Strategic ex-ante contracts: rent extraction and opportunity costs

Transcription

1 Strategc ex-ante contracts: rent extracton and opportunty costs Xnyu Hua Ths paper consders the possblty that a seller can contract wth one unnformed buyer pror to an aucton nolng two potental buyers. The seller s optmal strategc ex-ante contract more accurately reflects jont opportunty costs of the seller and the contracted buyer, and therefore extracts more rent from the entrant. Moreoer, ths ex-ante contract mtgates the seller s ex-post rent-seekng s-à-s the contracted buyer. Accordngly, t may create more socal welfare than the absence of ex-ante contracts, dependng upon the contracted buyer s fnancal constrant and the dstrbutons of trade surplus. Implementaton of the optmal strategc ex-ante contract and polcy mplcatons are dscussed. Department of Economcs, Hong Kong Unersty of Scence and Technology, Clear Water Bay, Kowloon, Hong Kong. Emal: xyhua@ust.hk. Ths paper s based on Chapter of my PhD dssertaton at Northwestern Unersty -- Kellogg School of Management. I would lke to thank Kathryn E. Sper for her aluable comments and precous encouragement. I also am grateful to Edtor Raymond Deneckere and an anonymous referee for ther ery helpful comments. I also would lke to thank Dad Besanko, Yeon-Koo Che, James Dana, Dad Dranoe, Peter Eso, Yuk-Fa Fong, Qang Gong, Sdartha Gordon, Kathleen Hagerty, Nko Matouschek, Rakesh Vohra, Joel Watson, Asher Wolnsky, Charles Zheng, the semnar partcpants at Kellogg School of Management at Northwestern Unersty, the Smon School of Busness at the Unersty of Rochester, Hong Kong Unersty of Scence and Technology, Unersty of Hong Kong, the 4 Internatonal Industral Organzaton Conference n Chcago, the 4 Summer Meetngs of the Econometrc Socety n Rhode Island, the Conference on Contract Theory n August, 4, at the Unersty of Calforna-San Dego, the 5 AEA Wnter Meetngs n Phladelpha, and the 6 Summer Workshop on Industral Organzaton and Management Strategy n Bejng, for ther ery helpful comments and dscussons. All mstakes are my own.

2 . Introducton Pre-sale and pre-acquston agreements are wdely adopted n sales and acqustons. In, Lask Vson Corp., a leadng North Amercan proder of laser son correcton serces, entered nto two pre-acquston agreements wth ICON Laser Eye Centers, Inc. for the sale of all of Lask s common stock. The agreements gae ICON an opton rght to buy Lask f there were no competng offers, and requred that any competng offers be at least % of ICON s strke prce. ICON also obtaned the rght of frst refusal, meanng that ICON had the rght to wn the target by matchng the terms of competng offers made by competng buyers. In return for grantng ICON ths prlege, Lask receed some payments n the form of optons to purchase certan shares of ICON s stock. Ths paper consders the prate ncentes of sellers and buyers to wrte contracts at an exante stage; that s, before they learn prate nformaton and before thrd partes enter the scenaro. 3 On one hand, ex-ante contracts may be used strategcally to extract rent from thrd partes, by affectng contractng partes or thrd partes ex-post behaors after they acqure addtonal nformaton. On the other hand, ex-ante contracts ncrease the probablty of effcent trade by mtgatng sellers ex-post rent seekng s-à-s contracted buyers. Wthout ex-ante contracts, sellers hae market power to seek rent from prately-nformed buyers, and trade may not occur een f t could brng poste surplus. 4 These strategc ex-ante contracts appear to be ant-compette or dscrmnatory -- they faor contracted buyers at the expense of subsequent competng buyers -- and they often are ltgated 5 or emerge n polcy debates. 