International Trade with Domestic Regulation under Asymmetric Information: A Simple General Equilibrium Approach

Transcription

1 Intenational Tade with Domestic Regulation unde Asymmetic Infomation: A Simple Geneal Equilibium Appoach David Matimot and Thiey Vedie Septembe 8, 2009 Abstact: This pape investigates the consequences of designing domestic incentive egulation unde asymmetic infomation in the geneal equilibium context of an open economy. We discuss the implications of such incentive egulation fo intenational specialization and the conditions fo tade openness to be still welfae-impoving. Moe specifically, we append to an othewise standad 2 2 Hecksche-Ohlin model of a small open economy a continuum of intemediate sectos poducing non-tadable goods used in tadable sectos. Those goods ae poduced by local fims which ae pivately infomed on thei technologies but ae egulated by a domestic egulato. Even when domestic egulation is optimally designed at the sectoal level, asymmetic infomation geneates distotions which cannot be coected. The small county becomes elatively iche in the facto which is infomationally sensitive so that asymmetic infomation might evese pattens of tade. Fee tade is Paeto-dominated by autaky when it exacebates the distotions due to asymmetic infomation. As an aside, ou methodology povides a constained Fist Welfae Theoem unde asymmetic infomation of geneal inteest beyond ou tade model. Keywods: Incentive egulation, tade, specialization, asymmetic infomation. JEL Classification: D82; F2; L5. We thank Yolande Hiiat, Humbeto Moeia and Macelo Olaeaga fo vey useful comments on an ealie daft. Financial suppot fom the Wold Bank is gatefully acknowledged. The usual disclaime applies. All eos ae ous. Toulouse School of Economics EHESS), Toulouse, and CEPR. Pais School of Economics EHESS), Pais, and CEPR.

2 Intoduction One of the founding pinciples of Neoclassical Tade Theoy is that fee tade impoves welfae unde pefect competition, in the absence of extenality, and when makets ae complete. Of couse, economists have long been awae that this esult may fail when any of those conditions no longe holds. Still, the common wisdom emains that, with enough policy instuments to coect fo domestic distotions, a small economy always benefits fom open bodes. This pape econsides this geneal pinciple in a famewok whee asymmetic infomation emains a fundamental obstacle to the coection of domestic distotions. A basic tenet of the Incentive Regulation liteatue is indeed that efficiency and edistibutive concens ae deeply linked unde asymmetic infomation. Any egulatoy policy aimed at coecting allocative distotions which could be necessay to enjoy the full the gains fom tade has necessaily stong distibutional consequences between those agents who etain pivate infomation and those who emain uninfomed. This basic pinciple of the Incentives liteatue stands in shap contast with the common wisdom that the absence of fictions in edistibuting gains fom tade between winnes and loses is a necessay condition to ensue the optimality of fee tade. With those conflicting insights in mind, this pape taces out the implications of asymmetic infomation within domestic makets fo the degee of intenational competitiveness and the choice of specialization faced by a small open county. Embedding the lessons of the Incentive Regulation liteatue into a geneal equilibium envionment, we deive nomative implications of a joint use of tade integation and optimal domestic egulation on tade pattens. Finally, we ask whethe tade openness emains welfaeimpoving compaed to autaky when asymmetic infomation is a fundamental obstacle to the design of efficient domestic egulations. Moe specifically, conside a small open economy with two factos capital and labo) and two final goods. Those goods ae taded on intenational makets and poduced by competitive sectos. In this typical Heckshe-Ohlin envionment, one of the final good sectos is capital intensive while the othe is instead labo intensive. Those sectos also use some non-tadable intemediate goods which ae poduced domestically. One may think of those goods as telecommunications, enegy, tanspotation, utilities and sevices. Each of those intemediate sectos is un by a local monopolist which, fo simplicity, uses capital as its sole input. Ownes of those monopolies have pivate infomation on thei technologies. Insights fom the Incentive Regulation liteatue 2 indicate that those ownes may withdaw some infomation ent fom being pivately infomed. To coect Laffont and Tiole 993) and Laffont and Matimot 2002) fo instance. 2 Laffont and Tiole 993) among othes. 2

3 theefoe fo the distotions due to maket and infomational powes, egulation of those intemediate sectos is needed. Howeve, any such coective policy emains by and lage constained by asymmetic infomation. 3 Pattens of tade. Ou fist contibution is to show how asymmetic infomation in egulated sectos affects this small county s patten of specialization. Two effects ae at play in explaining changes in the patten of tade. Fist, standad Incentives Theoy 4 teaches us that inducing infomation evelation fom pivately infomed fims equies to leave them some costly infomation ents. Moeove, those ents incease with poduction in those sectos. Optimal egulation educes thus infomation ents by downsizing poduction in egulated sectos. Since these sectos use capital only, moe capital becomes available fo the capital intensive tadable good. This makes that good elatively cheape to poduce. With asymmetic infomation, eveything happens thus as if the small county was elatively iche in the facto which is infomationally sensitive. This fist effect may change the patten of tade with the est of the wold compaed with what aises unde complete infomation. Second, in a geneal equilibium famewok, infomation ents end up being pocketed by a epesentative) consume and theefoe boost demands fo final tadable goods. In fine, unde asymmetic infomation, this consume enjoys not only his income associated to the usual facto endowments of this economy but also the equivalent of an infomational endowment eflecting the facto content of the infomation ents captued by intemediate sectos. With Cobb-Douglas pefeences and moe geneally homothetic pefeences), this additional wealth does not change the elative demand fo tadable goods. In such a context, the patten of tade is entiely dictated by the lowe poduction cost of the capital intensive good due to the infomationally induced contaction of output in the intemediate sectos. Fee tade may be welfae-deteioating. Ou second contibution consists in assessing the nomative implications of fee tade in this context with asymmetic infomation. A pioi, thee ae two possible souces of distotions in ou small open economy. Fist, monopolies in intemediate sectos might have maket powe and chage a mak-up. Second, asymmetic infomation might also affect the allocation of esouces. The fist distotion could easily be fixed unde complete infomation by means of convenient subsidies. In such a highly hypothetical context, fee tade would always dominate autaky fo a small open economy. The conventional wisdom that well-designed behind-the-bode policies do no conflict with fee tade would pevail. 3 Given that optimal egulation concens a non-tadable secto, that behind-the-bode policy is de facto non-disciminating against foeign fims. 4 Laffont and Tiole 993) and Laffont and Matimot 2002, Chapte 2) fo instance. 3

