No Firm Is An Island: The Institutional Structure of. Production in the Presence of the Price Mechanism

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1 USC FBE APPLIED ECONOMICS WORKSHOP presente by Richar Holen FRIDAY, March 7, 009 :30 pm - 3:00 pm, Room: HOH-506 No Firm Is An Islan: The Institutional Structure of Prouction in the Presence of the Price Mechanism Robert Gibbons, Richar Holen an Michael Powell March 6, 009 Abstract We analyze a rational-epectations moel of price formation in an intermeiategoo market. There is a continuum of yas, each consisting of an upstream party an a ownstream party. Both parties can make speci c inestments at priate cost. As in property-rights moels, i erent goernance structures inuce i erent inestments. As in rational-epectations moels, some parties may inest in acquiring information, which is then partially incorporate into the market-clearing price by the parties traing behaiors. The informatieness of the price mechanism a ects the returns to speci c inestments an hence the optimal goernance structure for iniiual yas; meanwhile, the goernance-structure choices by iniiual yas a ect the informatieness of the price mechanism. In equilibrium, rms an the market coeist an shape each other. In particular, the price mechanism can inuce e ante homogenous yas to choose heterogeneous goernance structures (JEL D0, D3). Gibbons: Massachusetts Institute of Technology an NBER, rgibbons@mit.eu. Holen: Massachusetts Institute of Technology an NBER, rholen@mit.eu. Powell: Massachusetts Institute of Technology, mlp@mit.eu. We thank Daron Acemoglu, Glenn Ellison, Olier Hart, Bengt Holmström an Olier Williamson for helpful comments an MIT Sloan s Program on Innoation in Markets an Organizations for nancial support.

2 Introuction Since Coase (937), economists hae sought to unerstan why rms eist, gien the power of the price mechanism as an informing an coorinating eice. As Coase argue, it is surely important to enquire why co-orination is the work of the price mechanism in one case an of the entrepreneur in the other (p. 359, emphasis ae). Signi cant progress has been mae in answering this question, incluing contributions by Williamson (97, 975, 979), Klein, Crawfor an Alchian (978), Grossman an Hart (986), Hart an Moore (990), an others. Yet scant attention has been pai to the interaction between D. H. Robertson s islans of conscious power an the ocean of unconscious cooperation in which he enisione such islans coagulating like lumps of butter in a pail of buttermilk (98: 85). That is, rms an markets hae typically been seen as alternatie ways of coorinating economic actiity, rather than as two institutions that shape each other. In this paper we take the latter iew, eploring the interaction between rms an the e ning feature of the market: the price mechanism. To eplore how these two institutions shape each other, our moel incorporates two, reciprocal consierations. First, rms operate in the contet of the market: the informatieness of the price mechanism a ects the relatie returns to the parties speci c inestments an hence parties optimal choice of goernance structure. Secon, a market (for an intermeiate goo) is mae up of rms: the parties goernance structures a ect how they buy an sell in the intermeiate-goo market an hence the informatieness of the price mechanism. In equilibrium, these reciprocal consierations must both be taken into account. Our emphasis on the interaction between rms an the price mechanism seems new. That is, while Coase was eplicit that the price mechanism is the chief alternatie to internal organization, an Williamson s (975) title famously emphasize Markets as the alternatie to hierarchy, oer the net 35 years, the market fae away. Instea, the literature focuse on non-integration ersus integration, with the iscussion of non-integration emphasizing

3 hol-up costs rather than the market s price mechanism. In fact, een Williamson (97: 4) aopte this approach, suggesting that at is frequently... more e cient [than] haggling, thereby emphasizing the haggling of non-integration rather than the price mechanism of the market. Similarly, Klein, Crawfor, an Alchian (978: 98) emphasize hol-up by arguing that as assets become more speci c an more appropriable quasi-rents are create..., we are more likely to obsere ertical integration. An Grossman an Hart (986: 590) began by asking What is a rm? an eelope an important answer inoling resiual rights of control, but pai less attention to the market, again emphasizing hol-up as the consequence of iie control. The ensuing literatures on transaction costs an property rights hae greatly enhance our unerstanings of the costs an bene ts of integration. Furthermore, both of these approaches hae been fruitfully applie in many other els of economics. But the literature on rms bounaries, with its focus on the consequences of iie control rather than on the price mechanism, has become completely iorce from both Coase s (937) original framing an the Markets aspect of Williamson s (975) apt title. In this paper, therefore, we bring the price mechanism back into the theory of rms bounaries. The conentional component of our moel is a simpli e ersion of the classic propertyrights theory (PRT) initiate by Grossman an Hart. Focusing for the moment on a single transaction conucte by a single ya, our moel inoles two parties an a single alienable asset. Regarless of who owns the asset, each party can make a speci c inestment, but the returns to these inestments epen on who owns the asset. Following the PRT (i.e., For sureys, see Hart (995) an Macher & Richman (008). Many make-or-buy questions hae been analyze in these terms, for eample: internal ersus eternal capital markets (Gertner et al. (994)), inhouse ersus outsource research an eelopment (Aghion & Tirole (994)), real ersus formal authority (Aghion & Tirole (997)), public ersus priate proision of serices (Hart et al. (997)), macroeconomic issues (Caballero & Hammour (998)), intra- rm ersus inter- rm international trae (Antràs (003)), an more. Grossman & Helpman (00) an Legros & Newman (008) analyze other interactions between rms an the market, but ones that o not inole the informatieness of the price mechanism. Grossman an Helpman emphasize the trae-o between between the costs of managing a ertically integrate rm that can manufacture the components it nees, an the costs of search an hol-up that specialize rms face. Legros an Newman focus on the interaction between organizational form an price leels for nal goos. 3

