Optimal Redistributive Taxation with both Labor Supply and Labor Demand Responses
|
|
- Ruth Price
- 7 years ago
- Views:
Transcription
1 Optiml Redistributive Txtion with both Lbor Supply nd Lbor Demnd Responses Lurence JACQUET NHH Preliminry version Etienne LEHMANN y CREST Bruno VAN DER LINDEN z IRES - UCLouvin nd FNRS Mrch 28, 2011 Abstrct This pper chrcterizes the optiml redistributive tx schedule in mtching unemployment frmework with endogenous (voluntry) nonprticiption nd (involuntry) unemployment. The optiml employment tx rte is given by n inverse employment elsticity rule. This rule depends on the globl response of the employment rte, which depends not only on the prticiption (lbor supply) responses, but lso on the vcncy posting (lbor demnd) responses nd on the product of these two types of responses. For plusible prmeters, our mtching environment induces much lower employment tx rtes thn the usul competitive prticiption model. JEL Clssi ction: D82; H21; J64. Keywords: Optiml txtion, Lbor mrket frictions, Unemployment. I Introduction This pper nlyzes the optiml income tx schedule with endogenous voluntry nonprticiption nd involuntry unemployment. Individuls decide whether to prticipte or not to the lbor force (the extensive mrgin). Becuse of mtching frictions à l Mortensen nd Pissrides (1999), prticipting individul my be involuntry unemployed. The probbility for prticipnt to be recruited is endogenous nd depends on the number of vcncies rms nd pro tble to crete (the lbor demnd mrgin). Individuls di er both in their skills nd their costs of serching job. The skill heterogeneity implies Lurence Jcquet is lso reserch ssocite t IRES nd t BETA nd reserch network fellow t CESifo. Lurence.Jcquet@nhh.no y Etienne Lehmnn is lso reserch ssocite t IRES nd reserch network fellow t IZA, IDEP nd CESifo. etienne.lehmnn@ense.fr z Bruno Vn der Linden is lso reserch ssocite t ERMES- University Pris 2 nd reserch fellow t IZA. bruno.vnderlinden@uclouvin.be. 1
2 tht employed workers ern distinct wges. Costs of serching di er cross individuls of the sme skill level, which ccounts for the extensive mrgin s in Dimond (1980), Sez (2002) or Choné nd Lroque (2005, 2011). The government observes only ernings, so the redistribution is constrined to be second-best. This pper is interested in the employment tx, de ned s the tx the worker pys plus the unemployment bene t. 1 A higher level of employment tx reduces the returns to prticiption, thereby inducing some individuls to give up serch. In the stndrd cse with only the extensive mrgin, the optiml employment tx is inversely relted to the elsticity of the lbor supply, s in the extensive response model of Sez (2002). A lrger elsticity reduces the mgnitude of the optiml employment tx. When the lbor demnd is introduced, the optiml employment tx is inversely relted to the globl elsticity of employment. The ltter is the sum of three terms: the lbor supply elsticity, the lbor demnd elsticity with respect to the rm surplus nd the product of these two terms. 2 Intuitively, rise in the employment tx reduces the net (fter-tx) wge nd increses the gross (pre-tx) wge. In competitive setting, wges re exible nd equlize the lbor demnd nd supply. Hence, the gross wge response rises only when the lbor supply is elstic. In contrst, our model fetures unemployment nd wges re negotited below the productivity of the job. We mke the simplifying ssumption tht the workers nd their employers receive xed frction of the totl surplus. An increse in the employment tx reduces the totl surplus, thereby both the worker s nd the rm s surplus. Therefore, rise in the employment tx increses the gross wge, even in the bsence of prticiption responses. Firms thus nd less pro tble to crete vcncies nd the number of txpyers decreses through this lbor demnd response. Hence, the lrger the elsticity of the lbor demnd to the surplus of the rm, the lower is the optiml employment tx. The optiml employment tx is lso inversely relted to the product of the lbor demnd nd supply elsticities. The intuition behind this intercting term is the following. When tx increse reduces the rm s incentives to hire workers, the probbility for job seekers to nd job is reduced which reduces the return of prticiption. Therefore, the lrger the product of the lbor demnd nd lbor supply elsticities, the lower the employment tx. We numericlly investigte how introducing the lbor demnd responses ects the 1 In the literture, the employment tx is trditionlly clled prticiption tx in the bsence of (involuntry) unemployment. 2 In n ppendix vilble upon request, we show tht in the full informtion cse, the optiml employment tx is inversely relted to the lbor demnd elsticity only. Intuitively, in such cse, the government cn use the conditioning of txtion on the cost of serching to enforce individuls prticiption decisions without ny distortion of the lbor supply. The lbor supply elsticity does then not pper in the optiml tx formul. 2
3 optiml employment tx rtes nd show tht our mtching environment induces much lower employment tx rtes thn the usul competitive extensive response model. Severl ppers study the optiml income tx model under serch frictions on the lbor mrket. The optiml tx in Boone nd Bovenberg (2002) nd in Bodwy, Cu nd Mrceu (2003) cts s Pigouvin tx to correct the ine ciency tht rises from the serch-congestion externlities. Hungerbühler, Lehmnn, Prmentier nd Vn der Linden (2006) nd Lehmnn, Prmentier nd Vn der Linden (2011) consider insted n environment where these externlities re perfectly internlized by the wge setting process in the no-tx economy. The role of txtion is therefore to redistribute income nd not to restore e ciency. Hungerbühler nd Lehmnn (2009) consider both the redistributive spects nd congestion externlities. In ll of these ppers except Bodwy, Cu nd Mrceu (2003), rise in the mrginl tx rte increses the shre of the surplus tht the employer receives: higher mrginl tx rte discourges workers to clim for higher wges, thereby reducing the gross wge negotited nd boosting the lbor demnd. In contrst, we neglect this wge-cum-lbor demnd mrgin to stress the role of the lbor demnd responses in the optiml tx formul. This pper is orgnized s follows. Section II presents the model. Section III derives the optiml tx formul nd contrsts it with the cse of competitive lbor mrket nd lbor supply responses long the extensive mrgin. Section IV concludes. II The generl frmework Assume risk-neutrl individuls endowed with distinct skill levels denoted by. exogenous skill distribution is given by the continuous density function f(), de ned on the support [ 0 ; 1 ], with 0 < 0 < 1 1. The size of the popultion is normlized to 1. Jobs re skill-speci c. A worker of skill produces units of output if nd only if she is employed in type- job, 3 otherwise her production is nil. This ssumption of perfect segmenttion is mde for trctbility nd seems more relistic thn the polr one of unique lbor mrket for ll skill levels. At ech skill level, some people choose to sty out of the lbor force while some others do prticipte to the lbor mrket. We integrte this feture by ssuming tht individuls of given skill level di er in their cost of serching job. The distribution of conditionl on skill level is described by the conditionl density H 0 (:j ) over the support R +. The We ssume tht H (:j ) is twice continuously di erentible nd strictly positive for ll 2 R +. The chrcteristics nd my be distributed independently or 3 Allowing n gent to work in ny occuption which requires skill below her type opens the possibility of monotonicity constrints nd pooling tht re studied in Choné nd Lroque (2010). 3
