ASSET OWNERSHIP AND IMPLICIT CONTRACTS*

Transcription

1 - 1 - ASSET OWNERSHIP AND IMPLICIT CONTRACTS* Iver Bragelen December 1998 Department of Fnance and Management Scence Norwegan School of Economcs and Busness Admnstraton N-5035 Bergen-Sandvken, Norway. E-mal: ver.bragelen@nhh.no Ph. (47) Fax (47) Abstract In a settng wth two managers/owners who both make relaton- and asset-specfc nvestments, I suggest a model where a lnear mplct contract can strengthen the ncentves to nvest, f the partes are suffcently patent. Otherwse, only asset ownershp can be used to nfluence the ncentves. Frst, I analyse the case where the mplct contract may nclude a fxed transfer, whch then must be pad by the manager wth the weakest barganng poston. I argue that ths arrangement s not observed n busness relatons, due to rsk averson, bounded ratonalty and socal norms. Therefore I focus on mplct contracts wthout fxed transfers n the rest of the paper. The same ownershp structure s then optmal under both spot governance and mplct contractng, unless an ownershp structure wth more symmetrcal barganng postons can support a better mplct contract. In fact, a frst-best mplct contract s self-enforcng only when the two managers enjoy smlar barganng postons, even f they are nfntely patent. Choosng between technologes, strong nterdependences can be good, snce the future losses assocated wth an mplct contract volaton then are large. * I thank Terje Lensberg, Frøysten Gjesdal, Trond Olsen, John Roberts and Steve Tadels for nsghtful comments on earler drafts of ths paper. A frst verson of the paper was completed durng my stay at Scancor, Stanford Unversty I would also lke to thank Jm March for hs support durng that perod.

2 Introducton Wllamson (1975, 1985) and Klen, Crawford and Alchan (1978) observed that specfc nvestments can play an mportant role to determne optmal asset ownershp. Buldng on ths dea, Grossman and Hart (1986), Hart and Moore (1990) and Hart (1995) suggest formal models to show the benefts and costs of ntegraton wth respect to the hold-up problem. These models are lmted to one-perod relatonshps. I am aware of only two workng papers that treat the mult-perod case, where reputaton effects can play an mportant role. 1 Halonen (1994) argues that ownershp rghts matter also n a long-term relatonshp, where the partes are dscplned by reputaton effects. In a model where (for some unexplaned reason) no transfer of ownershp can take place after one of the partes has cheated, the worst ownershp structure of the one-shot game s good n the repeated settng because t provdes strong punshment but bad because the gans from devaton also are large. The optmal ownershp structure can change from the one-shot game to the repeated settng. Baker, Gbbons and Murphy (1996) analyse the case where only one of the partes nvests. They dstngush between spot employment, frms, spot markets and relatonal contracts, and allow for a transfer of ownershp rghts f cooperaton breaks down. The results add to the argument by Coase (1937) that frms can arse only when markets perform suffcently poorly, as there must be enough surplus from engagng n an mplct contract that the temptaton to renege n one perod s offset by the fear of future economc losses. Ths paper s an attempt to further deepen our nsghts wth respect to optmal ownershp structures and mplct contracts (whch can be nterpreted as a knd of trust). In the sprt of the Grossman-Hart-Moore models I focus on a stuaton where both partes make relatonand asset-specfc nvestments. Then the model predctons become more realstc, for nstance wth respect to when frms should domnate relatonal contractng. Frst, I ntroduce a general framework for two assets and two managers/owners, where ownershp rghts and mplct contracts can govern transactons. In an accompanyng paper (Bragelen 1998) I dscuss how explct contracts and ownershp rghts are jontly determned by the partes rsk averson and the specfcty of ther nvestments n a one-perod settng. Together these two papers reflect Bradach and Eccles (1989) observaton that prce, authorty and trust mechansms are found both n markets and n frms. 1 Another nterestng dscusson of reputaton effects wth respect to the theory of the frm s found n Kreps (1990). He consders a stuaton wth one employer (owner) and many (rsk averse) employees. Unforeseen contngences render long-term complete contracts mpossble. Instead the employer s gven the authorty to decde on adaptatons as tme goes by and the envronment changes. Then the employees must have some knd of fath or trust n the fact that the authorty wll be used farly. As unforeseen contngences tend to follow patterns, the employer can buld up a reputaton for meetng the contngences n a certan way. Kreps argues that a corporate culture s partly charactersed by the prncples that govern such decson makng and partly by the means by whch the prncples are communcated.

3 - 3 - Then I develop the one-perod model. I assume rsk neutralty, lnearty, ndependent technologes and quadratc cost functons to neutralse all effects except for a smple verson of the hold-up problem found n Hart (1995). The basc model s a varaton of the one I use n Bragelen (1998) and s nspred by Holmstrom and Mlgrom s (1991) lnear moral hazard model. It s very dfferent from the models by Halonen and Baker, Gbbons and Murphy, especally n the way uncertanty and nvestment specfcty s modelled. In secton 4 I ntroduce an mplct contract that s lnear n the observable, but not verfable benefts of the two partes. Followng Baker, Gbbons and Murphy (1996) I assume that a spot relatonshp prevals forever after an mplct contract volaton, but that a transfer of ownershp rghts can take place. I focus on self-enforcng mplct contracts, whch n fact are expected never to be broken. Frst, n secton 5, I analyse the case where the mplct contract may nclude a fxed transfer. The manager wth the weakest barganng poston would then have to commt to a fxed payment n every perod. However, n actual busness relatons, payments typcally go the other way and are part of a verfable contract. The absence of fxed transfers n mplct contracts can be explaned by rsk averson, bounded ratonalty and socal norms. In secton 6 I therefore focus on mplct contracts wthout fxed transfers. I show that the manager wth the strongest barganng poston wll enjoy the strongest ncentves under both spot governance and mplct contractng. If the managers are suffcently patent, a selfenforcng mplct contract always exsts that s better than the spot governance relatonshp. However, frst-best s not always sustanable, even when the dscount rate goes to zero. A frst-best mplct contract can be self-enforcng only f the two managers enjoy relatvely smlar barganng postons. In other words, wth ths class of mplct contracts, symmetry can be good for the mplct contract, and ownershp matters even when the partes are nfntely patent (snce the barganng postons are determned by the ownershp structure). Choosng between ownershp structures, an mplct contract benefts from strong barganng postons, snce the temptaton to renege then s small. Strong barganng postons are good also under spot governance. The managers should therefore choose the same ownershp structure under both governance modes, unless another ownershp structure wth more symmetrcal barganng postons can sustan a better mplct contract. Choosng between technologes, weak barganng postons are good for the mplct contract under some crcumstances, snce the future losses assocated wth an mplct contract volaton then are large. Stronger nterdependences can thus be benefcal for a busness relaton, even f t does not lead to hgher returns on nvestments. In secton 7 I suggest some more structure wth respect to the nvestment specfcty technology. Ths s helpful to llustrate some well-known results n the spot governance mode from Hart and Moore (1990) and Hart (1995). Then I use ths nvestment specfcty structure n secton 8 to show how the optmal governance structure s jontly determned by

