European Regional Science Association 36th European Congress ETH Zurich, Switzerland August 1996
|
|
- Sharon Walton
- 5 years ago
- Views:
Transcription
1 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 98, JAPA ax: REE-RD, SCALE ECMY AD JT PRVS LCAL PUBLC D ABSTRACT: t s observed that each jursdcton does not necessarly have all types of local publc good. Therefore, some types of publc good may be used by people from other jursdctons. n ths stuaton, strategc local government may not provde ther own publc good and expect that ther resdents wll use the good n other jursdcton; we term ths nterjursdctonal free-rdng. Settng a two regon model, ths paper nvestgates ash equlbra of local governments wth respect to the provson of local publc good wth spll over effect. We dentfed the condtons under whch free-rdng occur as an equlbrum soluton. urthermore, we formulate the programmng problem to obtan socally optmal allocaton and compare wth ash equlbrum soluton. Dscusson about polcy nstruments are also provded.
2 ree Rdng, Scale Economy and Jont Provson of Local Publc ood by Se-l Mun and Mn-xue Wang. ntroducton t s observed that each jursdcton does not necessarly have all types of local publc good. Therefore, some types of publc goods may be used by people from other jursdctons, f the use of publc good s not excludable as postulated. n ths stuaton, strategc local governments may not provde ther own publc goods and expect that ther resdents wll use the goods n other jursdctons; we term ths nterjursdctonal free-rdng. The purpose of ths paper s to nvestgate the consequences of decentralzed decson makng by local governments ncludng the case of free-rdng, and to examne the effcency of such decentralzed system. The topc of ths paper s related to the lterature on local publc goods generatng spll-over effects(e.g. Wllams(966), Paully(97), ordon(983)). These authors ponted out that, under the presence of spll-over effects, decentralzed decson makng by local governments cannot acheve the effcent level of publc good, snce each local government does not take account of the beneft of non-resdents. They addressed varous ssues; how the equlbrum level of publc good devate from the optmal one, what the role of central government s, and so on. Recently, Wellsch(993) has demonstrated that ash equlbrum of competng local governments s socally effcent, f households are perfectly moble and local governments take account of the mgraton responses to ther polces. Most prevous works n ths feld, ncludng those mentoned above, are restrctve n the sense that they have focused only on nteror solutons n that each government necessarly provdes postve amount of publc good. To nvestgate the free-rdng problem, we should explctly deal wth corner solutons. Kuroda(989) and Tsukahara(995) are exceptons. Kuroda focused on the locaton of publc facltes as strategy of local government whle quantty of the publc goods are gven exogenously, and compared non-cooperatve and cooperatve solutons. Although he dentfed the case of corner soluton, t was elmnated from the man part of hs analyss; he consdered that the emergence of corner soluton should be avoded by central government. n contrast, Tsukahara shed lght on the corner soluton. He examned the case that two local governments jontly
3 provde one publc good, and derved the condton under whch local governments choose the jont provson nstead of ndependent provson. Snce the subject of our study s closely related to Tsukahara s work, we would dscuss t n more detal. rst, he assumed that resdents can use the publc facltes n other jursdctons only f ther government jons the coalton. Ths mples that free-rdng from other jursdcton s prohbted even f t s possble. Ths contradcts the basc character of publc good, non-excludablty. Second, n hs model, local governments are perfectly compettve n that each of them consders that ts behavor does not affect the behavor of others. Perfect competton s not compatble wth the fact that spll over effects are present among small number of neghborng jursdctons. Ths paper presents a dfferent approach to analyzng the smlar problem to that n Tsukahara s paper. We nvestgate not only jont provson as cooperatve soluton but also free-rdng resultng from non-cooperatve behavor of local government wth respect to the provson of local publc good wth spll over effect. We derve ash equlbra of local governments and dentfy the condtons under whch free-rdng occur as an equlbrum soluton. urthermore, we formulate the programmng problem to obtan socally optmal allocaton and compare wth ash equlbrum soluton. Dscusson about polcy nstruments are also provded.. The Model Suppose that the economy conssts of two regons(jursdctons). Total number of households n the economy s fxed at, and ther locaton dstrbuton, n( =, ) s exogenously gven. Thus followng relaton holds n+ n = () Each household supples one unt of labor force to the local frm. Each regon produces a sngle homogenous product, used as a numerare good. nputs for producton s labor; the producton functon s represented as Y = f ( n ), where f >, f < are assumed. ote that local populaton n s equvalent to the labor nput. All households have dentcal preferences and the utlty of a household n regon s a functon of ts consumpton x and servce level of local publc good, Z, denoted by ux (, Z). t s assumed that publc good n ether regon s accessble for all resdents n the economy, but ts servce level for resdents n other jursdcton s lower than that for resdents n the jursdcton where the good s provded. Ths reducton s, for example, attrbuted to the dstance or travel costs to vst facltes located n other jursdcton. We represent the
