Redistributing the Gains from Trade through Nonlinear. Lumpsum Transfers


 Victor Johns
 5 years ago
 Views:
Transcription
1 Redistributing the Gins from Trde through Nonliner Lumpsum Trnsfers Ysukzu Ichino Fculty of Economics, Konn University April 21, 214 Abstrct I exmine lumpsum trnsfer rules to redistribute the gins from free trde under incomplete informtion, where the government does not know the chrcteristics of individuls. By considering trnsfer rules tht mke the mount of trnsfer dependent on trnsctions of individuls under utrky, I show tht there is no incentivecomptible nd budgetblncing trnsfer rule to redistribute the gins from free trde successfully, if the discount fctor is sufficiently lrge. Also, the pper exmines whether the mount of trnsfer should be dependent on trnsctions under utrky or trnsctions under free trde, nd shows tht the former is better when the discount fctor is smll or the government hs enough budget for redistribution. *Address: Okmoto, Higshindku Kobe , Jpn. Emil: 1
2 1 Introduction It is well known tht free trde cretes winners nd losers. However, with n pproprite lumpsum trnsfer, Preto improvement cn be chieved s country moves from utrky to free trde, s shown by Kemp (1962), Kemp nd Wn (1972), nd Grndmont nd McFdden (1972), mong others. 1 Essentilly, the ide of Pretoimproving lumpsum trnsfers is to let wht ech individul consumed under utrky ffordble under free trde, too. 2 Lter, Dixit nd Normn (1986) pointed out prcticl difficulties of implementing such lumpsum trnsfers. In implementing lumpsum trnsfer to mke everyone better off fter free trde, the government hs to figure out not only who re txed nd who re subsidized, but lso how much is txed or subsidized for ech individul. To do so, the government needs to collect informtion bout the chrcteristics of individuls. Moreover, when sked by the government, ech individul my not revel his chrcteristics tht the government is going to use to clculte the mount of trnsfer. As Dixit nd Normn (1986) write, individuls hve n incentive to mnipulte their behvior so s to misled the plnner bout these chrcteristics nd secure lrger net trnsfer. How do they mnipulte their behvior? Does tht mnipultion mtter? 3 Wong (1997) studied these questions in generl setting, nd rgued tht mnipultion does not mtter if the utrkic price does not chnge by such mnipultion. Recently, however, exmining the sme question in simpler setting of twogoods exchnge economy with qusiliner utility, Ichino (212) showed tht due to consumers mnipultion the utrkic price chnges to the directions unfvorble to those who lose by free trde. As result, lumpsum trnsfer rule tht llows everyone to consume under free trde wht they used to consume under utrky becomes ineffective in redistributing the gins from free trde. Moreover, in Ichino (212) it is shown tht ny trnsfer rules tht re linerly 1 These studies work on models of perfect competition. Under imperfect competition such s oligopoly, whether there re gins from free trde is less unmbiguous. See, for exmple, Dong nd Yun (21) nd Kemp (21). 2 Using such lumpsum trnsfers hs been one of the stndrd techniques to mke welfre comprison. For textbook tretment, see Wong (1995; pp ). 3 Che nd Fcchini (27) studied this kind of mnipultion in context of mrket liberliztion, while we study the mnipultion in the context of trde liberliztion. 2
3 dependent on utrkic consumption cnnot chieve Preto gins from trde. In this pper, we consider more generl clss of lumpsum trnsfer rules, including trnsfer rules nonlinerly dependent on utrkic consumption, nd explore if there exist ny trnsfer rules tht cn successfully redistribute the gins from free trde to everyone. For this purpose, we pply contrcttheory technique used by Feenstr nd Lewis (1991) (herefter, we refer it s FL (1991)). As explined bove, since the government does not hve complete informtion on individuls chrcteristics, it hs to sk the individuls to revel such informtion in order to clculte the mount of trnsfer. Then, under such circumstnce, individuls hve n incentive to mnipulte their behvior, or misreport their chrcteristics if doing so increses the mount of trnsfer to be received. To prevent mnipultion or misreporting, the government hs to design trnsfer rule tht induces truth telling. We therefore formulte welfremximiztion problem in which trnsfer rules should stisfy the incentive comptible constrint s well s the government budget constrint nd the everyoneismdebetteroff constrint. By solving the welfre mximiztion problem, we firstpointoutthtiftrnsferrules re to relte the mount of trnsfer to the mount of consumption under utrky, then the utrkic consumption should be distorted to prevent mnipultion or misreporting of the individuls. Then, we show tht there is no incentivecomptible nd budgetblncing trnsfer rules to chieve Preto gins from free trde if the discount fctor is sufficiently lrge. Intuitively, this is becuse the mount of subsidies given to losers of free trde hs to be lrge enough to compenste him not only for his loss from free trde but lso for the loss from distorted consumption under utrky. At the sme time, the mount of txes collected from the giners of free trde is limited becuse of distorted consumption. Also, we compre the outcome of our model with the outcome of FL (1991). As mentioned bove, in this pper, we consider trnsfer rules dependent on the consumption under utrky. On the other hnd, in FL (1991), trnsfer rules re dependent on the consumption under free trde. By compring the resulting welfre of our model nd FL(1991) s, we show tht the former gives higher welfre thn the ltter when the discount fctor is smll or the government hs enough budget for redistribution. 3
4 2 The Model We consider n exchnge economy with two goods, good x nd good y, where good y is the numerire. In this economy, there is continuum of individuls with the popultion normlized to one. The individuls re ssumed identicl, except the endowment of good x. Withω denoting the endowment of good x, the individuls in the economy re indexed by ω. For simplicity, ssume tht ω is uniformly distributed over the rnge of [, 1]. The utility function of n individul hving ω units of the endowment of good x is given by u(x + ω)+y +ȳ where x nd y denote excess demnd of good x nd y respectively, nd ȳ is the endowment of good y (which is the sme for everyone). To hve explicit solution, we ssume tht the subutility function u( ) is qudrtic: u (x + ω) =k + (x + ω) b 2 (x + ω)2. where k, >, b>. In this model, we hve two periods: in period, the economy is under utrky; in period 1, the economy is under free trde. The utility mximiztion problem of n individul is given by mx U (x, p, ω) =u(x + ω) px +ȳ x since the budget constrint px + y is lwys binding. The firstorder condition is u (x + ω) =p, from which the excess demnd function x (p, ω) =( p) /b ω is derived. Then, the utrkic equilibrium price p is determined from the mrketclering condition R 1 x (p, ω) dω =.SinceR 1 ωdω =1/2, solving this condition gives p =(2 b) /2. Let x (ω) x (p, ω) denote the excess demnd (or, we cll it trnsction ) of individul ω in the utrkic equilibrium, nd define the indirect utility of individul ω in the utrkic equilibrium U (ω) U (x (ω),p, ω). In period 1, when the economy llows free trde, the price of good x is equl to the 4