4 my be correlted. Among individuls who prticipte to the lbor mrket, some fil to be recruited nd become unemployed. This involuntry unemployment is due to mtching frictions. The number of mtches between employers nd job seekers on the lbor mrket of skill is function of the stock of vcnt posts, V, nd the stock of job seekers, U, in the mrket (Mortensen nd Pissrides 1999). Therefore, M (V ; U ) denotes the mtching function on the lbor mrket of skill. If there were no frictions, the number of mtches would be determined by the short side of the mrket nd the mtching process would be e cient. But when job seekers nd employers hve to engge in costly nd time-consuming process of serch to nd ech other, the mtching function cptures the technology tht brings them together. The mtching process is ssumed not e cient hence M (V ; U ) < min(v ; U ). The mtching function M (V ; U ) is twice continuously di erentible on R 2 +, incresing nd concve in both rguments, veri es M (0; U ) = M (V ; 0) = 0 since mtches cnnot occur unless there re gents on both sides of the mrket nd exhibits constnt returns to scle. These ssumptions re lrgely empiriclly supported s discussed by Petrongolo nd Pissrides (2001). We ssume tht the government does neither observe individuls types (; ) nor the job-serch nd mtching processes. It only observes worker s gross wge w. Therefore, the tx T (:) : R + 7! R only depends on the gross wge w. Moreover, the government is unble to distinguish mong the non-employed individuls those who serched for job but filed to nd one (the involuntry unemployed) from the non prticipnts (the voluntry unemployed). Therefore, the government is constrined to give the sme level of welfre bene t b 2 R + to ll non-employed gents. The timing of the model is: 1. The government commits to tx system de ned s pir (T (:); b), with T (:) : R + 7! R which only depends on the gross wge w nd the welfre bene t b 2 R + for the non-employed. 2. For ech skill level, rms open vcncies. Creting vcncy of type costs > 0. Ech type -gent decides whether she prticiptes to the lbor mrket of type. 3. Mtching occurs. Once mtched, the rm nd the worker shre the rent hence set the wge. 4. Ech worker of skill produces units of goods, receives wge w = w nd pys txes or receive trnsfers. Txes nnce the ssistnce bene t b nd n exogenous mount of public expenditures R 0. Agents consume. 4
5 II.1 Prticiption decision An individul of type (; ) cn decide to sty out of the lbor force, in which cse her utility equls the welfre bene t b. Otherwise, she prticiptes. Then, she nds job with n endogenous probbility ` nd gets utility level equls to w T (w ) or she becomes unemployed with probbility 1 ` nd gets utility level equls to b. To prticipte, n gent of type (; ) should expect higher expected utility `(w T (w )) + (1 `) b thn in cse of non prticiption, b. Let = T (w ) + b denote the employment tx. We de ne the expected surplus of prticipnt of type s def ` (w T (w ) b) (1) i.e. the dditionl income she gets if she nds job rther thn being unemployed multiplied by the probbility of employment. Any individul of skill chooses to prticipte if her cost of serching job is lower thn the surplus she expects from nding job, i.e.. Let h denote the prticiption rte mong individuls of skill, i.e.: h = H ( j) Pr [ j ] (2) The mss of prticipnts of type equls U = h f(). We now de ne: P def H 0 ( j) H ( j) (3) s the elsticity of the prticiption rte mong individuls of skill with respect to the expected surplus of prticipnt, t =. Note tht P lso equls the elsticity of the prticiption rte mong individuls of skill with respect to di erence in income between employment nd unemployment w, controlling for chnges in the employment probbility `. The empiricl literture on the prticiption decisions is typiclly concerned with the ltter elsticity. II.2 Lbor demnd De ne mrket tightness s the rtio V =U : The probbility tht mtching is successful (i.e. the probbility of lling type- vcncy) equls m ( ) M (V ; U )=V = M (1; 1= ). Due to serch-mtching externlities, the mtching probbility decreses with the number of vcncies (V ) nd increse with the number of job-seekers (U ). Since M (V ; U ) exhibits constnt returns to scle, only tightness mtters nd m ( ) is decresing function of. Symmetriclly, the probbility tht job-seeker nds job is n incresing function of tightness m ( ) M (V ; U )=U = M ( ; 1) with the functions m ( ) nd m ( ) de ned from R + to (0; 1). Firms nd individuls being tomistic, they tke tightness s given. 5
6 When rm cretes vcncy of type, it lls it with probbility m ( ). The cretion of this vcncy costs > 0 to the rm. This cost includes the screening of pplicnts nd investment in equipment for the extr worker. The rm s expected pro t is m( ) ( w ). For given number of job-seekers, rise in the number of vcncies decreses this expected pro t becuse ech vcncy is lled with lower probbility. Firms crete vcncies until the free-entry condition m ( ) ( w ) = is met. This pins down the vlue of tightness s m 1 ( = ( w )). 4 In turn, it lso gives the probbility of nding job (or the lbor demnd) through m ( ) = L ( w ), where the lbor demnd function L (:) is de ned s: L ( w ) def At the equilibrium, one hs ` = L ( w ). m 1 w w (4) The L (:) function is reduced form tht cptures everything we need on the lbor demnd side. From the ssumptions mde on the mtching function, L (:) is twicecontinuously di erentible nd dmits vlues within (0; 1). As the wge w increses, rms get lower surplus ( w ) on ech lled vcncy, fewer vcncies re creted nd tightness decreses. This explins why the employment probbility ` decreses with the wge w. Moreover, due to the constnt-returns-to-scle ssumption, the probbility of being employed depends only on skill nd wge levels nd not on the number of prticipnts. If for given wge, there re twice more prticipnts, the free-entry condition leds to twice more vcncies, so the level of employment is twice higher nd the employment probbility is un ected. This property is in ccordnce with the empiricl evidence tht the size of the lbor force hs no lsting e ect on group-speci c unemployment rtes. Finlly, becuse lbor mrkets re perfectly segmented by skill, the probbility tht prticipnt of type nds job depends only on the wge level w nd not on wges in other segments of the lbor mrket. We then de ne the elsticity of the (type-) lbor demnd to the surplus of the rm w s: D def ( w ) L0 ( w ) L ( w ) = 1 ( ) > 0 (5) ( ) where (4) hs been used nd ( ) denotes the elsticity of the mtching function with respect to the mss of job-seekers U evluted t = m 1 ( = ( w )) (see Appendix A). The empiricl literture on lbor demnd is typiclly concerned with the elsticity of employment with respect to the level of wge. Controlling for prticiption decisions in our model, the ltter elsticity is negtive nd equls D (w = ( w )). 4 where m 1 (:) denotes the reciprocl of function 7! m (), holding constnt. 6
7 II.3 The wge setting: Exogenous shring of the rent Once rm nd worker re mtched, they shre the rent, i.e. the sum of the rm s surplus w nd of the worker s surplus w T (w ) b. In the bsence of n greement, nothing is produced nd the worker gets the welfre bene t b. The brgining process determines how the totl surplus S = T (w ) b is shred between the worker nd the rm. The result of the brgining cn be viewed s the outcome of the mximiztion of n objective (x; y) tht is incresing in the rm s x nd the employer s y surplus. For instnce, the generlized Nsh brgining frmework tkes the form (x; y) = x 1 y. However, di erent shpes cn be considered insted. In this pper, we consider Leontief h i speci ction (x; y) = min x 1 ; y to void n e ect of mrginl tx rtes on wges. This simpli ction enbles us to clerly identify the role of the lbor demnd responses in the optiml tx formul. The equilibrium wge solves: w w = rg mx min w 1 ; w T (w) b When the income tx function T (:) is di erentible with T 0 (:) 1 everywhere, the solution to this progrm is unique nd given by: w = + (1 ) (T (w ) + b) In this cse, it is equivlent 5 for the government to design n income tx function T (:), or to directly design the employment tx = T (w ) + b for ech skill level. Then w = + (1 ) (6) The gross wge w is incresing with the employment tx. An increse of the employment tx will reduce the employee s surplus hence the employee will o set her loss by lrger brgined wge w. Since w = (1 ) ( ) from (6), the employment probbility veri es: ` = L [(1 ) ( )] (7) 5 The government cn decentrlize n lloction chrcterized with di erentible 7! mpping by n income tx function w 7! T (w) when < 1 A given 7! leds to wge level given by (6). This wge is incresing in only when = (1 ) =@. Then, Eqution (6) cn be inverted to express skill s di erentible function = A (w) of the wge, with A 0 (w) = 1= [ + (1 =@]. The income tx function hs then to stisfy T (w) A(w), which implies: T 0 A0 (w) = This tx function veri es T 0 (w) 1 only =@ + 7