4 - 4 - the dscount rate and the relatve nvestment specfcty of the two managers n a specfc example. I do ths exercse both for one and two assets. The example demonstrates, for example, that partnershps are lkely to occur n settngs where the two partes have smlar technologes, they take a long-term perspectve and there s for all practcal purposes only one asset to own (e.g. the company name). These condtons seem to be satsfed for many law and management consultng frms, where partnershps are prevalent. Fnally, n secton 9 I dscuss the model and some of the results n a wder context. I argue that the model seems realstc from a bounded ratonalty perspectve, and that t does capture mechansms and trade-offs that are mportant also under more complex technologes. 2. A general framework In ths secton I suggest a general governance framework for two assets and two productve managers/owners. Both make unobservable asset- and relatonshp-specfc nvestments. When uncertanty s resolved, the two managers make some further non-contractble decsons (e.g. to trade a partcular good) nfluencng the actual outcome. It s mpossble (or too costly) to ex-ante contract on the ex-post decson, due to the hgh degree of uncertanty. Ths cycle of ex-ante nvestments and ex-post decsons and outcomes s repeated n future perods. A classcal nterpretaton of the model would be that manager 2 n combnaton wth asset 2 supples an nput to manager 1, who wth asset 1 uses ths nput to produce output that s sold on the output market (Hart 1995). The nvestments may stand for expendtures of money or tme n makng the manufacturng operatons more effectve and developng the output market respectvely. An asset could for nstance be a factory, a dstrbuton network or a company name, and a manager could nclude the whole management team. There are two nstruments avalable to nfluence the ncentves to nvest. The two partes can choose a specfc ownershp structure, n the sense that ownershp gves the owner(s) resdual control rghts (Grossman and Hart 1986). And, they can agree to an mplct contract on observable benefts. The benefts are not verfable, so a contract cannot be enforced by a thrd party, but n a repeated settng reputaton effects may dscplne the managers. Reputaton effects work only f the managers are suffcently patent. Otherwse they must rely on spot governance, where the partes worry only about the current perod when they make decsons. If that s the stuaton, assume that renegotatons always lead to effcent ex-post decsons, regardless of ex-ante nvestment levels and ownershp structure. The negotated monetary transfer depends on the partes barganng postons. The ownershp rghts wll nfluence these barganng postons, snce the value of a manager s outsde opton

5 - 5 - s affected. A manager s nvestment level wll thus reflect her margnal benefts after the antcpated renegotaton process. Defne asset ownershp as the rght to deny other partes access to the asset (Hart and Moore 1990). In that case there are fve dstnct ownershp structures. Ether manager 1 owns both assets (whch, followng Hart (1995), I call Type 1 ntegraton - T1), manager 2 owns both assets (Type 2 ntegraton - T2), each manager owns the asset most specfc to her nvestments (Non-ntegraton - NI), each manager owns the asset most specfc to the other manager s nvestments (Cross ownershp - CO), or, fnally, the two managers jontly own the two assets (Jont ownershp - JO). Under jont ownershp both partes must agree for any of them to have access to the asset. In other words, both have a form of veto power. Then there are altogether ten dfferent categores of governance. These are summarsed n fgure 1 below, where I also name the categores. 2 Contractng mode T1 Ownershp structure T2 NI CO JO Spot governance Spot Employment I Spot Employment II Spot Market Implct contracts Frm I Frm II Relatonal Contractng Mutual hostage takng Partnershp Fgure 1 Under spot employment one of the managers owns both assets, and n each perod she offers the other party a contract whch s unaffected by the past. Frms are charactersed by the same ownershp structure, but the partes are to some extent dscplned by reputaton effects. Under non-ntegraton I call the categores spot market and relatonal contractng. Whle cross ownershp and jont ownershp structures n the mplct contractng mode are called mutual hostage takng and partnershps respectvely. As the reader wll see when I defne the formal model, jont ownershp and cross ownershp are domnated by non-ntegraton n the spot governance mode, and these categores are therefore crossed out. However, jont ownershp and cross ownershp can be vable n an mplct contract mode. 2 The fgure s nspred by the framework for one asset and one-sded nvestments found n Baker, Gbbons and Murphy (1996). Note that the categores I call Spot Employment II and Frm II are comparable to the categores they choose to call Spot Market and Relatonal Contract respectvely.

6 - 6 - Non-ntegraton and cross ownershp are not relevant f there s only one asset. If there are more than two assets, more ownershp structures wll be avalable to the partes. In ths model, ownershp s only mportant n the sense that t decdes the partes relatve barganng postons. The more assets there are (that are specfc to nvestments), the more flexblty the partes have n fndng jontly favourable barganng postons. 3. The basc one-perod model There are two assets and two productve rsk-neutral partes, manager 1 and manager 2. At t = 0 the partes make non-observable nvestments n human captal (e 1 and e 2 ). The benefts at t = 1 for the two managers are observable to manager 1 and 2 but not verfable to a thrd party. 3 The benefts depend on the nvestments at t = 0, some stochastc varables and on whether the two partes choose to cooperate or not at t = 1. In the case of no cooperaton, the benefts wll further depend on the ownershp structure. The outsde opton s worth more to a manager f she has access to some of (or preferably all) the assets. Whether cooperaton has taken place or not s also observable to the two partes but not verfable to outsders. Assume ndependent technologes that are lnear n an agent s effort e j (j {1,2}). If they choose to cooperate, the two managers' value added (net of t = 1 costs) are gven by θ 1 C = e 1 + ε 1 θ 2 C = e 2 + ε 2 where e j 0, E[ε j ] = 0 and ε j [-ε, ε]. 4 In the more general case, θ C j could be a functon of both e 1 and e 2. However, the ndependent technology property s not necessarly unrealstc. Say that manager 2's manufacturng costs decde θ C 2 (after nvestng n producton competences), and that the prce manager 1 can take for the product n the end market decdes θ C 1 (after marketng nvestments). There s no reason to beleve that marketng nvestments should nfluence producton costs and that (frm-specfc) producton technology nvestments (that are unobservable to the buyers) should nfluence the prce n the output market. Note that I do not rule out correlaton between ε 1 and ε 2. If, however, the two partes choose not to cooperate, ther benefts are reduced to 3 Note that benefts (and costs) can be monetary n nature even f they are not verfable to thrd partes. 4 The assumpton that nvestment levels and the stochastc varables enter the beneft functons addtvely s nspred by Holmstrom and Mlgrom (1991). Alternatvely we could let the range of ε j depend on e j, for nstance so that ε j [-e j, e j ]. The results of ths paper would stll hold qualtatvely, and n fact the selfsustanng constrants (n secton 4) would then be smplfed.

