. Frst, we note that an ndvdual s unable to change the rce constructed, X. Second, the roducton lan n A X maxmzes rofts gven X ; thereby, an ndvdual s choce of t gves hm the largest budget set. Fnally, the choce of c and r leads to the most referred consumton bundle n the budget set. Therefore, changes n c, t or r wll not X mrove uon the x, y X. outcome for ndvdual.b The man features dstngushng mechansm A from other cost-allocaton methods s the Pareto otmalty of the outcome reached and the relaxaton of nformatonal assumtons. In contrast to other cost-sharng methods, our mechansm by vrtue of concdng wth comettve solutons yelds Pareto otmal levels of y. Furthermore, ts oeraton does not requre the desgner to know the technology, as assumed wth seral cost sharng. Mechansm A, on the other hand, s not mmune to coaltonal devatons lke the seral cost-sharng method and s more comlex than the revous methods suggested. The mechansm s otmalty of outcomes and exstence of a soluton crtcally deend uon the assumton of convexty of the technology. Ths henomena s arallel to the one encountered n a comettve economy. Secton 4 secfes soluton concets arorate for envronments wth ncreasng returns non-con- vextes. and dscusses ther mlementaton.
9 4. Increasng returns to scale In ths secton, we consder the allocaton of costs n envronments wth ncreasng returns to scale. We use the analogy of these cost allocaton roblems to economes wth ncreasng-returns-to-scale roducton to suggest a soluton. A common construct for such roducton economes s a margnal-cost-rcng equlbrum MCPE.. Ths conssts of dctatng the roducton lan of the frm and allowng the ndvduals to urchase goods at margnal cost after ayng for ther share of the frm s losses. Exstence of such equlbra under certan condtons has been shown n a seres of aers Mantel, 1979; Beato, 1982; Kamya, 1988a; Bonnsseau and Cornet, Also, the otmalty of these equlbra s guaranteed wth strngent enough condtons on the curvature of the ndfference curves and roducton ossblty fronters Derker, 1986; Qunz, Further results can be found n the work of Cornet Hence, a devce that leads to margnal-cost-rcng equlbra would be an nterestng soluton to cost-sharng roblems. As before, the standard constructon gnores the ossblty of manulaton by the ndvduals. To address ths ssue, we rovde a contnuous, feasble and fnte-dmensonal mechansm that realzes the MCPE soluton. Calsamgla demonstrates that n the resence of ncreasng returns to scale t s mossble to obtan Pareto otmal outcomes va a fnte-dmensonal mechansm. Our mechansm s comatble wth ths result, snce the MCPE that t yelds s not always Pareto otmal. In order to defne an MCPE soluton, we create a fcttous frm and endow w 3 ndvduals wth strctly ostve ownersh shares gven by a s. Alterna- j Ý js 1w tvely, we can choose a desred share structure a and redstrbute endowments as w sa Ý js1w j. An MCPE soluton s a feasble allocaton and a rce of y where the rce equals the margnal cost of roducton, the frm carres out the rescrbed roducton lan and the ndvduals maxmze utlty subject to ther budget constrants. These constrants ncororate both the rce and ther share of the X negatve rofts. Formally, the MCPE soluton s a feasble allocaton x, X. X X X X. X X. X y, x, y and rce where s c y and x, y X. s1 solves: max u x, y. x, y where s.t. x q X y Fw qa denotes the rofts of the frm. 3 The creaton of shares n ths manner revents ndvduals from gong bankrut when held resonsble for the frm s losses. Ths s a verson of the survval assumton, whch aears n the exstence roofs for MCPE Mantel, 1979; Beato, 1982; Kamya, 1988a; Bonnsseau and Cornet, A counter-examle for nonexstence when the survval assumton does not hold s rovded by Kamya 1988b..
10 The cost of roducton mosed on ndvdual by ths soluton s the sum of s exendture on y and s share n the losses. We cannot acheve these outcomes n a straghtforward manner due to ossble msreresentaton of references by the ndvduals. In order to revent these roblems, we offer a contnuous and feasble mechansm mlementng MCPE solutons Mechansm B Excet for the constructon of the budget sets, mechansm B s defned just lke the mechansm mlementng the comettve soluton. The frst constrant n the X y y constructon of B n Secton 2 s relaced wth z qz F2 a y yx. 1 2 ya y yx., where: ž y y j ž s1 j/1 ½ / 5 Ý Ý x, y s mn w, max 0, t, ½Ý ž Ý / 5 ž // y1 j c mn w, max 0, t s1 j/1 The RHS s twce the rofts of the frm at the roducton lan determned by the announcements of all ndvduals other than mnus the rofts of the frm at the roducton lan determned by the announcements of all ndvduals, wth all terms adjusted for feasblty. In equlbrum, all ndvduals announce the same roducton lan. When ths occurs, the desgner can construct the budget sets wth only the knowledge ganed from roducng the announced lan and does not need to know the whole technology as before, the desgner should be able to measure the outut that s eventually roduced.. Outsde of equlbrum, ndvduals may not announce the same roducton lan. In ths case, the desgner needs to know the technology at several onts, that s, he should be able to dscover the outut that would be roduced for several dfferent levels of nuts n order to construct the outcome functon. For some fnte cost he should be able to obtan ths nformaton, for nstance, by ether rerunnng the technology for several onts or stong the technology at several levels of nut. Dong so for the entre curve may ental nfnte costs, whch would not be a credble oton even outsde of equlbrum. These requrements both nsde and outsde equlbrum. are notceably weaker than havng to know the entre roducton technology. 4 4 An alternate route to revealng the entre technology can be acheved by aendng to the mechansm a game smlar to the Hurwcz Maskn Postlewate Hurwcz et al., 1995 construct.