8 Combining (1) nd (6), the expected surplus from prticipting equls: nd the skill-speci c prticiption rte equls: = ( ) L [(1 ) ( )] (8) h = H [ ( ) L [(1 ) ( )] j] (9) Finlly, the skill speci c employment rte e equls the product of the prticiption rte h by the probbility ` for ech prticipnt to nd job: e = ` h = L [(1 ) ( )] H [ ( ) L [(1 ) ( )] j] (10) The employment rte responds to tx ccording to de = D + P + D P e d (11) where we used elsticities de ned in (3) nd (5). We henceforth refer to the term in brckets in (11) s the globl elsticity of employment. The product D P enters this formul becuse ny increse in the lbor demnd gives dditionl incentives for individuls to enter the lbor force, so it reinforces the lbor supply. This complementrity between lbor demnd nd lbor supply is key insight of the unemployment mtching theory. II.4 The government We ssume tht the government cres bout the distribution of expected utilities, nmely, ` (w T (w )) + (1 `) b = + b (from (8)) for those who prticipte nd b for nonprticipting individuls. More precisely, the government hs the following Bergson-Smuelson socil welfre function: Z 1 Z ( + b ) dh ( j) + (b) (1 H ( j)) f () d (12) 0 0 where 0 (:) > 0, 00 (:) 0. 6 The stronger the concvity of (:) the more verse to inequlity is the government. Assuming 00 (:) = 0 corresponds to the Benthmite Utilitrin criterion tht sums the individul expected utilities. The government fces the following budget constrint Z 1 0 e f() d b R = 0 (13) tht is written so tht the welfre bene t b is provided to ll gents in the economy but for ech dditionl worker of skill, the government sves the welfre bene t b nd collects 6 (:) is n incresing function of the expected utility nd does not vry with the heterogeneous individuls chrcteristics (; ). Another vlue judgment could give distinct welfre weights to identicl utility levels obtined by individuls with distinct chrcteristics. This is left for future reserch. 8
9 txes T (w ) (the sum of these being ). Tking (2) nd (7) into ccount, this budget constrint cn be rewritten s Z 1 0 L [(1 ) ( )] H ( ( ) L [(1 ) ( )] j) f() d(14) = b + R III The optiml tx policies The optiml tx problem consists in nding the optiml level of bene t b nd of employment tx t ech skill level to mximize the socil objective (12) subject to the budget constrint (14), tking (7) into ccount. This problem is solved in Appendix B. Let be the Lgrnge multiplier of the budget constrint. We interpret s the mrginl socil cost of the public funds R nd we let g denote the mrginl socil welfre weight given to workers of skill, expressed in terms of public funds, i.e. g def R 0 0 ( + b ) H 0 ( j) d h (15) Intuitively, the government is indi erent between giving one more euro to ech of the gent of skill nd giving g euros of public funds. Symmetriclly, we de ne g N def 0 (b) (16) s the mrginl socil welfre weight of non-prticipting individuls expressed in terms of public funds. The optiml tx policy is given in the following proposition, which is proved in the ppendix. Proposition 1 For ny skill level 2 A, the optiml tx schedule stis es: Z 1 g h + g N (1 h ) f () d = 1 (17) 0 = 1 g 1 + D w [ D + P + D P (17b) ] or = 1 g 1 + D 1 g (1 + D ) + [ D + P + D P ] w (18) Eqution (17) sttes tht the mrginl cost of public funds is weighted verge of the socil mrginl utilities of the workers (g ) nd of the unemployed (g N ). Eqution (17b) leds to (18). Our generl model encompsses two speci c cses. First, one cn retrieve the pure extensive mrgin model when the mtching function veri es M (V; U) = U nd = 1. 9
10 When M (V; U) = U, ny job-seeker becomes employed, s in Dimond (1980), Sez (2002) nd Choné nd Lroque (2005, 2011). If in ddition the workers hve ll the brgining power (i.e. = 1), eqution (6) leds to the equlity between the skill level nd the gross wge w. Under these two ssumptions, to which we henceforth refer to s the pure extensive response model, Eqution (17b) becomes identicl to the one obtined by Sez (2002) in the bsence of intensive response, i.e. w = 1 g P (19) Second, our model lso encompsses the polr pure lbor response model with xed prticiption decisions P = 0. Equtions (17)-(17b) then become: Z 1 g ` f () d = 1 (20) 0 = 1 g 1 + D w D (20b) To derive Eqution (17b), we consider in the spirit of Sez (2002) perturbtion of the optiml tx function tht consists in smll increse 7 dt (w ) > 0 in the tx libility t wge w. For constnt level of bene t b, this increse induces rise d = dt (w ) in the employment tx pid by workers of skill level, which implies mechnicl e ect, n employment response e ect nd socil welfre e ect tht we now describe. III.1 Mechnicl e ect Absent ny behviorl chnge, the government levies d dditionl txes on ech job of skill. Their mss is e f (). From (13), the mechnicl increse in tx revenue equls: M = e f () d (21) This e ect is identicl in our generl model, in the pure extensive response nd in the pure lbor demnd responses cses. III.2 Employment response e ect The increse in the employment tx d > 0 induces reduction in the employment rte e = ` h tht is given by (11). Using (6), employment chnges by: de = D + P + D P e This reduction integrtes direct chnge in prticiption, direct lbor demnd response nd the e ect of the lbor demnd response on the incentives for individuls to serch 7 The cse where the employment tx is decresed is symmetric s only rst-order e ects re considered. w d 10
11 job. As ech dditionl worker of skill increses the government s revenue by the employment tx, the employment e ect equls E = D + P + D P e f () d (22) w There re two di erences with the pure extensive response cse. First, the globl elsticity of employment D + P + D P is reduced to the sole lbor supply elsticity P in the pure extensive response cse where the lbor demnd elsticity D is nil. Second, in the generl model, the employment response e ect is multiplied by the frction of the surplus tht occurs to the worker. This ltter term would not pper if we hd expressed (22) s function of the the totl surplus of the job insted of the surplus w tht the workers receive. In the pure extensive response cse, the two terms re equls, while in the generl model, the workers surplus w is frction of the totl surplus. In the pure lbor demnd response cse, the globl elsticity of employment D + P + D P is reduced to the sole lbor demnd elsticity D. III.3 Socil welfre e ect We now describe how the reform ects the socil welfre function (12). Given our ssumption tht the government cres bout the distribution of expected utilities, one should determine how the reform modi es the expected surplus de ned in (1). On the one hnd, there is direct e ect on the surplus w extrcted by the worker. From (6), this chnge mounts to d (w ) = d On the other hnd, the lbor demnd response implies reduction in the probbility for job-seeker to nd job. From (5) nd (7), this term equls d` = D 1 ` d Combining these two e ects, the expected surplus is reduced by d = 1 + D ` d This reduction induces some individuls to stop prticipting. However, these pivotl individuls re indi erent between prticipting or not, so the chnge in their prticiption decisions hs no rst-order e ect on the socil objective. Recll tht g is the mrginl socil welfre weight given to workers of skill, expressed in terms of public funds (see (15)), the socil welfre e ect equls: W = g 1 + D e f () d (23) 11