7 - 7 - θ 1 NC γ k θ 1 C θ 2 NC λ k θ 2 C where γ k, λ k [0,1) are constants that depend on the ownershp structure k K {T1, T2, NI, CO, JO}. Ths assumpton s strong n the sense that total and margnal benefts move together. That does not necessarly need to be the case, but t s consstent wth Hart and Moore (1990) and Hart (1995). 5 Further, the assumpton s strong n the sense that the nature of the uncertan varables s the same both under cooperaton and non-cooperaton. As s becomng standard n the lterature, assume a symmetrc Nash barganng soluton at t = 1. That s, cooperaton takes place after renegotatons, and the gans are splt 50:50. The rsk neutral managers then maxmse U 1 = ½ E [ θ 1 C + θ 1 NC + θ 2 C - θ 2 NC ] - c 1 (e 1 ) U 2 = ½ E [ θ 1 C - θ 1 NC + θ 2 C + θ 2 NC ] - c 2 (e 2 ) where c j (e j ) denotes manager j's prvate costs at t = 0 (n t = 1 dollars). To smplfy the analyss, assume quadratc cost functons c j (e j ) = ½ e j 2, j {1, 2}. 6 Defne ϕ k ½(1+γ k ) and ψ k ½(1+λ k ), whch can be nterpreted as the partes' respectve barganng postons (whch must not be confused wth the partes' barganng power n a Nash barganng sense). The maxmsaton problems of the two managers for a gven ownershp structure k then smplfy to e 1 k e 2 k = Argmax U 1 = Argmax { ϕ k e 1 + (1-ψ k ) e 2 - ½ e 2 1 } = ϕ k e 1 e 1 = ArgmaxU 2 = Argmax{ (1-ϕ k ) e 1 + ψ k e 2 - ½ e 2 2 } = ψ k e 2 e 2 Note that frst-best nvestment levels are e 1 * = e 2 * = 1, so the managers always undernvest n the spot governance mode. They should choose the ownershp structure (determnng specfc values of ϕ k and ψ k ) that maxmses the expected jont surplus Ω k (ϕ k,ψ k ) = e 1 (ϕ k ) + e 2 (ψ k ) - c 1 (e 1 (ϕ k )) - c 2 (e 2 (ψ k )) = ϕ k + ψ k - ½ ϕ k 2 - ½ ψ k 2 5 Baker, Gbbons and Murphy (1996) assume a dfferent knd of technology, where total and margnal benefts do not move together. Hence, n ther model over-nvestment s possble, whle n my model the partes always undernvest n the spot governance mode (although one of the managers may over-nvest under an mplct contract). 6 Most of the results n ths paper are robust wth respect to the form of the cost functon. A notable excepton s proposton 6.8 (that stronger nterdependences can be good), whch s not true f nvestments are very elastc (wth respect to the nvestment specfcty parameters).

8 - 8 - where e 1 (ϕ k ) and e 2 (ψ k ) denote the optmal nvestments of the two managers, for a gven nvestment specfcty. Although not necessary to generate the man results of the paper, t can be helpful to assume a rankng of the ownershp structures that I dscussed n secton 2, n the sense that 1 > γ T1 γ NI γ CO γ T2 = γ JO 0 1 > λ T2 λ NI λ CO λ T1 = λ JO 0 Then, t follows drectly from the defntons of ϕ and ψ that 1 > ϕ T1 ϕ NI ϕ CO ϕ T2 = ϕ JO ½ 1 > ψ T2 ψ NI ψ CO ψ T1 = ψ JO ½ Wth these assumptons, the value of the outsde opton ncreases (weakly) wth the number of assets the manager controls. Consder the set of nequaltes for manager 1. By defnton, there s a specal lnk between manager 1 and asset 1, and the outsde value s therefore assumed hgher for the manager f she owns her asset nstead of the other one (.e. γ NI γ CO ). Type 2 ntegraton and jont ownershp are equvalent wth respect to the outsde opton for manager 1, snce manager 2 has the rght to exclude her from both assets under both ownershp structures. The expected jont surplus ncreases n ϕ and ψ for the relevant range of these parameters. Jont ownershp and cross ownershp are therefore (weakly) domnated by non-ntegraton n the spot governance mode (snce ϕ NI ϕ CO ϕ JO and ψ NI ψ CO ψ JO ). 4. A lnear mplct contract An mplct contract s based on the realsatons of the observable, but non-verfable benefts of the two partes (θ 1 C and θ 2 C ). Assume that the mplct contract s restrcted to be lnear, n the form of a vector (a, b, t), where a s 1's share of θ 1 C, b s 2's share of θ 2 C and t s a fxed transfer, whch s postve when manager 1 s on the recevng end. Lnear contracts are attractve from a bounded ratonalty perspectve and to avod strategc behavour over tme (durng a perod). 7 After the uncertanty s resolved n a perod, the two partes can wrte a verfable contract on specfc amounts, so there s no rsk of one of the partes honourng the mplct contract expost whle the other does not. Ether the mplct contract s fulflled n ts entrety, or, f a party chooses to renege, the partes' barganng postons decde the dstrbuton of the surplus for that perod (as n the spot governance mode). 7 Holmstrom and Mlgrom (1987) argue convncngly for lnear explct ncentve contracts.