6 It wll be shown that the addtonal alue created by lmtng rent-seekng s-à-s contracted buyers may domnate the msallocaton loss. Consequently, strategc ex-ante contracts may be more effcent for socety than the absence of ex-ante contracts. The features of ex-ante contracts n facltatng future trade and extractng rent from entrants are not unque to pre-sales or pre-acquston agreements, but also are obsered n many longterm contracts, such as energy supply contracts, property rental contracts, executes compensaton contracts, and strategc allance contracts. For example, energy supples between ppelne companes and shppers face uncertanty about future trade surplus and frms may learn prate nformaton n future perods. Moreoer, there often are future entrants. Long-term energy-supply contracts prode greater commtment to future trade than short-term contracts or spot markets do and, addtonally, often use strategc terms such as rebates and the rght of frst refusal. These ex-ante contracts may nclude upfront transfers n cash or by other means, such as offerng stocks or optons and changng early perods prces. Formally, ths paper consders a framework n whch a sngle seller, hang one ndsble asset to sell, faces two subsequent buyers. Trade always s more effcent than hang no trade. 7 The requrement for competng offers s only for Lask s two bggest shareholders shares. Feb.,, CCN Dsclosure 3 In the ICON case, ICON mght not hae full nformaton on ts aluaton of the target at the tme of contractng. Howeer, t could learn prate nformaton after contractng. Durng ths tme, thrd partes such as other acqurers mght enter the scenaro. Ths scenaro s typcal for many other contracts. 4 Many auctons fal because sellers set hgh resere prces. For example, n, the Commttee on Sugar Conerson and Aucton held an aucton wth a hgh ndcate prce for the rght to mport sugar. Howeer, prate traders refused to submt mport proposals. (July 7,, Busness World. 5 Strategc contracts often are the subject of lawsuts, such as those nolng remedy clauses for breachng contracts (Shaell, 98, 984; The Palgrae Dctonary of Economcs and the Law, Stockton Press, For example, there are many polcy debates on strategc energy supply contracts. The US Federal Energy Regulatory Commsson (FERC remoed the term-match cap for the rght of frst refusal. Yet, the FERC has other regulatons prohbtng certan strategc contracts (Noember 8,, Platts Retal Energy. 7 Ths assumpton s made for smplcty. The results would extend to known costs at the tme of contractng. If the seller has uncertan alue for the asset or uncertan costs, ex-ante contracts mght lead to ex-post neffcent trade wth a negate surplus.

3 Before a second buyer enters the scenaro, the seller can negotate sale or pre-sale contracts wth the frst buyer, who s unnformed about hs aluaton for the asset and s fnancally constraned at the contractng stage. 8 After ths, each buyer prately learns hs aluaton for the asset. If an ex-ante contract has been sgned, the seller has to follow the contracted mechansm to sell the asset. Otherwse he can choose any mechansm wth short-term monopoly power (for examples, see Myerson, 98; Mlgrom and Weber, 98; McAfee and McMllan, 987. Ths paper wll examne the seller s optmal strategc ex-ante contract and, more mportantly, ts effects upon socal welfare. If there s no second buyer, n the absence of ex-ante contracts, the seller seeks rent from the prately nformed buyer and ths creates a deadweght loss, snce effcent trade mght not occur. In contrast, the seller s optmal ex-ante contract could aod ths by commttng to a hgher probablty of ex-post trade. It works as a two-part tarff: the seller requres a lower ared payment ex-post, so that the buyer s wllng to buy ex-post; and the seller requres a fxed upfront transfer from the buyer, who s unnformed ex-ante, to extract the addtonal surplus. If a second buyer does appear n the future, the seller s optmal strategc ex-ante contract stll facltates trade by mtgatng hs ex-post rent-seekng, s-à-s the frst buyer. Moreoer, ths exante contract, as opposed to the seller s optmal mechansm when there s no ex-ante contract, extracts more rent from the second buyer by creatng a certan compette adantage for the frst buyer. Ths contract more accurately reflects jont opportunty costs 9 for the contractng partes when sellng to the second buyer. Accordngly, ths contract ether forces the second buyer to pay more, or aods jontly unproftable trade wth the second buyer. The seller and the frst buyer could make an upfront transfer to achee dfferent splts of ther jont surplus. Snce the upfront transfer s lmted by the frst buyer s ex-ante wealth, the rent extracted and trade facltated also are restrcted. The seller can mplement hs optmal ex-ante contract by combnng some ndrect contract clauses. None of the commonly used contract clauses, such as a fxed