5 world price p (we ssume tht the economy is smll). Then, trnsction of individul ω in the freetrde equilibrium is given by x (ω) ( p ) /b ω, nd the indirect utility in the freetrde equilibrium by U (ω) U (x (ω),p, ω). We ssume tht p <p :theworld price of good x is smller thn the utrky price. 4 By this ssumption, x (ω) >x (ω). In ggregte, there re gins from free trde 5 : = = U (ω) dω U (ω) dω [U (x,p ) U (x,p )] dω + [U (x,p ) U (x,p )] dω +(p p ) [U (x,p ) U (x,p )] dω x dω > since the first term is positive (given p, the utilitymximizing trnsction is x )ndthe second term is zero becuse R 1 x dω =. However, the gins from trde do not fll eqully to everyone. Buyers of good x under utrky gin from free trde: U (ω) U (ω) =[U (x,p ) U (x,p )] + [U (x,p ) U (x,p )] =[U (x,p ) U (x,p )] + (p p ) x > since x >. On the other hnd, the sellers of good x under free trde lose from free trde: U (ω) U (ω) =[U (x,p ) U (x,p )] + [U (x,p ) U (x,p )] =(p p ) x +[U (x,p ) U (x,p )] <. provided tht x <. 4 For the prmeters of the utility function nd the world price, we impose the following restriction: (i) 2 >b. Thisistomketheutrkicpricepositive. (ii)p < (2 b) /2. This is from the ssumption of p <p. (iii) ( p ) /b < 1. This is to mke some individuls still sellers of good x under free trde. 5 Here, to simplify the nottion, we use expressions such s U (x,p ) to men U (x (ω),p, ω), by suppressing ω. Herefter, if there is likely no confusion, we write U (x, p) to denote U (x (ω),p,ω). 5
6 3 Lumpsum Trnsfers under incomplete informtion In order to redistribute the gins from trde, the government cn give the following lumpsum trnsfer z (ω) = (p p ) x (ω) to individul ω in period 1 (note tht z (ω) > is subsidy nd z (ω) < is tx). By this trnsfer, the budget constrint of individul ω in period 1 becomes p x + y (p p ) x (ω). It is esy to show tht this trnsfer mkes wht ech individul consumed under utrky ffordble under free trde s well: p x + y (p p ) x (ω) p x + y p x (ω) p x (ω) Therefore, everyone gets better off by free trde. Tht is, U (ω) +z (ω) >U (ω) for ll ω. In ddition, with this lumpsum trnsfer, the government budget is blnced since R 1 z (ω) dω = (p p ) R 1 x (ω) dω =. The discussion bove tht the free trde policy with the lumpsum trnsfer z (ω) mkes everyone better off, however, depends on n implicit ssumption tht the government cn figure out wht z (ω) s re. For the government to clculte z (ω), ithsto know ech individul s endowment. But this is not likely the cse. Without knowing the endowment of ech individul, the government is not ble to clculte x (ω), nd thus cnnot figure out z (ω). Then, the only wy for the government to find the mount of lumpsum trnsfer for ech individul is to observe his trnsction in period (under utrky). However, if ech individul knows tht the government is going to observe his trnsction in period to determine the mount of trnsfer for him, then he my wnt to chnge, or mnipulte his period trnsction in order to get lrger trnsfer in period 1. So, here is the question: Is it possible to chieve Preto gins from free trde through lumpsum trnsfers even when the government does not hve complete informtion on the chrcteristics of the individuls nd thus there cn be mnipultion of trnsction? To nswer the question formlly, let us now clrify the setting. As mentioned erlier, in the following nlysis we suppose tht the government does not know endowment of ech individul; the government just observes trnsction of ech individul in period (under utrky). In period, ll individuls know tht free trde will be llowed in period 6
7 1. They lso know tht lumpsum trnsfer z (x) will be given in period 1. Here, note tht the trnsfer depends on x, the observed trnsction of n individul in period. In this setting, the utility mximiztion problem of n individul should be n intertemporl one, nmely, mx x,x 1 U (x, p, ω)+δz (x)+δu x 1,p, ω (1) where x nd x 1 re respectively the period nd the period1 trnsction of good x, p is the previling price in period, nd δ is discount fctor δ 1 (we ssume everyone hs the sme discount fctor). By inspection of the mximiztion problem (1), it is obvious tht x 1 = x : the trnsction under free trde is the sme s the one we sw in Section 2. But the trnsction under utrky is now different from x becuse of the dependence of the lumpsum trnsfer on x. Thus, the utrkic equilibrium price, too, cn be different from p. We sy tht lumpsum trnsfer rule z (x) cn chieve Preto gins from free trde if the following inequlity holds for ll ω: mx x [U (x, p, ω)+δz (x)] + δu (ω) (1 + δ) U (ω). Ichino (212) exmined the cse of z (x) = (p p ) x, the lumpsum trnsfer rule to mke sure tht ll individuls cn consume under free trde wht they used to consume under utrky, nd found tht due to trnsction mnipultion Preto gins from trde cnnot be chieved by this trnsfer rule. Moreover, in Ichino (212) it is shown tht ny trnsfer rules tht re liner in x cnnot chieve Preto gins from trde. In this pper, we consider more generl clss of lumpsum trnsfers, including trnsfer rules nonlinerly dependent on x, nd explore if there re ny trnsfer rules tht cn successfully distribute the gins from free trde to everyone. For this purpose, we pply contrcttheory technique used by FL (1991), where the endowment of good x is tken s type of n individul not known to the government, nd the government is going to solve welfremximiztion problem to derive menu {x (ω),z(ω)}, i.e.,pirof trnsction nd trnsfer. 7
8 4 WelfreMximizing trnsfers 4.1 Welfre mximiztion problem Given menu {x (ω),z(ω)} for ω 1, if n individul whose endowment is ω picks prticulr pir {x (ω ),z(ω )}, his intertemporl utility is U x ω,p,ω + δz ω + δu (ω). By the reveltion principle, without loss of generlity we cn confine the set of pirs {x (ω),z(ω)} to be considered to those stisfying the following incentive comptibility (IC) constrints: U (x (ω),p,ω)+δz (ω) U x ω,p,ω + δz ω for ll ω, ω. (2) In ddition to the IC constrints, trnsctiontrnsfer menu {x (ω),z(ω)} hs to be designed so s to mke everyone better off by free trde. Tht is, the inequlity U (x (ω),p,ω)+δz (ω) U (ω)+δ (U (ω) U (ω)) for ll ω (3) hs to be stisfied. This is nlogous to the individul rtionlity (IR) constrint in stndrd contrcttheory model. So, in the pper we refer this s the IR constrint. Third, trnsfers should stisfy the government s budget (GB) constrint: z (ω) dω B (4) where B is some mount of budget the government cn use for trnsfer policy. Finlly, the mrketclering condition x (ω) dω = (5) determines the period equilibrium price p. 8