12 In the pure extensive response model where = 1 nd D = 0, the welfre e ect (23) tkes simple form s 1 + D = 1. In the generl model, the workers py only frction of the tx. Moreover rise in txtion lso ects the probbility for jobseeker to nd job through the lbor demnd e ect. Hence, unit rise of the employment tx pid by workers of skill decreses their expected surplus by n mount 1 + D. The equlity 1 + D = 1 only holds in the generl model under speci c restriction, nmely: 1 = D (24) From (5), this restriction leds to the equlity between the worker s shre of the totl surplus nd the elsticity of the mtching function with respect to unemployment, the so-clled Hosios (1990) condition. The ltter gives the right blend of congestion externlities tht re inherent to the mtching process. Intuitively, this equlity indirectly sets up the wges so tht they e ciently coordinte the serch decisions of workers nd rms in the frictionl lbor mrket. There is no prticulr reson why it should be stis ed since it reltes prmeter of the resolution of brgining con ict to prmeter of the technology of mtching, s rgued by Pissrides (2000, p.198). The term tht corresponds to devition from the Hosios condition does not pper in our optiml tx formul for e ciency resons, but for tx incidence ones. As the frction of the surplus tht ech prty received fter the wge brgining re ssumed exogenous, txtion cnnot correct for congestion externlities. III.4 Optiml employment tx rtes A smll chnge in the employment tx must imply no rst-order e ect. Adding (21), (22) nd (23) nd rerrnging terms gives (17b). Rerrnging terms gin led to the optiml employment tx rtes given in (18). The sign of the employment tx rte is given by the di erence between the mechnicl (21) nd the socil welfre e ects (23). Redistribution therefore occurs from workers whose weights g re lower thn 1= 1 + D to workers with weights lrger thn this vlue nd to non prticipnts. R 1 0 In the pure lbor demnd response cse, the weighted verge of socil welfre weights g f () d equls 1 (see (20)). Under concve socil welfre function (:), the socil welfre weights g re decresing in the skill levels under the plusible ssumption tht expected surplus is incresing in the skill level. Therefore, if one lso ssumes tht the Hosios condition (24) holds, the employment tx on the lest skilled workers is negtive, cse tht Sez (2002) de nes s n Erned Income Tx Credit (EITC). In the pure extensive response cse nd in the generl model, the welfre of nonpr- 12
13 ticipnts hs to be tken into ccount. From (15) nd (16), one hs g N > g whenever the socil welfre function (:) is concve. In prticulr, when the socil welfre function is close to Mximin objective, one typiclly obtins g N > 1 > g. Assuming gin tht the Hosios condition holds, n EITC is then ruled out. III.5 Quntittive insights In this section, we numericlly investigte how introducing the lbor demnd responses ects the optiml employment tx rtes. For this purpose, we compute optiml employment tx rtes =w from (18) for di erent clibrted vlues of P, D nd g. P g 0 0:5 D 0 0: : =3 0:5 1 2=3 0: % 75% 66:7% 100% 60% 50% 0:25 80% 63; 2% 57:1% 66:7% 46:2% 40% 0:5 66:7% 54:5% 50% 50% 37:5% 33:3% Tble 1: Optiml employment txes =w under the Hosios condition We consider in Tble 1 cses where the Hosios condition (24) holds. the rst nd fourth columns of Tble 1 give =w in the pure extensive response model (where D = 0) while the rst row provides vlues of =w in the pure lbor demnd model (where P = 0). Incresing the lbor demnd elsticity then implies two e ects on the optiml employment tx rtes. First, the globl elsticity of employment D + P + D P increses, which tends to reduce the mgnitude of the employment tx rtes. Second, the reduction in tht tkes plce to keep the Hosios condition vlid does not chnge the rtio between the optiml employment tx nd the skill level. However, it reduces the rtio of wges w over skill, hence it tends to increse employment tx rte =w. Tble 1 suggests tht the former e ect domintes, whtever the elsticity of prticiption P nd the vlue of the welfre weight g. A lrger lbor demnd elsticity substntilly reduces the optiml employment tx. For instnce, when P = 0:25, =w shrinks by 23 percentge points (from 80% to 57%) under Mximin nd by 33 percentge points (from 67% to 40%) with mrginl socil welfre weight g equls to 0:5. The empiricl literture does not usully distinguish between the distinct components of the globl elsticity of employment with respect to the employment tx. However, depending on the reltive importnce of the lbor demnd nd lbor supply elsticities in explining the globl employment elsticity, the optiml employment tx rtes vry. To illustrte this, we ssume tht the Hosios condition (24) is vlid. Incresing D requires 13
14 g 0 0:5 D 0 0:25 0:5 0 0:25 0:5 1 0:8 2=3 1 0:8 2=3 D + P + D P 0:5 66:7% 71:4% 75% 50% 55:6% 60% 0:7 58:8% 64:1% 68:2% 41:7% 47:2% 51:7% 1 50% 55:6% 60% 33:3% 38:5% 42:9% Tble 2: Optiml employment txes =w under the Hosios condition to reduce to keep the Hosios condition stis ed. Therefore, from (18) with g < 1, we expect tht the employment tx rte will increse with D, the globl elsticity being constnt. This is con rmed in Tble 2. In ech row of Tble 2, the globl employment elsticity D + P + D D P is xed nd equls 0:5, 0:7 nd 1 respectively. Then, incresing from 0 to 0:5 increses the employment tx by bout 9 or 10 percentge points when g = 0. Employment tx rtes re lower when g = 0:5, nd decrese in D similr extent. P g 0:5 1 D 1 1 0:3 0:5 0:7 0:3 0:5 0:7 0 70% 50% 30% 57:1% 0 133:3% 0:25 60:9% 40% 22:2% 47:1% 0 61:5% 0:5 53:8% 33:3% 17:6% 40% 0 40% Tble 3: Otiml employment tx rtes =w when the Hosios condition is violted by Finlly, Tble 3 studies the impct of deviting from the Hosios condition (24), in prticulr when the worker s shre of the totl surplus increses. The elsticity D is ssumed constnt nd equls 1 nd the mrginl socil welfre weight g is equl to 0:5. Intuitively, given increse of the employment tx hs lrger impct on the welfre of the workers when is higher. Therefore, the optiml employment tx decreses with. Tble 3 con rms this intuition nd highlights tht the quntittive impct is substntil. For instnce, when P = 0:25 nd g = 0:5, incresing the worker s shre of the totl surplus from 0:3 to 0:7 divides the employment tx rte by nerly three (from 61% to 22%). The chnges re even lrger when g = 1. Under the Hosios condition, optiml employment tx rtes re nil since the numertor of (18) is equl to zero with these vlues of g, nd D. When P = 0:25, incresing the worker s shre of the totl surplus from 0:3 to 0:7 shifts the optiml employment tx rte from positive 47:1% to negtive 61:5%; n EITC then previls. 14
15 IV Conclusion The optiml tx schedule derived in the optiml tx model with lbor supply long the extensive mrgin is drsticlly modi ed when lbor demnd in frictionl economy is lso modeled. The employment tx is still n inverse elsticity rule however the elsticity term encpsultes not only lbor supply responses (s in the stndrd model) but lso lbor demnd responses nd the crossed e ects between lbor demnd nd lbor supply, both being neglected in the stndrd frmework. For plusible prmeters, mtching unemployment frictions induce much lower employment tx rtes thn the ones found in the usul competitive model. References [1] Bodwy R., Cu K. nd N. Mrceu (2003), Redistribution nd employment policies with endogenous unemployment, Journl of Public Economics, 87, [2] Choné, P. nd G. Lroque (2005), Optiml Incentives for Lbor Force Prticiption, Journl of Public Economics, 89 (2-3), [3] Choné, P. nd G. Lroque (2011), Optiml Txtion in the Extensive Model, Journl of Economic Theory, Forthcoming. [4] Dimond P. (1980), Income Txtion with Fixed Hours of Work, Journl of Public Economics, 13, [5] Dimond P. nd E. Sheshinski (1996), Economic Aspects of Optiml Disbility Bene ts, Journl of Public Economic Theory, 57, [6] Hosios, A. (1990), On the E ciency of Mtching nd Relted Models of Serch nd Unemployment, Review of Economic Studies, 57, [7] Hungerbühler, M., Lehmnn, E. (2009), On the Optimlity of Minimum Wge: New Insights from Optiml Tx Theory, Journl of Public Economics, 93 (3-4), [8] Hungerbühler, M., Lehmnn, E., Prmentier, A. nd B. Vn der Linden (2006), Optiml Redistributive Txtion in Serch Equilibrium Model, Review of Economic Studies, 2006, 73 (3), [9] Lehmnn, E., Prmentier, A. nd B. Vn der Linden (2011), Optiml income txtion with endogenous prticiption nd serch unemployment, CESifo Discussion Pper