4 Asymmetic infomation is a moe seious concen even when the lagest set of egulatoy policies is available. Asymmetic infomation is indeed the souce of a mak-up that emains even afte policy intevention. Given the dead-weight loss associated to those distotions, fee tade may not always dominate autaky. When consumes have Cobb-Douglas pefeences, we povide conditions unde which fee tade dominates autaky even unde asymmetic infomation. Howeve, fee tade can now be sometimes Paeto infeio to autaky. The intuition is quite simple. To minimize infomation ents in intemediate sectos, optimal egulation educes output in those sectos. If tade openness induces a patten of specialization which einfoces this domestic distotion, this additional distotionay effect may outweigh the taditional gains fom tade. Fee tade is then dominated by autaky. Liteatue eview. This pape lies at the the intesection of the Tade and Regulation liteatues and boows insights fom both. Stating with Bhagwati 97), the Tade liteatue has built an analytical famewok that allows to assess distotions away fom fee tade and discuss how such distotions can be coected. 5 Following Bhagwati s taxonomy, distotions found in the absence of non-pecuniay extenalities might aise fom maket impefections o fom misguided policy inteventions which ae exogenously set. In both cases, well-designed policies could avoid the distotion. Asymmetic infomation ceates instead a moe basic souce of distotions which has so fa been ovelooked in geneal equilibium envionments. Incentive compatibility constaints limit the set of feasible allocations even when the most complete set of policy instuments is available. Distotions ae not a pioi imposed by exogenously esticting those instuments as in the ealie tade liteatue. They ae instead deeply linked to the undelying infomation stuctue. This last point is in fact closely elated to a bugeoning liteatue that analyzes optimal taxation in open economies Naiko 996, Gabaix 997a and 997b, Guesneie 998 and 200 and Specto 200). This liteatue has investigated also how asymmetic infomation imposes limits on domestic edistibutive policies. Extending the famewok developed by Stiglitz 982) to a 2 2 tade model, these papes show that fee-tade can be socially infeio, at least locally, to autaky. In these papes, the demand side of the economy has pivate infomation on the souce of facto income skilled vesus unskilled labo income) and incentive compatibility constaints affect the tade-off between consumption and leisue. Ou model of optimal egulation investigates instead infomational asymmeties on the poduction side of the economy. Focusing on the poduction side makes welfae analysis much moe tactable. On top, it facilitates ou deivation of a constained Fist Welfae Theoem: the competitive equilibium of the economy unde 5 See Sinavasan 987) fo instance. 4

5 asymmetic infomation also solves a social planne poblem whee feasibility constaints ae conveniently modified to account fo infomational endowment. No such esult was available in the Taxation liteatue quoted above. Beyond ou specific tade model, ou methodology can be used elsewhee to deive welfae popeties of competitive equilibium unde asymmetic infomation. This pape builds also on the Incentive Regulation liteatue developed by Baon and Myeson 982), Laffont and Tiole 993) and Amstong and Sappington 2005) among othes. One of its impotant insight is that, unde asymmetic infomation, thee is always a fundamental tade-off between giving up to egulated fims some infomation ents which ae socially costly and eaching allocative efficiency. Although this liteatue has poved to be paticulaly useful in assessing sectoal inteventions, it is cast in a patial equilibium famewok and nothing is known on the consequences of such sectoal egulations in open economies. This is clealy an impotant issue given the cuent globalization tend and the ole that domestic egulated sectos like local tanspotation, telecommunications, electicity, utilities and vaious accounting and financial sevices play in shaping the whole poduction patten of counties. In othe wods, ou pape contibutes to a bette undestanding of how behind-the-bode egulations affect pattens of tade. Section 2 descibes both the domestic and intenational sides of the economy. Section 3 discusses the benchmak economy unde complete infomation. Section 4 consides an economy with asymmetic infomation. It stats with a chaacteization of the autakic equilibium and goes on by chaacteizing how pattens of tade with the est of the wold ae affected by infomational asymmeties. Section 5 consides the nomative implications of openness. Section 6 concludes. Poofs ae elegated to an Appendix. 2 The Model Ou model has two building blocks. The fist one descibes tade between a small economy and the est of the wold. The second one analyzes the design of optimal egulation fo intemediate sectos within that county. On the tade side, we conside a standad Heckshe-Ohlin model with two tadable goods, manufactues M and agicultual poducts A, and two factos, labo and capital. On top of these standad featues, we add a continuum of intemediate sectos un by domestic monopolies which use only capital as an input. 6 One can think of those non-tadable inputs as electicity, telecommunication, tanspotation and utilities which ae poduced locally, egulated, and not taded on intenational makets. Those examples show that capital geneally unde the fom of infastuctues) is the main input fo poducing those intemediate goods and this aspect 6 Given the symmety of ou model, all conclusions ae evesed if intemediate sectos use only labo. 5