9 The welfre mximiztion problem of the government is set s follows: mx x(ω),z(ω) [U (x (ω),p,ω)+δz (ω)] dω + δb s.t. (2), (3), (4), nd (5), δz (ω) dω (6) where the objective function is the sum of the individul s utility nd the government surplus. Problem (6) is nturl extension of Ichino (212). However, here we do not solve problem (6). Insted, we solve somewht different problem defined below. mx x(ω),z(ω) [U (x (ω),p, ω)+δz (ω)] dω + δb [δz (ω) (p p ) x (ω)] dω (7) s.t. U (x (ω),p, ω)+δz (ω) U x ω,p, ω + δz ω for ll ω, ω, U (x (ω),p, ω)+δz (ω) U (ω)+δ (U (ω) U (ω)) for ll ω. δz (ω) dω (p p ) x (ω) dω δb. The welfre mximiztion problem (7) is different from problem (6) in how the period price is determined. In problem (6), the period price p is determined by the utrkic mrketclering condition R 1 x (ω) dω =. Therefore, the utrkic equilibrium price my be different from p, depending on the shpe of x (ω). On the other hnd, in problem (7), the period price is supported by the government t p, the utrkic equilibrium price under the complete informtion cse. To support the price t p, the government impose n import triff (if x (ω) > ) ornexportsubsidy(ifx (ω) < ) withthesizeof(p p ). Thtiswhywehveterm R 1 (p p ) x (ω) dω in the government s budget constrint. Simply put, in problem (6) utrky is mintined by prohibition of interntionl trde, while utrky is mintined by prohibitive triff (or export subsidy) in problem (7). Below, we present n outline of solving problem (7). Problem (6) is solved in similr fshion since it hs the sme structure s problem (7). Lter, we explin why we focus on problem (7) insted of problem (6). To mke expressions simpler, by busing nottion little bit, we define U (ω) 9
10 U (x (ω),p, ω)+δz (ω). As explined by FL (1991), the IC constrints of problem (7) is equivlent to (i) U (ω) =u (x (ω)+ω) nd (ii) x (ω) is nonincresing. By using condition (i) for the IC constrint, we cn construct the following constrined Hmiltonin by treting x (ω) nd z (ω) s control vribles nd U (ω) s stte vrible: H = [U (ω)+δb δz (ω)+(p p ) x (ω)] (8) +γ (ω) u (x (ω)+ω) +μ (ω)(u (ω) U (ω) δ (U (ω) U (ω))) +ρ (ω)(u (x (ω),p, ω)+δz (ω) U (ω)) +λ (δb δz (ω)+(p p ) x (ω)), where the second line is condition (i) of the IC constrint, nd gives the eqution of motion for U (ω) (we confirm tht condition (ii) of the IC constrint is stisfied fter hving derived solution). The third line is the IR constrint, the fourth line defines U (ω), ndthefifth line is the GB constrint. The mximum principle requires tht H x = (p p )+γ (ω) u + ρ (ω) u (x (ω)+ω) p + λ (p p )=, (9) H z = δ + ρ (ω) δ λδ =, (9b) H U = 1 μ (ω)+ρ (ω) =γ (ω), (9c) nd the trnsverslity conditions re γ () [U () U () δ (U () U ())] =, nd γ (1) [U (1) U (1) δ (U (1) U (1))] =. We let x (ω),z (ω) ª denote the solution, nd U (ω) utility level chieved by the solution. Here, we present n outline of deriving the solution. For the detil, see the ppendix. From (9b), ρ (ω) =1+λ is derived. Substituting this into (9c) gives γ (ω) =γ () 1
11 R ω μ (t) dt + λω. Then, pplying these expressions to (9), we cn derive eqution determining the trnsction schedule x (ω) u x (ω)+ω p = γ () R ω μ (t) dt + λω u, (1) 1+λ For the time being, ssume tht the IR constrint is binding only t ω =1(Lter, we explin it is ctully the cse when the government s budget B is lrge enough). Then, γ () = by the trnsverslity condition nd R ω μ (t) dt =since the IR constrint is not binding for ll ω < 1. Thus, (1) is simplified to u x (ω)+ω p = u mω where m = λ/ (1 + λ). Solvingforx, the following expression x (ω) =x n (ω) p b (m +1)ω (11) is derived. Here, we hve defined x n (ω) s solution when the IR constrint is not binding for ll ω < 1 (the superscript n for not binding ). Since the multiplier λ, x n (ω) is decresing in ω, stisfying condition (ii) of the IC constrint. Once x n (ω) is derived, from the IC constrint, nd from the IR constrint binding t ω =1,theperiod utility is determined s follows: U (ω) =U n (ω) U (1) + δ (U (1) U (1)) ω u (x n (ω)+t) dt. We cn interpret U (ω) s trget level of utility to be chieved, with trnsfer z (ω). On the other hnd, without trnsfer, the period utility of individul ω is U (x n (ω),p, ω). The trnsfer schedule is thus determined so s to fill the gp between the trget level nd the withouttrnsfer level: δz (ω) =δz n (ω) U n (ω) U (x n (ω),p, ω). (12) 11
12 Then, we cn clculte the GB constrint δz n (ω) dω (p p ) x n (ω) dω = δb, nd from this we cn determine m. This completes the solution. Now, we explin why we solved problem (7) insted of problem (6). Lemm 1 shows tht wht is chieved by solving problem (6) is chievble by problem (7). Lemm 1 Consider solution {ˆx (ω), ẑ (ω)} of problem (6) nd the welfre level chieved by the solution. There exists some z (ω) by which the sme welfre level nd the sme ˆx (ω) is implemented such tht {ˆx (ω),z(ω)} stisfies the constrints of problem (7). Proof. Consider solution {ˆx (ω), ẑ (ω)} of problem (6). In problem (6), the utility level of individul ω is equl to U (1) + δ (U (1) U (1)) R 1 ω u (ˆx (t)+t) dt. To chieve this trget level, the trnsfer schedule ẑ (ω) is clculted s follows: δẑ (ω) =U (1) + δ (U (1) U (1)) ω u (ˆx (t)+t) dt U (ˆx (ω),p,ω). With the sme ˆx (ω), the sme trget level of utility cn be chieved in problem (7) by the following trnsfer schedule δz (ω). δz (ω) =U (1) + δ (U (1) U (1)) ω u (ˆx (t)+t) dt U (ˆx (ω),p, ω). Since R 1 ˆx (ω) dω =by the mrket clering condition in problem (6), the ggregte trnsfers re the sme for ẑ (ω) nd z (ω), ndthetriff revenue in problem (7) is zero. Therefore, R 1 δẑ (ω) dω = R 1 δz (ω) dω R 1 (p p )ˆx (ω) dω. 4.2 Chrcteriztion of the solution Now we chrcterize the solution x (ω),z (ω) ª s follows, noticing tht the solution depends on the size of the government s budget B. When B is lrge nd the GB constrint is not binding, the solution is trivil. Since 12
13 m = λ/ (1 + λ) =if the GB constrint is not binding, from (11) we see tht x (ω) = ( p ) /b ω = x (ω). Thtis,thegovernmentcnchievethemostefficient outcome by letting everyone consume good x of the mount under the free trde. However, s the individuls consume x (ω)+ω when fcing p, their period utility without trnsfer is U (x (ω),p, ω), which is less thn U (ω). Since U (ω) <U (ω)+δ (U (ω) U (ω)) for lrge ω, the government hs to give positive trnsfer to those individuls to stisfy the IR constrint (see Figure 1). In prticulr, individuls with ω =1need to be compensted t lest by U (1) + δ (U (1) U (1)) U (x (1),p, 1) in order for the IR constrint to be stisfied. Suppose tht the government gives the individuls with ω =1exctly this mount of trnsfer so tht the IR constrint is just binding t ω =1. Then, the IC constrint requires tht the trget level of utility U (ω) hs slope of u (x (ω)+ω) =p sinceeveryoneconsumesx (ω) +ω. Nmely, U (ω) hs to be prllel upwrd shift of U (ω) by the mount of (1 + δ)(u (1) U (1)). By this construction, for ll ω the trget level of utility is bove the utility without trnsfer. Therefore, the government hs to give positive trnsfers to everyone to chieve the trget level of utility. The sum of the trnsfers is δz (ω) dω = U (ω) dω +(1+δ)(U (1) U (1)) U (x (ω),p, ω) dω. On the other hnd, becuse x (ω) >x (ω), in ggregte there is imports of good x so tht the government erns triff revenue R 1 (p p ) x (ω). Thus, the overll government expenditure needed to implement the trnsctiontrnsfer schedule is = δz (ω) dω (p p ) x (ω) U (ω) dω +(1+δ)(U (1) U (1)) = (1+δ)(U (1) U (1)). U (x,p ) dω (p p ) x (ω) So, when B =(1+δ)(U (1) U (1)), the government hs just enough budget to implement x (ω) with the IR constrint binding only t w =1. In other words, when the 13