4 analyzing one ya in isolation) reeals that the optimal ownership structure is etermine by the marginal returns to these inestments. In our moel all yas are homogeneous e ante, so a PRT analysis of a single ya woul then prescribe that all yas choose the same ownership structure. Relatie to the PRT, the noel component of our moel is the inclusion of the price mechanism, which enogenizes the returns to the parties speci c inestments an hence creates an inustry-leel eterminant of an iniiual ya s choice of goernance structure. This is the sense in which, in our moel, rms operate in the contet of a market. In the spirit of Hayek (945), we iew the market as informing an coorinating through the price mechanism. We therefore eelop a rational-epectations moel in the spirit of Grossman an Stiglitz (976, 980) but esigne to apply to goos markets (as oppose to nancial markets), with positie prices an quantities an no noise traers. In Gibbons, Holen, an Powell (009; hereafter GHP), we eelope such a rational-epectations moel for a goos market, but for the Grossman-Stiglitz case of iniiual inestors. Relatie to rational-epectations pricing moels such as Grossman-Stiglitz (an GHP), the noel component in this paper is the analysis of alternatie goernance structures. Speci cally, we enrich GHP to allow for prouction by the yas escribe aboe, so there are now two feasible goernance structures (epening on which party owns the alienable asset) rather than only iniiual inestors. In summary, our moel integrates two familiar approaches: rational epectations (where an imperfectly informatie price mechanism both permits rational inferences by some parties an inuces costly information acquisition by others) an property rights (where inestments epen on the parties goernance structure an asset ownership is chosen to inuce seconbest inestments). Our main result is that, een though all yas are homogeneous e ante (an thus woul choose the same goernance structure in a PRT analysis) in the presence of the price mechanism the inustry equilibrium typically inoles i erent yas choosing i erent goernance structures. To eplain this result, we rst escribe the moel in more etail. 4

5 In each ya the two parties are upstream an ownstream in a prouction process that can transform an intermeiate goo (a wiget ) into a nal goo. Upstream parties may be enowe with a wiget. Upstream parties that are enowe with a wiget can sell it in the wiget market, an any party may purchase a wiget from the market. The alienable asset is a machine that can transform one wiget into one nal goo (at a cost). Upstream parties may make inestments that reuce the cost of operating the machine; we therefore think of upstream parties as haing human capital that is releant to the prouction of nal goos. Downstream parties may make inestments that elier information about the alue of a nal goo in the consumer market; we therefore think of ownstream parties as haing human capital that is releant to the marketing of nal goos. As in the PRT, the parties incenties to make inestments epen on asset ownership. In particular, yas that choose ownstream ownership then inest in information about the alue of the nal goo, whereas those that choose upstream ownership inest instea in cost reuction an rely solely on the price mechanism for information about the alue of the nal goo. Naturally, if the price mechanism is more informatie, the returns to inesting in information are lower so yas hae a greater incentie to choose upstream ownership an inest instea in cost reuction. As in rational-epectations moels, when fewer parties inest in informatie, the price mechanism becomes less information, thereby making ownstream ownership more attractie. An inustry equilibrium must balance these two forces. We show that a unique equilibrium eists an is typically interior. In this sense, the price mechanism inuces heterogenous behaior among homogeneous yas. The remainer of the paper procees as follows. In Section we specify an iscuss the moel. Section 3 analyzes the integration ecision of a single ya in isolation, an Section 4 analyzes the price mechanism. Section 5 then combines the property-rights an rational-epectations aspects of the preious two sections, analyzing the equilibrium choices of goernance structures for all the yas in the inustry an hence eriing our main result. Section 6 iscusses some implications of the moel an section 7 conclues. 5

6 The Moel. Statement of the Problem There is a unit mass of risk-neutral yas that are eogenously matche to each other. Each ya i [0; ] consists of two parties, which we enote U i an D i ; an a machine that is capable of eeloping one intermeiate goo (a wiget ) into one nal goo at cost c i U [c; c] : The machine can be owne by either party, but it is relationship-speci c (i.e., the machine is useless outsie its intene ya). If party U i owns the machine, we say that the goernance structure in ya i is g i = U; an if party D i owns the machine, we say that g i = D: Final goos hae an uncertain alue. Party D i can inest at priate cost K D to learn the alue of a nal goo in the market, U [; ] : If he incurs this cost, U i knows that D i is informe but oes not herself obsere : Party U i can inest at cost K U in reucing the cost of operating the ya s machine. If she incurs this cost, both parties obsere that c i is reuce to c i, where c: We embe these yas in our rational-epectations moel of price formation in goos markets from Gibbons, Holen an Powell (009). A fraction y of the yas is enowe with a wiget. In particular, U i is enowe with w i = wigets if i y an w i = 0 if i > y; where y is taken to be an eogenous (an commonly known) aggregate enowment. Parties not enowe with a wiget may purchase one in the wiget market, an those who are enowe with one may sell it into the market. Aitionally, there is a set of rms outsie this inustry of uncertain mass z; each of whom emans one wiget inelastically at any price p : We think of this eman as coming from a nearby inustry that has an alternatie use for wigets. Assume z U [z; z] ; an e ne = y z U [; ] to be the net enowment of wigets in the inustry we analyze (where = y z an = y z are such that [; ] [0; ]). Equilibrium in the market for wigets occurs at the price p that equates supply an 6