4 servce level of the publc good n regon as follows Z = max{, h }, j () j where s quantty of publc good provded n jursdcton, and h s a parameter rangng h. The above formulaton mples that households choose to use the publc good wth the hghest servce level. C ( ) = R S T + a, f >, f = The cost for producton of publc good n jursdcton s gven by where s the fxed cost and a s a constant representng the margnal cost. (3) 3. Decentralzed decson makng of local governments and ash equlbra 3. Decson makng of a local government The objectve of a local government s to maxmze the utlty of ther resdents. Wthout any nterventon of central government or nterregonal transfer, the followng resource constrant must be satsfed n each regon. Y nx C( ) = (4) The local government has two alternatve strateges: (A) to provde postve amount of by collectng tax from ther resdents, and (B) not to provde publc good and expect that ther resdents free rde on the publc good n another jursdcton. f the government takes the former strategy (A), t wll choose the quantty of publc good such that Max u Y C ( ), (5) n The frst order condton for optmzaton s n u u x KJ = C (6) Let be the soluton to the above equaton and V the utlty level correspondng to the soluton. n the other hand, f the government takes the free-rdng strategy (B), the resdents enjoy the utlty level gven by uy ( / n, h). The government wll choose the strategy that gves hgher j utlty. Decson makng of government depends on the strategy of another jursdcton j. Let j be the quantty of publc good n j satsfyng the followng relaton 3
5 uy ( / n, h ) = V (7) j When j s greater than j, the utlty for the free-rdng strategy (B) s greater than that for strategy (A). Thus the government wll not provde the publc good n the jursdcton. n the other hand, when j s smaller than j, the government wll provde ts own publc good accordng to the manner specfed n (5). The optmal polcy for the local government, as reactons to the strateges of another jursdcton j, can be summarzed as follows R S f > = T,, f j j j j (8) 3. ash equlbra ash equlbra concernng the provson of publc good by two local governments can be classfed to four cases. As llustrated n gure (a)-(d), the relatve poston of,, and determne whch case s emerged. below The condtons under whch each case s emerged are descrbed Case : nly jursdcton provdes postve quantty of publc good and resdents n jursdcton free-rde on the good n. Ths case emerges f > and < and the equlbrum soluton s (, ) = (, ). Case : Both jursdctons provde ther own publc good, thus nether spll-over nor free-rdng occurs. Ths case emerges f < and < (, ) = (, ). and the equlbrum soluton s Case 3: nly jursdcton provdes postve quantty of publc good and resdents n jursdcton free-rde on the good n. Ths case emerges f < and > and the equlbrum soluton s (, ) = (, ). Case 4: n ths case, as shown n the gure (d), the equlbrum soluton s not unque. Both governments seek to be free-rder. Ths case emerges f > and > and the equlbrum solutons are (, ) = (, ) and (, ) (, = ). 4
6 = h = h = h = h (a) Case (b) Case = h = h = h = h (c) Case 3 (d) Case 4 Equlbrum pont reacton of regon reacton of regon URE our cases of ash equlbrum 3.3 Propertes of ash equlbra To obtan the explct results, we specfy the form of utlty functon as ux (, Z) = log x+ ( ) log Z (9) where s a constant satsfyng < <. By usng the specfcaton above, we solve the equatons (6) and (7) to obtan = ( Y ) a 5 ()
7 = Yj j ah K J H Y K J j d,. () Then we derve explctly the condtons under whch each case emerges, as follows Case : Substtutng ()() nto the condtons, > and <, we rewrte them as h > h and h< h where h h Y Y b g ( Y ). () = H K J Y Y b g ( Y ). (3) = H K J Smlarly, condtons for the emergence of the remanng cases are: Case : h Case 3: h Case 4: h < h and h< h < h and h> h > h and h> h The values of h and h depend on varous parameters and we term them case boundary functons. To nvestgate the relaton between case emergence and populaton dstrbuton, we dfferentate (), (3) wth respect to n. h n h n = h = h L M L M l q f P< (4a) Y Q l( ) + q f + P> (4b) Y Y Y Q f ( ) Y ( )( Y ) Y f Y ( )( ) And we see from (),(3) that h = h when Y = Y,.e., n = n = /. urthermore, h (h ) as n, and h (h ) as n. Based on the above nformaton, we depct n gure the case boundary functons and show the range of h and n n whch each case emerges. rom the fgure, t s seen that free-rdng cases, such as cases,3 and 4, are lkely to emerge when the degree of spll-over, h s hgh and populaton dstrbuton s uneven. Hgher value of h mples that the declne n servce level due to dstance s not sgnfcant. n other words, two regons are not so dstant each other, or transportaton system s mproved. 6
8 Case 4 h Case 3 Case h h Case n n URE Parameters and cases of ash equlbrum Another mportant parameter affectng case dvson s the fxed cost for provson of the publc good. h Dfferentatng () wth respect to gves ( )( Y ) ( Y ) = h ( )( Y )( Y ) l q (5) Although the sgn of the RHS of (5) s ambguous n general, at least t s negatve when n > n. As shown n gure, h curve as the boundary between free-rdng case(case ) and ndependent provson case(case ) s meanngful only when n > n. Wthn ths range, ncrease n fxed cost shfts the curve downward. Smlar argument apples to the effect on h curve. Consequently, the lkelhood of free-rdng cases s ncreased as fxed cost becomes larger. nally we would make a remark on case 4, the case of multple equlbra. n ths case, we cannot predct whch soluton s realzed. But we can evaluate whch soluton s more socally preferable than the other. Some scholars clamed that players are lkely to choose the strategy such that preferable soluton s attaned when nformaton on focal pont s provded, or preplay communcaton s made. But ths s not always the case. The central government may play an mportant role n provdng the nformaton on focal pont, or coordnatng the pre-play communcaton, even f t does not ntervene by means of fscal polces. 7