14 government hs lrge enough budget such tht B (1 + δ)(u (1) U (1)), themost efficient trnsction x (ω) is implemented, with the GB constrint not binding. As B flls below (1 + δ)(u (1) U (1)), letting everyone consume x (ω)+ω is no longer comptible with the IR constrint. To stisfy the IR constrint with the smller mount of the budget vilble to the government, now the trnsfer hs to be mde smller for the individuls with low ω (since they re the ones who gin from free trde, there is room to shve the trnsfer for them). Then, with smller trnsfer for low ω, if x (ω) =x (ω) were offered, the individuls with low ω would hve n incentive to pretend tht his ω is higher thn wht ctully is in order to get lrge trnsfer. To prevent it, trnsction schedule x (ω) hs to be distorted in such wy tht consumption x (ω) +ω is no longer the sme for everyone but smller for high ω. Thisisseenby eqution (11): consumption x (ω) +ω is equl to x n (ω) +ω, which is distorted from x (ω)+ω by mω. Put differently, we cn explin the following trdeoffs of distorting consumption. Tke prticulr individul with < ω 1. As consumption is distorted to be smller thn the free trde level, his period utility without trnsfer is decresed. This mkes trnsfer needed to be given to this prticulr individul lrger. However, such distortion steepens the slope of the trget utility u (x n (ω)+ω), which lowers the trget utility levelofthell individuls below ω. This mkes trnsfers needed to be given to those individuls smller. In ggregte, the ltter effect outweighs the former effect, nd thus the government expenditure for trnsfers is mde smller by such distortion. In prticulr, for the individuls with lrge ω, the ltter effect is dominting. This is why distortion is lrge for lrge ω, s illustrted in Figure 4. The trget utility level is depicted in Figure 2. It is now steeper thn the one when the GB constrint is not binding, but the IR constrint is still binding only t ω =1. As the government budget gets more stringent, consumption of good x is more distorted nd the slope of the trget level utility gets steeper. Eventully, the trget utility becomes s steep s the right hnd side (RHS) of the IR constrint t ω =1. Then, consumption of good x cnnot be lowered without violting the IR constrint for high 14
15 ω. In this cse, the IR constrint becomes binding not only t ω =1but lso for lrge ω such tht ω ω < 1, where ω is threshold vlue. Nmely, for ω ω < 1, the trnsction schedule is chosen so s to mke the trget utility s steep s the RHS of the IR constrint: u (x (ω)+ω) =p + δ (p p ) (see Figure 3). Letting x b (ω) (b for binding ) denote the trnsction schedule stisfying this equlity, we hve x b (ω) = p b δ (p p ) b ω for ω ω < 1. (13) Since the trget utility is U (ω)+δ (U (ω) U (ω)), the trnsction schedule for ω ω < 1 is given by δz b (ω) U (ω)+δ (U (ω) U (ω)) U(x b (ω),p, ω). (14) On the other hnd, for ω < ω, the trnsction schedule is the sme s (11), while the trget utility is modified to U ( ω)+δ (U ( ω) U ( ω)) R ω ω u (x n (t)+t) dt. Therefore, the trnsction schedule for ω < ω is Z ω δ z n (ω) U ( ω)+δ (U ( ω) U ( ω)) u (x n (t)+t) dt U (x n (ω),p, ω). (15) ω The threshold vlue ω is determined by equting x n (ω) nd x b (ω). Thtis, ω solves the equlity p b (m +1) ω = p b δ (p p ) b ω, (16) tht is, ω =(1+δ)(p p ) /bm. (17) The more stringent the government budget constrint becomes, m rises, nd ω flls, mening tht the more individuls re mde just indifferent between utrky nd free trde. Then, nturlly, the following question rises. No mtter how smll the budget B is,sy,evenwhenb =, cn some individuls be mde strictly better off by free trde? Proposition 1 clims tht the nswer is no: when B =, the gins from free trde 15
16 cn be distributed to mke someone strictly better off nd no one worse off only when δ is sufficiently smll. If δ is lrge enough nd B is smll enough, there is no solution to problem (7). See Figure 6 for grphicl presenttion. Proposition 1 There is vlue δ (, 1) such tht for δ δ problem (7) hs solution for ny B. On the other hnd, for δ > δ, there is threshold function B (δ) > such tht B (δ) > nd for B< B (δ) problem (7) hs no solution. The proof is given in the ppendix. Here, we provide intuitive explntion in the following three steps. First, we show tht in problem (7), even when mking everyone just indifferent between utrky nd free trde, the government needs positive budget. With the trnsctiontrnsfer pir x b (ω),z b (ω) ª for ll ω, the government expenditure for individul ω is written s δz b (ω) (p p ) x b (ω) =U (ω)+δ (U (ω) U (ω)) U(x b,p ) Adding nd subtrcting U (ω), wehve ³ δz b (ω) (p p ) x b (ω) =(1+δ)(U (ω) U (ω)) + U (ω) U(x b,p ) The first term is negtive when it is ggregted, while the second term is positive since U (ω) =U (x,p ). By decomposing the first term by dding nd subtrcting U (x,p ), we hve δz b (ω) (p p ) x b (ω) ³ = (1+δ)(U (ω) U (x,p )+U (x,p ) U (ω)) + U (ω) U(x b,p ) (18) ³ = (1 + δ)(p p ) x (1 + δ)(u (x,p ) U (x,p )) + U (x,p ) U(x b,p ). The first term disppers when ggregted over ω 1. The second term is negtive: it represents, in terms of per cpit, the gins from free trde llowed in the both periods 16
17 (with the negtive sign in front of it). By giving everyone the IRbinding level of utility insted of the freetrde level of utility, the government cn collect this mount of tx revenue. The third term is positive, which is interpreted s the loss of the individuls induced to consume distortedly smll mount of x b +ω due to the IC constrint, insted of consuming the free trde level of x + ω. So, the government hs to compenste this loss to the individuls. Grphiclly (see Figure 5), the third term is big tringle representing the chnge in the consumer surplus by consuming x b + ω t p rther thn consuming x + ω t p.for the second term, (U (ω) U (x,p )) is smll tringle representing the chnge in the consumer surplus by consuming x +ω t p rther thn x +ω t p. Multiplied by (1 + δ), it becomes the second term. Since (x + ω) x b + ω =(1+δ)((x + ω) (x + ω)), the big tringle representing the third term is lwys lrger thn the tringles representing the second term. Therefore, expression (18) is positive, mening tht it requires positive government budget to mke everyone just indifferent between utrky nd free trde (i.e., mking the IR constrint binding for ll ω). Of course, mking the IR constrint