11 The ash equlbra resultng from mechansm B are shown to be MCPE solutons n Prooston 4. In Prooston 5, we show that any MCPE soluton for the cost allocaton roblem can be realzed as a ash equlbrum of the mechansm. Prooston 4. For any cost-allocaton roblem n I, the ash equlbra of mechansm B yeld an MCPE soluton. Proof. The roof concdes wth the roof of Prooston 2 excet for Lemmata 2 and 4. X Lemma 2. B ( ) contans net trades leadng to strctly ostõe consumton bundles for ndõdual. Proof. We consder three dstnct cases:. y Case 1: 0-x -Ýs1w Indvdual can, by adjustng the t announcement, set ysy y and x sx y, hence both x and y are strctly ostve. Lettng z1syw and z2s0 turns the X w X frst nequalty n the defnton of B. nto yw F yyx. or 0 Ýs 1w w X s1 s1 Ýs 1w X 1 2 F Ý w yx q y. The RHS s strctly ostve snce x -Ý w. Hence, Bcontans net trades where z ) yw and z ) 0. These net trades lead to strctly ostve consumton bundles for ndvdual. y Case 2: x s Ýs1w Once more, ndvdual can by adjustng the t announcement set ysy y and x sx y. Indvdual would then have an ndvdual budget constrant for X B. mentoned above. that would allow for ostve consumton of both X goods. However, the aggregate constrants n B. would restrct the ndvdual to receve zero consumton of the x good. By submttng n a smaller t such that x -x y, the ndvdual can relax the aggregate constrants whle stll keeng the ndvdual budget constrant not bndng. Ths would allow strctly ostve consumton of both goods. y Case 3: x s 0 The frst term on the RHS s zero leavng ya yyx. Snce w )0 and X )0 ndvdual can, just as before, choose a strctly ostve roducton lan X that leaves hm wth strctly ostve ncome ncludng w.. Thus, B. contans net trades leadng to strctly ostve consumton bundles.b
12 Lemma 4. The roducton lan ( x, y ) s such that c ( y ) s. X X X X X Proof. The negatve roft of the frm s n the ndvdual budget constrant for X B.. By the same argument as n Lemma 4 of Secton 3, the ndvdual would be able to exand hs budget set f losses were not maxmzed. Maxmzaton of X X X losses mles the condton c y. s.b Ths demonstrates that the ash equlbra outcomes of mechansm B consttute MCPE solutons.b Prooston 5. For any cost-allocaton roblem n I, the set of MCPE solutons s contaned n the set of ash equlbra outcomes of mechansm B. Proof. Smlar to revous roofs.b 5. Conclusons In ths aer, we study the allocaton of costs for envronments wth both decreasng and ncreasng returns to scale. In the decreasng-returns-to-scale case, we construct a mechansm that leads to Pareto otmal outcomes, correctly recognzng the ncentves of ndvduals. In the ncreasng-returns-to-scale case, Pareto otmalty s harder to acheve. We construct a mechansm that leads to margnal-cost-rcng equlbra that generate Pareto otmal outcomes under certan condtons. The exstence of such a constructon further justfes the MCPE concet. The outcomes of revously suggested mechansms are not guaranteed to be Pareto otmal even n the decreasng-returns-to-scale case. Furthermore, n contrast to revous mechansms, our cost-sharng mechansms do not requre the desgner to know ether the technology or ndvdual references. Whether or not there exsts a mechansm that s sueror to ours for envronments where MCPE outcomes fal to be Pareto otmal s a queston of nterest. One also may be nterested n the equty roertes of our mechansm. Such ssues can be used to determne share ownersh wth decreasng-returns-to-scale. Ths s not an oton n our mechansm for ncreasng-returns-to-scale where share ownersh s roortonal to endowments; however, snce rofts are negatve, ndvduals wth hgher endowments bear a larger cost. The constructon technque we use s not lmted to the secfed envronment. Extendng the mechansm to envronments wth more than two goods or multle technologes s straghtforward. Creatng a smlar mechansm to allocate resources when externaltes are resent s also ossble. Modfyng the mechansm to handle asymmetrcally nformed ndvduals nvolves major changes as well as movng to the Bayes ash equlbrum concet and remans a toc of further research.