9 4. Socal optmum 4. The problem formulaton n ths secton, we formulate and solve the problem as f the central government (or socal planner) can control everythng. We wll consder n the next secton the polcy nstruments n decentralzed settng. We choose the Benthamte socal welfare as the objectve functon to be maxmzed. As n the prevous secton, three cases are expected to emerge: () only regon provdes the publc good, () both regons provde, () only regon provdes. We wll solve the problem by two step; the frst step s to solve three problems, n each of whch one of three cases s supposed, the next s to choose the case that gves the hghest value of objectve functon. We start by descrbng the problem of each case n the frst step. Case : The problem under case s formulated as follows Max nu ( x, ) + nu ( x, h) (6) x, subject to Y + Y n x n x C( ) = (7) The frst order condtons for optmzaton are u = u (8a) x x n u u x n hu + = C (8b) u x (8b) states that the quantty of publc good n regon should be determned such that the sum of margnal beneft for all resdents n the economy s equal to margnal cost. n the decentralzed provson as descrbed by (6), the second term n LHS of (8b) s not appeared. Ths mples that decentralzed provson s not effcent because t gnores the beneft of non-resdents. Let x, x and be the soluton to the above problem, then the optmal value of the objectve functon n case s calculated as follows W = nu( x, ) + n u( x, h ) Case : Max nu ( x, ) + nu ( x, ) (9) x, subject to Y+ Y nx nx C ( ) C ( ) = () The frst order condtons for optmzaton are u = u (a) x x 8
10 n u u x = C, =, (b) And optmal value s W = nu( x, ) + n u( x, ) Case : Ths case s symmetry to Case. Thus we omt explanaton about ths case. Suppose that the optmal values, W, W and W are obtaned. Then the next task of the planner s to choose the optmal case. The planner should choose case f W > W and W > W ; case f W > W and W > W ; Case f W > W and W > W. 4. Propertes of optmal soluton The analyss n ths secton s based agan on the specfcaton of log-lnear utlty functon. By usng the explct solutons(see Appendx for detals), we derve the condtons under whch each case s chosen as optmal polcy. Case : The condtons, W > W and W > W become h> h and n > n, where h n n = H K J H K J + n n ( ) n Y Y Y + Y KJ. () Case : The condtons, W > W and W > W become h h < and h< h, where h n n = H K J H K J + n n ( ) n Y Y Y + Y KJ. (3) Case : The condtons, W > W and W > W become n > n and h> h. n cases and, quantty of publc good s determned takng account of the beneft of the resdents n both regons and. And n case (case ), regon (regon ) bears porton of the cost for provdng publc good, although the publc good s not located n ts terrtory. Therefore, we can regard cases and as jont provson. As n the analyss of ash equlbra, we nvestgate the shape of the case boundary functons, h and h, to see the relatons between parameters and the optmal polcy. Dfferentatng (), (3) wth respect to n, we have 9
11 h n h n = h = h ( f f ) n ( ) n ( Y + Y )( Y + Y ) R S T R S T ( f f ) n ( ) n ( Y + Y )( Y + Y ) + H K J + n H K J + U KJV W U KJV W n Y Y log (4a) Y + Y Y Y log (4b) Y + Y rom the assumpton of concave producton functon, f f s postve (negatve) when n < n (n > n). urthermore, n Y+ Y <, ( =, ), and <. Then we conclude that Y + Y h n <, f n > n and h n >, f n > n. Based on the above nformaton, we depct n gure 3 the case boundary curves and the area n whch each case s chosen as optmal polcy. t s seen n gure 3 that the jont provson cases are lkely to be optmal when h s hgh and populaton dstrbuton s uneven. Ths s smlar result to that n ash equlbrum. The decson rule concernng the choce between cases and s qute smple; the publc good should be provded by the regon wth larger populaton. As for the effect of fxed cost,, we obtan h = h Y+ Y ( ) n ( Y + Y )( Y + Y ) W < R S T Same result holds for h. U V These results mply that, as the fxed cost s larger, jont provson s (5) h Case Case n h o Case h o n URE 3 Parameters and cases of optmal solutons
12 more lkely to be optmal. 4. Comparson between ash equlbrum and optmum We frst examne whether the parameter range for the emergence of jont provson cases n optmum s larger than that of free-rdng cases n ash equlbrum. Ths comparson s meanngful because jont provson and free-rdng have common features n the sense that two regons have one publc good. gure 4 shows case boundary curves for equlbrum and optmum. n the fgure, free-rdng cases n ash equlbrum emerge n the area above h optmum emerges n the area above h and h curves, whle jont provson n and h curves. t s seen that the area of jont provson case s larger than that of free-rdng case, snce h and h curves are located above h and h curves unless the populaton dstrbuton s extremely uneven. n other words, the economy may produce two publc goods n ash equlbrum even though havng one publc good s optmal. ext, we examne whether the total quantty of publc good n the economy as a whole s larger n optmum than n equlbrum. The comparson was made for all possble combnatons of cases. After the drect comparson usng the explct solutons, () n ash equlbrum and (A)(A5)(A8) n optmal, we obtan + + where s the socally optmal quantty of publc good n jursdcton, and the good provded by jursdcton n ash equlbrum. the quantty of The above relaton mples that the total quantty of publc good n optmum s not smaller than that n ash equlbrum. Equalty holds only for the combnaton of case n equlbrum and case n optmum, although quantty n each jursdcton s dfferent. ote that the total quantty under case n equlbrum s smaller than that under case or n optmum; the sum of two publc good s smaller than one. Ths occurs n the range below h h curves(or lne A A A ) and above h h curves(or lne 3 B B B3) n gure 4. urthermore, n ths case, total expendture n ash equlbrum s larger than that n optmum ; ash equlbrum may cause excessve expendture for smaller publc good provson, snce fxed cost s double n case.