break-up fee, the non-compete clause, a stock lockup, by tself s optmal. The seller s optmal ex-ante contract can hae two effects upon socal effcency compared to the absence of ex-ante contracts. Frst, the contract facltates more trade. Second, ths optmal exante contract affects the allocaton between the two buyers, because the frst buyer enjoys a compette adantage. Both effects are enhanced when the frst buyer s less fnancally constraned. Socal polces should balance these two effects. The trade-off depends upon the frst buyer s fnancal constrants and the dstrbuton of trade surplus. The seller s optmal strategc ex-ante contract may ncrease socal welfare. In partcular, f all possble alues of trade surplus are hgh enough, strategc ex-ante contracts are less effcent than the absence of ex-ante contracts. When the buyers aluatons follow a unform dstrbuton, the seller s optmal strategc ex-ante contract s more effcent than the absence of ex-ante contracts, f the contracted buyer has low ex-ante wealth and f all possble alues of trade surplus are not ery hgh. Polcy makers or courts should consder ths effcency of ex-ante contracts n facltatng trade and, thereby, allow ex-ante contracts n certan crcumstances. Ths paper also dscusses more flexble polcy choces and shows that the welfare effects of strategc ex-ante contracts are robust, when buyers hae ex-post fnancal constrants and when the frst buyer, ex-ante, learns prate sgnals, as long as the sgnals are not ery nformate about hs aluaton. Ths paper contrbutes to the lterature on strategc contracts. Contracts can be used as strategc tools to deter entry or to extract rent from entrants. Ths proposton ntally was made 8 If the frst buyer had unlmted ex-ante wealth, the seller would smply make an ex-ante sale to the frst buyer and the buyer can resell the asset to the second buyer ex-post. Howeer, n realty, many contractng partes are ex-ante fnancally constraned. Smlar results hold wth other contractng constrants. 9 Ths s the frst buyer s aluaton n ths paper. In the ICON case, the rght of frst refusal guaranteed that entrants payment would be hgher than the jont opportunty costs for ICON and Lask. The opton rght restrcts Lask from ex-post rent-seekng.

4 by Aghon and Bolton (987. Many other studes consder specfc strategc clauses. Cho (6, for example, dly ponts out that the rght of frst refusal could be used to extract rent from entrants. Strategc contracts could mtgate hold-up problems and presere ncentes for relatonshp-specfc nestments, whch may be a good justfcaton for socal effcency of these contracts (Rogerson, 984, 99; Chung, 99; Sper and Whnston, 995; Che and Chung, 999; Che and Hausch, 999; Segal and Whnston, ; Hua, 5; Che and Lews, 7. Strategc contracts also could facltate early trade by mposng lower alues on outsde optons (Matouschek and Ramezzana, 7. Most of the aboe papers assume that the contracted buyer does not learn prate nformaton and that the seller has no ex-post commtment power. In contrast, ths paper consders that the contracted buyer can learn prate nformaton after contractng, and that the seller has ex-post monopoly power. Furthermore, ths paper analyzes strategc ex-ante contracts wth a drect reelaton mechansm. Second, ths paper adds a new twst to the lterature regardng a monopolst s ex-ante contractng wth unnformed buyers ersus ex-post sellng to prately nformed buyers. Courty (3 demonstrates that a monopolst would not sell both to nformed and unnformed buyers. Courty and L ( dscuss the use of ex-ante contracts to screen buyers who hae nosy nformaton, ex-ante. These papers do not nclude entrants and assume that the seller can make long-term commtments. Instead, ths paper consders strategc effects of ex-ante contracts aganst entrants. Moreoer, the seller cannot make long-term commtments wthout ex-ante contracts. Thrd, ths paper dscusses contractng or mechansm desgn when buyers hae fnancal constrants and prate aluatons. Laffont and Robert (996 dere the ex-post reenuemaxmzng mechansm when dfferent buyers hae the same commonly-known budget. Malakho and Vohra (5 characterze a seller s reenue-maxmzng mechansm when two buyers hae dscrete alues and only one buyer s budget-constraned. Buyers also may hae prate nformaton about ther budgets (Che