7 eman (from informe, uninforme, an outsie parties). In making supply or eman ecisions for wigets, yas that are not irectly informe about (because party D i chose not to inest K D ) make rational inferences about from the market price for wigets. Dyas choose their goernance structures (i.e. machine ownership) taking into account the information that will be inferre from the market price an hence the relatie returns from the two parties inestments.. Timing an Assumptions We now state the timing an assumptions of the moel more precisely. We comment on these assumptions in Section.3. There are seen perios. Nature chooses an z Specific inestments Price formation Payoffs Dyas choose goernance structure Wiget enowment Prouction Figure : Timeline In the rst perio, inustry-leel uncertainty is resole: the alue of the nal goo is rawn from U [; ] an the outsie eman z is rawn from U [z; z] ; but neither of these ariables is obsere by any parties. In the secon perio, each ya negotiates a goernance structure g i fu; Dg: uner g i = U; party U i owns the machine that can eelop one wiget into one nal goo; uner g i = D; party D i owns this machine. This negotiation occurs ia Nash bargaining. In the thir perio, parties U i an D i simultaneously choose whether to make relationship speci c inestments (or not) at costs K U an K D ; respectiely. In partial accorance with the PRT, we assume that the acts of making these inestments are obserable but not eri able, but we epart from the PRT (in a manner that is natural in our setting) by assuming that the outcome of the ownstream party s inestment (namely, learning ) is 7

8 obserable to only D i ; not U i : In an aitional eparture from the PRT we assume that, once the speci c inestments hae been mae, regarless of who owns the machine, its use is non-contractible (i.e., only the party who owns the machine may operate it to transform a wiget into a nal goo), an its ownership cannot be renegotiate. In the fourth perio, yas learn their ine, i; an all U i with i y are enowe with w i = wiget. In the fth perio, price formation takes place, in three steps. In perio 5a, the parties U i an D i commonly obsere c i U [c; c], the raw cost of running their machine, as well as i f0; g, the amount of cost reuction achiee by U i s speci c inestment. Also, D i (but not U i ) obseres ' i f;; g ; a signal about the alue of the nal goo, where ' i = ; is the uninformatie signal that obtains if party D i has not ineste K D in perio 3, an ' i = is the perfectly informatie signal receie if K D has been ineste. It is useful to introuce the following notation for the parties information sets: s D i = (c i ; i ; ' i ) ; s U i = (c i ; i ; ;) ; an s i = s D i ; s U i : Then, in perio 5b, a mass z of outsie parties each emans a single wiget at any price p : Finally, in perio 5c, the market for wigets clears at price p: In particular: (i) any party may buy a wiget, an (ii) any upstream party enowe with a wiget may sell it (insie or outsie the ya). These possibilities yiel eight possible outcomes after the market closes, epening on whether upstream has a wiget, ownstream has a wiget, an who owns the machine. As the analysis in section 4 shows, howeer, the only releant issue is whether the machine owner has a wiget. In the sith perio, prouction occurs: if the machine owner in ya i has a wiget he or she can run machine to eelop the wiget into a nal goo at cost c i i. We enote the ecision to prouce a nal goo by q i = ; an the ecision not to o so by q i = 0: O the equilibrium path, one party might own the machine an the other a wiget, in which case the parties bargain oer the wiget an then the machine owner makes the prouction ecision. 8

9 Finally, in the seenth perio, nal goos sell for an payo s are realize. These payo s are g i U i = pw i + fgi =Ug fqi =g E js U i ; p (; ) = p p (c i i ) ; an g i D i = fgi =Dg fqi =g E js D i ; p (; ) = p p (c i i ) :.3 Discussion of the Moel Before proceeing with the analysis, we pause to comment on some of the moeling choices we hae mae. First, we assume that the machine is ya-speci c. This assumption allows us to focus on the market for wigets by eliminating the market for machines. Secon, we hae only one alienable asset, in contrast to the classic PRT setting. Our choice here is rien purely by parsimony; etening the moel to allow more alienable assets (an hence more goernance structures) coul be interesting. Thir, we hae binary inestments in cost reuction an information acquisition (at costs K U an K D ; respectiely), rather than continuous inestment opportunities. It seems straightforwar to allow the probability of success (in cost reuction or information acquisition) to be an increasing function of the inestment leel, which in turn has cone cost. Fourth, we assume that once the speci c inestments hae been mae, the use of the machine is non-contractible an its ownership cannot be renegotiate. These assumptions eliminate the possibility of bargaining uner asymmetric information within the ya. Fifth, we assume that the aggregate enowment y is known an eogenous, an whether an iniiual ya receies a wiget is not reeale until perio 4. The eogeneity of y eliminates inferences about aggregate enowments base on iniiual enowments. Reealing iniiual enowments in perio 4 eliminates conitioning the choices of goernance structure or speci c inestments on the ya s enowment. 9