13 Acknowledgements We wsh to thank Andrew Postlewate and a referee for helful comments. We are grateful to the artcants of the Stony Brook Internatonal Conference on Game Theory w1996 x. Also, we gratefully acknowledge the suort from the Kretman Foundaton and the Monaster Center for Economc Research. References Abreu, D., Sen, A., Subgame erfect mlementaton: a necessary and almost suffcent condton. Journal of Economc Theory 50, Abreu, D., Sen, A., Vrtual mlementaton n ash equlbrum. Econometrca 59, Beato, P., The exstence of margnal cost rcng equlbra wth ncreasng returns. The Quarterly Journal of Economcs 89, Bonnsseau, J.-M., Cornet, B., Exstence of margnal cost rcng equlbra n economes wth several nonconvex frms. Econometrca 58, Brown, D., Equlbrum analyss wth non-convex technologes. In: Hldenbrand, W., Sonnenschen, H. Eds.., Handbook of Mathematcal Economcs, Vol. 4, Cha. 36. orth-holland, Amsterdam, Calsamgla, X., Decentralzed resource allocaton and ncreasng returns. Journal of Economc Theory 14, Cornet, B., Margnal cost rcng and areto otmalty. In: Essays n honor of Edmond Malnvaud, Vol. 1. MIT Press, Cambrdge, MA. Derker, E., When does Margnal Cost Prcng lead to Pareto-effcency? Zetschrft fur atonalokonome 5, Hong, L., ash mlementaton n roducton economes. Economc Theory 5, Hurwcz, L., Outcome functons yeldng Walrasan and Lndahl allocatons at ash equlbrum onts. Revew of Economc Studes 46, Hurwcz, L., Maskn, E., Postlewate, A., Feasble ash mlementaton of socal choce rules when the desgner does not know endowments or roducton sets. In: Ledyard, J.O. Ed.., The Economcs of Informaton Decentralzaton: Comlexty, Effcency, and Stablty. Kluwer Academc, Boston, Kamya, K., 1988a. Exstence and unqueness of equlbra wth ncreasng returns. Journal of Mathematcal Economcs 17, Kamya, K., 1988b. On the survval assumton n margnal cost. rcng. Journal of Mathematcal Economcs 17, Mantel, R., Equlbro con rendmento crecentes a escala. Anales de la Asocaton Argentne de Economa Poltca 1, Matsushma, H., A new aroach to the mlementaton roblem. Journal of Economc Theory 45, Moore, J., Reullo, R., Subgame erfect mlementaton. Econometrca 56, Mouln, H., Shenker, S., Seral cost sharng. Econometrca 60, Mouln, H., Shenker, S., Average cost rcng versus seral cost sharng: an axomatc aroach. Journal of Economc Theory 64, Mouln, H., Watts, A., Two versons of the tragedy of the commons. Economc Desgn 2, Palfrey, T., Srvastava, S., ash mlementaton usng undomnated strateges. Econometrca 59,
14 Postlewate, A., Wettsten, D., Contnuous and feasble mlementaton. Revew of Economc Studes 56, Qunz, M., Effcency of margnal cost rcng equlbra. In: Majundar, M. Ed.., Equlbrum and Dynamcs: Essays n Honour of Davd Gale, Cha. 14. St. Martn s Press, ew York, Schmedler, D., Walrasan analyss va strategc outcome functons. Econometrca 48, Varan, H., A soluton to the roblem of externaltes when agents are well nformed. Amercan Economc Revew 84, Young, H.P., Cost allocaton. In: Aumann, R.J., Hart, S. Eds.., Handbook of Game Theory, Vol. 2, Cha. 36. orth-holland, Amsterdam,
The economics of climate change
The Economcs of Clmate Change C 175 The economcs of clmate change C 175 Chrstan Traeger Part 2: Effcency, Publc Goods, Externaltes Suggested background readng for emergng questons: olstad, Charles D. (2000),
More informationThe Dixit-Stiglitz demand system and monpolistic competition.
The Dxt-Stgltz demand system and monolstc cometton. Economcs students are generally well traned n erfectly comettve markets. Such markets are often thought to be characterzed by well defned utlty functons
More information- contrast so-called first-best outcome of Lindahl equilibrium with case of private provision through voluntary contributions of households
Prvate Provson - contrast so-called frst-best outcome of Lndahl equlbrum wth case of prvate provson through voluntary contrbutons of households - need to make an assumpton about how each household expects
More informationElements of Economic Analysis II Lecture VI: Industry Supply
Elements of Economc Analyss II Lecture VI: Industry Supply Ka Hao Yang 10/12/2017 In the prevous lecture, we analyzed the frm s supply decson usng a set of smple graphcal analyses. In fact, the dscusson
More informationENDOGENOUS TRADE POLICIES IN A DEVELOPING ECONOMY
ENDOGENOUS TRADE POLICIES IN A DEVELOPING ECONOMY BY NGUYEN MANH HUNG AND NGUYEN VAN QUYEN Ths aer examnes the formaton of trade olcy for a small oen develong economy where lobbyng actvtes may be carred
More informationLecture 7. We now use Brouwer s fixed point theorem to prove Nash s theorem.
Topcs on the Border of Economcs and Computaton December 11, 2005 Lecturer: Noam Nsan Lecture 7 Scrbe: Yoram Bachrach 1 Nash s Theorem We begn by provng Nash s Theorem about the exstance of a mxed strategy
More informationA political-economic analysis of free-trade agreements: Comment
A oltcal-economc analyss of free-trade agreements: Comment By ueeng u Abstract: n hs aer n the Amercan Economc Reve, evy (997) develos a oltcal economy model of free-trade agreements (s). He emhaszes that
More informationApplications of Myerson s Lemma
Applcatons of Myerson s Lemma Professor Greenwald 28-2-7 We apply Myerson s lemma to solve the sngle-good aucton, and the generalzaton n whch there are k dentcal copes of the good. Our objectve s welfare
More informationA Utilitarian Approach of the Rawls s Difference Principle
1 A Utltaran Approach of the Rawls s Dfference Prncple Hyeok Yong Kwon a,1, Hang Keun Ryu b,2 a Department of Poltcal Scence, Korea Unversty, Seoul, Korea, 136-701 b Department of Economcs, Chung Ang Unversty,
More informationTaxation and Externalities. - Much recent discussion of policy towards externalities, e.g., global warming debate/kyoto
Taxaton and Externaltes - Much recent dscusson of polcy towards externaltes, e.g., global warmng debate/kyoto - Increasng share of tax revenue from envronmental taxaton 6 percent n OECD - Envronmental
More informationJeffrey Ely. October 7, This work is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License.