binding for ll ω my not minimize the government expenditure. In fct, strting from the IR constrint binding for everyone (i.e., strting from ω =), the government cn improve its budget by giving someone strictly positive gins from trde (i.e., by incresing ω). So, second, we explin this. Tke prticulr individul with ω very smll. As ω increses from zero so tht his ω becomes below ω, his consumption is now less distorted, nd thus his utility level without trnsfer increses. By this, the government cn collect more txes from him (or needs to give less subsidy to him), with the government expenditure getting smller. On the other hnd, however, n increse in ω rises his trget utility level. This hppens becuse due to the less distorted (incresed) consumption, the slope of the trget utility of, not only him, but lso ll individuls between his ω nd ω, getsfltter. By this, the government cn collect less txes from him (or needs to give more subsidy to him), with the government expenditure getting lrger. Since the ltter effect is smll when ˆω is smll, the former effect is dominting so tht the government expenditure flls by n increse in ω from ω =. Eventully, 17
18 however, s ω is incresed sufficiently lrge, the government expenditure hits the bottom, since the ltter effect is getting bigger nd comes to outweigh the former. Third, we explin tht (18) is lrge when δ is lrge. This is seen by inspecting Figure 5. When δ is lrge, the distnce between p + δ(p p ) nd p is lrge, nd so is the distnce between x + ω nd x b + ω. Therefore, the re of the big tringle not covered by the smll tringles gets lrger. This mens tht (18) is lrge. Then, lthough the government expenditure decreses s ω increses, the lowest government expenditure is still positive if δ is lrge. So, when B is smller thn the lowest government expenditure, the government cnnot implement the trnsfer policy to redistribute the gins from free trde. 4.3 Should the trnsfers be dependent on trnsctions under utrky or under free trde? So fr, we hve considered trnsfer rules under which the mount of trnsfer is dependent on the trnsction mde in period. Tht is, the government offers trnsctiontrnsfer menu x (ω),z (ω) ª,wherex (ω) is the trnsction in period nd z (ω) is the trnsfer given in period 1. In our nlysis, the resulting intertemporl utility cn be written s U x (ω),p, ω + δz (ω)+δu (ω). (19) On the other hnd, in order to redistribute the gins from free trde, we could consider trnsfer rules dependent on trnsctions mde in period 1. Nmely, the government could offer trnsctiontrnsfer menu x 1 (ω),z 1 (ω) ª,wherex 1 (ω) is the trnsction in period 1 nd z 1 (ω) is the trnsfer given in period 1. In fct, this trnsfer rule is the one studied by FL (1991). Formlly, menu x 1 (ω),z 1 (ω) ª is solution to the 18
19 welfremximiztion problem formulted s follows: mx x(ω),z(ω) [U (x (ω),p, ω)+z (ω)] dω + B z (ω) dω (2) s.t. U (x (ω),p, ω)+z (ω) U x ω,p, ω + z ω for ll ω, ω, U (x (ω),p, ω)+z (ω) U (ω) for ll ω. z (ω) dω B. The solution to this problem, denoted by x 1 (ω),z 1 (ω) ª, is qulittively similr to x (ω),z (ω) ª, the solution to problem (7) we derived in the previous section. Nmely, when B is sufficiently lrge, the GB constrint is not binding nd the trnsction schedule is efficient: x 1 (ω) =x (ω). As B flls, the GB constrint becomes binding nd the trnsction is distorted so tht consumption is smller for lrge ω, whiletheirconstrint is binding only t ω =1. Then, s B flls further, eventully the IR becomes binding for some ω < 1. However, different from problem (7), there is lwys solution to problem (2), s shown by FL (1991). This is becuse, in problem (2), mking the IR constrint binding for ll ω (tht is, forcing everyone consume x + ω) cn be implemented by blnced budget (i.e., with B =). Therefore, strting from the IR binding for everyone, the government cn let some individuls with smll ω consume more thn x + ω to mke them strictly better off by trde, nd still the GB constrint is stisfied even when B = (See Proposition 4 of FL (1991)). By the trnsfer rule x 1 (ω),z 1 (ω) ª, the intertemporl utility is given by U (ω)+δz 1 (ω)+δu x 1 (ω),p, ω. (21) Compring (19) nd (21), we cn see tht in (19) the government does not intervene trnsctions in period 1, leving the period1 utility U (ω) intct, while in (21) the government does not intervene trnsctions in period with leving the period utility U (ω) intct. Then, we sk the following question: by which trnsfer rules cn the welfre be mde higher? In other words, to redistribute the gins from free trde to everyone 19
20 with stisfying the IC constrint, which is less hrmful, distorting period trnsctions, or distorting period1 trnsctions? The proposition below shows tht the nswer depends onthesizeofb. If the government hs lrge budget for trnsfer, the former is better, nd if it hs smll budget, the ltter is better. Proposition 2 If B (1 + δ)(u (1) U (1)), the trnsfer rule dependent on trnsctions in period gives higher welfre thn the trnsfer rule dependent on trnsctions in period 1. If B< B (δ), the trnsfer rule dependent on trnsctions in period 1 gives higher welfre thn the trnsfer rule depending on trnsctions in period. Proof. When B (1 + δ)(u (1) U (1)), the GB constrint is not binding for problem (7) nd x = x. Letting W denote the resulting intertemporl welfre of problem (7), W = = U x (ω),p, ω + δz (ω)+δu (ω) δz (ω)+(p p ) x (ω)+δb dω (U (ω)+δu (ω)+δb) dω. For problem (2), note tht the GB constrint is not binding if B U (1) U (1) (The reson comes from the sme logic discussed in Section 4.2). Therefore, when B (1 + δ)(u (1) U (1)), the government cn implement x 1 = x. Let W 1 denote the resulting welfre for problem (2). We hve W 1 = = U (ω)+δz 1 (ω)+δu x 1 (ω),p, ω δz 1 (ω)+δb dω (U (ω)+δu (ω)+δb) dω. Since R 1 U (ω) dω > R 1 U (ω) dω, it holds tht W >W 1. If B< B (δ), there is no solution to problem (7). So, the best thing the government cn do is to sty utrky in both periods, thus W = R 1 (U (ω)+δu (ω)+δb) dω. On the other hnd, for problem (2), the government cn give some individuls strictly 2
21 positive gins from trde. Therefore, W 1 = U (ω)+δu x 1 (ω),p, ω + δb dω > (U (ω)+δu (ω)+δb) dω = W. Moreover, since W nd W 1 re continuous in B B (δ),evenwhenb<(1 + δ)(u (1) U (1)), s long s B is lrge enough, W stys bove W 1. This cn be seen in Figure 6, where W is higher thn W 1 even when B is fr below (1 + δ)(u (1) U (1)). 5 Concluding remrks We hve considered twoperiod model where in period the utrky price is mintined ndinperiod1freetrdeisllowed. Tochieve Preto gins from trde, the government designs trnsfer rule to collect txes from giners nd give subsidies to losers from free trde. By considering trnsfer rules tht mke the mount of trnsfer dependent on trnsctions in the utrky period, we hve shown tht there is no incentive comptible trnsfer rules tht successfully redistribute the gins from free trde if the discount fctor is sufficiently lrge or if the government budget vilble for redistribution is limited. Nmely, our finding tells tht redistributing the gins from free trde is often very costly under incomplete informtion; redistribution uses up ll gins from free trde nd still not ble to mke everyone better off. 21