6 will be a basic point of ou modeling. In those intemediate sectos, poduction technologies ae highly idiosyncatic and ownes of those fims have pivate infomation on thei technologies. In the shot-un, competition by potential entants in those sectos is of little value and domestic egulation is the only device to limit maket powe. Even though egulatos face no estiction in thei choice of instuments to cub maket powe, such intevention is nevetheless constained by thei incomplete knowledge of the poduction technology. We analyze each building block in tun and we descibe the equilibium unde autaky. Then, we intoduce maket openness and analyze its ole on the patten of tade. Pefeences. To simplify the analysis and make it as tactable as possible, consumes have pefeences ove consumptions of tadable goods M and A given by a standad Cobb-Douglas utility function: UC M, C A ) = αlnc M + α)lnc A whee α 0, ). Final Sectos. Final goods M and A ae poduced by competitive fims. We denote by p the pice of the manufactued good wheeas the agicultual good is taken as the numeaie. Each final secto uses a continuum of intemediate non-tadable inputs and poduction factos. In lines with standad tade facto endowment theoy, we assume that secto M is capital intensive while secto A is labo intensive. Moe pecisely, the poduction functions in each secto ae espectively given by whee β 0, ) and D i = Y M = D β M K and Y A = D β A L, x 0 ji ) dj with > fo i = M, A. The amount of intemediate good j used in the final secto i is denoted by x ji. The index j vaies continuously on [0, ]. is the elasticity of substitution between any two intemediate goods in the poduction pocess of good i. The assumption of a continuum of intemediate sectos is made fo tactability only. Late on, it allows us to use the Law of Lage Numbes to simply chaacteize optimal egulation in those sectos and to define an aggegate poductivity index that paameteizes the whole economy. 7 With such a fomulation, all non-tadable intemediate inputs ente symmetically in the poduction of the tadable sectos. 8 This small economy is endowed with espectively L units of labo and K units of capital. Let be the ental ate of capital and w the wage. 7 A moe cumbesome analysis could be done with a finite numbe of those sectos. 8 Beaking this symmety leads to a moe complex analysis without changing the main insights of the pape. 6

7 We denote t jm and t ja the payments made by the final sectos to intemediate ones to obtain the inputs needed in thei poduction pocesses. Pofits in each final good secto can thus be witten espectively as: and Π M = p 0 Π A = 0 ) β x jm dj K K ) β x ja dj L wl 0 0 t jm dj t ja dj. Unde asymmetic infomation, it is a significant loss of geneality to estict the payments of the final sectos to be linea in the quantity of intemediate goods they buy. Incentives Theoy teaches us that menus of options ae useful devices to sceen infomed paties accoding to thei pivate infomation. We discuss below the pecise fom of those incentive payments. Fo the time being, it is only useful to see those payments as being decided by the egulato in chage of egulating intemediate sectos. Intemediate Sectos. Poducing x j units of intemediate good j equies j x j units of capital. 9 The poductivity of each intemediate secto j is affected by a andom shock j. Ove the whole continuum of sectos, these shocks ae independently and identically distibuted on a set Θ = {, } with espective pobabilities ν and ν. Those pobabilities ae common knowledge. Let E ) be the expectation opeato w..t.. Poduction shocks in secto j ae obseved only by fim j s ownes. This assumption is motivated by the fact that the technology fo each intemediate secto is highly specific to that secto and cannot be easily compaed with technologies fo poducing othe intemediate inputs. 0 Without egulation, fims in the intemediate sectos would fix pices above thei maginal costs. Such maket powe calls fo egulatoy policies whose goal is to impove allocative efficiency by shifting down pice close to maginal costs and inceasing demand of the final secto fo the intemediate goods. Howeve, asymmetic infomation in intemediate sectos still ceates impotant tade-offs between allocative efficiency 9 Ou assumption that sevices ae poduced with capital only and that the manufactue and agicultue sectos use eithe labo o capital but not both is just made fo analytical convenience. What mattes is the elative intensities in these thee sectos and, especially in ou context, which of the two tadable sectos uses moe intensively the input facto also used in the egulated sectos. 0 The eade may find ou epesentative custome a little bit schizophenic. On the one hand, as an owne of the intemediate sectos, he is pivately infomed on the shocks hitting each of these sectos. On the othe hand, as an owne of the fims in the final secto and a consume, he ignoes this piece of infomation. This modeling difficulty can easily be avoided by consideing diffeent classes of ownes knowing diffeent pieces of infomation but having the same Cobb-Douglas utility function. Thee would be as much classes as intemediate sectos. Using Goman aggegation ule, it is standad to show that the behavio of those agents can be aggegated and summaized by the behavio of a single epesentative agent having the whole the endowment of the economy. 7

8 and extaction of the monopolies infomation ents even when an optimal egulation is designed. Given the payments eceived fom the final sectos, pofits in the intemediate secto j can be witten as: U j = t jm + t ja j x jm + x ja ), fo j [0, ]. To ensue that fims in the intemediate sectos beak-even, the egulatoy payments eceived by those fims must cove thei costs. This yields the condition U j 0. To model a meaningful tade-off between efficiency and ent extaction, we follow the Incentive Regulation liteatue and assume that the egulatoy agency in chage with cubing maket powe in intemediate secto j maximizes the pofits of the final sectos which consume those intemediate goods fo thei own poduction pocess, namely: W = Π M + Π A. As the sequel will make clea, this egulato takes final goods pices and facto pices as given when designing an optimal egulatoy scheme. In othe wods, this means that the egulato has no tools to influence what happens on the final secto. This fits with egulatoy policies used in pactice fo electicity, telecommunication o tanspots whee egulatoy agencies have esticted sectoal objectives diectly elated to the inteests of customes of those egulated sectos hee the tadeable sectos). Thee is theefoe still significant scope fo makets and pices to equilibate aggegate supply and demand in the economy even afte egulatoy tools have been set up. Although the egulato maximizes the pofit of fims in the final secto, he does not intoduce any distotion in the elationship with consumes. Instead, his sole concen is to educe as much as possible distotions due to the intemediate fims behavio. Indeed, unde complete infomation, the egulato would like to ensue that intemediate sectos chage a pice equal to maginal cost so that poduction decisions in the final sectos ae not distoted. Because the egulato is only concened by pofits in the final sectos, he wants also to minimize the infomation ent left to the intemediate sectos. This will induce some distotions and a wedge between pice and maginal cost in the intemediate sectos. Expessing pofits in the final secto as a function of the infomation ents of the intemediate ones, the egulato s objective function can be ewitten as: ) β p x ) β jm dj K + x ) ja dj L wl j x jm + x ja )dj + K }{{} Allocative Efficiency Baon and Myeson 982), Laffont and Tiole 993) and Amstong and Sappington 2005). 8