October 7, 2012 Ths work s lcensed under the Creatve Commons Attrbuton-NonCommercal-ShareAlke 3.0 Lcense. Recap We saw last tme that any standard of socal welfare s problematc n a precse sense. If we want
More informationECE 586GT: Problem Set 2: Problems and Solutions Uniqueness of Nash equilibria, zero sum games, evolutionary dynamics
Unversty of Illnos Fall 08 ECE 586GT: Problem Set : Problems and Solutons Unqueness of Nash equlbra, zero sum games, evolutonary dynamcs Due: Tuesday, Sept. 5, at begnnng of class Readng: Course notes,
More informationPrice and Quantity Competition Revisited. Abstract
rce and uantty Competton Revsted X. Henry Wang Unversty of Mssour - Columba Abstract By enlargng the parameter space orgnally consdered by Sngh and Vves (984 to allow for a wder range of cost asymmetry,
More informationUNIVERSITY OF NOTTINGHAM
UNIVERSITY OF NOTTINGHAM SCHOOL OF ECONOMICS DISCUSSION PAPER 99/28 Welfare Analyss n a Cournot Game wth a Publc Good by Indraneel Dasgupta School of Economcs, Unversty of Nottngham, Nottngham NG7 2RD,
More informationIntroduction to game theory
Introducton to game theory Lectures n game theory ECON5210, Sprng 2009, Part 1 17.12.2008 G.B. Ashem, ECON5210-1 1 Overvew over lectures 1. Introducton to game theory 2. Modelng nteractve knowledge; equlbrum
More informationOPERATIONS RESEARCH. Game Theory
OPERATIONS RESEARCH Chapter 2 Game Theory Prof. Bbhas C. Gr Department of Mathematcs Jadavpur Unversty Kolkata, Inda Emal: bcgr.umath@gmal.com 1.0 Introducton Game theory was developed for decson makng
More informationPREFERENCE DOMAINS AND THE MONOTONICITY OF CONDORCET EXTENSIONS
PREFERECE DOMAIS AD THE MOOTOICITY OF CODORCET EXTESIOS PAUL J. HEALY AD MICHAEL PERESS ABSTRACT. An alternatve s a Condorcet wnner f t beats all other alternatves n a parwse majorty vote. A socal choce
More informationProvision of public goods in a large economy
Economcs Letters 61 (1998) 229 234 Provson of publc goods n a large economy Mark Gradsten* Ben-Guron Unversty and the Unversty of Pennsylvana, Pennsylvana, USA Receved 13 Aprl 1998; accepted 25 June 1998
More informationMechanisms for Efficient Allocation in Divisible Capacity Networks
Mechansms for Effcent Allocaton n Dvsble Capacty Networks Antons Dmaks, Rahul Jan and Jean Walrand EECS Department Unversty of Calforna, Berkeley {dmaks,ran,wlr}@eecs.berkeley.edu Abstract We propose a
More informationTests for Two Correlations
PASS Sample Sze Software Chapter 805 Tests for Two Correlatons Introducton The correlaton coeffcent (or correlaton), ρ, s a popular parameter for descrbng the strength of the assocaton between two varables.
More informationAppendix - Normally Distributed Admissible Choices are Optimal
Appendx - Normally Dstrbuted Admssble Choces are Optmal James N. Bodurtha, Jr. McDonough School of Busness Georgetown Unversty and Q Shen Stafford Partners Aprl 994 latest revson September 00 Abstract
More informationAn Efficient Nash-Implementation Mechanism for Divisible Resource Allocation
SUBMITTED TO IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS 1 An Effcent Nash-Implementaton Mechansm for Dvsble Resource Allocaton Rahul Jan IBM T.J. Watson Research Center Hawthorne, NY 10532 rahul.jan@us.bm.com
More informationreferences Chapters on game theory in Mas-Colell, Whinston and Green
Syllabus. Prelmnares. Role of game theory n economcs. Normal and extensve form of a game. Game-tree. Informaton partton. Perfect recall. Perfect and mperfect nformaton. Strategy.. Statc games of complete
More information15-451/651: Design & Analysis of Algorithms January 22, 2019 Lecture #3: Amortized Analysis last changed: January 18, 2019
5-45/65: Desgn & Analyss of Algorthms January, 09 Lecture #3: Amortzed Analyss last changed: January 8, 09 Introducton In ths lecture we dscuss a useful form of analyss, called amortzed analyss, for problems
More informationEquilibrium in Prediction Markets with Buyers and Sellers
Equlbrum n Predcton Markets wth Buyers and Sellers Shpra Agrawal Nmrod Megddo Benamn Armbruster Abstract Predcton markets wth buyers and sellers of contracts on multple outcomes are shown to have unque
More informationHedging Greeks for a portfolio of options using linear and quadratic programming
MPRA Munch Personal RePEc Archve Hedgng reeks for a of otons usng lnear and quadratc rogrammng Panka Snha and Archt Johar Faculty of Management Studes, Unversty of elh, elh 5. February 200 Onlne at htt://mra.ub.un-muenchen.de/20834/
More informationCS 286r: Matching and Market Design Lecture 2 Combinatorial Markets, Walrasian Equilibrium, Tâtonnement
CS 286r: Matchng and Market Desgn Lecture 2 Combnatoral Markets, Walrasan Equlbrum, Tâtonnement Matchng and Money Recall: Last tme we descrbed the Hungaran Method for computng a maxmumweght bpartte matchng.
More informationComparing welfare effects of different regulation schemes: an application to the electricity distribution industry
Comarng welfare effects of dfferent regulaton schemes: an alcaton to the electrc dstrbuton ndustr Mara Kosakangas-Savolanen and Raul Svento Unvers of Oulu, Deartment of Economcs and Martt Ahtsaar Instute
More informationPerformance attribution involves
STUART MORGA s an analyst at Wngate Asset Management n Melbourne, Australa. stuart.morgan@wngategrou. com.au Performance Attrbuton of Otons: Defnng Sngle-Stock Oton Exosures and Understandng the Brnson-Fachler
More informationGames and Decisions. Part I: Basic Theorems. Contents. 1 Introduction. Jane Yuxin Wang. 1 Introduction 1. 2 Two-player Games 2
Games and Decsons Part I: Basc Theorems Jane Yuxn Wang Contents 1 Introducton 1 2 Two-player Games 2 2.1 Zero-sum Games................................ 3 2.1.1 Pure Strateges.............................