9 - 9 - Further assume that both partes and the assets lve forever (or de together at a random date). There s a common postve dscount rate, r, whch s constant over all perods. In other words, the partes are equally patent wth respect to when they would lke ther benefts. The mplct contract s contnued as long as both partes respect t. But f one party chooses to renege on the contract, all trust s destroyed, and the partes wll be unable to agree upon any new mplct contract afterwards. 8 There are three major scenaros wth respect to the future relatons of the two partes when an mplct contract s broken. The most extreme would be that they become so angry wth each other that no transacton s possble whatsoever. Or, they could agree to deal wth each other n a spot governance mode wthout beng allowed to change the ownershp structure, even f another structure would yeld a hgher expected jont surplus (as n Halonen 1994). Fnally, they could transfer the ownershp rghts (f that s desrable), and then settle n a spot governance mode under the best possble ownershp structure for that mode (as n Baker, Gbbons and Murphy 1996). Theoretcally, the second scenaro s odd, because the ownershp structure under the mplct contract also decdes the jont surplus after the mplct contract s broken. In other words, the partes could agree upon a very dsadvantageous ownershp structure to ncrease the expected punshment assocated wth renegng on the contract. In my opnon, the thrd scenaro s more consstent wth the basc assumptons. If the partes could have agreed upon a renegotaton soluton under spot governance n the frst place, then t s dffcult to understand why they cannot agree upon an ownershp transfer and a future spot relatonshp after an mplct contract s broken. The ownershp transfer does only requre that they agree upon a fxed payment, whch s verfable and can be enforced by a court. And the spot governance mode as such does not requre any trust at all, so the fact that there has been an mplct contract n place should not stop the partes from enterng a spot relatonshp afterwards (at least n a world wthout heated emotons). 9 Assume therefore that an ownershp transfer s possble after one of the partes reneges on the mplct contract. Index the best ownershp structure under an mplct contract K, and the best ownershp structure under spot governance s K. Usng the expresson for the expected jont surplus from secton 3, the dscounted value added ( ) from the transfer of ownershp rghts s gven by = 1 / r [ { ϕ s - ½ ϕ s 2 + ψ s - ½ ψ s 2 } - { ϕ - ½ ϕ 2 + ψ - ½ ψ 2 } ] 8 Later I wll focus on self-enforcng mplct contracts, where the probablty of an mplct contract volaton actually occurrng s zero. 9 Note that under spot governance, f the transacton nvolves a transfer of a good ex-post, the partes must be able to wrte a verfable contract at ths pont of tme on the transfer of the good. Then the uncertanty s already resolved (for that perod) and the partes can descrbe n detal the characterstcs of the good and the fxed payment for the transfer. (Whle the uncertanty ex-ante makes contngent contracts too costly to wrte.)

10 By defnton 0. Assume a 50:50 splt of the value added from such a transfer. Note that although we allow a transfer of ownershp rghts after an mplct contract volaton, t turns out that t usually wll be optmal to base the mplct contract on the same ownershp structure as under spot governance anyway (so that = 0). The case where the partes ndeed do expect a transfer of ownershp rghts s mportant for the choce of ownershp structure, whle the case where they do not expect such a transfer s relevant for the ntal choce of technology For an mplct contract to hold, t must be ncentve compatble for the two managers both ex-ante and ex-post n every perod. Ex-ante, a manager can follow three strateges. Frst, she can plan to keep the mplct contract forever. Gven that the other manager follows the same strategy, the managers effort levels are then e 1 = Argmax { a e 1 + (1-b) e 2 + t - ½ e 2 1 } = a e 1 e 2 = Argmax{ (1-a) e 1 + b e 2 - t - ½ e 2 2 } = b e 2 Second, she can ex-ante choose to not accept the mplct contract and communcate ths to the other manager. Then a transfer of assets wll occur mmedately (f that s optmal), and there wll be a spot relatonshp from perod one. For the two managers to nstead prefer the mplct contract (and follow the frst strategy), the followng nequaltes must be satsfed (1a) (1b) 1 / r { ½ a 2 + b(1-b) + t } 1 / r { ½ ϕ 2 + ψ (1-ψ ) } + ½ 1 / r { ½ b 2 + a(1-a) - t } 1 / r { ½ ψ 2 + ϕ (1-ϕ ) } + ½ Thrd, the manager can pretend that she accepts the mplct contract but plan to renege on t. Say that manager 1 follows ths strategy whle manager 2 nvests accordng to the mplct contract. Manager 1 then nvests ϕ, whch wll also be her share of her own (reduced) value added. On the other hand, she expects to end up wth a hgher share of manager 2's value added. In future perods the spot governance mode prevals. The followng nequaltes must thus hold for the two managers to prefer to be honest (and follow the frst strategy) (2a) (2b) (1 + 1 / r ){ ½ a 2 + b(1-b) + t } ½ ϕ 2 + b(1-ψ ) + 1 / r { ½ ϕ 2 + ψ (1-ψ ) } + ½ (1 + 1 / r ){ ½ b 2 + a(1-a) - t } ½ ψ 2 + a(1-ϕ ) + 1 / r { ½ ψ 2 + ϕ (1-ϕ ) } + ½ Ex-post, after the uncertanty for that perod s resolved, a manager may be tempted to renege on the mplct contract, f the value added of the other manager s unexpectedly hgh whle her own value added s low. Then the spot barganng soluton (ϕ, ψ) can be better for her n that partcular perod than the mplct contract (a, b). On the other hand, f she reneges, a spot relatonshp prevals forever after whch (n expectancy) mples lower future benefts,

11 as gven by (1a) and (1b). So for both managers to honour the contract ex-post, the followng two nequaltes must hold n any gven perod (3a) a(e 1 (a) + ε 1 ) + (1-b)(e 2 (b) + ε 2 ) + t + 1/r [ ae 1 (a) + (1-b)e 2 (b) + t - c 1 (e 1 (a)) ] ϕ (e 1 (a) +ε 1 ) + (1-ψ )(e 2 (b) + ε 2 ) + 1/r [ ϕ e 1 (ϕ ) + (1-ψ )e 2 (ψ ) - c 1 (e 1 (ϕ )) ] + ½ (3b) (1-a)(e 1 (a) + ε 1 ) + b(e 2 (b) + ε 2 ) - t + 1/r [ (1-a)e 1 (a) + be 2 (b) - t - c 2 (e 2 (b)) ] (1-ϕ )(e 1 (a) + ε 1 ) + ψ (e 2 (b) + ε 2 ) + 1/r [ (1-ϕ )e 1 (ϕ ) + ψ e 2 (ψ ) - c 2 (e 2 (ψ )) ] + ½ DEFINITION 4.1: An mplct contract s self-enforcng f (3a) and (3b) hold for all possble realsatons of the uncertan varables ε 1 and ε Later I wll show that a ϕ and b ψ n all optmal mplct contracts. For now, just assume that ths s true. Remember that ε j [-ε, ε]. For an mplct contract to be selfenforcng, (3a) must hold for (ε 1, ε 2 ) = (-ε, ε) and (3b) must hold for (ε 1, ε 2 ) = (ε, -ε). (3a) and (3b) are then satsfed for all possble combnatons of ε 1 and ε 2. Note that we do not have to decde the partcular probablty dstrbutons of ε 1 and ε 2. We know that (e 1, e 2 ) = (ϕ, ψ ) under spot governance and (e 1, e 2 ) = (a, b) f the mplct contract s expected to hold. When a ϕ and b ψ, the self-enforcng constrants can thus be wrtten as (4a) (4b) (b-ψ )(b+ε) - (a-ϕ )(a-ε) - t 1/r [ ½ a 2 + b(1-b) + t - ½ ϕ 2 - ψ (1-ψ ) ] - ½ (a-ϕ )(a+ε) - (b-ψ )(b-ε) + t 1/r [½ b 2 + a(1-a) - t - ½ ψ 2 - ϕ (1-ϕ ) ] - ½ In other words, the gans from renegng n that partcular perod (that are gven on the lefthand sdes of the nequaltes) must be offset by the expected future losses (that are gven on the rght hand sdes). Observe that the constrants are strengthened (for the same values of ϕ and ψ ) f a transfer of ownershp rghts s expected after an mplct contract s broken (.e. > 0), compared to the case where no such transfer s expected (.e. = 0), snce the punshment s reduced. It s straghtforward to show that (4a) and (4b) are stronger than the ex-ante constrants (1a), (1b), (2a) and (2b) f 2 2 (a - ϕ ) (b - ψ ) a(a - ϕ ) - b(b - ψ ) - t (5) ε Max,, 2(a - ϕ + b - ψ ) 2(a - ϕ + b - ψ ) a - ϕ + b - ψ All the major results of ths paper are vald, rrespectve of whether t s the ex-ante or the expost constrants that are bndng (although a couple of the propostons must be slghtly 10 Self-enforcement s a strong condton (whch s also used by Baker, Gbbons and Murphy 1996). In a more realstc verson of the model, the partes could be wllng to engage n an mplct contract that s broken n a gven perod wth some postve probablty. However, ths extenson does not seem to add sgnfcant nsghts.