13 h A h B h o h o h B A A 3 B 3 n n ash equlbrum ptmum URE 4 Case boundares n equlbrum and optmum 5. scal polces toward effcent allocaton 5. rst best polcy n the last secton, t s shown that ash equlbrum of decentralzed decson makng cannot attan the socal optmal allocaton. ne polcy response s that the central government tself provdes the publc good by collectng tax from resdents. t s true that by choosng the tax optmally ths scheme attans the frst best allocaton. To verfy ths, we demonstrate below the problem and soluton for central provson of local publc good. Supposng case, the problem to be solved by the central government s formulated as Max T, T, nu Y T n u Y T, +, h (6) n KJ n KJ subject to T + T C( ) = (7) where T( =, ) s the total amount of tax leved n regon. As shown n (7), tax revenue s used to fnance the expendture for publc good provson. By manpulatng the frst order
14 condtons for the above problem, the dentcal expressons wth (8a)(8b) are easly derved. or log-lnear utlty, optmal tax n case s obtaned as T = ( p ) Y py + pc( ) j = ( p ) Y p ( Y ),, j =, ; j where p = n /. j (8) We can solve the problems n other cases by repeatng the same procedure. 5. Decentralzed decson makng wth tax-subsdy: a second best polcy f the central government tself provdes local publc good as supposed n the prevous secton, local governments may lose ther rason d'etre $. Advocatng the centralzaton s not our ntenton. n ths secton, we wll present an alternatve scheme n that central government collects tax and subsdze the regon provdng the publc good; on the sde of local government, t chooses the level of publc good gven the subsdy. Local governments are authorzed to provde publc goods accordng to ther own nterests; maxmzng the utlty of ther resdents. The central government optmally chooses the tax-subsdy, takng account of the above stated behavor of local governments. As we wll see later, ths scheme cannot attan the frst best allocaton. Thus we term ths the second best polcy. Suppose that case s chosen. The problem s formulated as Max n u Y T + ( ), +, h T, T, S n KJ n KJ (9) subject to T+ T S = (3) u Y T S C + ( ) = arg max, (3) n where S s the amount of subsdy gven to regon where publc good s provded. Consderng (3), the above problem s equvalent to the problem to determne the optmal transfer between regons and. or the log-lnear utlty functon, (3) s solved as = ( Y+ T ) (3) a Subsequently, we have KJ 3
15 x x = ( n Y T + ) (33) = ( n Y T ) (34) By usng the above relatons, the problem (9)-(3) s reduced to Max n T L M L M R S U V n Y T log ( + ) ( ) log ( Y T ) T W + + a R S U V RST RST + T W + n + n Y T h log ( ) ( ) log ( Y T ) a (35) Solutons to the above problem s n T Y n Y = K J ( ) (36) whch s dentcal to the frst best soluton obtaned by (8). Substtutng (36) nto (3)-(34), we obtan the quantty of publc good and consumpton under the second best polcy, as follows x n = a = K J + n n + KJ ( Y Y ) (37a) ( Y Y ) (37b) x Y Y = ( + ) (37c) t s seen that (37a)-(37c) do not concde wth the frst best solutons (A)(A). n other words, transfer gven by (36) cannot acheve the frst best soluton; resource allocaton s dstorted by decson makng of local government concernng the quantty of publc good. By comparng the second best solutons (37a)-(37c) wth the frst best soluton (A)(A) and ash soluton (), we obtan the followng relatons < < (38a) x < x < x (38b) x = x < x (38c) Under the second best polcy, publc good n regon s larger than that n ash equlbrum but stll undersuppled compared wth the frst best soluton. n case we have dfferent concluson; snce no spll-over effect exsts n ths case, the frst best polcy s chosen by local governments who consder the welfare of ther resdent only. Case 4 UVWQ P UVWQ P
16 s symmetry of case. Choosng the optmal case s the job of the central government; t performs that job by choosng the regon to be subsdzed. The procedure to fnd out the optmal case s same as n the prevous secton; dervng the case boundary functons and the condtons under whch each case s emerged. ootnotes. n case, by usng (A)(A), t s seen that Y n x > and Y n x C( ) < The above relatons mply that the resource s transferred from regon to. Thus we can say that resdents n regon bear the porton of cost for publc good n regon. Smlar argument apples to case.. Expendture for publc good provson n case of ash equlbrum s calculated by usng the soluton () as a + ( + ) = ( )( Y + Y ) + n the other hand, n case of optmal soluton, by usng (A), we have + a = ( )( Y + Y ) + t s obvous that the expendture n the former case s larger than that n the latter case. Appendx: Socally optmal solutons By usng the log-lnear utlty functon, we obtaned the soluton to the optmzaton problems and the optmal value functons of three cases as follows. Case : 5
17 x = x = ( Y + Y ) (A) = ( Y + Y ) (A) a W = log( Y+ Y ) + log + ( ) log + ( ) n log h (A3) a Case : x x Y Y = = ( + ) (A4) ( ) n = ( Y+ Y ), =, (A5) a n W Y Y n a n n = log( + ) + log + ( ) log + ( ){ log + log } (A6) Case : x = x = ( Y + Y ) (A7) = ( Y + Y ) (A8) a W = log( Y+ Y ) + log + ( ) log + ( ) n log h (A9) a References ordon, R. H., 983, An optmal taxaton approach to fscal federalsm, Quarterly Journal of Economcs 98, Kuroda, T., 989, Locaton of publc facltes wth spllover effects: Varable locaton and parametrc scale, Journal of Regonal Scence 9, Pauly, M. V., 97, ptmalty, publc goods, and local governments: A general theoretcal analyss, Journal of Poltcal Economy 78, Tsukahara, K., 995, ndependent and jont provson of optonal publc servces, Regonal Scence and Urban Economcs 5, Wellsch, D., 993, n the decentralzed provson of publc goods wth spll overs n the presence of household moblty, Regonal Scence and Urban Economcs 3,