More informationOptimal Income Tax Schedules under Action Revelation
Optmal Income Tax Schedules under Acton Revelaton Jonathan Hamlton and Steven Slutsky Department of Economcs Warrngton College of Busness Unversty of Florda Ganesvlle FL 36-740 USA Aprl 03 Earler versons
More informationProblems to be discussed at the 5 th seminar Suggested solutions
ECON4260 Behavoral Economcs Problems to be dscussed at the 5 th semnar Suggested solutons Problem 1 a) Consder an ultmatum game n whch the proposer gets, ntally, 100 NOK. Assume that both the proposer
More informationUtilitarianism. Jeffrey Ely. June 7, This work is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License.
Utltaransm June 7, 2009 Ths work s lcensed under the Creatve Commons Attrbuton-NonCommercal-ShareAlke 3.0 Lcense. Utltaransm Why Utltaransm? We saw last tme that any standard of socal welfare s problematc
More informationQuadratic Games. First version: February 24, 2017 This version: August 3, Abstract
Quadratc Games Ncolas S. Lambert Gorgo Martn Mchael Ostrovsky Frst verson: February 24, 2017 Ths verson: August 3, 2018 Abstract We study general quadratc games wth multdmensonal actons, stochastc payoff
More informationQuadratic Games. First version: February 24, 2017 This version: December 12, Abstract
Quadratc Games Ncolas S. Lambert Gorgo Martn Mchael Ostrovsky Frst verson: February 24, 2017 Ths verson: December 12, 2017 Abstract We study general quadratc games wth mult-dmensonal actons, stochastc
More informationA MODEL OF COMPETITION AMONG TELECOMMUNICATION SERVICE PROVIDERS BASED ON REPEATED GAME
A MODEL OF COMPETITION AMONG TELECOMMUNICATION SERVICE PROVIDERS BASED ON REPEATED GAME Vesna Radonć Đogatovć, Valentna Radočć Unversty of Belgrade Faculty of Transport and Traffc Engneerng Belgrade, Serba
More informationLecture Note 1: Foundations 1
Economcs 703 Advanced Mcroeconomcs Prof. Peter Cramton ecture Note : Foundatons Outlne A. Introducton and Examples B. Formal Treatment. Exstence of Nash Equlbrum. Exstence wthout uas-concavty 3. Perfect
More informationWages as Anti-Corruption Strategy: A Note
DISCUSSION PAPER November 200 No. 46 Wages as Ant-Corrupton Strategy: A Note by dek SAO Faculty of Economcs, Kyushu-Sangyo Unversty Wages as ant-corrupton strategy: A Note dek Sato Kyushu-Sangyo Unversty
More informationCh Rival Pure private goods (most retail goods) Non-Rival Impure public goods (internet service)
h 7 1 Publc Goods o Rval goods: a good s rval f ts consumpton by one person precludes ts consumpton by another o Excludable goods: a good s excludable f you can reasonably prevent a person from consumng
More informationEconomics 1410 Fall Section 7 Notes 1. Define the tax in a flexible way using T (z), where z is the income reported by the agent.
Economcs 1410 Fall 2017 Harvard Unversty Yaan Al-Karableh Secton 7 Notes 1 I. The ncome taxaton problem Defne the tax n a flexble way usng T (), where s the ncome reported by the agent. Retenton functon:
More informationProblem Set 6 Finance 1,
Carnege Mellon Unversty Graduate School of Industral Admnstraton Chrs Telmer Wnter 2006 Problem Set 6 Fnance, 47-720. (representatve agent constructon) Consder the followng two-perod, two-agent economy.
More information2. Equlibrium and Efficiency
. Equlbrum and Effcency . Introducton competton and effcency Smt s nvsble and model of compettve economy combne ndependent decson-makng of consumers and frms nto a complete model of te economy exstence
More informationVanderbilt University Department of Economics Working Papers
Vanderblt Unversty Department of Economcs Workng Papers 17-00015 Majorty Rule and Selfshly Optmal Nonlnear Income Tax Schedules wth Dscrete Skll Levels Crag Brett Mt. Allson Unversty John A Weymark Vanderblt
More informationOptimal Service-Based Procurement with Heterogeneous Suppliers
Optmal Servce-Based Procurement wth Heterogeneous Supplers Ehsan Elah 1 Saf Benjaafar 2 Karen L. Donohue 3 1 College of Management, Unversty of Massachusetts, Boston, MA 02125 2 Industral & Systems Engneerng,
More informationElton, Gruber, Brown, and Goetzmann. Modern Portfolio Theory and Investment Analysis, 7th Edition. Solutions to Text Problems: Chapter 9
Elton, Gruber, Brown, and Goetzmann Modern Portfolo Theory and Investment Analyss, 7th Edton Solutons to Text Problems: Chapter 9 Chapter 9: Problem In the table below, gven that the rskless rate equals
More informationConsumption Based Asset Pricing
Consumpton Based Asset Prcng Mchael Bar Aprl 25, 208 Contents Introducton 2 Model 2. Prcng rsk-free asset............................... 3 2.2 Prcng rsky assets................................ 4 2.3 Bubbles......................................