10 Sith, as in GHP, we assume inelastic eman z from an outsie inustry at any price p : This uncertain eman makes the market price for wigets only partially informatie about ; so that parties may bene t from costly acquisition of information about : Seenth, again as in GHP, our assumptions that all the ranom ariables are uniform allow us to compute a close-form (inee, piece-wise linear) solution for the equilibrium price function at the inustry leel. This tractability is ery useful in the computing the returns to alternatie goernance structures, at the ya leel. Eighth, as in Grossman-Stiglitz an the ensuing literature, our moel of price formation is not an etensie-form moel of strategic ecision-making (incluing information transmission), but rather a reuce-form moel of price-taking behaior. See GHP for an etene iscussion. 3 Iniiual Dya Behaior As a builing block for our ultimate analysis, we rst analyze the behaior of a single ya taking the market price p as gien. To begin, e ne the gross surplus for ya i as GS i = g i U i + g i D i = pw i + fqi =g [E [js g i i ; p (; ) = p] p (c i i )] ; from which it follows that the e cient prouction ecision is q i p + c i i : = if E ; [j s g i i ; p] Working backwars, in perio 6, there are three possible cases of interest: if w i = 0; then the party with the machine may purchase a wiget at price p; if w i = an g i = U; then U i may keep the wiget or sell it into the market at price p; an if w i = an g i = D; then the parties bargain oer whether to transfer the wiget from U i to D i an at what price. In the last case, since U i can sell the wiget on the market at price p; an D i can buy a wiget at p; any plausible bargaining protocol leas to the wiget will be trae from U i to D i at 0

11 price p; an illustration of the Law of One Price. In all three of these situations the e cient prouction ecision will be taken. De ne the maimum gross surplus as GS i = E ; [( c i + i p) q i (g i ; s i ; p)j s g i i ; p] : The analysis is straightforwar if w i = 0: the party who owns the machine gets GS i an the other party obtains a zero payo. Similarly, if w i = an U i owns the machine then she gets GS i + p an D i obtains a zero payo. Finally if w i = an D i owns the machine then U i receies p an D i obtains GS i : In sum, the machine-owner always receies GS i an the non-owner receies a constant, an these payo s etermine the parties inestment incenties in perio 3, as follows. Let the subscript pairs (I; 0) enote the situation in which D i ineste an hence is informe about an U i i not inest in cost reuction, (U; ) enote the situation in which D i i not inest but U i i, hence reucing prouction costs by ; an (U; 0) enote the situation in which neither ineste. Now e ne the following: I;0 = E ci [GS i (D; s i )] if ' i = ; i = 0; U; = E ci [GS i (U; s i )] if ' i = ;; i = ; an U;0 = E ci [GS i (g i ; s i )] if ' i = ;; i = 0: Since one party s payo is inepenent of its inestment, at most one party will inest. If U i owns the machine she will inest if U; K U U;0 : Similarly, if D i owns the machine (g i = D); he will inest if I;0 K D U;0 : We assume that K U an K D are small relatie to the bene ts of inestment, so at least one party will inest. 3 These epectations are 3 This conition can be state in terms of primities of the moel, but since this is the economic assumption we are making, we state it in this fashion.

12 hence triple integrals oer (c i ; ; ) space. Formally, I;0 = Z Z Z c p(;) ( p (; ) c i ) F (c i ; ; ) ; U; = Z Z Z E[ jp] c p(;)+ ( p (; ) + c i ) F (c i ; ; ) ; an U;0 = Z Z Z E[ jp] c p(;) ( p (; ) c i ) F (c i ; ; ) ; where F is the joint istribution function. Obiously, we nee to compute p (; ) : This inoles analyzing the behaior of other yas, an it is to this task which we now turn. 4 Rational Epectations in the Market for Intermeiate Goos Recall that there is a unit mass of yas inee by i [0; ]. Who sells on the market an who buys? Dyas with su ciently low eelopment costs an no wiget may purchase one, an yas with a wiget an su ciently high eelopment costs may sell one. De ne c D (; p) = p to be the highest cost at which a ownstream party that has ineste in information (an hence knows ) woul be prepare to prouce a nal goo, an similarly let c U (p) = E [j p] p+ be the highest cost at which an upstream party that has ineste in cost reuction (but not information) woul be prepare to prouce. Supposing (as we will enogenize below) that a fraction of yas hae D ownership (an hence know ), whereas fraction hae U ownership (an costs reuce by ) the buyers an sellers of wigets are then illustrate in the following iagram.

13 Figure : Supply an Deman Formally, ya i sells on the market if it receies a wiget (which occurs for a mass y of yas) an its eelopment costs c i i are too high to warrant prouction (i.e. E ; [j s i ; p] p < c i i ). Similarly, ya i buys on the market if it oes not receie a wiget (which occurs with probability y) an its eelopment costs are su ciently low (i.e. E ; [j s i ; p] p c i i ). Then, since e ante inestment incenties are ientical for all yas, supply of wigets is gien by y Pr [E ; [j s i ; p (; ) = p] p < c i i ] 6 Pr [ p < c i ] = y 4 + ( ) Pr [E [j p (; ) = p] p < c i ] = y p c ( ) c c E [j p (; ) = p] + p c c c ; an eman for wigets is gien by 3

14 ( y) Pr [c i i E ; [j s i ; p (; ) = p] p] = ( y) [ Pr [c i p] + ( ) Pr [c i E [j p (; ) = p] p]] = ( y) p c E [j p (; ) = p] + p c + ( ) ; c c c c as well as z from the outsie inustry. The market-clearing price equates eman an supply, so substituting = y yiels p = ( ) E [j p (; ) = p] + (c c) + ( ) c: The conitional epectation of gien p therefore must satisfy E [j p (; ) = p] p + (c c) + c ( ) ; () where the equialence relation remins us that () hols as an ientity in an : De nition Assume fractions I; ; I;0 ; U; ; U;0 of yas are, respectiely, informe an hae cost reuction, informe an o not hae cost reuction, uninforme an hae cost reuction, an uninforme an o not hae cost reuction. Let = I; ; I;0 ; U; ; U;0. A rational epectations equilibrium ( REE ) is a price function p (; ) an a prouction allocation fq i g i[0;] such that. q i = q i for all i; an. The market for wigets clears for each (; ) [; ] [; ]: The aboe analysis implies I; = 0; an K U an K D small implies U;0 = 0. Let = I;0 an = U; : The problem of ning a rational-epectations price function in this moel becomes one of ning a e point of (). In Gibbons, Holen an Powell 4