16 [10] Meghir, C. nd D. Phillips (2008), Lbour supply nd txes, IZA Discusssion Pper Series, N [11] Mortensen, D. nd Pissrides, C. (1999), New developments in models of serch in the Lbor Mrket, in O. Ashenfelter nd D. Crd (eds.), Hndbook of Lbor Economics, vol 3, B, North-Hollnd, Amsterdm. [12] Petrongolo, B. nd Pissrides, C.A. (2001), Looking into the blck box: survey of the mtching function, Journl of Economic Literture, 39, [13] Pissrides, C. A (2000), Equilibrium Unemployment Theory, 2 nd Edition, Cmbridge: MIT Press. [14] Rubinstein, A. (1982), Perfect Equilibrium in Brgining Model, Econometric, 50(1): [15] Sez, E. (2002), Optiml Income Trnsfer Progrms:Intensive Versus Extensive Lbor Supply Responses, Qurterly Journl of Economics, 117, [16] Sez, E. (2003), The E ect of Mrginl Tx Rtes on Income: A Pnel Study of Brcket Creep, Journl of Public Economics, 87: [17] Thomson, W. (1994), Coopertive Models of Brgining, in Hndbook of Gme Theory, vol.2, R. umnn nd S. Hrt eds. Appendices A Link between the elsticity of the lbor demnd nd the elsticity of the mtching function Let (:) denote the elsticity of the mtching function M (:; :) with respect to the mss of job-seekers U. Becuse the mtching function is incresing in both rguments nd exhibits constnt returns to scle, depends only on the level of tightness nd one must hve () 2 (0; 1) for ll. From the de nition m () = M (1; 1=), the elsticity of the probbility of lling vcncy to the tightness level (i.e. ( =m ) (@m () =@ )) equls (). Hence the elsticity of the reciprocl m 1 (:) equls 1= m 1 (:). The log-di erentition of the L function (4) with respect to the rm s surplus w gives: dl L = ( ) d ( w ) w which leds to the second equlity in (5). The inequlity holds becuse () 2 (0; 1). 16
17 B Proof of Proposition 1 The Lgrngin of the optiml tx problem cn be written s Z 1 0 L ( ; b; ) f () d b R where L ( ; b; ) def Z 1 0 Z ( )L [(1 )( )] 0 ( ( ) L [(1 ) ( )] + b ) dh ( j) + (b) (1 H ( ( ) L [(1 ) ( )] j)) + L [(1 ) ( )] H ( ( ) L [(1 ) ( )] j) The rst-order condition with respect to b is written s ( Z ) ( )L [(1 )( )] 0 ( + b ) dh ( j) + 0 (b) (1 h ) f () d = 0 Using (15) nd (16) gives (17). The rst-order condition with respect to writes ( ; b; ), which gives, using (3) nd (5) Z 0 = 1 + D ` 0 ( + b D 1 + D ) dh ( j) P ` h Dividing both sides by h ` nd using (15) nd w = ( ) from (6) gives (17b). 17
Econ 4721 Money and Banking Problem Set 2 Answer Key
Econ 472 Money nd Bnking Problem Set 2 Answer Key Problem (35 points) Consider n overlpping genertions model in which consumers live for two periods. The number of people born in ech genertion grows in
More informationAll pay auctions with certain and uncertain prizes a comment
CENTER FOR RESEARC IN ECONOMICS AND MANAGEMENT CREAM Publiction No. 1-2015 All py uctions with certin nd uncertin prizes comment Christin Riis All py uctions with certin nd uncertin prizes comment Christin
More informationBasic Analysis of Autarky and Free Trade Models
Bsic Anlysis of Autrky nd Free Trde Models AUTARKY Autrky condition in prticulr commodity mrket refers to sitution in which country does not engge in ny trde in tht commodity with other countries. Consequently
More informationUNIVERSITY OF NOTTINGHAM. Discussion Papers in Economics STRATEGIC SECOND SOURCING IN A VERTICAL STRUCTURE
UNVERSTY OF NOTTNGHAM Discussion Ppers in Economics Discussion Pper No. 04/15 STRATEGC SECOND SOURCNG N A VERTCAL STRUCTURE By Arijit Mukherjee September 004 DP 04/15 SSN 10-438 UNVERSTY OF NOTTNGHAM Discussion
More informationDlNBVRGH + Sickness Absence Monitoring Report. Executive of the Council. Purpose of report
DlNBVRGH + + THE CITY OF EDINBURGH COUNCIL Sickness Absence Monitoring Report Executive of the Council 8fh My 4 I.I...3 Purpose of report This report quntifies the mount of working time lost s result of
More informationEducation and Optimal Dynamic Taxation: The Role of Income-Contingent Student Loans
University of Zurich Deprtment of Economics Center for Institutions, Policy nd Culture in the Development Process Working Pper Series Working Pper No. 421 Eduction nd Optiml Dynmic Txtion: The Role of
More informationWeek 7 - Perfect Competition and Monopoly
Week 7 - Perfect Competition nd Monopoly Our im here is to compre the industry-wide response to chnges in demnd nd costs by monopolized industry nd by perfectly competitive one. We distinguish between
More informationMath 135 Circles and Completing the Square Examples
Mth 135 Circles nd Completing the Squre Exmples A perfect squre is number such tht = b 2 for some rel number b. Some exmples of perfect squres re 4 = 2 2, 16 = 4 2, 169 = 13 2. We wish to hve method for
More informationRedistributing the Gains from Trade through Non-linear. Lump-sum Transfers
Redistributing the Gins from Trde through Non-liner Lump-sum Trnsfers Ysukzu Ichino Fculty of Economics, Konn University April 21, 214 Abstrct I exmine lump-sum trnsfer rules to redistribute the gins from
More informationGraphs on Logarithmic and Semilogarithmic Paper
0CH_PHClter_TMSETE_ 3//00 :3 PM Pge Grphs on Logrithmic nd Semilogrithmic Pper OBJECTIVES When ou hve completed this chpter, ou should be ble to: Mke grphs on logrithmic nd semilogrithmic pper. Grph empiricl
More informationExample 27.1 Draw a Venn diagram to show the relationship between counting numbers, whole numbers, integers, and rational numbers.
2 Rtionl Numbers Integers such s 5 were importnt when solving the eqution x+5 = 0. In similr wy, frctions re importnt for solving equtions like 2x = 1. Wht bout equtions like 2x + 1 = 0? Equtions of this
More informationMATH 150 HOMEWORK 4 SOLUTIONS
MATH 150 HOMEWORK 4 SOLUTIONS Section 1.8 Show tht the product of two of the numbers 65 1000 8 2001 + 3 177, 79 1212 9 2399 + 2 2001, nd 24 4493 5 8192 + 7 1777 is nonnegtive. Is your proof constructive
More informationThis paper considers two independent firms that invest in resources such as capacity or inventory based on
MANAGEMENT SCIENCE Vol. 5, No., December 006, pp. 93 99 issn 005-909 eissn 56-550 06 5 93 informs doi 0.87/mnsc.060.0574 006 INFORMS Strtegic Investments, Trding, nd Pricing Under Forecst Updting Jiri
More informationEducation and Optimal Dynamic Taxation: The Role of Income-Contingent Student Loans
Eduction nd Optiml Dynmic Txtion: The Role of Income-Contingent Student Lons Sebstin Findeisen University of Mnnheim Dominik Schs CGS, University of Cologne First version: October 2, 20 This version: November
More informationTreatment Spring Late Summer Fall 0.10 5.56 3.85 0.61 6.97 3.01 1.91 3.01 2.13 2.99 5.33 2.50 1.06 3.53 6.10 Mean = 1.33 Mean = 4.88 Mean = 3.
The nlysis of vrince (ANOVA) Although the t-test is one of the most commonly used sttisticl hypothesis tests, it hs limittions. The mjor limittion is tht the t-test cn be used to compre the mens of only
More information9 CONTINUOUS DISTRIBUTIONS
9 CONTINUOUS DISTIBUTIONS A rndom vrible whose vlue my fll nywhere in rnge of vlues is continuous rndom vrible nd will be ssocited with some continuous distribution. Continuous distributions re to discrete
More informationUse Geometry Expressions to create a more complex locus of points. Find evidence for equivalence using Geometry Expressions.