12 rephrased). It turns out to be more convenent to work wth the ex-post constrants. Therefore assume that ε s large enough so that (5) s satsfed. Then the ex-ante constrants can be gnored. Note that the rght hand sde of (5) typcally s qute small compared to nvestment levels, so there s not much uncertanty that s needed for t to hold. An optmal self-enforcng mplct contract then solves Max { a - ½ a 2 + b - ½ b 2 }, subject to (4a) and (4b). (a,b,t ) Defne I 3 / 2 (ϕ 2 - ψ 2 ) - (ϕ - ψ ). Note that ϕ < ψ I < 0 for ϕ, ψ [½, 1). I can be nterpreted as a measure of manager 1's barganng poston relatve to manager 2, gven the ownershp structure under the mplct contract. Remember from secton 3 that the expected jont surplus n the spot governance mode s gven by Ω s ϕ s + ψ s - ½ (ϕ s 2 + ψ s 2 ). Settng n for, (4a) and (4b) can then be reformulated as (6a) (b-ψ )(b+ε) - (a-ϕ )(a-ε) - t 1/r [½ a 2 + b(1-b) + t - ½ I - ½ Ω s ] (6b) (a-ϕ )(a+ε) - (b-ψ )(b-ε) + t 1/r [½ b 2 + a(1-a) - t + ½ I - ½ Ω s ] where Ω s = Ω f no transfer of ownershp rghts s expected after an mplct contract volaton. The Lagrangan for the optmal self-enforcng mplct contract s gven by (7) L(a, b, t, λ 1, λ 2 ) = a - ½ a 2 + b - ½ b 2 - λ 1 { (b-ψ )(b+ε) - (a-ϕ )(a-ε) - t - 1/r [ ½ a 2 + b(1-b) + t - ½ I - ½ Ω s ] } - λ 2 { (a-ϕ )(a+ε) - (b-ψ )(b-ε) + t - 1/r [ ½ b 2 + a(1-a) - t + ½ I - ½ Ω s ] } where λ 1 and λ 2 denote the Lagrange multplers for (6a) and (6b) respectvely. Remember that ths expresson s vald only when a ϕ and b ψ. 5. The optmal mplct contract wth a fxed transfer The mplct contract defned n the prevous secton could nclude a fxed transfer (as n Baker, Gbbons and Murphy 1996). I wll later argue that such transfers are not observed n busness relatons due to rsk averson, bounded ratonalty and socal norms. However, from a theoretcal pont of vew, t s nterestng to study how such mplct contracts would have performed. In secton 4 I assumed that ncentves are stronger under the mplct contract for both managers. Now I need to show that ths result n fact does hold.

13 PROPOSITION 5.1: An optmal mplct contract (wth a fxed transfer) provdes (weakly) stronger ncentves for both the two managers compared to the spot governance mode under the same ownershp structure (.e. a ϕ and b ψ ). PROOF: Proof by contradcton. Say that a < ϕ. Then b > ψ, snce the mplct contract otherwse s worse than the spot governance mode. For the mplct contract to be selfenforcng, (3a) must hold for (ε 1, ε 2 ) = (ε, ε) and (3b) must hold for (ε 1, ε 2 ) = (-ε, -ε). The Lagrangan for the optmal mplct contract s then gven by L(a, b, t, λ 1, λ 2 ) = a - ½ a 2 + b - ½ b 2 - λ 1 { (b-ψ )(b+ε) + (ϕ -a)(a+ε) - t - 1/r [ ½ a 2 + b(1-b) + t - ½ I - ½ Ω s ] } - λ 2 { -(ϕ -a)(a-ε) - (b-ψ )(b-ε) + t - 1/r [ ½ b 2 + a(1-a) - t + ½ I - ½ Ω s ] } where λ 1 and λ 2 denote the Lagrange multplers for the two self-enforcement constrants. The frst-order condton wth respect to t mples that λ 1 = λ 2 λ for the optmal contract. Then L / a = 1-a + λ{2ε + 1/r(1-a)}, whch s postve for a < ϕ (< 1). In other words, n the optmal contract a should be set at least equal to ϕ. But ths result contradcts the assumpton that a < ϕ, whch thus cannot hold. Smlar for b < ψ. QED. We can therefore use (7) from the prevous secton to fnd the optmal mplct contract. But we must check that the soluton does satsfy the requrement that a ϕ and b ψ. As n the proof of proposton 5.1, the frst-order condton wth respect to t mples that λ 1 = λ 2 λ. The fxed transfer t s used to make the 'margnal costs' of each constrant the same. (6a) and (6b) can therefore be combned to one constrant (8) 2ε (a + b - ϕ - ψ ) 1/r (a - ½a 2 + b - ½b 2 - Ω s ) If ths constrant s satsfed, some t always exsts, so that both (6a) and (6b) hold. Frst, consder the stuaton where a > ϕ and b > ψ. The frst-order condtons wth respect to a and b then mply that the managers wll enjoy equal ncentves, even f they have very dfferent barganng postons (.e. a = b α). Equal ncentves are good, snce the managers have dentcal convex cost functons. The soluton to the optmsaton problem s gven by 2 (9) α = Mn( 1,1-2εr + (1-2εr) + 2εr( ϕ + ψ ) Ω ) Before we go on, consder under what crcumstances frst-best s sustanable. PROPOSITION 5.2: A frst-best mplct contract s always sustanable f the two partes are suffcently patent (.e. the dscount rate s suffcently low), when the mplct contract can nclude a fxed transfer. s