More informationDynamic Analysis of Knowledge Sharing of Agents with. Heterogeneous Knowledge
Dynamc Analyss of Sharng of Agents wth Heterogeneous Kazuyo Sato Akra Namatame Dept. of Computer Scence Natonal Defense Academy Yokosuka 39-8686 JAPAN E-mal {g40045 nama} @nda.ac.jp Abstract In ths paper
More informationFormation of Coalition Structures as a Non-Cooperative Game
Formaton of Coalton Structures as a Non-Cooperatve Game Dmtry Levando Natonal Research Unversty Hgher School of Economcs, Moscow, Russa dlevando@hse.ru Abstract. The paper proposes a lst of requrements
More informationAn introduction to quasi-random numbers
An ntroducton to quas-random numbers By George Levy, umercal Algorthms Grou Ltd. Introducton Monte-Carlo smulaton and random number generaton are technques that are wdely used n fnancal engneerng as a
More informationSingle-Item Auctions. CS 234r: Markets for Networks and Crowds Lecture 4 Auctions, Mechanisms, and Welfare Maximization
CS 234r: Markets for Networks and Crowds Lecture 4 Auctons, Mechansms, and Welfare Maxmzaton Sngle-Item Auctons Suppose we have one or more tems to sell and a pool of potental buyers. How should we decde
More informationTests for Two Ordered Categorical Variables
Chapter 253 Tests for Two Ordered Categorcal Varables Introducton Ths module computes power and sample sze for tests of ordered categorcal data such as Lkert scale data. Assumng proportonal odds, such
More informationGOAL-ORIENTED ADJUSTMENT MECHANISMS FOR STABILIZATION AND DEVELOPMENT OF TRANSITION ECONOMIES
ISAHP 2001, Berne, Swtzerland, August 2-4, 2001 GOAL-ORIENTED ADJUSTMENT MECHANISMS FOR STABILIZATION AND DEVELOPMENT OF TRANSITION ECONOMIES Vasa Toroyan Head of Deartment of Mathematcal Modelng of Economy
More informationMechanism Design in Hidden Action and Hidden Information: Richness and Pure Groves
1 December 13, 2016, Unversty of Tokyo Mechansm Desgn n Hdden Acton and Hdden Informaton: Rchness and Pure Groves Htosh Matsushma (Unversty of Tokyo) Shunya Noda (Stanford Unversty) May 30, 2016 2 1. Introducton
More informationMeaningful cheap talk must improve equilibrium payoffs
Mathematcal Socal Scences 37 (1999) 97 106 Meanngful cheap talk must mprove equlbrum payoffs Lanny Arvan, Luıs Cabral *, Vasco Santos a b, c a Unversty of Illnos at Urbana-Champagn, Department of Economcs,
More informationState-dependent Preferences in Prediction Markets and Prices as Aggregate Statistic
State-deendent Preferences n Predcton Markets and Prces as Aggregate Statstc Urmee Khan 1 Abstract If traders n redcton markets have state-deendent references so that margnal utlty of money vares across
More informationStatic (or Simultaneous- Move) Games of Complete Information
Statc (or Smultaneous- Move) Games of Complete Informaton Nash Equlbrum Best Response Functon F. Valognes - Game Theory - Chp 3 Outlne of Statc Games of Complete Informaton Introducton to games Normal-form
More informationBenefit-Cost Analysis
Chapter 12 Beneft-Cost Analyss Utlty Possbltes and Potental Pareto Improvement Wthout explct nstructons about how to compare one person s benefts wth the losses of another, we can not expect beneft-cost
More informationAppendix for Solving Asset Pricing Models when the Price-Dividend Function is Analytic
Appendx for Solvng Asset Prcng Models when the Prce-Dvdend Functon s Analytc Ovdu L. Caln Yu Chen Thomas F. Cosmano and Alex A. Hmonas January 3, 5 Ths appendx provdes proofs of some results stated n our
More informationTHE IMPORTANCE OF THE NUMBER OF DIFFERENT AGENTS IN A HETEROGENEOUS ASSET-PRICING MODEL WOUTER J. DEN HAAN
THE IMPORTANCE OF THE NUMBER OF DIFFERENT AGENTS IN A HETEROGENEOUS ASSET-PRICING MODEL WOUTER J. DEN HAAN Department of Economcs, Unversty of Calforna at San Dego and Natonal Bureau of Economc Research
More informationVolume 30, Issue 1. Partial privatization in price-setting mixed duopoly. Kazuhiro Ohnishi Institute for Basic Economic Science, Japan
Volume 3, Issue 1 Partal prvatzaton n prce-settng mxed duopoly Kazuhro Ohnsh Insttute for Basc Economc Scence, Japan Abstract Ths paper nvestgates a prce-settng mxed model nvolvng a prvate frm and a publc
More informationPayment Cards and Cash.
Interchange Fees and Ine cences n the Substtuton between Payment Cards and Cash. Maranne Verder May 16, 2010 Abstract Ths artcle exlans why the collectve determnaton of nterchange fees n ayment latforms
More informationCoalition-Proof Equilibrium
GAMES AD ECOOMIC BEHAVIOR 7, 802 996 ARTICLE O. 0095 Coalton-Proof Equlbrum Dego Moreno Departamento de Economıa, Unersdad Carlos III de Madrd, 28903 Getafe ( Madrd ), Span and John Wooders Department
More informationAn Efficient Mechanism for Network Bandwidth Auction
1 An Effcent Mechansm for Network Bandwdth Aucton Rahul Jan IBM T.J. Watson Research Center Hawthorne, NY 10532 rahul.jan@us.bm.com Jean Walrand EECS Department, Unversty of Calforna, Berkeley wlr@eecs.berkeley.edu
More informationContests with Group-Specific Public-Good Prizes
Contests wth Group-Specfc Publc-Good Przes Kyung Hwan ak * Department of Economcs Sungkyunkwan Unversty Seoul 110-745 South Korea September 2005 Abstract I examne the equlbrum effort levels of ndvdual
More informationFall 2017 Social Sciences 7418 University of Wisconsin-Madison Problem Set 3 Answers