9 U j dj 0 }{{} Infomation Rents This expession stesses the tade-off faced by the egulato. On the one hand, the egulato is concened by an efficient use of esouces, namely finding the vecto of inputs K, L, x jm, x ja ) which maximizes aggegated pofits in all poduction sectos fist backeted tem). On the othe hand, the egulato is also inteested in minimizing the infomation ents left to the intemediate sectos. 2,3. 3 Tade and Regulation unde Complete Infomation Let us stat with the case of complete infomation. This will povide a useful benchmak against which one can assess how asymmetic infomation might change tade pattens. Supply Side. Suppose that the egulato is fully infomed on the whole vecto of shocks =,..., j,...) hitting intemediate sectos. Given that thee is a continuum of symmetic intemediate sectos, the Law of Lage Numbe applies and we have: [ D i = 0 ] x ji dj = E x ji ) )) i = M, A, whee x ji ) is the output of the intemediate goods j fo secto i when the poductivity shock hitting this secto is. Because of symmety, all sectos poduce the same outputs in equilibium when they ae hit by simila shocks. Theefoe, the index j can be omitted and we can denote x ji ) = x i ) fo any. Similaly, we also denote by U) the pofit o infomation ent of a given intemediate secto when it is hit by shock. Unde complete infomation, the egulato s poblem is thus given by: max p E {K,L,x i ),U )} x M ) )) β K + E x A ) wl K E x M ) + x A ))) E U)) )) β L subject to U) 0, fo all in Θ ) 2 Ou modeling of the egulato s objective function could nevetheless be extended, at the cost of an inceased complexity, to the case whee a positive, but less than one, weight is given to the intemediate sectos. See Baon and Myeson 982) fo that assumption in a patial equilibium model. An altenative intepetation of such assumption is that one cannot finance the infomational ents left to manages of the intemediate sectos though non-distotionay taxation Laffont and Tiole, 993). 3 With this egulatoy objective, eveything happens as if the incentive contacts given to the intemediate sectos wee actually offeed by the final sectos poduces in an unegulated famewok. This intepetation of the model gives a boade scope to ou analysis. 9

10 whee ) ae paticipation constaints in the intemediate sectos. 4 Solving this poblem is staightfowad. The coesponding solution chaacteizes the supply side of this economy when egulation takes place unde complete infomation. Poposition Unde complete infomation, the optimal egulation of the intemediate sectos entails the following popeties. Fo any ealization of the poductivity shock, fims in the intemediate sectos get zeo infomation ent: U F I ) = 0, fo all in Θ. Zeo-pofit conditions in the final sectos yield β w = β) β β Θ β 2) and whee Θ = facto pice. ) E ) p = ω ) 3) is an aggegate poductivity index and ω = w is the elative Unde complete infomation, the optimal egulation of the supply side of the economy maximizes the whole pofit of the vetically integated stuctue obtained by meging final and intemediate sectos. Eveything happens as if intemediate sectos wee selling thei inputs at maginal cost to final good poduces and making zeo pofit. Because of constant etuns to scale, the whole pofit of this integated stuctue will also be zeo. Fims in the intemediate sectos poduce moe when they ae hit by a good shock than by a bad shock. Accodingly, we shall efe in the sequel to the efficient esp. inefficient) fim esp. ). Impotantly, 2) defines a downwad sloping cuve, = F I w) which captues the zeo pofit condition on the agicultual secto unde constant etuns to scale: a highe wage must be compensated by a lowe cost of capital. We will efe to that cuve as the zeo pofit locus. The paamete Θ eflects the poductivity of this economy. As Θ inceases, poduction of intemediate goods out of capital becomes moe difficult. This deceases the demand fo complementay inputs, capital and labo, emanating fom the final sectos. 4 Note again that the pices ae taken as given by the egulato since he is only concened by tansactions between the final and the intemediate sectos. We nevetheless slightly abuse and simplify notations by omitting the dependence of the optimization vaiables on the pice vecto. 0