14 PROOF: From (8) we see that frst-best can be sustaned when 2ε(2 - ϕ - ψ ) 1/r(1 - Ω s ), whch s always satsfed for r 0, snce Ω s < 1 for all ϕ s, ψ s [½, 1). QED. Second, assume that α < Max(ϕ, ψ ). Say for nstance that ψ < ϕ, so that ψ < α < ϕ. From the proof of proposton 5.1 we then know that a* = ϕ. Set ths value of a nto the constrant (8), and solve for the optmal value of b Smlarly, consder the case where ϕ < ψ, so that b = ψ. Then the optmal a s gven by 2 2 (10) b = 1-2εr + (1-2εr) + 2ϕ ϕ + 4εrψ 2Ωs 2 2 (11) a = 1-2εr + (1-2εr) + 2ψ ψ + 4εrϕ 2Ωs The ncentves under the optmal mplct contract are thus gven by ( α, α) (a*,b*) = ( ϕ, b) (a, ψ ) f f f Max( ϕ, ψ ψ ϕ < α < ϕ < α < ψ ) α where α, a and b are defned n (9), (10) and (11). Now consder the fxed transfer of the contract. PROPOSITION 5.3: The manager wth the best barganng poston wll receve the fxed transfer, f such a transfer s part of the optmal mplct contract (.e. ϕ > ψ t 0 and ϕ < ψ t 0). PROOF: Frst, assume that (a*, b*) = ( α, α ), and that (6a) and (6b) bnd. Subtract each sde of (6b) from the respectve sde of (6a) to fnd t t = 1 2 I + ( ϕ ψ 1+ r ) αr Snce ϕ > ψ I > 0, t follows drectly that t must be postve f ϕ > ψ, and vce versa. If the constrants are not bndng, then a non-zero t s not needed n the mplct contract. Second, consder the stuaton where ψ < α < ϕ. Then (6a) and (6b) wth (a*,b*) = (ϕ, b ) mply that t = ( 1 2 b ψ )(rb (b + ψ ) 1+ r ) whch also must be postve, snce b > ψ ½. Smlarly, ϕ < α < ψ mples that t < 0. QED.

15 An mplct contract wth fxed transfers does not seem very realstc, snce t s always the party wth the worst barganng poston that must commt to a recurrng fxed payment. Such transfers are usually not observed n busness transactons. Rsk consderatons and wealth constrants are probably mportant reasons, snce the weakest party can have dffcultes payng n perods where profts are low due to uncertan (external) factors. It can also conflct wth the partes socal norms (wth respect to equty), f t s not consdered far to take advantage of another party s hgh nvestment specfcty to secure a fxed payment n addton to a large share (up to 100 percent) of own value added. Fnally, the managers may have dffcultes understandng the role fxed payments could play n mplct contracts, whle t s straghtforward that a hgher share of own value added strengthens the ncentves to nvest. Instead managers and owners tend to focus on the respectve shares of the value added that the dfferent unts are enttled to. In the next secton I wll therefore study a verson of the model where a fxed transfers s not allowed as part of the mplct contract. Note that I do not clam that fxed transfers are not mportant n busness relatons. But, I would argue that when there s such a recurrng payment, t s usually part of a verfable contract, and t s pad to the weaker party as part of a rsk sharng arrangement. 6. The optmal mplct contract wthout a fxed transfer As I dscussed above, a model where the mplct contract does not nclude a fxed transfer does seem to better conform to actual busness practce. Assume, therefore, that t must be set equal to zero. It s then not possble to derve a smple closed-form soluton to the optmsaton problem that was gven by the Lagrangan (7) n secton 4. We must nstead show the results n a somewhat more ndrect way. It turns out that the ex-ante constrants (1a) and (1b), where t = 0, now are useful to prove that ncentves are stronger for both the managers under the mplct contract. PROPOSITION 6.1: A vable mplct contract (wthout a fxed transfer) provdes stronger ncentves for both the two managers compared to the spot governance mode under the same asset ownershp structure (.e. a > ϕ and b > ψ ). PROOF: (1a) and (1b) must also hold for = 0 (snce 0). Set = 0, multply each nequalty wth r (whch s postve) and reformulate to get (12a) ½(a - ϕ )(a + ϕ ) - (b - ψ )(b + ψ - 1) 0 (12b) ½(b - ψ )(b + ψ ) - (a - ϕ )(a + ϕ - 1) 0

16 Frst, note that at least one of the nequaltes a > ϕ and b > ψ must hold for an mplct contract to yeld a hgher jont surplus than the spot governance mode. Suppose a > ϕ. The second term of (12b) s then negatve (snce ϕ ½). For the nequalty to hold, the frst term must therefore be postve. That s, a > ϕ b > ψ. Smlarly, a > ϕ must hold for (12a) to be satsfed f b > ψ. QED. In other words, we can agan use the optmsaton problem as t s stated n (7), but we do not need to check for a ϕ and b ψ anymore, snce the optmal contract always wll satsfy those condtons. From constrants (6a) and (6b) we can calculate the maxmum dscount rate for a gven mplct contract to be feasble (when t = 0). r [ ½ a 2 + b(1-b) - ½ I - ½ Ω s ] / [ (b-ψ )(b+ε) - (a-ϕ )(a-ε) ] f(a, b, ϕ, ψ, Ω s ) r [ ½ b 2 + a(1-a) + ½ I - ½ Ω s ] / [ (a-ϕ )(a+ε) - (b-ψ )(b-ε) ] g(a, b, ϕ, ψ, Ω s ) That s, r Mn{f( ), g( )}. It can be shown that for a vable mplct contract, f a, g b > 0 and f b, g a < PROPOSITION 6.2: The manager wth the strongest barganng poston wll also (weakly) have the strongest ncentves to nvest under the optmal mplct contract (.e. ϕ > ψ a b and ϕ < ψ a b). PROOF: Suppose ϕ > ψ. If a = b, then g( ) > f( ) r for a vable mplct contract. Snce f a > 0 and g a < 0, the coeffcent a can be ncreased untl g( ) = f( ). That wll be a better mplct contract, snce manager 1's ncentves are strengthened, unless a and b already take the frst-best values. a < b wll never be optmal, snce g( ) > f( ) then too. (To reach an optmal mplct contract, both a and b should be ncreased, but a must be ncreased more than b.) Smlar for ϕ < ψ. QED. COROLLARY: Managers wth equal barganng postons wll enjoy the same ncentve strength under an mplct contract (.e. ϕ = ψ a = b). PROOF: From the proof of proposton 6.2 t s clear that ϕ ψ a b and ϕ ψ a b. a = b must therefore hold for ϕ = ψ. QED. Note that proposton 6.2 and ts corollary are true only when the producton technologes of the two managers are symmetrcal n nature. That s, the beneft and cost functons must be dentcal, and the ranges of the two error terms must be the same. PROPOSITION 6.3: For suffcently low dscount rate r (.e. the partes are suffcently patent), a self-enforcng mplct contract always exsts that s better than the optmal spot governance relatonshp. 11 To show the sgn of these dervatves, remember that a > ϕ ½, b > ψ ½ and f( ), g( ) > 0.