18 Wllams, A., 966, ptmal provson of publc goods n a system of local government, Journal of Poltcal Economy 74,
Welfare 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 informationEndogenous timing in a mixed oligopoly consisting of a single public firm and foreign competitors. Abstract
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
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 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 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 informationOnline 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 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 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 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 informationAssortment Optimization under MNL
Assortment Optmzaton under MNL Haotan Song Aprl 30, 2017 1 Introducton The assortment optmzaton problem ams to fnd the revenue-maxmzng assortment of products to offer when the prces of products are fxed.
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 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 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 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 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 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 informationDifference Equations
Dfference Equatons c Jan Vrbk 1 Bascs Suppose a sequence of numbers, say a 0,a 1,a,a 3,... s defned by a certan general relatonshp between, say, three consecutve values of the sequence, e.g. a + +3a +1
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 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 informationSupporting Materials for: Two Monetary Models with Alternating Markets
Supportng Materals for: Two Monetary Models wth Alternatng Markets Gabrele Camera Chapman Unversty Unversty of Basel YL Chen Federal Reserve Bank of St. Lous 1 Optmal choces n the CIA model On date t,
More informationSupporting Information for: Two Monetary Models with Alternating Markets
Supportng Informaton for: Two Monetary Models wth Alternatng Markets Gabrele Camera Chapman Unversty & Unversty of Basel YL Chen St. Lous Fed November 2015 1 Optmal choces n the CIA model On date t, gven
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 informationSolutions to exam in SF1811 Optimization, Jan 14, 2015
Solutons to exam n SF8 Optmzaton, Jan 4, 25 3 3 O------O -4 \ / \ / The network: \/ where all lnks go from left to rght. /\ / \ / \ 6 O------O -5 2 4.(a) Let x = ( x 3, x 4, x 23, x 24 ) T, where the varable
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 informationThe Multiple Classical Linear Regression Model (CLRM): Specification and Assumptions. 1. Introduction
ECONOMICS 5* -- NOTE (Summary) ECON 5* -- NOTE The Multple Classcal Lnear Regresson Model (CLRM): Specfcaton and Assumptons. Introducton CLRM stands for the Classcal Lnear Regresson Model. The CLRM s also
More informationAdditional Codes using Finite Difference Method. 1 HJB Equation for Consumption-Saving Problem Without Uncertainty
Addtonal Codes usng Fnte Dfference Method Benamn Moll 1 HJB Equaton for Consumpton-Savng Problem Wthout Uncertanty Before consderng the case wth stochastc ncome n http://www.prnceton.edu/~moll/ HACTproect/HACT_Numercal_Appendx.pdf,
More informationManaging Capacity Through Reward Programs. on-line companion page. Byung-Do Kim Seoul National University College of Business Administration
Managng Caacty Through eward Programs on-lne comanon age Byung-Do Km Seoul Natonal Unversty College of Busness Admnstraton Mengze Sh Unversty of Toronto otman School of Management Toronto ON M5S E6 Canada
More informationIndeterminate pin-jointed frames (trusses)
Indetermnate pn-jonted frames (trusses) Calculaton of member forces usng force method I. Statcal determnacy. The degree of freedom of any truss can be derved as: w= k d a =, where k s the number of all
More informationEconomics 2450A: Public Economics Section 10: Education Policies and Simpler Theory of Capital Taxation
Economcs 2450A: Publc Economcs Secton 10: Educaton Polces and Smpler Theory of Captal Taxaton Matteo Parads November 14, 2016 In ths secton we study educaton polces n a smplfed verson of framework analyzed
More information2E Pattern Recognition Solutions to Introduction to Pattern Recognition, Chapter 2: Bayesian pattern classification
E395 - Pattern Recognton Solutons to Introducton to Pattern Recognton, Chapter : Bayesan pattern classfcaton Preface Ths document s a soluton manual for selected exercses from Introducton to Pattern Recognton
More informationGames of Threats. Elon Kohlberg Abraham Neyman. Working Paper
Games of Threats Elon Kohlberg Abraham Neyman Workng Paper 18-023 Games of Threats Elon Kohlberg Harvard Busness School Abraham Neyman The Hebrew Unversty of Jerusalem Workng Paper 18-023 Copyrght 2017
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 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 informationA NOTE ON CES FUNCTIONS Drago Bergholt, BI Norwegian Business School 2011
A NOTE ON CES FUNCTIONS Drago Bergholt, BI Norwegan Busness School 2011 Functons featurng constant elastcty of substtuton CES are wdely used n appled economcs and fnance. In ths note, I do two thngs. Frst,