11 Demand Side. Given the Cobb-Douglas pefeences of the epesentative consume, demands fo both consumption goods ae espectively C M = αrf I p and C A = α)r F I, whee R F I is the consume s total income unde complete infomation. With constant etuns to scale in the poduction sectos, this income comes fom the facto endowment only and R F I = w L + K. Autaky. Unde autaky, the equilibium conditions on the agicultual and labo makets yield α)w L + K) = X β L A = w β L whee the second equality comes fom expessing labo demand in the agicultual secto. This can be simplified as: ω = w = L ) K α) β). 4) Those maket cleaing conditions define thus an upwad sloping elationship = 2 F I w) linking the ental ate of capital and the labo wage: the autaky locus. The elative facto pice ω is invesely popotional to the elative endowment of factos. As capital becomes moe scace, the ental ate of capital appeciates in elative tems. An autaky equilibium is obtained when 2), 3) and 4) hold altogethe. Next poposition ensues existence of such an equilibium and povides useful compaative statics. Poposition 2 Thee exists a unique equilibium unde autaky and complete infomation. It is chaacteized by the pice system p F I, w F I, F I ) solving 2), 3) and 4). As Θ inceases, the zeo-pofit locus F I ) is shifted downwads and the autaky locus F I 2 ) emains unchanged. Thee is a downwad shift in the facto pices w F I and F I. As the poductivity index deteioates Θ inceasing), the demand fo intemediate goods deceases and demands fo both capital and labo diminish. This leads to a lowe ental ate of capital and lowe wages. See Figue.) Since intemediate sectos ente in the same way in the poduction technologies of both tadable sectos, the whole impact of a change in the poductivity index comes fom a shift in the zeo-pofit locus 2). When the poductivity index inceases, the autaky locus 4) is unchanged and the elative facto pice emains the same, namely L K ). In the sequel, we will be paticulaly α)) inteested in the impact of asymmetic infomation on the poductivity index. Fee Tade. Let us now conside the case whee this small county opens up tade with the est of the wold. Unde fee tade, the elative pice of final goods is fixed on

12 the wold maket at some exogenous level p. Note that 2) and 3) ae still valid so that emaining pices in the open economy ae completely defined. Define the epesentative consume s indiect utility function V F I p) as follows: P F I ) : V F I p) max {C M,C A,X M,X A,x m ),x a )} αlnc M + α)lnc A subject to px β M K + X β L A pc M + C A 5) ) X M = E x 6) X A = E M x A ) ) K = K + E x M ) + x A ))). 8) 7) Constaint 5) is a tade-balance condition wheeas 6), 7) and 8) ae standad feasibility conditions fo goods M, A and capital espectively. Fom the Fist Welfae Theoem, V F I ) is also the consume s utility when domestic makets fo input factos ae competitive. The solution to P F I ) eplicates indeed the competitive equilibium. By definition, V F I ) is thus minimum at p F I such that the makets fo final goods ae on autaky i.e., C M = X β M K and C A = X β L A ) since indeed imposing those exta conditions coesponds to a moe constained optimization. Theefoe, fee tade is always welfae supeio. Moe fomally, let us denote by γp) the non-negative multiplie of the tade-balance condition 5) at wold pice p. The Envelope Theoem yields: ) V F I p) = γp) X β M p)k p) C M p) whee the dependence of all vaiables on the maket pice p is made explicit. Of couse, that ight-hand side is pecisely woth 0 at p F I since domestic poduction is equal to domestic consumption unde autaky. Going into moe details and using the specific Cobb-Douglas pefeences, we can easily compute whee Finally, V F I ) is minimized fo V F I p) = αlnα + α)ln α) lnγp) αlnp γp) = RF I = β β β) Θ β p K ) + p β L. p F I = )) L K α) β). 9) 2

13 Unde complete infomation, one ecoves the taditional esult that, once domestic egulation is optimally designed, fee tade is always Paeto-supeio to autaky. Pattens of tade. When the wold pice diffes fom p F I, two cases ae possible. p > p F I. The wold pice of manufactues is geate than unde autaky. The small county expots good M which is capital intensive and impots good A which is labo intensive final good. An incease in p inceases the demand fo capital and aises its ental ate above its autaky level. At the same time, the wage ate deceases to guaantee zeo pofit in the final sectos unde constant etuns to scale: w < w F I and > F I. p < p F I. The wold pice fo M is lowe than its value unde autaky. By symmety, we get: w > w F I and < F I. Figue below summaizes gaphically the two cases. F I F I Θ > Θ = p w > p F I = F I 2 w) Θ w w F I w F I w = p w < p F I = F I w) w Figue : Autaky and fee-tade equilibia unde complete infomation. 3

14 4 Tade and Regulation unde Asymmetic Infomation Conside now the case of asymmetic infomation. Ownes of fims in the intemediate sectos ae pivately infomed on the poductivity shocks that hit those sectos. Supply Side. Poductivity shocks in any intemediate secto ae not obseved by the egulato. The egulato has to ely on incentive egulation to induce fims in those sectos to tuthfully eveal thei poductivity paamete. Fom the Revelation Pinciple 5 such an incentive scheme stipulates how much each intemediate secto has to poduce as a function of its announcement on its efficiency shock. In full geneality, and given that poduction in the final sectos depend on the whole vecto of input factos poduced by intemediate sectos, the tansfe t j and the output x j in secto j should depend on the whole announcement ˆ made by each secto. Given that thee is a continuum of symmetic intemediate sectos with i.i.d. shocks, we will use the Law of Lage Numbes to appoximate the optimal contact by a vecto of incentive contacts fo each secto which depends only on the announcement of that secto. We thus envision a collection of bilateal egulatoy contacts fo each secto which take the fom {tˆ), xˆ)}ˆ {, } whee ˆ is the announced poductivity paamete in that secto, tˆ) and xˆ) being espectively the payment and the poduction of that secto. It is a by-now standad esult in the Theoy of Incentives 6 that, in two types advese selection models, the binding incentive constaint at the optimum is that of an efficient fim wheeas the binding paticipation constaint is that of an inefficient fim. Still, using symmety among all sectos, those constaints can be witten espectively as U) t M ) + t A ) x M ) + x A ) ) = U ) + x M ) + x A ) ), 0) and U ) 0. ) Unde asymmetic infomation, the egulato s poblem becomes: max p E {K,L,x i ),U )} x M ) )) β K + E x A ) wl K E x M ) + x A ))) E U)) subject to 0) and ). 5 Myeson 982). 6 Laffont and Matimot 2002, Chapte 2) fo instance. )) β L 4