Lerning Objectives Loci nd Conics Lesson 3: The Ellipse Level: Preclculus Time required: 120 minutes In this lesson, students will generlize their knowledge of the circle to the ellipse. The prmetric nd
More informationPublic Capital Maintenance and Congestion: Long-Run Growth and Fiscal Policies
Public Cpitl Mintennce nd Congestion: Long-Run Growth nd Fiscl Policies Evngelos Dioikitopoulos nd Srntis Klyvitis y Athens University of Economics nd Business Mrch 2008 z Forthcoming in Journl of Economic
More informationPolynomial Functions. Polynomial functions in one variable can be written in expanded form as ( )
Polynomil Functions Polynomil functions in one vrible cn be written in expnded form s n n 1 n 2 2 f x = x + x + x + + x + x+ n n 1 n 2 2 1 0 Exmples of polynomils in expnded form re nd 3 8 7 4 = 5 4 +
More informationMathematics. Vectors. hsn.uk.net. Higher. Contents. Vectors 128 HSN23100
hsn.uk.net Higher Mthemtics UNIT 3 OUTCOME 1 Vectors Contents Vectors 18 1 Vectors nd Sclrs 18 Components 18 3 Mgnitude 130 4 Equl Vectors 131 5 Addition nd Subtrction of Vectors 13 6 Multipliction by
More informationFirm Objectives. The Theory of the Firm II. Cost Minimization Mathematical Approach. First order conditions. Cost Minimization Graphical Approach
Pro. Jy Bhttchry Spring 200 The Theory o the Firm II st lecture we covered: production unctions Tody: Cost minimiztion Firm s supply under cost minimiztion Short vs. long run cost curves Firm Ojectives
More informationCEO Pay and the Lake Wobegon Effect
CEO Py nd the Lke Wobegon Effect Rchel M. Hyes nd Scott Schefer December 11, 2008 Forthcoming in Journl of Finncil Economics Abstrct The Lke Wobegon Effect, which is widely cited s potentil cuse for rising
More informationLecture 3 Gaussian Probability Distribution
Lecture 3 Gussin Probbility Distribution Introduction l Gussin probbility distribution is perhps the most used distribution in ll of science. u lso clled bell shped curve or norml distribution l Unlike
More informationSPECIAL PRODUCTS AND FACTORIZATION
MODULE - Specil Products nd Fctoriztion 4 SPECIAL PRODUCTS AND FACTORIZATION In n erlier lesson you hve lernt multipliction of lgebric epressions, prticulrly polynomils. In the study of lgebr, we come
More informationVectors 2. 1. Recap of vectors
Vectors 2. Recp of vectors Vectors re directed line segments - they cn be represented in component form or by direction nd mgnitude. We cn use trigonometry nd Pythgors theorem to switch between the forms
More informationParticipation and investment decisions in a retirement plan: the influence of colleagues choices
Journl of Public Economics 85 (2002) 121 148 www.elsevier.com/ locte/ econbse Prticiption nd investment decisions in retirement pln: the influence of collegues choices Esther Duflo,b, *, Emmnuel Sez MIT,
More informationEconomics Letters 65 (1999) 9 15. macroeconomists. a b, Ruth A. Judson, Ann L. Owen. Received 11 December 1998; accepted 12 May 1999
Economics Letters 65 (1999) 9 15 Estimting dynmic pnel dt models: guide for q mcroeconomists b, * Ruth A. Judson, Ann L. Owen Federl Reserve Bord of Governors, 0th & C Sts., N.W. Wshington, D.C. 0551,
More informationDistributions. (corresponding to the cumulative distribution function for the discrete case).
Distributions Recll tht n integrble function f : R [,] such tht R f()d = is clled probbility density function (pdf). The distribution function for the pdf is given by F() = (corresponding to the cumultive
More informationSmall Business Networking
Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd processes. Introducing technology
More informationPROF. BOYAN KOSTADINOV NEW YORK CITY COLLEGE OF TECHNOLOGY, CUNY
MAT 0630 INTERNET RESOURCES, REVIEW OF CONCEPTS AND COMMON MISTAKES PROF. BOYAN KOSTADINOV NEW YORK CITY COLLEGE OF TECHNOLOGY, CUNY Contents 1. ACT Compss Prctice Tests 1 2. Common Mistkes 2 3. Distributive
More informationCollege Admissions with Entrance Exams: Centralized versus Decentralized
Is E. Hflir Rustmdjn Hkimov Dorothe Kübler Morimitsu Kurino College Admissions with Entrnce Exms: Centrlized versus Decentrlized Discussion Pper SP II 2014 208 October 2014 (WZB Berlin Socil Science Center
More informationCOMPARISON OF SOME METHODS TO FIT A MULTIPLICATIVE TARIFF STRUCTURE TO OBSERVED RISK DATA BY B. AJNE. Skandza, Stockholm ABSTRACT
COMPARISON OF SOME METHODS TO FIT A MULTIPLICATIVE TARIFF STRUCTURE TO OBSERVED RISK DATA BY B. AJNE Skndz, Stockholm ABSTRACT Three methods for fitting multiplictive models to observed, cross-clssified
More informationExperiment 6: Friction
Experiment 6: Friction In previous lbs we studied Newton s lws in n idel setting, tht is, one where friction nd ir resistnce were ignored. However, from our everydy experience with motion, we know tht
More informationDoes Trade Increase Employment? A Developing Country Perspective
Does Trde Increse Employment? A Developing Country Perspective By Sugt Mrjit City University of Hong Kong nd Center for Studies in Socil Sciences, Indi Hmid Beldi University of Texs t Sn Antonio 005 Address
More informationEQUATIONS OF LINES AND PLANES
EQUATIONS OF LINES AND PLANES MATH 195, SECTION 59 (VIPUL NAIK) Corresponding mteril in the ook: Section 12.5. Wht students should definitely get: Prmetric eqution of line given in point-direction nd twopoint
More informationSmall Business Networking
Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd business. Introducing technology
More information3 The Utility Maximization Problem
3 The Utility Mxiiztion Proble We hve now discussed how to describe preferences in ters of utility functions nd how to forulte siple budget sets. The rtionl choice ssuption, tht consuers pick the best
More informationCredit Ratings, Collateral, and Loan Characteristics: Implications for Yield*
Kose John New York University Anthony W. Lynch New York University nd Ntionl Bureu of Economic Reserch Mnju Puri Stnford University nd Ntionl Bureu of Economic Reserch Credit Rtings, Collterl, nd Lon Chrcteristics:
More informationLINEAR TRANSFORMATIONS AND THEIR REPRESENTING MATRICES
LINEAR TRANSFORMATIONS AND THEIR REPRESENTING MATRICES DAVID WEBB CONTENTS Liner trnsformtions 2 The representing mtrix of liner trnsformtion 3 3 An ppliction: reflections in the plne 6 4 The lgebr of
More informationSmall Business Networking
Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd business. Introducing technology
More informationpersons withdrawing from addiction is given by summarizing over individuals with different ages and numbers of years of addiction remaining:
COST- BENEFIT ANALYSIS OF NARCOTIC ADDICTION TREATMENT PROGRAMS with Specil Reference to Age Irving Leveson,l New York City Plnning Commission Introduction Efforts to del with consequences of poverty,
More informationCOMPONENTS: COMBINED LOADING
LECTURE COMPONENTS: COMBINED LOADING Third Edition A. J. Clrk School of Engineering Deprtment of Civil nd Environmentl Engineering 24 Chpter 8.4 by Dr. Ibrhim A. Asskkf SPRING 2003 ENES 220 Mechnics of
More informationSmall Businesses Decisions to Offer Health Insurance to Employees
Smll Businesses Decisions to Offer Helth Insurnce to Employees Ctherine McLughlin nd Adm Swinurn, June 2014 Employer-sponsored helth insurnce (ESI) is the dominnt source of coverge for nonelderly dults
More informationThe Development and Structure of Financial Systems
The Development nd Structure of Finncil Systems Shnkh Chkrborty y Tridip Ry z Revised: September 2006 Abstrct Firms rise externl nnce vi monitored bnk lons nd non-monitored borrowing in dynmic generl equilibrium
More informationSmall Business Networking
Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd processes. Introducing technology
More informationLower Bound for Envy-Free and Truthful Makespan Approximation on Related Machines