More informationPHYS 705: Classical Mechanics. Calculus of Variations II
1 PHYS 705: Classcal Mechancs Calculus of Varatons II 2 Calculus of Varatons: Generalzaton (no constrant yet) Suppose now that F depends on several dependent varables : We need to fnd such that has a statonary
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 informationLecture Notes on Linear Regression
Lecture Notes on Lnear Regresson Feng L fl@sdueducn Shandong Unversty, Chna Lnear Regresson Problem In regresson problem, we am at predct a contnuous target value gven an nput feature vector We assume
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 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 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 informationThe equation of motion of a dynamical system is given by a set of differential equations. That is (1)
Dynamcal Systems Many engneerng and natural systems are dynamcal systems. For example a pendulum s a dynamcal system. State l The state of the dynamcal system specfes t condtons. For a pendulum n the absence
More informationKernel Methods and SVMs Extension
Kernel Methods and SVMs Extenson The purpose of ths document s to revew materal covered n Machne Learnng 1 Supervsed Learnng regardng support vector machnes (SVMs). Ths document also provdes a general
More informationStatistical Hypothesis Testing for Returns to Scale Using Data Envelopment Analysis
Statstcal Hypothess Testng for Returns to Scale Usng Data nvelopment nalyss M. ukushge a and I. Myara b a Graduate School of conomcs, Osaka Unversty, Osaka 560-0043, apan (mfuku@econ.osaka-u.ac.p) b Graduate
More informationPsychology 282 Lecture #24 Outline Regression Diagnostics: Outliers
Psychology 282 Lecture #24 Outlne Regresson Dagnostcs: Outlers In an earler lecture we studed the statstcal assumptons underlyng the regresson model, ncludng the followng ponts: Formal statement of assumptons.
More informationLinear Regression Analysis: Terminology and Notation
ECON 35* -- Secton : Basc Concepts of Regresson Analyss (Page ) Lnear Regresson Analyss: Termnology and Notaton Consder the generc verson of the smple (two-varable) lnear regresson model. It s represented
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 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 informationThe Order Relation and Trace Inequalities for. Hermitian Operators
Internatonal Mathematcal Forum, Vol 3, 08, no, 507-57 HIKARI Ltd, wwwm-hkarcom https://doorg/0988/mf088055 The Order Relaton and Trace Inequaltes for Hermtan Operators Y Huang School of Informaton Scence
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 informationx i1 =1 for all i (the constant ).
Chapter 5 The Multple Regresson Model Consder an economc model where the dependent varable s a functon of K explanatory varables. The economc model has the form: y = f ( x,x,..., ) xk Approxmate ths by
More informationSection 8.3 Polar Form of Complex Numbers
80 Chapter 8 Secton 8 Polar Form of Complex Numbers From prevous classes, you may have encountered magnary numbers the square roots of negatve numbers and, more generally, complex numbers whch are the
More informationChapter Newton s Method
Chapter 9. Newton s Method After readng ths chapter, you should be able to:. Understand how Newton s method s dfferent from the Golden Secton Search method. Understand how Newton s method works 3. Solve
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 informationSIMPLE LINEAR REGRESSION
Smple Lnear Regresson and Correlaton Introducton Prevousl, our attenton has been focused on one varable whch we desgnated b x. Frequentl, t s desrable to learn somethng about the relatonshp between two
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 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 informationLECTURE 9 CANONICAL CORRELATION ANALYSIS
LECURE 9 CANONICAL CORRELAION ANALYSIS Introducton he concept of canoncal correlaton arses when we want to quantfy the assocatons between two sets of varables. For example, suppose that the frst set of
More informationModule 9. Lecture 6. Duality in Assignment Problems
Module 9 1 Lecture 6 Dualty n Assgnment Problems In ths lecture we attempt to answer few other mportant questons posed n earler lecture for (AP) and see how some of them can be explaned through the concept
More informationUnit 5: Government policy in competitive markets I E ciency
Unt 5: Government polcy n compettve markets I E cency Prof. Antono Rangel January 2, 2016 1 Pareto optmal allocatons 1.1 Prelmnares Bg pcture Consumers: 1,...,C,eachw/U,W Frms: 1,...,F,eachw/C ( ) Consumers
More informationAppendix for Causal Interaction in Factorial Experiments: Application to Conjoint Analysis
A Appendx for Causal Interacton n Factoral Experments: Applcaton to Conjont Analyss Mathematcal Appendx: Proofs of Theorems A. Lemmas Below, we descrbe all the lemmas, whch are used to prove the man theorems
More informationIntroduction to Vapor/Liquid Equilibrium, part 2. Raoult s Law:
CE304, Sprng 2004 Lecture 4 Introducton to Vapor/Lqud Equlbrum, part 2 Raoult s Law: The smplest model that allows us do VLE calculatons s obtaned when we assume that the vapor phase s an deal gas, and
More informationThe Geometry of Logit and Probit
The Geometry of Logt and Probt Ths short note s meant as a supplement to Chapters and 3 of Spatal Models of Parlamentary Votng and the notaton and reference to fgures n the text below s to those two chapters.