15 (009), we sole for this e point, ning it to be piecewise-linear oer three regions of (; ) space: a low-price region, a moerate-price region, an a high-price region. Proposition Gien ; there eists an REE characterize by a price function p (; ) = f(;)r g p (; ) + f(;)r g p3 (; ) + f(;)r 3 g p3 (; ) ; where p j (; ) = j 0 + j + j for j = ; ; 3: To buil some intuition for this result, consier the gure below, which shows the three regions of (; ) space, R j for j = ; ; 3: The low-price region R begins from the lowest feasible price, p L at (; ) an etens up to the price p at (; ) : The moerate-price region R then etens from price p up to the price p at (; ) ; an the high-price region R3 etens from p up to the highest feasible price p H at (; ) : Figure : Conitional Epectation of gien p: Within each region, the iso-price loci are linear. In particular, soling p j (; ) = p for yiels = j j + p j 0 j as an iso-price line in (; ) space. Because an are inepenent an uniform, eery (; ) point on this line is equally likely. Thus, after obsering p; an informe party projects 5

16 this line onto the ais an conclues that the conitional istribution of gien p is uniform, with support epening on which region p is in. For eample, if p < p then the lower boun on is an the upper boun is some (p) < : Alternatiely, if p < p < p then the lower an upper bouns on are an ; so p is uninformatie. Finally, if p > p then the lower boun is some (p) an the upper boun is : Gien this uniform conitional istribution of gien p; the conitional epectation on the left-han sie of () is then the aerage of these upper an lower bouns on : The coe cients j 0; j ; an j can then be compute by substituting p j (; ) for p on both sies of () an equating coe cients on the like terms so that () hols as an ientity. 5 Inustry Equilibrium To recapitulate, section 3 analyze the prouction ecision, taking p (; ) as eogenous, an section 4 enogenize prices. In this section, we enogenize the goernance structure choices of each ya an e ne an inustry equilibrium as follows. De nition An inustry equilibrium is a set of yas of mass ; a price function p (; ) ; an a prouction allocation fq i g i[0;] such that. Each ya optimally chooses g i ; with a fraction choosing g i = D;. Each party optimally chooses whether or not to inest; 3. q i = qi ; an 4. The market for wigets clears for each (; ) [; ] [; ] The choice in perio is between the two possible goernance structures: g i = U or g i = D: The payo s from choosing the two goernance structures are gien by T S U () = U; () K U ; an T S D () = I;0 () K D. 6

17 In an interior equilibrium, yas must be ini erent between the two goernance structures. Thus our goal is to n such that T S U ( ) = T S D ( ) an to characterize how aries as we change the parameters of the moel. For simplicity we assume that K U = K D = K 4 ; so we seek such that I;0 ( ) = U; ( ) ; or equialently, I;0 ( ) U;0 ( ) = U; ( ) U;0 ( ) : () To keep notation compact, let = p ( ) an = p ( ) : We will make use of the following fact (which is erie in the appeni). Fact Assume (c c). Then c c c c I;0 () U;0 () = U; () U;0 () = c c c c + : ; an Obsere that the rst epression is ecreasing in ; an the secon is increasing in : This leas to the following characterization of inustry equilibrium. Proposition Assume (c an inustry equilibrium. Further, c). For all c; c; ; ; > 0 with c ; there eists = + (c c) = c c + (3) if the right-han sie of (3) is in [0; ]. If the right-han sie of (3) is less than 0, then = 0; if it is greater than, then =. Proof. If (c c) ; then U;0 (0) U; (0) an thus since the left han sie is ecreasing in, it follows that = 0. Similarly, if c c (c c) +, 4 The case where K U 6= K D is iscusse in section 6. 7

18 then U;0 () U; (), an since the right han sie is increasing in, we must hae that =. Otherwise, we want to n such that 0 = T S U T S D ( ) = + (c c) (c c) (c c) = c c + ; which yiels the epression in the statement of the proposition. Proposition is our main result, establishing that there eists a unique inustry equilibrium an proiing an eplicit epression for the proportion of yas who choose each of the goernance structures. As the proposition makes clear, this proportion may well be interior. Recall, howeer, that our yas are homogeneous e ante, so a PRT analysis (taking each ya in isolation) woul prescribe that they all choose the same goernance structure. In this sense, the price mechanism can inuce heterogeneous behaiors from homogenous yas. We are also able to raw some conclusions about comparatie statics. First, when the e ante leel of funamental uncertainty increases (i.e. is higher), the return to inesting in acquiring information increases, so increases to the point where the price mechanism has become su ciently informatie to counteract the increase in : Secon, an increase in noise (i.e. is higher) has an ientical e ect. Finally, an increase in has two e ects. The rst is the simple partial equilibrium channel through which an increase in the bene ts of choosing upstream ownership (an hence inesting in cost reuction) make upstream ownership relatiely more appealing, reucing. In an inustry equilibrium, howeer, there is also a price e ect. For a e fraction of parties that inest in cost reuction, an increase in makes wigets more aluable, which in turn increases eman an hence aerage prices. Since yas with upstream ownership purchase wigets oer a larger region of the c i space than yas with ownstream ownership, they face this increase in aerage price leel relatiely more than yas with ownstream ownership, so the price e ect will ten towars an increase in : Which of these two e ects ominates epens on 8