Lower Bound for Envy-Free nd Truthful Mespn Approximtion on Relted Mchines Lis Fleischer Zhenghui Wng July 14, 211 Abstrct We study problems of scheduling jobs on relted mchines so s to minimize the mespn
More informationTechnical Appendix: Multi-Product Firms and Trade Liberalization (Not For Publication)
Technicl Appenix: Multi-Prouct Firms n Tre Liberlition (Not For Publiction) Anrew B. Bernr Tuck School of Business t Drtmouth, CEPR & NBER Stephen J. Reing Princeton University & CEPR Peter K. Schott Yle
More informationand thus, they are similar. If k = 3 then the Jordan form of both matrices is
Homework ssignment 11 Section 7. pp. 249-25 Exercise 1. Let N 1 nd N 2 be nilpotent mtrices over the field F. Prove tht N 1 nd N 2 re similr if nd only if they hve the sme miniml polynomil. Solution: If
More informationHealth insurance exchanges What to expect in 2014
Helth insurnce exchnges Wht to expect in 2014 33096CAEENABC 02/13 The bsics of exchnges As prt of the Affordble Cre Act (ACA or helth cre reform lw), strting in 2014 ALL Americns must hve minimum mount
More information** Dpt. Chemical Engineering, Kasetsart University, Bangkok 10900, Thailand
Modelling nd Simultion of hemicl Processes in Multi Pulse TP Experiment P. Phnwdee* S.O. Shekhtmn +. Jrungmnorom** J.T. Gleves ++ * Dpt. hemicl Engineering, Ksetsrt University, Bngkok 10900, Thilnd + Dpt.hemicl
More informationHealth insurance marketplace What to expect in 2014
Helth insurnce mrketplce Wht to expect in 2014 33096VAEENBVA 06/13 The bsics of the mrketplce As prt of the Affordble Cre Act (ACA or helth cre reform lw), strting in 2014 ALL Americns must hve minimum
More informationThe Velocity Factor of an Insulated Two-Wire Transmission Line
The Velocity Fctor of n Insulted Two-Wire Trnsmission Line Problem Kirk T. McDonld Joseph Henry Lbortories, Princeton University, Princeton, NJ 08544 Mrch 7, 008 Estimte the velocity fctor F = v/c nd the
More informationHow To Network A Smll Business
Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd processes. Introducing technology
More informationHow To Find Out How A Worker'S Work Ethic Is Related To The Ability To Get A Job
RtSWD Reserch Notes Reserch Note No. 11 Previously relesed s RtSWD Working Pper No. 15 Popultion Aging nd Trends in the Provision of Continued Eduction Regin T. Riphhn, Prvti Trübswetter 2007 Reserch Notes
More information4.11 Inner Product Spaces
314 CHAPTER 4 Vector Spces 9. A mtrix of the form 0 0 b c 0 d 0 0 e 0 f g 0 h 0 cnnot be invertible. 10. A mtrix of the form bc d e f ghi such tht e bd = 0 cnnot be invertible. 4.11 Inner Product Spces
More informationOperations with Polynomials
38 Chpter P Prerequisites P.4 Opertions with Polynomils Wht you should lern: Write polynomils in stndrd form nd identify the leding coefficients nd degrees of polynomils Add nd subtrct polynomils Multiply
More informationModule 2. Analysis of Statically Indeterminate Structures by the Matrix Force Method. Version 2 CE IIT, Kharagpur
Module Anlysis of Stticlly Indeterminte Structures by the Mtrix Force Method Version CE IIT, Khrgpur esson 9 The Force Method of Anlysis: Bems (Continued) Version CE IIT, Khrgpur Instructionl Objectives
More informationIntegration by Substitution
Integrtion by Substitution Dr. Philippe B. Lvl Kennesw Stte University August, 8 Abstrct This hndout contins mteril on very importnt integrtion method clled integrtion by substitution. Substitution is
More informationBayesian Updating with Continuous Priors Class 13, 18.05, Spring 2014 Jeremy Orloff and Jonathan Bloom
Byesin Updting with Continuous Priors Clss 3, 8.05, Spring 04 Jeremy Orloff nd Jonthn Bloom Lerning Gols. Understnd prmeterized fmily of distriutions s representing continuous rnge of hypotheses for the
More informationPHYSICAL AND HUMAN CAPITAL INVESTMENT: RELATIVE SUBSTITUTES IN THE ENDOGENOUS GROWTH PROCESS * Jorge Durán and Alexandra Rillaers **
PHYSICAL AND HUMAN CAPITAL INVESTMENT: RELATIVE SUBSTITUTES IN THE ENDOGENOUS GROWTH PROCESS * Jorge Durán nd Alexndr Rillers ** WP-AD 2002-18 Corresponding uthor: Jorge Durán, Deprtmento de Fundmentos
More informationAREA OF A SURFACE OF REVOLUTION
AREA OF A SURFACE OF REVOLUTION h cut r πr h A surfce of revolution is formed when curve is rotted bout line. Such surfce is the lterl boundr of solid of revolution of the tpe discussed in Sections 7.
More informationThe elasticity of taxable income: evidence and implications
Journl of Public Economics 84 (2002) 1 32 www.elsevier.com/ locte/ econbse The elsticity of txble income: evidence nd implictions Jon Gruber,c, *, Emmnuel Sez Deprtment of Economics, Msschusetts Institute
More informationOptimal Execution of Open-Market Stock Repurchase Programs
Optiml Eecution of Open-Mrket Stock Repurchse Progrms Jcob Oded This Drft: December 15, 005 Abstrct We provide theoreticl investigtion of the eecution of open-mrket stock repurchse progrms. Our model suggests
More informationLabor Productivity and Comparative Advantage: The Ricardian Model of International Trade
Lbor Productivity nd omrtive Advntge: The Ricrdin Model of Interntionl Trde Model of trde with simle (unrelistic) ssumtions. Among them: erfect cometition; one reresenttive consumer; no trnsction costs,
More informationThe Impact of Oligopolistic Competition in Networks
OPERATIONS RESEARCH Vol. 57, No. 6, November December 2009, pp. 1421 1437 issn 0030-364X eissn 1526-5463 09 5706 1421 informs doi 10.1287/opre.1080.0653 2009 INFORMS The Impct of Oligopolistic Competition
More informationHelicopter Theme and Variations
Helicopter Theme nd Vritions Or, Some Experimentl Designs Employing Pper Helicopters Some possible explntory vribles re: Who drops the helicopter The length of the rotor bldes The height from which the
More informationHumana Critical Illness/Cancer
Humn Criticl Illness/Cncer Criticl illness/cncer voluntry coverges py benefits however you wnt With our criticl illness nd cncer plns, you'll receive benefit fter serious illness or condition such s hert
More informationPhysics 43 Homework Set 9 Chapter 40 Key
Physics 43 Homework Set 9 Chpter 4 Key. The wve function for n electron tht is confined to x nm is. Find the normliztion constnt. b. Wht is the probbility of finding the electron in. nm-wide region t x
More informationEstimating Exchange Rate Exposures:
Estimting Exchnge Rte Exposures: Issues in Model Structure * Gordon M. Bodnr ** Pul H. Nitze School of Advnced Interntionl Studies, The Johns Hopkins University 1740 Msschusetts Avenue NW Wshington, DC
More informationLump-Sum Distributions at Job Change, p. 2
Jnury 2009 Vol. 30, No. 1 Lump-Sum Distributions t Job Chnge, p. 2 E X E C U T I V E S U M M A R Y Lump-Sum Distributions t Job Chnge GROWING NUMBER OF WORKERS FACED WITH ASSET DECISIONS AT JOB CHANGE:
More information5.2. LINE INTEGRALS 265. Let us quickly review the kind of integrals we have studied so far before we introduce a new one.
5.2. LINE INTEGRALS 265 5.2 Line Integrls 5.2.1 Introduction Let us quickly review the kind of integrls we hve studied so fr before we introduce new one. 1. Definite integrl. Given continuous rel-vlued
More informationIs Competition Among Charities Bad?
Is Competition Among Chrities Bd? Inkyung Ch nd Willim Neilson Tes A&M University, College Sttion, TX 7783 December Abstrct This pper studies tht the eect o incresed competition mong chrities or dontions,
More informationAppendix D: Completing the Square and the Quadratic Formula. In Appendix A, two special cases of expanding brackets were considered:
Appendi D: Completing the Squre nd the Qudrtic Formul Fctoring qudrtic epressions such s: + 6 + 8 ws one of the topics introduced in Appendi C. Fctoring qudrtic epressions is useful skill tht cn help you
More informationUnderstanding Basic Analog Ideal Op Amps
Appliction Report SLAA068A - April 2000 Understnding Bsic Anlog Idel Op Amps Ron Mncini Mixed Signl Products ABSTRACT This ppliction report develops the equtions for the idel opertionl mplifier (op mp).