More informationThe Minimum Universal Cost Flow in an Infeasible Flow Network
Journal of Scences, Islamc Republc of Iran 17(2): 175-180 (2006) Unversty of Tehran, ISSN 1016-1104 http://jscencesutacr The Mnmum Unversal Cost Flow n an Infeasble Flow Network H Saleh Fathabad * M Bagheran
More informationLinear Approximation with Regularization and Moving Least Squares
Lnear Approxmaton wth Regularzaton and Movng Least Squares Igor Grešovn May 007 Revson 4.6 (Revson : March 004). 5 4 3 0.5 3 3.5 4 Contents: Lnear Fttng...4. Weghted Least Squares n Functon Approxmaton...
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 informationCOMPARISON OF SOME RELIABILITY CHARACTERISTICS BETWEEN REDUNDANT SYSTEMS REQUIRING SUPPORTING UNITS FOR THEIR OPERATIONS
Avalable onlne at http://sck.org J. Math. Comput. Sc. 3 (3), No., 6-3 ISSN: 97-537 COMPARISON OF SOME RELIABILITY CHARACTERISTICS BETWEEN REDUNDANT SYSTEMS REQUIRING SUPPORTING UNITS FOR THEIR OPERATIONS
More informationCS294 Topics in Algorithmic Game Theory October 11, Lecture 7
CS294 Topcs n Algorthmc Game Theory October 11, 2011 Lecture 7 Lecturer: Chrstos Papadmtrou Scrbe: Wald Krchene, Vjay Kamble 1 Exchange economy We consder an exchange market wth m agents and n goods. Agent
More informationCredit Card Pricing and Impact of Adverse Selection
Credt Card Prcng and Impact of Adverse Selecton Bo Huang and Lyn C. Thomas Unversty of Southampton Contents Background Aucton model of credt card solctaton - Errors n probablty of beng Good - Errors n
More informationNumerical Heat and Mass Transfer
Master degree n Mechancal Engneerng Numercal Heat and Mass Transfer 06-Fnte-Dfference Method (One-dmensonal, steady state heat conducton) Fausto Arpno f.arpno@uncas.t Introducton Why we use models and
More informationHidden Markov Models
Hdden Markov Models Namrata Vaswan, Iowa State Unversty Aprl 24, 204 Hdden Markov Model Defntons and Examples Defntons:. A hdden Markov model (HMM) refers to a set of hdden states X 0, X,..., X t,...,
More informationLaboratory 1c: Method of Least Squares
Lab 1c, Least Squares Laboratory 1c: Method of Least Squares Introducton Consder the graph of expermental data n Fgure 1. In ths experment x s the ndependent varable and y the dependent varable. Clearly
More informationModule 3 LOSSY IMAGE COMPRESSION SYSTEMS. Version 2 ECE IIT, Kharagpur
Module 3 LOSSY IMAGE COMPRESSION SYSTEMS Verson ECE IIT, Kharagpur Lesson 6 Theory of Quantzaton Verson ECE IIT, Kharagpur Instructonal Objectves At the end of ths lesson, the students should be able to:
More informationACTM State Calculus Competition Saturday April 30, 2011
ACTM State Calculus Competton Saturday Aprl 30, 2011 ACTM State Calculus Competton Sprng 2011 Page 1 Instructons: For questons 1 through 25, mark the best answer choce on the answer sheet provde Afterward
More informationNegative Binomial Regression
STATGRAPHICS Rev. 9/16/2013 Negatve Bnomal Regresson Summary... 1 Data Input... 3 Statstcal Model... 3 Analyss Summary... 4 Analyss Optons... 7 Plot of Ftted Model... 8 Observed Versus Predcted... 10 Predctons...
More informationChapter 9: Statistical Inference and the Relationship between Two Variables
Chapter 9: Statstcal Inference and the Relatonshp between Two Varables Key Words The Regresson Model The Sample Regresson Equaton The Pearson Correlaton Coeffcent Learnng Outcomes After studyng ths chapter,
More informationSimultaneous Optimization of Berth Allocation, Quay Crane Assignment and Quay Crane Scheduling Problems in Container Terminals
Smultaneous Optmzaton of Berth Allocaton, Quay Crane Assgnment and Quay Crane Schedulng Problems n Contaner Termnals Necat Aras, Yavuz Türkoğulları, Z. Caner Taşkın, Kuban Altınel Abstract In ths work,
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 informationSolutions HW #2. minimize. Ax = b. Give the dual problem, and make the implicit equality constraints explicit. Solution.