22 Appendix A. Solution to problem (7). (i) When the IR constrint is binding only t ω =1: From eqution (11) nd (12), the government expenditure is clculted s follows: δz (ω) dω (p p ) x (ω) dω =(1+δ)(U (1) U (1)) mb (2 m) 6 where U (1) U (1) = µ 1 2 (p p ) (p p ) 2b nd m = λ/ (1 + λ). The GB constrint is thus (1 + δ)(u (1) U (1)) mb (2 m) 6 = δb. Solving this for m, weget m = b p b 2 6b ((1 + δ)(u (1) U (1)) δb). b Note tht m is decresing in B. So, s B flls, m increses, x (ω) decreses, nd therefore the trget utility gets steeper. As B flls enough tht the trget utility is s steep s the RHS of the IR constrint t ω =1, the IR constrint becomes binding other thn ω =1.ThebordervlueofB below which this hppens is derived by u x (1) + 1 = p + δ (p p ) p + mb = p + δ (p p ). Solving this for B, we hve the border vlue of B: µ B = 1 (2 δ) (p p ) (1 + δ)(p p ). b 6δ From our ssumption tht ( p ) /b =1/2 < ( p ) /b < 1, wehve(p p ) /b < 1/2. So, the B bove is lwys positive, mening tht for ny prmeter vlues, if B is 22
23 smll enough, the IR constrint becomes binding for ω ω 1. (ii) When the IR constrint is binding for ω ω 1: For ω ω 1, the trnsction schedule nd the trnsfer schedule re respectively given by eqution (13) nd (14). For ω < ω, since the IR constrint is not binding, nd γ () = by trnsverslity condition, the trnsction schedule is given by (11), nd thus the trnsfer schedule is by (15). From these, the government expenditure is clculted s ³ δz b (ω) (p p ) x b (ω) ω µ ω = (1+δ)(p p 2 ) Z ω dω + 2 ((1 + δ) ω δ)(p p ) 2b (δ z n (ω) (p p ) x n (ω)) dω µ bm 3 bm2 ω 3. (22) 6 The threshold vlue ω is determined s follows. For ω ω 1, x b (ω) should stisfy (1): u (x b (ω)+ω) p = R ω ω μ (t) dt + λω b. 1+λ Here, we used tht γ () = nd μ (ω) =for ω < ω (the IR constrint is not binding for this rnge of ω). At the sme time, by the IC constrint, we hve u (x b (ω) +ω) = p + δ (p p ).Thus, Z ω ω μ (t) dt = λω (1 + λ) (1 + δ)(p p ). b Especilly, when ω = ω, it holds tht Z ω ω μ (t) dt = λ ω (1 + λ) (1 + δ)(p p ) b =. Solving this for ω gives ω =(1+δ)(p p ) /bm. Substituting this into (22), nd rrnging, we hve the following GB constrint: (1 + δ)(p p ) ω 2 (1 + δ)2 (p p ) 2 ω + δ (1 + δ)(p p ) 2 6 3b 2b = δb. (23) Combined with ω =(1+δ)(p p ) /bm, thisissolvedfor ω nd m. 23
24 B.ProofofProposition1. Consider the determinnt of the qudrtic eqution (23). It is nonnegtive if B (1 + δ)(p p ) 2 6bδ Ã! 3δ (1 + δ)2 (p p ). (24) b Define the RHS of (24) s B (δ). If B< B (δ), there is no solution to problem (7). Note tht B (δ) is negtive if 3δ (1 + δ)2 (p p ) b <. (25) Since the inequlity (25) holds when δ =, violted when δ =1, nd the LHS of (25) is incresing in δ, there is unique δ (cll it δ) belowwhich B (δ) <. Thus, for δ δ, there is solution to problem (7) for ny B. Forδ > δ, B (δ) > nd B (δ) = B (δ) (1 + δ) + (1 δ)(1+δ)2 (p p ) 3 6b 2 δ 2 >. 24
25 References [1] Che, Jihu nd Giovnni Fcchini, Dul Trck Reforms: with nd without Losers, Journl of Public Economics 91 (27): [2] Dixit, Avinsh nd Victor Normn, Gins from Trde without LumpSum Compenstion, Journl of Interntionl Economics 21 (1986): [3] Dong, Bomin nd Lsheng Yun, The Loss from Trde under Interntionl Cournot Oligopoly with Cost Asymmetry, Review of Interntionl Economics 18 (21): [4] Feenstr, Robert C. nd Trcy R. Lewis, Distributing the Gins from Trde with Incomplete Informtion, Economics nd Politics 3 (1991): [5] Grndmont, JenMichel nd Dniel McFdden, A Technicl Note on Clssicl Gins from Trde, Journl of Interntionl Economics 2 (1972): [6] Ichino, Ysukzu, Trnsction Flsifiction nd the Difficulty of Achieving Pretoimproving Gins from Trde through Lumpsum Trnsfers, Review of Interntionl Economics 2 (212): [7] Kemp, Murry C., The Gin from Interntionl Trde, Economic Journl 72 (1962): [8] Kemp, Murry C., The Gins from Trde in CournotNsh Trding Equilibrium, Review of Interntionl Economics 18 (21): [9] Kemp, Murry C. nd Henry Y. Wn, Jr., The Gins from Free Trde, Interntionl Economic Review 13 (1972): [1] Wong, Kryiu, Interntionl Trde in Goods nd Fctor Mobility, Cmbridge: MIT Press, [11] Wong, Kryiu, Gins from Trde with LumpSum Compenstion. Jpnese Economic Review 48 (1997):
26 U U ( ) when the GB is not binding. U ( ) U *( ) (slope = p ) (slope = p* ) U ( x*( ), p, ) U ( ) ( U ( ) U * ( )) (slope = p ( p p*) ) 1 Figure 1: U (ω) when the GB constrint is not binding 26
27 U U ( U ( ) when the GB is binding nd the IR is binding only t 1. ) when the GB is not binding. U ( ) (slope = p ) U *( ) (slope = p* ) U ( ) ( U ( ) U * ( )) (slope = p ( p p*) ) 1 Figure 2: U (ω) when the GB constrint is binding nd the IR constrint is binding only t ω =1 27
28 U U ( ) when the IR is binding for some 1. U ( ) U *( ) (slope = p ) (slope = p* ) U ( ) ( U ( ) U * ( )) (slope = p ( p p*) ) 1 Figure 3: U (ω) when the IR constrint is binding for some ω < 1 28
29 x( ) x * ( ) x ( ) b x ( ) x ( ) when the IR is binding only t 1. x ( ) when the IR is binding for some 1. 1 Figure 4: Consumption of good x 29
30 p b U ( x*, p*) U ( x, p*) p ( p p*) p ( U( x*, p*) U( x, p*)) U( x*, p*) U( x, p*) p * u ( x ) b x x x * x Figure 5: 3
31 B.3.25 * B (1 )( U (1) U (1)) : bove this curve, the GB constrint is not binding Below this curve, the IR constrint is binding for some 1. Above this curve, W >W 1 : the trnsfer rule in our model gives higher welfre thn FL(1991) s..5 B( ): no solution below this curve A numericl exmple: when =2, b=1, p*=5/4 Figure 6: 31
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 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 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 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 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 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 10438 UNVERSTY OF NOTTNGHAM Discussion
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 informationAll pay auctions with certain and uncertain prizes a comment
CENTER FOR RESEARC IN ECONOMICS AND MANAGEMENT CREAM Publiction No. 12015 All py uctions with certin nd uncertin prizes comment Christin Riis All py uctions with certin nd uncertin prizes comment Christin
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 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 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 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 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 pointdirection nd twopoint
More informationand thus, they are similar. If k = 3 then the Jordan form of both matrices is
Homework ssignment 11 Section 7. pp. 24925 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 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 ttest is one of the most commonly used sttisticl hypothesis tests, it hs limittions. The mjor limittion is tht the ttest cn be used to compre the mens of only