ublc Affars 854 enze D. Chnn Fall 07 Socal Scences 748 Unversty of Wsconsn-adson roblem Set 3 Answers Due n Lecture on Wednesday, November st. " Box n" your answers to the algebrac questons.. Fscal polcy
More informationFORD MOTOR CREDIT COMPANY SUGGESTED ANSWERS. Richard M. Levich. New York University Stern School of Business. Revised, February 1999
FORD MOTOR CREDIT COMPANY SUGGESTED ANSWERS by Rchard M. Levch New York Unversty Stern School of Busness Revsed, February 1999 1 SETTING UP THE PROBLEM The bond s beng sold to Swss nvestors for a prce
More informationAn inductive proof for a closed form formula in truncated inverse sampling
Journal of Proagatons n Probablty and Statstcs Vol. No. August Internatonal ed.. 7- An nductve roof for a closed for forula n truncated nverse salng Kuang-Chao Chang Fu Jen Catholc Unversty Abstract Inverse
More informationRaising Food Prices and Welfare Change: A Simple Calibration. Xiaohua Yu
Rasng Food Prces and Welfare Change: A Smple Calbraton Xaohua Yu Professor of Agrcultural Economcs Courant Research Centre Poverty, Equty and Growth Unversty of Göttngen CRC-PEG, Wlhelm-weber-Str. 2 3773
More informationINTERNATIONAL TRADE AND ITS IMPACT ON BIOLOGICAL DIVERSITY
INTERNATIONAL TRADE AND ITS IMPACT ON BIOLOGICAL DIVERSITY RAFAT ALAM Unversty of Ottawa N.V. QUYEN Unversty of Ottawa Abstract Usng a general equlbrum model, ths aer shows how free trade can have negatve
More informationGeneral Examination in Microeconomic Theory. Fall You have FOUR hours. 2. Answer all questions
HARVARD UNIVERSITY DEPARTMENT OF ECONOMICS General Examnaton n Mcroeconomc Theory Fall 2010 1. You have FOUR hours. 2. Answer all questons PLEASE USE A SEPARATE BLUE BOOK FOR EACH QUESTION AND WRITE THE
More informationON THE DYNAMICS OF GROWTH AND FISCAL POLICY WITH REDISTRIBUTIVE TRANSFERS
O THE DYAMICS OF GROWTH AD FISCAL POLICY WITH REDISTRIBUTIVE TRASFERS by* Hyun Park Unversty of Essex and Apostols Phlppopoulos Athens Unversty of Economcs and Busness May 25, 999 Abstract: Ths paper formalzes
More informationTradable Emissions Permits in the Presence of Trade Distortions
85 Tradable Emssons Permts n the Presence of Trade Dstortons Shnya Kawahara Abstract Ths paper nvestgates how trade lberalzaton affects domestc emssons tradng scheme n a poltcal economy framework. Developng
More informationECON 4921: Lecture 12. Jon Fiva, 2009
ECON 4921: Lecture 12 Jon Fva, 2009 Roadmap 1. Introducton 2. Insttutons and Economc Performance 3. The Frm 4. Organzed Interest and Ownershp 5. Complementarty of Insttutons 6. Insttutons and Commtment
More informationPrivatization and government preference in an international Cournot triopoly
Fernanda A Ferrera Flávo Ferrera Prvatzaton and government preference n an nternatonal Cournot tropoly FERNANDA A FERREIRA and FLÁVIO FERREIRA Appled Management Research Unt (UNIAG School of Hosptalty
More informationProduction and Supply Chain Management Logistics. Paolo Detti Department of Information Engeneering and Mathematical Sciences University of Siena
Producton and Supply Chan Management Logstcs Paolo Dett Department of Informaton Engeneerng and Mathematcal Scences Unversty of Sena Convergence and complexty of the algorthm Convergence of the algorthm
More informationOn Competitive Nonlinear Pricing
On Compettve Nonlnear Prcng Andrea Attar Thomas Marott Franços Salané July 4, 2013 Abstract A buyer of a dvsble good faces several dentcal sellers. The buyer s preferences are her prvate nformaton, and
More informationQuiz on Deterministic part of course October 22, 2002
Engneerng ystems Analyss for Desgn Quz on Determnstc part of course October 22, 2002 Ths s a closed book exercse. You may use calculators Grade Tables There are 90 ponts possble for the regular test, or
More informationA Noncooperative View of Consistent Bankruptcy Rules*
Ž. GAMES AND ECONOMIC BEHAVIOR 18, 5572 1997 ARTICLE NO. GA970526 A Noncooperatve Vew of Consstent Bankruptcy Rules* Nr Dagan Department of Economcs, Unerstat Pompeu Fabra, Barcelona, Span and Roberto
More informationc slope = -(1+i)/(1+π 2 ) MRS (between consumption in consecutive time periods) price ratio (across consecutive time periods)
CONSUMPTION-SAVINGS FRAMEWORK (CONTINUED) SEPTEMBER 24, 2013 The Graphcs of the Consumpton-Savngs Model CONSUMER OPTIMIZATION Consumer s decson problem: maxmze lfetme utlty subject to lfetme budget constrant
More informationTrading Volume, Price Autocorrelation and Volatility under Proportional Transaction Costs
Tradng Volume, Prce Autocorrelaton and Volatlty under Proortonal Transacton Costs Hua Cheng Unversty of Pars Dauhne - Deartment of Economcs SDF (Fnancal Strateges & Dynamcs), P33A, Deartment of Economcs,
More informationPricing Mechanisms for Economic Dispatch: A Game-Theoretic Perspective
Prcng Mechansms for Economc Dspatch: A Game-Theoretc Perspectve Wenyuan Tang a, Rahul Jan a a Unversty of Southern Calforna, Los Angeles, CA 90089, USA Abstract The economc dspatch problem s to determne
More informationGlobal Optimization in Multi-Agent Models
Global Optmzaton n Mult-Agent Models John R. Brge R.R. McCormck School of Engneerng and Appled Scence Northwestern Unversty Jont work wth Chonawee Supatgat, Enron, and Rachel Zhang, Cornell 11/19/2004