Solutons HW #2 Dual of general LP. Fnd the dual functon of the LP mnmze subject to c T x Gx h Ax = b. Gve the dual problem, and make the mplct equalty constrants explct. Soluton. 1. The Lagrangan s L(x,
More informationLecture 4. Instructor: Haipeng Luo
Lecture 4 Instructor: Hapeng Luo In the followng lectures, we focus on the expert problem and study more adaptve algorthms. Although Hedge s proven to be worst-case optmal, one may wonder how well t would
More informationSome modelling aspects for the Matlab implementation of MMA
Some modellng aspects for the Matlab mplementaton of MMA Krster Svanberg krlle@math.kth.se Optmzaton and Systems Theory Department of Mathematcs KTH, SE 10044 Stockholm September 2004 1. Consdered optmzaton
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 informationProblem Set 9 Solutions
Desgn and Analyss of Algorthms May 4, 2015 Massachusetts Insttute of Technology 6.046J/18.410J Profs. Erk Demane, Srn Devadas, and Nancy Lynch Problem Set 9 Solutons Problem Set 9 Solutons Ths problem
More informationStatistics for Economics & Business
Statstcs for Economcs & Busness Smple Lnear Regresson Learnng Objectves In ths chapter, you learn: How to use regresson analyss to predct the value of a dependent varable based on an ndependent varable
More informationLecture 10 Support Vector Machines II
Lecture 10 Support Vector Machnes II 22 February 2016 Taylor B. Arnold Yale Statstcs STAT 365/665 1/28 Notes: Problem 3 s posted and due ths upcomng Frday There was an early bug n the fake-test data; fxed
More informationLaboratory 3: Method of Least Squares
Laboratory 3: Method of Least Squares Introducton Consder the graph of expermental data n Fgure 1. In ths experment x s the ndependent varable and y the dependent varable. Clearly they are correlated wth
More informationCOMPLEX NUMBERS AND QUADRATIC EQUATIONS
COMPLEX NUMBERS AND QUADRATIC EQUATIONS INTRODUCTION We know that x 0 for all x R e the square of a real number (whether postve, negatve or ero) s non-negatve Hence the equatons x, x, x + 7 0 etc are not
More informationLecture 10 Support Vector Machines. Oct
Lecture 10 Support Vector Machnes Oct - 20-2008 Lnear Separators Whch of the lnear separators s optmal? Concept of Margn Recall that n Perceptron, we learned that the convergence rate of the Perceptron
More informationCanonical transformations
Canoncal transformatons November 23, 2014 Recall that we have defned a symplectc transformaton to be any lnear transformaton M A B leavng the symplectc form nvarant, Ω AB M A CM B DΩ CD Coordnate transformatons,
More informationELASTIC WAVE PROPAGATION IN A CONTINUOUS MEDIUM
ELASTIC WAVE PROPAGATION IN A CONTINUOUS MEDIUM An elastc wave s a deformaton of the body that travels throughout the body n all drectons. We can examne the deformaton over a perod of tme by fxng our look
More informationMaximizing Overlap of Large Primary Sampling Units in Repeated Sampling: A comparison of Ernst s Method with Ohlsson s Method
Maxmzng Overlap of Large Prmary Samplng Unts n Repeated Samplng: A comparson of Ernst s Method wth Ohlsson s Method Red Rottach and Padrac Murphy 1 U.S. Census Bureau 4600 Slver Hll Road, Washngton DC
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 informationUncertainty in measurements of power and energy on power networks
Uncertanty n measurements of power and energy on power networks E. Manov, N. Kolev Department of Measurement and Instrumentaton, Techncal Unversty Sofa, bul. Klment Ohrdsk No8, bl., 000 Sofa, Bulgara Tel./fax:
More informationChapter 6. Supplemental Text Material
Chapter 6. Supplemental Text Materal S6-. actor Effect Estmates are Least Squares Estmates We have gven heurstc or ntutve explanatons of how the estmates of the factor effects are obtaned n the textboo.
More informationLecture 5 Decoding Binary BCH Codes
Lecture 5 Decodng Bnary BCH Codes In ths class, we wll ntroduce dfferent methods for decodng BCH codes 51 Decodng the [15, 7, 5] 2 -BCH Code Consder the [15, 7, 5] 2 -code C we ntroduced n the last lecture
More informationLecture 7: Boltzmann distribution & Thermodynamics of mixing
Prof. Tbbtt Lecture 7 etworks & Gels Lecture 7: Boltzmann dstrbuton & Thermodynamcs of mxng 1 Suggested readng Prof. Mark W. Tbbtt ETH Zürch 13 März 018 Molecular Drvng Forces Dll and Bromberg: Chapters
More informationCIS526: Machine Learning Lecture 3 (Sept 16, 2003) Linear Regression. Preparation help: Xiaoying Huang. x 1 θ 1 output... θ M x M
CIS56: achne Learnng Lecture 3 (Sept 6, 003) Preparaton help: Xaoyng Huang Lnear Regresson Lnear regresson can be represented by a functonal form: f(; θ) = θ 0 0 +θ + + θ = θ = 0 ote: 0 s a dummy attrbute
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 informationChapter 13: Multiple Regression
Chapter 13: Multple Regresson 13.1 Developng the multple-regresson Model The general model can be descrbed as: It smplfes for two ndependent varables: The sample ft parameter b 0, b 1, and b are used to
More informationIII. Econometric Methodology Regression Analysis
Page Econ07 Appled Econometrcs Topc : An Overvew of Regresson Analyss (Studenmund, Chapter ) I. The Nature and Scope of Econometrcs. Lot s of defntons of econometrcs. Nobel Prze Commttee Paul Samuelson,
More informationWeek3, Chapter 4. Position and Displacement. Motion in Two Dimensions. Instantaneous Velocity. Average Velocity
Week3, Chapter 4 Moton n Two Dmensons Lecture Quz A partcle confned to moton along the x axs moves wth constant acceleraton from x =.0 m to x = 8.0 m durng a 1-s tme nterval. The velocty of the partcle
More information