More informationCEP Discussion Paper No 975 May 2010
ISSN 2042-2695 CEP Discussion Pper No 975 My 200 Trde Liberliztion nd Heterogeneous Firm Models: An Evlution Using the Cnd - US Free Trde Agreement Holger Breinlich nd Alejndro Cuñt Abstrct We exmine the
More informationThe mean-variance optimal portfolio
ALEXANDRE S. DA SILVA is vice president in the Quntittive Investment Group t Neuberger ermn in New York, NY. lexndre.dsilv@nb.com WAI LEE is the chief investment officer nd hed of the Quntittive Investment
More informationModule Summary Sheets. C3, Methods for Advanced Mathematics (Version B reference to new book) Topic 2: Natural Logarithms and Exponentials
MEI Mthemtics in Ection nd Instry Topic : Proof MEI Structured Mthemtics Mole Summry Sheets C, Methods for Anced Mthemtics (Version B reference to new book) Topic : Nturl Logrithms nd Eponentils Topic
More informationGAO HIGHER EDUCATION. Improved Tax Information Could Help Families Pay for College. Report to the Committee on Finance, U.S.
GAO United Sttes Government Accountbility Office Report to the Committee on Finnce, U.S. Sente My 2012 HIGHER EDUCATION Improved Tx Informtion Could Help Fmilies Py for College GAO-12-560 My 2012 HIGHER
More informationPension funds allocations to hedge funds: an empirical. analysis of US and Canadian de ned bene t plans
Pension funds lloctions to hedge funds: n empiricl nlysis of US nd Cndin de ned bene t plns Vincent Bouvtier y Sndr Rigot z August 2011 Abstrct This pper investigtes the chrcteristics of US nd Cndin pension
More informationRotating DC Motors Part II
Rotting Motors rt II II.1 Motor Equivlent Circuit The next step in our consiertion of motors is to evelop n equivlent circuit which cn be use to better unerstn motor opertion. The rmtures in rel motors
More informationLectures 8 and 9 1 Rectangular waveguides
1 Lectures 8 nd 9 1 Rectngulr wveguides y b x z Consider rectngulr wveguide with 0 < x b. There re two types of wves in hollow wveguide with only one conductor; Trnsverse electric wves
More informationReasoning to Solve Equations and Inequalities
Lesson4 Resoning to Solve Equtions nd Inequlities In erlier work in this unit, you modeled situtions with severl vriles nd equtions. For exmple, suppose you were given usiness plns for concert showing
More informationPension funds allocation to hedge funds: an empirical. analysis on US and Canadian de ned bene t plans
Pension funds lloction to hedge funds: n empiricl nlysis on US nd Cndin de ned bene t plns Vincent Bouvtier y Sndr Rigot z Preliminry drft Jnury 2011 Abstrct This pper investigtes the chrcteristics of
More informationOnline Multicommodity Routing with Time Windows
Konrd-Zuse-Zentrum für Informtionstechnik Berlin Tkustrße 7 D-14195 Berlin-Dhlem Germny TOBIAS HARKS 1 STEFAN HEINZ MARC E. PFETSCH TJARK VREDEVELD 2 Online Multicommodity Routing with Time Windows 1 Institute
More informationOr more simply put, when adding or subtracting quantities, their uncertainties add.
Propgtion of Uncertint through Mthemticl Opertions Since the untit of interest in n eperiment is rrel otined mesuring tht untit directl, we must understnd how error propgtes when mthemticl opertions re
More informationHealth insurance exchanges What to expect in 2014
Helth insurnce exchnges Wht to expect in 2014 33096CAEENABC 11/12 The bsics of exchnges As prt of the Affordble Cre Act (ACA or helth cre reform lw), strting in 2014 ALL Americns must hve minimum mount
More informationMODULE 3. 0, y = 0 for all y
Topics: Inner products MOULE 3 The inner product of two vectors: The inner product of two vectors x, y V, denoted by x, y is (in generl) complex vlued function which hs the following four properties: i)
More informationThe Impact of Negative Cash Flow and In uential Observations on Investment-Cash Flow Sensitivity Estimates
The Impct of Negtive Csh Flow nd In uentil Observtions on Investment-Csh Flow Sensitivity Estimtes George Allynnis Drden Grdute School of Business, University of Virgini PO Box 6550, Chrlottesville, VA
More informationExample A rectangular box without lid is to be made from a square cardboard of sides 18 cm by cutting equal squares from each corner and then folding
1 Exmple A rectngulr box without lid is to be mde from squre crdbord of sides 18 cm by cutting equl squres from ech corner nd then folding up the sides. 1 Exmple A rectngulr box without lid is to be mde
More informationSection 7-4 Translation of Axes
62 7 ADDITIONAL TOPICS IN ANALYTIC GEOMETRY Section 7-4 Trnsltion of Aes Trnsltion of Aes Stndrd Equtions of Trnslted Conics Grphing Equtions of the Form A 2 C 2 D E F 0 Finding Equtions of Conics In the
More informationLECTURE #05. Learning Objective. To describe the geometry in and around a unit cell in terms of directions and planes.
LECTURE #05 Chpter 3: Lttice Positions, Directions nd Plnes Lerning Objective To describe the geometr in nd round unit cell in terms of directions nd plnes. 1 Relevnt Reding for this Lecture... Pges 64-83.
More informationExponential and Logarithmic Functions
Nme Chpter Eponentil nd Logrithmic Functions Section. Eponentil Functions nd Their Grphs Objective: In this lesson ou lerned how to recognize, evlute, nd grph eponentil functions. Importnt Vocbulr Define
More informationNational Health Insurance and precautionary saving: evidence from Taiwan
Journl of Public Economics 87 (003) 1873 1894 www.elsevier.com/ locte/ econbse Ntionl Helth Insurnce nd precutionry sving: evidence from Tiwn b c, * Shin-Yi Chou, Jin-Tn Liu, Jmes K. Hmmitt Deprtment of
More informationBinary Representation of Numbers Autar Kaw
Binry Representtion of Numbers Autr Kw After reding this chpter, you should be ble to: 1. convert bse- rel number to its binry representtion,. convert binry number to n equivlent bse- number. In everydy
More informationEnterprise Risk Management Software Buyer s Guide
Enterprise Risk Mngement Softwre Buyer s Guide 1. Wht is Enterprise Risk Mngement? 2. Gols of n ERM Progrm 3. Why Implement ERM 4. Steps to Implementing Successful ERM Progrm 5. Key Performnce Indictors
More informationThe Tradeoff Between Inequality and Growth
ANNALS OF ECONOMICS AND FINANCE 4, 329 345 2003 The Trdeoff Between Inequlity nd Growth Jess Benhbib Deprtment of Economics, New York University 269 Mercer Street, 7th floor, New York, NY 10003, USA. E-mil:
More informationAn Undergraduate Curriculum Evaluation with the Analytic Hierarchy Process
An Undergrdute Curriculum Evlution with the Anlytic Hierrchy Process Les Frir Jessic O. Mtson Jck E. Mtson Deprtment of Industril Engineering P.O. Box 870288 University of Albm Tuscloos, AL. 35487 Abstrct
More information6.2 Volumes of Revolution: The Disk Method
mth ppliction: volumes of revolution, prt ii Volumes of Revolution: The Disk Method One of the simplest pplictions of integrtion (Theorem ) nd the ccumultion process is to determine so-clled volumes of
More informationSan Mateo County ACCEL Adult-Education College and Career Educational Leadership AB 86 Adult Education Consortium Project Management Plan 24, 2014 -
A Sn Mteo County ACCEL Adult-Eduction College nd Creer Eductionl Ledership AB 86 Adult Eduction Consortium Project Mngement Pln - Februry 24, 2014 - This project mngement pln presents ACCEL s process frmework
More informationOptiml Control of Seril, Multi-Echelon Inventory (E&I) & Mixed Erlng demnds
Optiml Control of Seril, Multi-Echelon Inventory/Production Systems with Periodic Btching Geert-Jn vn Houtum Deprtment of Technology Mngement, Technische Universiteit Eindhoven, P.O. Box 513, 56 MB, Eindhoven,
More information