17 PROOF: Suppose that the partes choose the best ownershp structure for the spot governance mode as a bass for the mplct contract, so that = 0. In ths settng, we must show that for any combnaton (ϕ, ψ ), where ϕ, ψ [½, 1), there always exsts a par (a, b), where a (ϕ, 1] and b (ψ, 1], so that the rght hand sdes of (4a) and (4b) both are postve, when t = 0. Then the nequaltes wll hold f r s suffcently low. The followng two nequaltes are suffcent condtons for the rght hand sdes of (4a) and (4b) to be postve when = 0 2 a > ϕ + ψ (1 ψ ) 2b(1 b) h(b) a < ½ + ½ + 2b 2ψ 4ϕ (1 ϕ ) k(b) 1 b ψ h(b), k(b) ϕ and k'(b) > h'(b) > 0. Then some b > ψ must exst, so that there s a non-empty range (h(b), k(b)) from whch a > ϕ can be chosen to satsfy both these condtons. QED. In a frst-best mplct contract (a, b) = (1, 1). The self-enforcng constrants can then be wrtten as r ½ r ½ (1 ψ (1 ϕ 1 I Ω )(1 + ε) (1 ϕ 1+ I Ω )(1 + ε) (1 ψ s s )(1 ε) )(1 ε) f FB (ϕ, ψ, Ω s ) g FB (ϕ, ψ, Ω s ) Snce ϕ < ψ f FB ( ) > g FB ( ) for ϕ, ψ [½, 1), t s only the self-enforcng constrant for the manager wth the strongest barganng poston that s relevant for a frst-best mplct contract. PROPOSITION 6.4: Frst-best s not always sustanable, even f the dscount rate goes to zero, when the mplct contract cannot nclude a fxed transfer. PROOF: Let r 0. (4a) and (4b) are then reduced to the ex-ante constrants (1a) and (1b). Wth t = 0, = 0 and a = b = 1, these constrants mply that ½ + ½ 2ψ 2 1 ϕ 2ψ (1 ψ ) for ψ > ½. 1 For ψ ½, only the second nequalty s relevant. Note that the values ϕ can take always nclude ψ. Say that ψ = Then ϕ must hold for a frst-best mplct contract to be sustanable. The constrants wll be even strcter for > 0. If ϕ has a value outsde the crtcal range, frst-best s not sustanable. QED.

18 The proof of proposton 6.4 ndcates that for a frst-best mplct contract to be selfenforcng, the two managers must enjoy relatvely smlar barganng postons. The next proposton shows that equal barganng postons are good to sustan frst-best, snce devatons from such symmetry always wll ncrease one of the partes temptaton to renege on the mplct contract. PROPOSITION 6.5: Suppose that an ownershp structure can be chosen where the managers have equal barganng postons (ϕ = ψ), and that the managers are just suffcently patent for frst-best to be sustaned wth an mplct contract (wthout fxed transfer) for that ownershp structure. That s, r = f FB ( ) = g FB ( ). A one-sded change n barganng postons would then requre the partes to be more patent for the frst-best mplct contract to stll be self-enforcng (snce f FB ( ) or g FB ( ) must decrease). PROOF: Say that ϕ = ψ. Then f FB ( ) = g FB ( ). It s straghtforward to verfy that f ϕ FB, g ψ FB < 0 and f ψ FB, g ϕ FB > 0, both when a transfer of ownershp rghts s expected after an mplct contract s broken and when t s not expected (as long as f FB ( ), g FB ( ) > 0). A onesded ncrease or decrease n ϕ or ψ must therefore reduce ether f FB ( ) or g FB ( ). QED. The basc results that were stated n propostons 6.1, 6.2 and 6.3 are vald regardless of whether the mplct contract can nclude a fxed transfer or not. That s not true for propostons 6.4 and 6.5. As proposton 5.2 ndcated, symmetry s not mportant for frstbest mplct contracts wth a fxed transfer. But, wthout such a transfer, the mplct contract s no longer as effectve. It s then more dffcult to provde the managers wth equal ncentves (whch s good because the managers have equal convex cost functons). That means that the choce of ownershp structure becomes more mportant. Ownershp structures wth symmetrcal barganng postons are good, because t s then easer to acheve smlar ncentve strengths for the two managers. a) The choce of ownershp structure Now consder the choce of ownershp structure n some more detal. Assume that technology s gven, so that the only way the managers can nfluence ther respectve barganng postons s through ther common choce of ownershp structure. To nvestgate whether t n general s optmal to choose an ownershp structure dfferent from the one that s optmal under spot governance, consder the optmsaton problem gven n (7) when a transfer of ownershp rghts s expected to take place after an mplct contract volaton ( > 0). Due to the envelope theorem, L/ ϕ and L/ ψ express the change n the maxmum jont surplus for a one-sded strengthenng of manager 1 s and manager 2 s barganng postons respectvely. (13a) L / ϕ = - λ 1 { a - ε + ½ (3ϕ -1) / r } + λ 2 { a + ε + ½ (3ϕ -1) / r }