15 Since the last two constaints ae binding at the optimum, the agency costs coming fom asymmetic infomation can be identified with the positive amount of expected infomation ent that must be left to fims in the intemediate sectos, namely E U)) = ν x M ) + x A ) ) whee emembe again that those optimization vaiables depend on the equilibium pice vecto but this dependence has been omitted fo notational simplicity. This expected ent, which is view as an exta cost by the egulato, is popotional to the poduction of inefficient fims in the intemediate sectos. This is whee the tadeoff between allocative efficiency and distibution bites: the moe poduction is equested fom the intemediate sectos, the moe infomation ent must be left to those sectos. Inseting this expession of the expected infomation ent into the egulato s objective function, one can easily see that eveything happens as if the egulato s optimization poblem was the same as unde complete infomation with the only change coming fom the fact that the tue poductivity paamete is now eplaced by a so-called vitual paamete = + ν which is geate. At the same time, the vitual poductivity ν of the efficient fim is kept unchanged =. As a esult, we can diectly impot ou pevious esults fom Poposition to chaacteize the supply side of this economy. Poposition 3 Unde asymmetic infomation, the optimal egulation of the intemediate sectos entails the following popeties. Fims in the intemediate sectos get a positive infomation ent if and only if they ae hit by a good poductivity shock ; U AI ) = x AI M ) + x AI A )), and U AI ) = 0. 3) still holds wheeas 2) is eplaced by is now geate than the full info- whee the vitual poductivity index Θ = mation poductivity index Θ. β w = β) β β β Θ β ) E ) 2) Unde asymmetic infomation, the egulato wants to educe the intemediate sectos fims incentives to epot being less efficient than what they eally ae. To induce paticipation by the least efficient fim, the egulato must incease the oveall payments fom the final sectos fo the inputs poduced by those fims. This inceases the incentives of an efficient fim to petend being less efficient and eap such lage payments. If it does so, it 5

16 can poduce the same output than an inefficient fim by using less capital and benefitting fom the high pice offeed to the inefficient fims. Ownes of efficient fims enjoy then a positive infomation ent as it can be seen fom 0). Those infomation ents ae peceived as costly by the egulato. Howeve, he can educe that cost by simply equesting less poduction x M ) and x A ) than unde complete infomation values keeping the ental pice of capital as given). That exta distotion amounts to an implicit tax on inefficient fims which is fomally captued by eplacing and Θ espectively by thei vitual values and Θ. Because of asymmetic infomation, eveything happens as if thee wee now a wedge between the unit pice at which inefficient fims in the intemediate sectos can sell thei goods and thei maginal cost. Output is inefficiently low fo those fims. Asymmetic infomation ceates a dead-weight loss in the economy. Moeove, because infomation ents ae popotional to the ental ate of capital, the dead-weight loss inceases with. This latte effect is paticulaly impotant fo what follows. Asymmetic infomation does not change the oveall tend between the ental pice of capital and labo wage. The zeo-pofit condition fo final sectos 2) still yields a cuve = AI w) which is still downwad sloping exactly as unde complete infomation. Howeve, asymmetic infomation eplaces the poductivity index by a geate vitual poductivity index. The cuve 2) is shifted downwads below 2). Oveall, zeo-pofit is obtained at lowe pices fo capital and labo. Howeve, this is not the only effect of asymmetic infomation in a geneal equilibium model. Infomation ents in the intemediate sectos ae also edistibuted to the epesentative consume as an owne of those intemediate sectos. That consume enjoys thus income flows not only fom the standad capital and labo endowments in this economy but also fom an additional infomational endowment. In othe wods, the poceeds of the implicit tax that asymmetic infomation imposes on the poduction of inefficient fims ae pocketed by the epesentative consume who owns intemediate sectos. Demand Side. Unde asymmetic infomation, the total endowment of the epesentative consume can be then witten as: R AI = w } L {{ + K } + ν x AI M ) + x AI A )). 3) }{{} Standad Endowment Infomational Endowment Using the expessions of the intemediate sectos outputs given in the Appendix equation A0)), we get: R AI = w L + K) + µλ ) 4) + µ ) whee λ =. ν β and µ = ν + ν) ν + ν) ν + ν) 6

17 Eveything happens thus as if, because of his infomational endowment, the tue income peceived by the epesentative custome was now scaled up by a facto + µλ +µ. Thanks to Cobb-Douglas pefeences, such change in evenue does not affect the elative demand fo the two final goods, it modifies only thei magnitudes. Fo the est of the pape, we will assume that the following condition holds: Assumption α) β) > + µλ + µ. Tedious computations show that this condition is always satisfied when is small enough, i.e., when the advese selection poblem is not too significant. Assumption ensues existence of a a competitive equilibium as we see below Autaky We ae now eady to chaacteize equilibium pices unde autaky. conditions on the agicultual and labo makets yield: α)r AI = X β A L = w β L Maket cleaing whee the second equality comes fom expessing labo demand in the agicultual secto. Using the expession fo R AI given in 4), we obtain: ω = w = K ). 5) L α) β) + µλ +µ When Assumption ) holds, the maket equilibium equation 5) still defines an autaky locus unde asymmetic infomation = AI 2 w) which is upwad sloping. Howeve, AI 2 ) is always below F I 2 ). The intuition comes fom a caeful analysis of the supply and demand cuves on the agicultual maket. Fist, emembe that the epesentative consume s income is scaled up unde asymmetic infomation. Theefoe, the demands fo both final goods incease and, given the Cobb-Douglas pefeences, they do so at the same ate. This income effect is captued by the scale facto + µλ +µ on the l.h.s. of 5). Second, poduction on the agicultual maket is popotional to labo wages exactly as unde complete infomation and up to changes in the equilibium level of 7 Had it not hold, asymmetic infomation would be incompatible with competitive behavio. We leave the analysis of this inteesting case fo futhe eseach. 7