19 the parameters of the moel. Proposition 3 Assume (c c). For all c; c; ; ; > 0 with c an (0; ) ; we hae that: (i) is increasing in ; (ii) is increasing in ; (iii) is ecreasing in ; an (i) If < (c c), then is ecreasing in ; otherwise there eists a ^ satisfying 0 ^ (c c) 3+(c c) such that is ecreasing in wheneer > ^ an increasing in wheneer < ^ : Proof. See appeni. 6 Implications 6. PRT Meets REE Property-rights theory emphasizes the importance of speci c inestments for the choice of goernance structure: whicheer party s inestment is more important shoul own the releant asset. We can mimic the PRT by eliminating the role of the price mechanism in our moel, by supposing that a ya beliees p (; ) p for all ; ; an hence oes not recognize that prices are informatie. Fact If p (; ) p for all ; ; then the bene ts from choosing g i = U are gien by U;0 U;0 = c c ; an the bene ts from choosing g i = D are U; U;0 = + ( p c) : c c The ya therefore chooses ownstream ownership if > + ( p c) ; chooses upstream ownership if < + ( p c) ; an is ini erent if the inequality is replace with an equality. Generically, one of these two inequalities must hol, so the PRT 9

20 prescription will be either that all yas are integrate or that all yas are non-integrate (because the yas are ientical e ante). In our moel, howeer, the informatieness of the price mechanism enogenizes the returns to speci c inestments. In particular, yas that woul hae chosen to inest in information acquisition (by choosing ownstream ownership of the machine) uner the assumptions of Fact may now free-rie on the information containe in the market price an choose instea to inest in cost reuction (by choosing to hae upstream ownership of the machine). More speci cally, as we began to eplain after Proposition, the equilibrium fraction of yas choosing ownstream ownership in our moel, in (3), is often interior, not zero or one, as in a PRT analysis. Inee, the price mechanism might inuce homogeneous goernance-structure choices by all yas in our moel, but the opposite of what the PRT woul preict, such as when + (c c) < 0 (so that = 0 in our moel) but > + ( p c) (so that all yas woul hae ownstream ownership in a PRT analysis). Of course, rms may well not be e ante ientical, an thus a miture of these two e ects may etermine the choice of goernance structure. This obseration suggests that empirical tests of PRT that focus solely on the importance of speci c inestments may be misleaing, by failing to consier the role that the price mechanism plays in enogenizing the returns to speci c inestments. 6. TCE Meets REE Foreshaowing the spirit of many subsequent moels an commentaries, Williamson (97: 3) obsere that market intermeiation is generally preferre...when markets may be sai to work well. 5 Our moel allows us to assess this obseration, if we can be precise about two things: (i) what work well means, an (ii) what is meant by market intermeiation. 5 In a similar spirit, an eplicitly commenting on Hayek s (945) iscussion of the price mechanism, Williamson (975: 5) argues that price often o not qualify as su cient statistics an that a substitution of internal organization (hierarchy) for maket-meiate echange often occurs on this account. 0

21 A natural way to think about the rst of these is the following. De nition 3 The equilibrium informatieness of the price system is the epecte i reuction in ariance E ; h jp that is obtaine by conitioning on prices. In our moel, the informatieness of the price system is gien by E jp = = c c : An in our moel market intermeiation also has a natural interpretation: it means relying on information about from the price mechanism, rather than acquiring it irectly (i.e., upstream ownership rather than ownstream). In these terms, Williamson s obseration h i can be state as: falls when E increases. jp To analyze Williamson s obseration, consier an increase in : Certainly the informatieness of the price mechanism increases, an it is also the case [ U I0 ] =@ > 0; so the returns to upstream ownership increase. But, of course, is enogenous, so it matters what causes to increase an what other e ects that unerlying change has. For eample, if increases then it can be shown that informatieness ecreases an increases, as Williamson conjecture. On the other han, many other changes in eogenous ariables can lea simultaneously to an increases in informatieness an an increase in : That is, it is possible for the price system to work better at the same time be use less. For eample, it is straightforwar to see that an increase in ecreases an ecreases informatieness. An an increase in c c can o likewise, as reporte in the following result. Proposition 4 Assume (c < + ; jp] (c Proof. See appeni. c) an (0; ). De ne! = c c. If > > 0:!!+ + (c c) <

22 6.3 REE Meets PRT A nal obseration is that the theory of the rm shes new light on the functioning of the price mechanism. Partially-reealing REE moels compare the bene ts of acquiring information to the eogenously speci e costs of acquiring information. As our moel shows, what matters is not only these eogenous costs K D ; but also the opportunity cost of choosing a goernance structure that proies incenties to inest in information (namely, the foregone opportunity for cost reuction). To analyze this issue, consier the epression for when K U 6= K D : = + (c c) ( + K D K U ) = : + c c Note the presence of prouction parameters, such as an K U ; which hae nothing per se to o with market clearing or price formation. More importantly, note that comparatie statics regaring the informatieness of the price mechanism, such =@K D ; can epen on parameters such as : In aition to comparatie statics that illustrate the potential e ects of prouction parameters on rational-epectations equilibrium, we can also say something about how the prouction enironment e ects markets. For eample, in GHP we showe that (as in Grossman an Stiglitz, 980) market thickness epens on ; with concomitant implications for economic e ciency an welfare. 7 Conclusion Transaction-cost economics an the property-rights theory hae mae major contributions to our unerstaning of why some economic actiity occurs within rms. For almost four ecaes, howeer, these theories of rms bounaries hae emphasize the hol-up costs of non-integration (at the transactor leel), rather than the functioning of the price mechanism