and Gale, 996,. Lews and Sappngton (,, n prncpal-agent schemes, dscuss contractng wth agents who hae prate knowledge of ther wealth and abltes. Ths paper examnes the seller s optmal ex-ante contract wth a drect reelaton mechansm when the frst buyer s fnancally constraned ex-ante. Moreoer, the result that ex-ante contracts may ncrease socal welfare s robust een f the buyers hae ex-post fnancal constrants. The next secton presents the model. The thrd secton llustrates the socal welfare effects of strategc ex-ante contracts wth a specfc contract. The fourth secton examnes the seller s optmal strategc ex-ante contract, explores ts effects on socal effcency, and llustrates ts mplementaton through ndrect clauses. The ffth secton prodes an assessment on robustness and more polcy dscusson. The last secton offers concludng remarks. All proofs n ths paper are n the appendx.. The model There are three rsk-neutral players: the seller (S, the frst buyer (B, and the subsequent buyer (B. S has one ndsble asset to sell. S s outsde alue for the asset and hs costs are normalzed to zero. Ths would not affect the results, as long as the outsde alue and the costs are commonly known by the three players. Thus, trade always brngs poste surplus. Cho (6, and Che and Lews (7 dscuss specfc strategc clauses n gen auctons when buyers learn prate nformaton. Other papers on strategc contracts nclude Noldeke and Schmdt (995, Bulow, Huang, and Klemperer (999, and Burch (. Ths paper s also related to colluson n auctons. Klemperer (999 conducts sureys on the aucton theory lterature. The studes that hae been done on colluson mostly consder colluson among bdders. In contrast, ths paper addresses the optmal colluse contract between a seller and a bdder before auctons. 3

5 B s and B s aluatons (, of the asset are ndependently3 drawn from dstrbutons F, F ( on [, ], wth monotone hazard rates: H = F ( f ( s decreasng ( ( ( n. Although these dstrbutons are commonly known to all three players, the realzaton,, s prately obsered by B after the contractng stage. The tmng s as follows: At date : S and B hae symmetrc nformaton, 4 and B has lmted wealth, k. 5 S and B know that B wll enter at date, but nether has access to B at ths contractng stage. S offers a sale or pre-sale contract wth a drect or ndrect sellng mechansm to B. 6 The contract also ncludes an upfront transfer from B to S. If B accepts ths contract, he pays the specfed upfront transfer. Howeer, f B refuses, no ex-ante contract s sgned. At date : B prately learns hs aluaton,, for the asset; B enters and prately learns hs aluaton,. Both aluatons are non-erfable. At date 3: f there s an ex-ante contract between S and B, S has to follow the specfed mechansm to sell the asset; 7 f there s no ex-ante contract, S can choose any mechansm to sell the asset. At ths tme, f B or B wns the asset, he would hae enough wealth to pay for t. 8 Ther outsde optons are normalzed to zero. Wthout loss of generalty, assume that S has all the barganng power at the contractng stage and monopoly power at the sellng stage. 9 Yet, n the long run he cannot commt to a sellng mechansm f there s no ex-ante contract. Ths paper further assumes that ex-post renegotaton of the ex-ante contract ether s mpossble or too costly to mantan. Ths model assumes that nether S nor B has access to B at date. The contractng partes do not know who the entrants are. For example, n mergers and acqustons, one buyer frst dentfes and approaches a target. Ths acton tself would attract other potental buyers, who mght not show any nterest n the target unless some buyer approaches t frst. For another example, n long-term contracts such as energy-supply contracts, the seller needs only one buyer for each perod. For any future perod, entrants may come from many potental buyers. Another assumpton s that B s fnancally constraned at date. Howeer, f he wns the asset at date 3, he wll hae enough wealth to pay S. Ths represents many scenaros. Frst of all, the captal market may not prode enough ex-ante fnancng, snce the alues and the control rght are not realzed ex-ante, whle B s budget or fnancng abltes may ncrease ex-post, especally after he controls the asset. Second, n long-term contracts such as supply contracts or 3 The common alue of the asset s easer to be learned by all players. Therefore, the buyers dosyncratc alues are crucal to the scenaro. If the buyers aluatons are correlated and the buyers hae lmted lablty, the ntuton n ths paper stll holds. Further dscusson wll be n Secton 5. 