18 wages) is unchanged. Hence, equilibium on the agicultual maket can only be obtained when the ental ate of capital deceases so that the demand boost due to the income effect is compensated by a deceased in income fom facto endowments. Assumption ensues that this elative pice adjustment mechanism is stong enough to ovecome the income effect due to the existence of endogenous) infomation ents. If it wee not the case, then the income effect associated to infomation ents would poduce an inceased equilibium ental ate of capital which in tun would feed back into inceased infomation ents. This multiplie effect would ende impossible the existence of a competitive equilibium. We can now complete the desciption of ou autakic equilibium. Poposition 4 When Assumption ) holds, thee always exists a unique equilibium unde autaky and asymmetic infomation. It is chaacteized by the pice system p AI, w AI, AI ) that solves 3), 2) and 5). Fist, obseve that the autaky pice of the manufactued good deceases with asymmetic infomation. Indeed asymmetic infomation contacts intemediate sectos which use capital as an input. Moe capital becomes available fo the capital intensive final good which becomes cheape. p AI = L K α) β) + µλ +µ ) < p F I. 6) A pioi, it is had to compae autaky input facto pices unde complete and asymmetic infomation. On the one hand, the downwad shift of the zeo-pofit locus 2) due to the deteioation of the poductivity index suggests that the equilibium ental ate of capital and wage ae lowe unde asymmetic infomation. On the othe hand, the downwad shift of the autaky locus inceases the equilibium wage see Figue 2 below). The total impact of asymmetic infomation on the ental ate of capital ends up being unambiguous. Howeve, its impact on wages depends on the paametes as shown below. 8

19 Figue 2: Equilibium unde autaky with and without asymmetic infomation. Poposition 5 Unde asymmetic infomation, capital is always cheape than unde complete infomation, AI < F I. Wages ae lowe, i.e., w AI < w F I, if and only if ) Θ + µλ α) β)) Θ > +µ ). 7) + µλ α) β) +µ Using Taylo expansions in the limiting case of small degees of asymmetic infomation i.e., small enough), it can be veified that condition 7) amounts to Assumption. Changes in input pices ae thus mostly explained by changes in the poductivity index so that both and w deceases with asymmetic infomation. 4.2 Fee Tade Unde fee tade, p is again fixed on the wold maket at an exogenous value. Following the same logic as unde complete infomation, the patten of tade can be immediately deived and depends on whethe p is above o below p AI. 9

20 Poposition 6 Assume that p F I > p > p AI, then unde complete infomation, the small economy contacts its poduction of the capital intensive good and expands that of the labo intensive one wheeas it is the evese unde asymmetic infomation. Unde those cicumstances, asymmetic infomation changes the patten of tade. To bette undestand this esult, it is useful to come back on the definition of p AI and ewite ) ) ) L p AI = K α) β) whee ) L K = L K + µλ +µ α) β) α) β) < L K. That expession highlights that, unde asymmetic infomation, the elative facto endowment L K of the economy has to be eplaced by its vitual value which is lowe. ) L K With asymmetic infomation, eveything happens thus as if the small county was elatively iche in the facto which is moe intensively used by sectos affected by agency poblems. Indeed, since these sectos contact thei activity, capital is elatively cheape and the small county specializes moe easily in the capital intensive good. Asymmetic infomation induces a specialization bias. 8 5 Nomative Analysis The taditional nomative conclusions of Tade Theoy change unde asymmetic infomation. One should not always expect fee tade to be necessaily welfae-impoving even fo a small open economy that has optimally designed its domestic egulation. Define fist now the epesentative consume s indiect utility function V AI p) in the open economy unde asymmetic infomation as follows: P AI ) : V AI p) max αlnc M + α)lnc A {C M,C A,X M,X A,x m ),x a )} subject to 5), 6), 7) and ν x M, p) + x A, p)) + K ) = K + E xm ) + x A )) 8) whee x M, p) and x A, p) solve the maximization poblem above. The following poposition holds. 8 In ou model, capital is the only facto affected by asymmetic infomation issues. Moe geneally, what mattes fo tade pattens is the elative facto endowment of the economy, adjusted fo the facto content of infomation ents. 20