More informationFactoring Polynomials
Fctoring Polynomils Some definitions (not necessrily ll for secondry school mthemtics): A polynomil is the sum of one or more terms, in which ech term consists of product of constnt nd one or more vribles
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 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 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 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 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, crossclssified
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 informationIntegration. 148 Chapter 7 Integration
48 Chpter 7 Integrtion 7 Integrtion t ech, by supposing tht during ech tenth of second the object is going t constnt speed Since the object initilly hs speed, we gin suppose it mintins this speed, but
More informationBabylonian Method of Computing the Square Root: Justifications Based on Fuzzy Techniques and on Computational Complexity
Bbylonin Method of Computing the Squre Root: Justifictions Bsed on Fuzzy Techniques nd on Computtionl Complexity Olg Koshelev Deprtment of Mthemtics Eduction University of Texs t El Pso 500 W. University
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 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 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 informationWeek 7  Perfect Competition and Monopoly
Week 7  Perfect Competition nd Monopoly Our im here is to compre the industrywide response to chnges in demnd nd costs by monopolized industry nd by perfectly competitive one. We distinguish between
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 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 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 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 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 informationAlgebra Review. How well do you remember your algebra?
Algebr Review How well do you remember your lgebr? 1 The Order of Opertions Wht do we men when we write + 4? If we multiply we get 6 nd dding 4 gives 10. But, if we dd + 4 = 7 first, then multiply by then
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 informationThe Velocity Factor of an Insulated TwoWire Transmission Line
The Velocity Fctor of n Insulted TwoWire 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 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 informationHow To Set Up A Network For Your Business
Why Network is n Essentil Productivity Tool for Any Smll Business TechAdvisory.org SME Reports sponsored by Effective technology is essentil for smll businesses looking to increse their productivity. Computer
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 information200506 Second Term MAT2060B 1. Supplementary Notes 3 Interchange of Differentiation and Integration
Source: http://www.mth.cuhk.edu.hk/~mt26/mt26b/notes/notes3.pdf 256 Second Term MAT26B 1 Supplementry Notes 3 Interchnge of Differentition nd Integrtion The theme of this course is bout vrious limiting
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 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 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 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 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. nmwide region t x
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 relvlued
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 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 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 informationg(y(a), y(b)) = o, B a y(a)+b b y(b)=c, Boundary Value Problems Lecture Notes to Accompany
Lecture Notes to Accompny Scientific Computing An Introductory Survey Second Edition by Michel T Heth Boundry Vlue Problems Side conditions prescribing solution or derivtive vlues t specified points required
More informationLecture 5. Inner Product
Lecture 5 Inner Product Let us strt with the following problem. Given point P R nd line L R, how cn we find the point on the line closest to P? Answer: Drw line segment from P meeting the line in right
More informationSection 74 Translation of Axes
62 7 ADDITIONAL TOPICS IN ANALYTIC GEOMETRY Section 74 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 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 informationSolving BAMO Problems
Solving BAMO Problems Tom Dvis tomrdvis@erthlink.net http://www.geometer.org/mthcircles Februry 20, 2000 Abstrct Strtegies for solving problems in the BAMO contest (the By Are Mthemticl Olympid). Only
More informationWarmup for Differential Calculus
Summer Assignment Wrmup for Differentil Clculus Who should complete this pcket? Students who hve completed Functions or Honors Functions nd will be tking Differentil Clculus in the fll of 015. Due Dte:
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 informationA.7.1 Trigonometric interpretation of dot product... 324. A.7.2 Geometric interpretation of dot product... 324
A P P E N D I X A Vectors CONTENTS A.1 Scling vector................................................ 321 A.2 Unit or Direction vectors...................................... 321 A.3 Vector ddition.................................................
More information2 DIODE CLIPPING and CLAMPING CIRCUITS
2 DIODE CLIPPING nd CLAMPING CIRCUITS 2.1 Ojectives Understnding the operting principle of diode clipping circuit Understnding the operting principle of clmping circuit Understnding the wveform chnge of
More informationCHAPTER 11 Numerical Differentiation and Integration
CHAPTER 11 Numericl Differentition nd Integrtion Differentition nd integrtion re bsic mthemticl opertions with wide rnge of pplictions in mny res of science. It is therefore importnt to hve good methods
More informationOptimal Redistributive Taxation with both Labor Supply and Labor Demand Responses
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
More informationRegular Sets and Expressions
Regulr Sets nd Expressions Finite utomt re importnt in science, mthemtics, nd engineering. Engineers like them ecuse they re super models for circuits (And, since the dvent of VLSI systems sometimes finite
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 information2. Transaction Cost Economics
3 2. Trnsction Cost Economics Trnsctions Trnsctions Cn Cn Be Be Internl Internl or or Externl Externl n n Orgniztion Orgniztion Trnsctions Trnsctions occur occur whenever whenever good good or or service
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 Employersponsored helth insurnce (ESI) is the dominnt source of coverge for nonelderly dults
More informationHomework 3 Solutions
CS 341: Foundtions of Computer Science II Prof. Mrvin Nkym Homework 3 Solutions 1. Give NFAs with the specified numer of sttes recognizing ech of the following lnguges. In ll cses, the lphet is Σ = {,1}.