23 (at the market leel). Motiate by Robertson (98) an Coase (937), we iew rms an the market not only as alternatie ways of organizing economic actiity, but also as institutions that interact an shape each other. In particular, by combining features of the property-rights theory of rms bounaries an the rational-epectations theory of the price mechanism, we hae eelope a moel that incorporates two, reciprocal consierations. First, rms operate in the contet of the market (speci cally, the informatieness of the price mechanism a ects parties optimal goernance structures). An secon, the market for an intermeiate goo is mae up of rms (speci cally, parties goernance structures a ect how they buy an sell in this market an hence the informatieness of the price mechanism). To eelop an analyze our moel, we hae impose seeral strong assumptions that might be relae in future work. For eample, to eliminate the market for machines, we assume that machines are ya-speci c. Also, to eliminate the possibility of bargaining uner asymmetric information, we assume that, once the speci c inestments hae been mae, the use of the machine is non-contractible an its ownership cannot be renegotiate. Finally, as in our paper on price formation (where we analyze iniiual inestors instea of yas), we ignore the possibility of strategic information transmission before or uring the price-formation process. In aition to relaing our current assumptions, it woul also be interesting to epan this line of argument beyon our current application (to rms bounaries). For eample, a host of internal organizational structures an processes seem likely to be in uence by the information aailable from the price mechanism (incluing transfer pricing, resource allocation, an empowerment), but our elemental property-rights moel of a ya is too simple to aress these internal issues. Also, as well as inestigating the impact of the market on rms, there may be more to say about the impact of rms on the market. For eample, it woul be interesting to know whether the equilibrium informatieness of the price mechanism is socially e cient an (assuming it is not) what features of rms prouction 3

24 enironment facilitate better performance by the market. 4

25 References Aghion, Philippe, & Tirole, Jean The Management of Innoation. Quarterly Journal of Economics, 09(4), Aghion, Philippe, & Tirole, Jean Formal an Real Authority in Organizations. Journal of Political Economy, 05(), 9. Antràs, Pol Firms, Contracts an Trae Structure. Quarterly Journal of Economics, 8(4), Caballero, Ricaro J., & Hammour, Mohama L The Macroeconomics of Speci city. Journal of Political Economy, 06(4), Coase, Ronal The Nature of the Firm. Economica, Gertner, Robert H., Scharfstein, Dai S., & Stein, Jeremy C Internal Versus Eternal Capital Markets. Quarterly Journal of Economics, 09(4), 30. Gibbons, Robert, Holen, Richar, & Powell, Michael A Rational Epectations Moel of Goos Markets. Massachusetts Institute of Technology working paper. Grossman, Gene M., & Helpman, Elhanan. 00. Integration Versus Outsourcing in Inustry Equilibrium. Quarterly Journal of Economics, Grossman, Sanfor J., & Hart, Olier D The Costs an Bene ts of Ownership: A Theory of Vertical an Lateral Integration. Journal of Political Economy, 94(4), Grossman, Sanfor J., & Stiglitz, Joseph E Information an Competitie Price Systems. American Economic Reiew, 66(), Grossman, Sanfor J., & Stiglitz, Joseph E On the Impossibility of Informationally E cient Markets. American Economic Reiew, 70(4),

26 Hart, Olier Firms, Contracts an Financial Structure. New York: Ofor Uniersity Press. Hart, Olier, & Moore, John Property Right an the Nature of the Firm. Journal of Political Economy, 98(6), Hart, Olier, Shleifer, Anrei, & Vishny, Robert W The Proper Scope of Goernment: Theory an an Application to Prisons. Quarterly Journal of Economics, (4), 7 6. Hayek, F. A The Use of Knowlege in Society. American Economic Reiew, 35(4), Klein, Benjamin, Crawfor, Robert G., & Alchian, Armen A Vertical Integration, Appropriable Rents, an the Competitie Contracting Process. Journal of Law an Economics, (), Legros, Patrick, & Newman, Anrew F Competing for Ownership. Journal of the European Economic Association, 6(6), Macher, Je rey T., & Richman, Barak D Transaction Cost Economics: An Assessment of Empirical Research in the Social Sciences. Business an Politics, 0. Robertson, D. H. 98. The Control of Inustry. Nisbet & Co. Lt. Williamson, Olier Markets an Hierarchies: Analysis an Antitrust Implications. New York: Free Press. 6

27 8 Appeni 8. Deriation of Fact E ;;ci [ U;0 ()] E ;;ci [ U;0 ()] = c c i = E ; h jp = c c Z Z c c jp c c ; which is continuous an strictly ecreasing in an similarly, E ;;ci [ U; ()] E ;;ci [ U;0 ()] = (c c) + E ; jp (; ) c E ; [p (; )] (c c) = c c (c c) + ; which is continuous an strictly increasing in. For the last equalities in these two epressions, we use the following three facts: E ; jp = ; E ; jp = c c ; an E ; [p (; )] = + ( ) (c c) c; which we now proe as claims. Claim E ; jp = Proof. Follows irectly from the Law of Iterate Epectations. i Claim E ; h jp = 7