21 Poposition 7 Unde asymmetic infomation, V AI p) is the epesentative consume s utility function when the wold pice of manufactued good is p. In othe wods, the allocation of esouces that solves P AI ) is the maket equilibium unde asymmetic infomation in the open economy. Poposition 7 chaacteizes a constained Fist Welfae Theoem unde asymmetic infomation. It shows that the equilibium allocation is in fact the solution to a centalized poblem P AI ) povided that the esouce constaint fo the infomationally sensitive input 8), hee capital, is caefully modified. That modification encapsulates implicitly the constaints that asymmetic infomation imposes in edistibuting wealth fom the epesentative consume viewed as an infomed shaeholde of the intemediate secto to the epesentative consume viewed as an uninfomed playe. As unde complete infomation, the esouce constaint 8) accounts fo the capital endowment K but it diffes fom 8) on both sides. Fist, the new exta tem ν x M, p) + x A, p)) has been added on the esouce side. Second, the efficiency paamete has been eplaced by its vitual value on the ight-hand side. The intuition fo these modifications is staightfowad. Unde asymmetic infomation, vitual efficiency paametes ae the ight concept to evaluate the maginal oppotunity cost of using esouces. Hence, any centalized maximization poblem that aims at eplicating the behavio of competitive makets fo input factos must take into account those vitual efficiency paametes. Going fom efficiency paametes to thei vitual countepats amounts to an implicit tax ν counted hee in units of capital) on the use of capital ν by inefficient fims of the intemediate sectos. In a geneal equilibium envionment, the poceeds of that tax have to be included on the esouce side which explains the newly added tem ν x M, p) + x A, p)) on the left-hand side of 8). Finally, x M, p) and x A, p) ae obtained as fixed-points out of the optimization P AI ). This poblem is self-geneating in the sense that some of its constaints itself depends on the solution. Let us again denote by γp) the non-negative multiplie of the tade-balance condition 5) and by γp)p) the non-negative multiplie of the feasibility condition 8) at wold pice p fo the manufactued good. The Envelope Theoem gives us: [ ] V AI p) = γp) X β xm M p)k p) C M p) + p)ν p, p) + x )) A p, p). At the autaky pice p AI, only the fist backeted tem is zeo since domestic poduction is equal to domestic consumption of that manufactued good. Intuitively, moving away fom the autaky pice by a small amount has now a fist-ode effect on welfae since it changes infomation ents in the intemediate sectos. Slightly inceasing p above p AI boosts the domestic poduction of good M. This aises demand fo capital and inceases its ental ate which finally deceases poduction 2

22 by inefficient fims in intemediate sectos. Stating fom the autaky pice, opening bodes inceases expotation but this also educes infomation ents and welfae. Using the specific Cobb-Douglas pefeences, we can go futhe and easily compute whee now V AI p) = αlnα + α)ln α) lnγp) αlnp γp) = RAI p) = β β β) Θ β + µλ ) p + µ K ) + p β L. V AI ) is again U-shaped and minimized, as V F I ), fo p F I which is geate than p AI. Hence, V AI p AI ) < 0. The following poposition follows immediately. Poposition 8 Unde asymmetic infomation, fee tade is welfae-deceasing when p AI < p < p F I wheeas it is welfae-inceasing when p < p AI < p F I. The intuition fo this poposition is staightfowad. Remembe that optimal egulation contacts the output of the intemediate sectos. If opening bodes induces a specialization which einfoces this domestic distotion, the additional distotionay effect offsets any gains fom tade. A fee tade egime is eventually Paeto infeio to autaky. When p > p AI, the domestic economy has a compaative advantage in the capital intensive tadable good. Fee tade induces specialization in that secto. By inceasing the demand fo capital, fee tade inceases the ental ate of capital and educes output in the intemediate good sectos. This specialization exacebates the initial downwad output distotion of the intemediate sectos due to asymmetic infomation. This additional social cost has to be evaluated against the taditional gains fom tade in poduction and consumption of the Heckshe-Ohlin famewok. When p < p AI, the economy has a compaative advantage in the labo intensive agicultual good. Fee tade induces a specialization in that secto and a eduction of poduction of the capital intensive tadable good. This, in tun, expands intemediate sectos. This expansion mitigates the initial downwad output distotion due to asymmetic infomation. Opening bodes impoves the allocation of esouces in the economy and inceases welfae. In that case, fee tade geneates two souces of social gains: the usual Heckshe-Ohlin gains fom tade and the educed domestic distotions associated with the existence of infomation ents. Fee tade is bette than autaky. Poposition 8 shows how asymmetic infomation may damatically change the standad positive and nomative pedictions of tade models. Unde complete infomation, tade openness allows a bette specialization of a small county and optimal egulation 22

23 does not affect the patten of tade. The incease in income of the expot secto moe than offset the loss incued by the impot secto. The utility of the epesentative consume inceases. All efficiency gains coming fom a bette specialization can be passed onto the epesentative custome. Of couse, this equies that thee is no constaint on edistibuting wealth between ownes of the tadable good who win fom tade openness and ownes of the secto who lose fom it. The key diffeence unde asymmetic infomation comes fom the existing endogenous dead-weight loss which makes such edistibution costly. Asymmetic infomation ceates a wedge between pice and maginal cost. Even though, in fine, the epesentative consume pockets both the pofits of final good sectos and the infomation ent of intemediate ones, the total size of this cake is less than unde complete infomation. 6 Conclusion Standad esults fom Tade Theoy must be modified when asymmetic infomation makes it impossible to fully edistibute gains fom tade within the domestic county. Fist, fee tade even when accompanied by a set of optimally designed domestic egulations may no longe be welfae-impoving even fo a small economy. Second, that county s compaative advantages may be evesed compaed to complete infomation. The basic eason fo this challenge of two of the most familia insights fom the Tade liteatue is simple: asymmetic infomation in intemediate sectos poducing key inputs fo tadeable goods intoduces distotions that cannot be eliminated even when the lagest set of policy instuments ae available to egulate those sectos. Tade openness impoves welfae only when it mitigates distotions induced by asymmetic infomation. It wosens welfae othewise. Because asymmetic infomation ceates a wedge between pices and maginal costs in intemediate sectos, its impact on the gains fom tade looks, at a ough level, like what one would obtain if we had instead assumed complete infomation but left intemediate sectos unegulated. In that case also, a decease in the pice of the capital intensive good inceases also the pice of capital in the small economy. This in tun inceases the deadweight loss of monopoly picing and may finally decease welfae. It should be stessed that, unde complete infomation, thee is no obstacle to implement coective policies. Implicit in any such analysis of the distotions associated with monopoly picing in intemediate sectos unde complete infomation is the idea that the egulato faces exogenous constaints when choosing his instuments. Ou famewok with asymmetic infomation clealy endogenizes those constaints by giving them infomational foundations and makes 23