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 informationOptimal Execution of OpenMarket Stock Repurchase Programs
Optiml Eecution of OpenMrket Stock Repurchse Progrms Jcob Oded This Drft: December 15, 005 Abstrct We provide theoreticl investigtion of the eecution of openmrket stock repurchse progrms. Our model suggests
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 soclled volumes of
More informationIIMK/WPS/121/FIN/2013/07. Abhilash S. Nair 1
IIMK/WPS/2/FIN/203/07 EXISTENCE OF CAPITAL MARKET EQUILIBRIUM IN THE PRESENCE OF HERDING AND FEEDBACK TRADING Abhilsh S. Nir Assistnt Professor, Indin Institute of Mngement Kozhikode, IIMK Cmpus PO, Kozhikode
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 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 information9.3. The Scalar Product. Introduction. Prerequisites. Learning Outcomes
The Sclr Product 9.3 Introduction There re two kinds of multipliction involving vectors. The first is known s the sclr product or dot product. This is soclled becuse when the sclr product of two vectors
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 informationOnline Multicommodity Routing with Time Windows
KonrdZuseZentrum für Informtionstechnik Berlin Tkustrße 7 D14195 BerlinDhlem Germny TOBIAS HARKS 1 STEFAN HEINZ MARC E. PFETSCH TJARK VREDEVELD 2 Online Multicommodity Routing with Time Windows 1 Institute
More informationWeek 11  Inductance
Week  Inductnce November 6, 202 Exercise.: Discussion Questions ) A trnsformer consists bsiclly of two coils in close proximity but not in electricl contct. A current in one coil mgneticlly induces n
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 informationRIGHT TRIANGLES AND THE PYTHAGOREAN TRIPLETS
RIGHT TRIANGLES AND THE PYTHAGOREAN TRIPLETS Known for over 500 yers is the fct tht the sum of the squres of the legs of right tringle equls the squre of the hypotenuse. Tht is +b c. A simple proof is
More informationpiecewise Liner SLAs and Performance Timetagment
i: Incrementl Cost bsed Scheduling under Piecewise Liner SLAs Yun Chi NEC Lbortories Americ 18 N. Wolfe Rd., SW3 35 Cupertino, CA 9514, USA ychi@sv.nec lbs.com Hyun Jin Moon NEC Lbortories Americ 18 N.
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 informationVersion 001 Summer Review #03 tubman (IBII20142015) 1
Version 001 Summer Reiew #03 tubmn (IBII20142015) 1 This printout should he 35 questions. Multiplechoice questions my continue on the next column or pge find ll choices before nswering. Concept 20 P03
More informationAnswer, Key Homework 10 David McIntyre 1
Answer, Key Homework 10 Dvid McIntyre 1 This printout should hve 22 questions, check tht it is complete. Multiplechoice questions my continue on the next column or pge: find ll choices efore mking your
More informationOn the Robustness of Most Probable Explanations
On the Robustness of Most Probble Explntions Hei Chn School of Electricl Engineering nd Computer Science Oregon Stte University Corvllis, OR 97330 chnhe@eecs.oregonstte.edu Adnn Drwiche Computer Science
More informationLumpSum Distributions at Job Change, p. 2
Jnury 2009 Vol. 30, No. 1 LumpSum Distributions t Job Chnge, p. 2 E X E C U T I V E S U M M A R Y LumpSum Distributions t Job Chnge GROWING NUMBER OF WORKERS FACED WITH ASSET DECISIONS AT JOB CHANGE:
More informationbaby on the way, quit today
for mumstobe bby on the wy, quit tody WHAT YOU NEED TO KNOW bout smoking nd pregnncy uitting smoking is the best thing you cn do for your bby We know tht it cn be difficult to quit smoking. But we lso
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 informationThe Relative Advantages of Flexible versus Designated Manufacturing Technologies
The Reltive Advntges of Flexible versus Designted Mnufcturing Technologies George Normn Cummings Professor of Entrepreneurship nd Business Economics Tufts University Medford MA 055 USA emil: george.normn@tufts.edu
More informationThe Definite Integral
Chpter 4 The Definite Integrl 4. Determining distnce trveled from velocity Motivting Questions In this section, we strive to understnd the ides generted by the following importnt questions: If we know
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 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 005909 eissn 56550 06 5 93 informs doi 0.87/mnsc.060.0574 006 INFORMS Strtegic Investments, Trding, nd Pricing Under Forecst Updting Jiri
More informationProtocol Analysis. 17654/17764 Analysis of Software Artifacts Kevin Bierhoff
Protocol Anlysis 17654/17764 Anlysis of Softwre Artifcts Kevin Bierhoff TkeAwys Protocols define temporl ordering of events Cn often be cptured with stte mchines Protocol nlysis needs to py ttention
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 information19. The FermatEuler Prime Number Theorem
19. The FermtEuler Prime Number Theorem Every prime number of the form 4n 1 cn be written s sum of two squres in only one wy (side from the order of the summnds). This fmous theorem ws discovered bout
More informationWhy is the NSW prison population falling?
NSW Bureu of Crime Sttistics nd Reserch Bureu Brief Issue pper no. 80 September 2012 Why is the NSW prison popultion flling? Jcqueline Fitzgerld & Simon Corben 1 Aim: After stedily incresing for more thn
More informationffiiii::#;#ltlti.*?*:j,'i#,rffi
5..1 EXPEDTNG A PROJECT. 187 700 6 o 'o' 600 E 500 17 18 19 20 Project durtion (dys) Figure 66 Project cost vs. project durtion for smple crsh problem. Using Excel@ to Crsh Project T" llt ffiiii::#;#ltlti.*?*:j,'i#,rffi
More information4 Approximations. 4.1 Background. D. Levy
D. Levy 4 Approximtions 4.1 Bckground In this chpter we re interested in pproximtion problems. Generlly speking, strting from function f(x) we would like to find different function g(x) tht belongs to
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 informationFUNDING OF GROUP LIFE INSURANCE
TRANSACTIONS OF SOCIETY OF ACTUARIES 1955 VOL. 7 NO. 18 FUNDING OF GROUP LIFE INSURANCE CHARLES L. TROWBRIDGE INTRODUCTION T RADITIONALLY the group life insurnce benefit hs been finnced on yerly renewble
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 informationThe Impact of Oligopolistic Competition in Networks
OPERATIONS RESEARCH Vol. 57, No. 6, November December 2009, pp. 1421 1437 issn 0030364X eissn 15265463 09 5706 1421 informs doi 10.1287/opre.1080.0653 2009 INFORMS The Impct of Oligopolistic Competition
More information