28 Proof. Note that, gien prices p, the conitional ariance is 8 >< jp = >: ( (p) ) ( ) ( (p)) p < p 0 p 0 < p < p 00 p 00 < p; where (p) an (p) sole p (; (p)) = p (; ) p 3 (; (p)) = p 3 (; ) or (; ) (p (; )) = (; ) (p (; )) = 3 p (; ) p 3 (; ) 0 + = + ( ) = ( ) so it is possible to compute the epecte conitional ariance E ; jp = Z = Z + R R 3 Z Z + () Z Z () + Z ( ) F (; ) + F (; ) + ( ) + ( ) + ( ) F (; ) + Z R ( ) F (; ) R ( ) F (; ) where () an () sole, respectiely p ( () ; ) = p 0 = p (; ) p 3 ( () ; ) = p 00 = p 3 (; ) 8

29 or () = ( ) () = + ( ) : We therefore hae E ; jp = Z Z ( ) ( ) + ( ) ( ) + ( ) ( ) Z Z + ( ) + + = ( 3) ( 3) 4 + ( ( ) ) ( ) + ( 3) ( 3) 4 = : ( ) Claim 3 E ; jp p (; ) = ( ) : Proof. First note that E ; jp p (; ) = + + Z Z Z Z ( ) Z ( ) ( ) + Z + ( ) jp (; ) p (; ) jp (; ) p (; ) 3 jp (; ) p 3 (; ) ; 9

30 where (p (; )) + jp (; ) = jp (; ) = + = ; 3 + (p (; )) jp (; ) = = = + + ( ) ; ( ) ; an p (; ) = p (; ) + ( ) p (; ) = ( ) ( + ) + p 3 (; ) = p (; ) ( ) ( ) + ( ) : so that if we substitute an epan, we obtain = E ; jp p (; ) Z Z Z Z Z Z Z Z ( ) ( ) ( + ) + ( ) Z ( ) + ( ) Z ( ) + Z Z Z ( ) Z ( ) + ( ) ( ) ( ) ( ) ( )! ( ) ( ) ( ) ( + ) +! ( ) ( ) ( + ) +! ( ) ( )! ( ) ( ) ( ) ( ) 30

31 There are four major epressions here. It can be shown that Z Z ( ) ( ) ( + ) + = + + ( ) ; () = Z Z Z ; ( ) Z + ( ) ( ) ( ) ( ) ( ) ( ) ( ) () Z Z Z ( ) Z + ( )! ( ) ( ) ( ) ( + ) +! ( ) ( + ) + = ; an (3) = + Z Z Z : ( ) Z + ( ) (! ) ( ) ( )! ( ) ( ) ( ) (4) 3

32 Thus, our epression is simply () + () + (3) + (4) or E ; jp p (; ) = ( ) : Claim 4 E ; [p (; )] = + ( ) Proof. Using similar logic as in the preious claim, we hae E ; [p (; )] = = Z Z Z Z Z Z Z Z Z = + ( ) ( ) Z ( ) ( ) + Z + ( ) p (; ) p (; ) ( ) Z ( ) + p (; ) p 3 (; ) ( ) ( ) ( ) ( ) Claim 5 E ; jp p (; ) = 0 Proof. This follows irectly from the preious two claims, since E ; jp p (; ) = E ; jp p (; ) + E ; [p (; )] = ( ) + + ( ) = 0: 3

33 8. Deriation of Fact Eplicit computation yiels the following bene t for choosing g = U E [ U;0 ] E [ U;0 ] = c c c c = c c = c c ; Z Z Z p c Z Z Z Z Z c ( p c i ) c i p ( p c i ) c i ( ) an similarly the bene ts for choosing g = D are E [ U; ] E [ U;0 ] = = = c c c c c c Z Z Z c Z Z Z Z Z + ( p c) : c c c p+ p ( p + c i ) c i ( p c i ) c i ( p) c Omitte Proofs Proof of Proposition 3. To establish that is increasing in, note that at = 0, the gains from choosing integration (an hence becoming informe) instea of non-integration (an hence enjoying a cost reuction) are gien by T S U T S D ( = 0) = + (c c) (c c) 33

34 an at = ; the gains from choosing integration oer non-integration are T S U T S D ( = ) = (c c) = + (c c) : c c (c c) Since we are at an interior solution, T S U T S D ( = 0) > 0 an T S U T S D ( = ) < 0. Net, note that T S U T S D ( = 0) is increasing in an T S U T S D ( = ) is increasing in if (c c) > 3, which is true since (c c) 4 >. Since T S U T S D () is linear in, this then implies that is increasing in. The comparatie statics with respect to an are straightforwar. Finally, = (c c) = : c c + When < (c c), this is clearly negatie. Otherwise, if, note that at = 0, = (c c), so this epression is positie. For > (c c), the epression 3+(c c) is negatie. (c c) 3+(c Since is increasing in, this implies that there is a cuto alue 0 ^ c), a function of the other parameters of the moel, for which < ^ > 0 an > ^ < 0: Proof of Proposition 4. Note that wheneer ; h i =! > 0! +! +! +! < < +! ; =! + + so that equilibrium informatieness is always increasing in!:!! +! > 0; 34