More informationOsaka University of Economics Working Paper Series No Hart Mas-Colell Implementation of the Discounted Shapley Value
Osaka Unversty of Economcs Workng Paper Seres No 2014-2 Hart Mas-Colell Implementaton of the Dscounted Shapley Value Tomohko Kawamor Faculty of Economcs, Osaka Unversty of Economcs November, 2014 Hart
More informationEconomic Design of Short-Run CSP-1 Plan Under Linear Inspection Cost
Tamkang Journal of Scence and Engneerng, Vol. 9, No 1, pp. 19 23 (2006) 19 Economc Desgn of Short-Run CSP-1 Plan Under Lnear Inspecton Cost Chung-Ho Chen 1 * and Chao-Yu Chou 2 1 Department of Industral
More informationAutomatica. An efficient Nash-implementation mechanism for network resource allocation
Automatca 46 (2010 1276 1283 Contents lsts avalable at ScenceDrect Automatca ournal homepage: www.elsever.com/locate/automatca An effcent Nash-mplementaton mechansm for networ resource allocaton Rahul
More informationA Microeconomic Foundation for Optimum Currency Areas: The Case for Perfect Capital Mobility and Immobile Labor Forces
Theoretcal Economcs Letters 202 2 395-399 htt://dx.do.org/0.4236/tel.202.24073 Publshed Onlne October 202 (htt://www.scrp.org/journal/tel) A Mcroeconomc Foundaton for Otmum Currency Areas: The Case for
More informationDiscussion Papers Department of Economics University of Copenhagen
Dscusson Papers Department of Economcs Unversty of Copenhagen No. 09-12 Incomplete Fnancal Markets and Jumps n Asset Prces Hervé Crès, Tobas Markeprand, and Mch Tvede Øster Farmagsgade 5, Buldng 26, DK-1353
More informationFinancial mathematics
Fnancal mathematcs Jean-Luc Bouchot jean-luc.bouchot@drexel.edu February 19, 2013 Warnng Ths s a work n progress. I can not ensure t to be mstake free at the moment. It s also lackng some nformaton. But
More informationFlight Delays, Capacity Investment and Welfare under Air Transport Supply-demand Equilibrium
Flght Delays, Capacty Investment and Welfare under Ar Transport Supply-demand Equlbrum Bo Zou 1, Mark Hansen 2 1 Unversty of Illnos at Chcago 2 Unversty of Calforna at Berkeley 2 Total economc mpact of
More informationBilateral Bargaining with Externalities
Unversty of Toronto From the SelectedWorks of Joshua S Gans October, 2007 Blateral Barganng wth Externaltes Catherne C de Fontenay, Melbourne Busness School Joshua S Gans Avalable at: https://works.bepress.com/joshuagans/14/
More informationMoney, Banking, and Financial Markets (Econ 353) Midterm Examination I June 27, Name Univ. Id #
Money, Bankng, and Fnancal Markets (Econ 353) Mdterm Examnaton I June 27, 2005 Name Unv. Id # Note: Each multple-choce queston s worth 4 ponts. Problems 20, 21, and 22 carry 10, 8, and 10 ponts, respectvely.
More informationCyclic Scheduling in a Job shop with Multiple Assembly Firms
Proceedngs of the 0 Internatonal Conference on Industral Engneerng and Operatons Management Kuala Lumpur, Malaysa, January 4, 0 Cyclc Schedulng n a Job shop wth Multple Assembly Frms Tetsuya Kana and Koch
More information2) In the medium-run/long-run, a decrease in the budget deficit will produce:
4.02 Quz 2 Solutons Fall 2004 Multple-Choce Questons ) Consder the wage-settng and prce-settng equatons we studed n class. Suppose the markup, µ, equals 0.25, and F(u,z) = -u. What s the natural rate of
More informationSecond-Degree Price Discrimination on Two-Sided Markets
MPRA Munch Personal RePEc Archve Second-Degree Prce Dscrmnaton on Two-Sded Markets Enrco Böhme 30. August 0 Onlne at http://mpra.ub.un-muenchen.de/4095/ MPRA Paper No. 4095, posted 30. August 0 09:0 UTC
More informationReal Exchange Rate Fluctuations, Wage Stickiness and Markup Adjustments
Real Exchange Rate Fluctuatons, Wage Stckness and Markup Adjustments Yothn Jnjarak and Kanda Nakno Nanyang Technologcal Unversty and Purdue Unversty January 2009 Abstract Motvated by emprcal evdence on
More informationIntensive vs Extensive Margin Tradeo s in a Simple Monetary Search Model
Intensve vs Extensve Margn Tradeo s n a Smple Monetary Search Model Sébasten Lotz y Unversty of Pars 2 Andre Shevchenko z Mchgan State Unversty Aprl 2006 hrstopher Waller x Unversty of Notre Dame Abstract
More informationBargaining over Strategies of Non-Cooperative Games
Games 05, 6, 73-98; do:0.3390/g603073 Artcle OPEN ACCESS games ISSN 073-4336 www.mdp.com/ournal/games Barganng over Strateges of Non-Cooperatve Games Guseppe Attanas, *, Aurora García-Gallego, Nkolaos
More informationCOS 511: Theoretical Machine Learning. Lecturer: Rob Schapire Lecture #21 Scribe: Lawrence Diao April 23, 2013
COS 511: Theoretcal Machne Learnng Lecturer: Rob Schapre Lecture #21 Scrbe: Lawrence Dao Aprl 23, 2013 1 On-Lne Log Loss To recap the end of the last lecture, we have the followng on-lne problem wth N
More informationOnline Appendix for Merger Review for Markets with Buyer Power
Onlne Appendx for Merger Revew for Markets wth Buyer Power Smon Loertscher Lesle M. Marx July 23, 2018 Introducton In ths appendx we extend the framework of Loertscher and Marx (forthcomng) to allow two
More informationTwo Period Models. 1. Static Models. Econ602. Spring Lutz Hendricks
Two Perod Models Econ602. Sprng 2005. Lutz Hendrcks The man ponts of ths secton are: Tools: settng up and solvng a general equlbrum model; Kuhn-Tucker condtons; solvng multperod problems Economc nsghts:
More information