19 (13b) L / ψ = λ 1 { b + ε + ½ (3ψ -1) / r } - λ 2 { b - ε + ½ (3ψ -1) / r } PROPOSITION 6.6: Say that r s suffcently low so that a self-enforcng mplct contract exsts that s better than the best spot governance relatonshp. Then t s always optmal to margnally strengthen one of the partes' barganng postons (whle the other s held constant), as long as both coeffcents of the optmal mplct contract are below the frst-best level (a, b < 1), a transfer of ownershp rghts s expected to take place after an mplct contract s broken and the barganng postons under the spot governance mode are not affected. PROOF: λ 1, λ 2 > 0 f both constrants are bndng. In (13a) use the expressons for λ 1 and λ 2, that are found from L / a = 0 and L / b = 0, to fnd L / ϕ > 0 (1-a) (a + 2b - ψ + 3(b + ϕ ) 2 ) + (1-b) (a - ϕ + 2r 3 (a ϕ ) ) > 0 2r The latter nequalty s always satsfed when a, b < 1, snce a > ϕ ½ and b > ψ ½. Smlar for L / ψ. QED. Strong barganng postons are n general good for the mplct contract, snce the temptaton to renege then s weak for a gven mplct contract (as ϕ s close to a and ψ s close to b). That means that there wll be a tendency to choose the ownershp structure under an mplct contract wth as strong barganng postons as possble. Ths tendency s also present under spot governance, snce the expected jont surplus, Ω s = ϕ s + ψ s - ½ (ϕ s 2 + ψ s 2 ), ncreases n ϕ s and ψ s for the relevant range of these parameters. These two results held together show that the same ownershp structure tends to maxmse the expected jont surplus both under spot governance and mplct contractng. However, as propostons 6.4 and 6.5 ndcate, an mplct contract can also beneft from symmetry n the barganng postons. Hence, f another ownershp structure mples more symmetrcal barganng postons, t can be optmal to choose that structure nstead of the one that s optmal under spot governance. 12 To llustrate how an mplct contract can beneft from symmetry, assume that the best ownershp structure n a spot governance mode s (ϕ s, ψ s ) = (0.9, 0.6), so that Ω s = 0.915, and set ε = ½. A frst-best mplct contract s then self-enforcng for a gven set of (ϕ, ψ ), f the dscount rate (r) s not hgher than the values gven n table 1. Some boxes are left blank. These combnatons of ϕ and ψ are not relevant for the gven value of Ω s, snce f they were avalable n the mplct contract mode, they would also be avalable as spot governance structures yeldng a hgher Ω s. Negatve values ndcate that the frst-best mplct contract s not self-enforcng even f the dscount rate s zero. 12 There s also a tendency to choose the same ownershp structures for both governance modes f the mplct contract can nclude a fxed transfer, but then more asymmetrcal barganng postons can support a better mplct contract under some settngs.

20 ϕ ψ JO 0.11 CO T NI T Table 1. Observe that a one-sded weakenng of a party s barganng poston now can be good to sustan a frst-best contract, snce t leads to more symmetrcal barganng postons. Ths may seem counter to proposton 6.6, but the reader should remember that the proposton was vald only for a, b < 1. It can be optmal to set one of the coeffcents hgher than one, f the barganng postons are very dfferent (and the mplct contract s relatvely close to acheve frst-best). Then the neffcences due to over-nvestment are outweghed by the strengthened ncentves to nvest for the manager wth the weakest barganng postons. Over-nvestment s necessary to keep the mplct contract self-enforcng. Weakenng the strongest barganng poston can then be good, snce over-nvestment s reduced and at the same tme the other (under-nvestng) manager s ncentves can be strengthened. Snce technology s fxed, the two managers can only choose between fve sets of (ϕ, ψ ), that correspond to the fve ownershp structures defned n secton 2. In the table I have ndcated fve boxes wth grey shadng, so that the basc assumptons of secton 3 wth respect to barganng postons for the dfferent ownershp structures are satsfed (ϕ T1 ϕ NI ϕ CO ϕ T2 = ϕ JO and ψ T2 ψ NI ψ CO ψ T1 = ψ JO ). Ths example s summarsed n table 2. Ownershp structure ϕ ψ Max r to sustan frst-best T NI CO T JO Table 2. Say for nstance that the dscount rate s Then jont ownershp (partnershp) s optmal, snce that s the only structure where frst-best can be sustaned. But f we change the assumptons wth respect to what barganng postons that each ownershp structure mples,

21 the rankng can change. Say that (ϕ CO, ψ CO ) = (0.65, 0.65), whle the other assumptons reman the same. Then cross ownershp (mutual hostage takng) domnates the other structures to acheve frst-best. Smlarly, f (ϕ NI, ψ NI ) = (0.70, 0.70), non-ntegraton (a relatonal contract) would be better. In ths way we can also change around the assumptons so that type 1 or type 2 ownershp (frm 1 and frm 2) would be optmal. PROPOSITION 6.7: The optmal ownershp structure for the mplct contract mode can be dfferent from the optmal structure under spot governance. No ownershp structure can be ruled out before the correspondng barganng postons are known. PROOF: One can easly construct examples from table 1 that satsfy the assumptons wth respect to the relatve barganng postons of the dfferent ownershp structures, so that n each example a dfferent ownershp structure s optmal under the mplct contract, whle the structure that s optmal under spot governance remans unchanged. QED. To sum up, the two managers should choose the same ownershp structure under the mplct contract as they would have done under spot governance, unless another ownershp structure wth more symmetrcal barganng postons can support a better mplct contract. The assumptons we have taken so far are n general not enough to rule out any of the ownershp structures as the optmal one under mplct contractng (whle jont ownershp and cross ownershp are domnated by non-ntegraton under spot governance). b) The choce of technology Above I assumed that technology was gven, so that only the choce of ownershp structure could nfluence the barganng postons. Now consder the stuaton where the managers can choose between technologes. For smplcty, assume that the managers choose the ownershp structure for the mplct contract that yelds the hghest expected jont surplus also n the spot governance mode. Then no transfer of ownershp rghts s expected after an mplct contract volaton ( = 0). Focus on the nterestng specal case where the two managers have equal barganng postons n the frst place. PROPOSITION 6.8: Suppose that the two managers have equal barganng postons ϕ = ψ k. Assume that the dscount rate r s suffcently low, so that a self-enforcng mplct contract exsts for that settng, but that frst-best s not sustanable. Then the expected jont surplus can be ncreased through a weakenng of one of the partes barganng postons (whle the other s held constant), when a transfer of ownershp rghts s not expected to take place after an mplct contract s broken. PROOF: Set ϕ ϕ = ϕ s and ψ ψ = ψ s. If ϕ = ψ k, then a = b α (from the corollary to proposton 6.2) and λ 1 = λ 2 λ n the Lagrangan for the optmsaton problem (snce everythng s symmetrcal). If α < 1, both constrants must be bndng, so that λ > 0. L/ ϕ and L/ ψ express the change n the maxmum jont surplus for a one-sded strengthenng of