4 When B has ex-ante prate and nosy sgnals about hs aluaton, the results hold f hs ex-ante sgnals are not so nformate. Further dscusson wll be n Secton 5. 5 The model can be extended to hae other contractng constrants, such as lmted resale probabltes. Generally the resale probabltes are lmted and the barganng may not be effcent. Strategc ex-ante contracts stll cause the trade-off of more trade and msallocaton between the buyers. 6 Drect reelaton mechansms would specfy the wnnng probabltes and the payments of the buyers accordng to ther reported aluatons at date 3. The ndrect mechansm may use contract clauses such as a breakup fee, the rght of frst refusal, an opton, et cetera. 7 For example, courts would enforce the contract or mpose hgh remedes for breachng the contract. 8 Howeer, the contract cannot force the buyers to make ex-post payments hgher than ther aluatons. 9 The results are not qualtately affected so long as S has some market power ex-post. Note that B has prate nformaton after date. Thus, renegotaton mght not maxmze the jont surplus of S and B. Instead, n the renegotaton, S would seek rent from the prately nformed B. Accordngly, the ex-ante contract could facltate trade when ex-post renegotaton s not effcent. If S could contract wth both buyers at date, hs optmal ex-ante contract stll would lead to more trade by mtgatng ex-post rent-seekng. 4

6 property rental contracts, B may generate more ex-post wealth from transactons or operaton n current perods. Thrd, frms often use equty or debt fnancng, and t takes tme to fnance from the captal market or banks. Ths s partcularly true n mergers and acqustons. A longer fnancng perod would secure more captal, but other buyers would be more lkely to enter. Therefore, many frms negotate pre-sales or pre-acquston contracts when they hae lmted captal. For example, n 3, before ts completon of $4 mllon fnancng, Enerplus Resources Fund sgned a strategc pre-acquston agreement wth Ice Energy Lmted. In sum, there s no nconsstency between B s ex-ante and ex-post fnancal constrants. Moreoer, as wll be dscussed n Secton 5, the results n ths paper would not be changed qualtately when the buyers hae ex-post fnancal constrants. Note that the ex-ante contract may nclude an upfront transfer from B to S. In realty, upfront payments depend more on buyers ex-ante wealth and the barganng power of S and B. Upfront transfers can be n cash. For example, n 998, Poneer Natural Resources Company sgned a pre-sales agreement wth Costlla Energy, Inc., whch proded Costlla wth an excluse opton rght to purchase certan ol and gas propertes. Costlla pad Poneer an rreocable upfront cash payment of $4 mllon. In 999, unable to rase enough fnancng, Costlla dd not exercse the opton. 3 Strategc allance contracts also nclude upfront cash payments or adjustments of partners equty stakes (for example, see Robnson and Stuart, 7. Upfront transfers also can take other means such as stocks, optons, or changng prces of current or sde transactons. As n the ICON example, pre-acquston agreements may offer sellers optons, stocks or remedy protectons. Long-term energy-supply or property rental contracts can requre dfferent prces for current perod transactons when offerng contracted buyers commtment or strategc clauses wth respect to future perods. Fnally, the ex-ante contract can be ether a sale contract ncludng a specfed prce, or smply a pre-sale agreement wthout a specfed prce. 4 Moreoer, ths model assumes that there s no nestment. There s ample research on the use of strategc contracts to protect nestments. The objecte here, howeer, s to analyze the use of contracts to facltate trade and to extract rent from entrants. 3. Illustraton--the ex-ante contract wth rght of frst refusal and no resere prce To llustrate the effects of strategc ex-ante contracts, ths secton consders one specfc contract. The contract requres that B pays an upfront transfer to hold the rght of frst refusal, whch says that the seller must reeal B s bd to B, and B has the rght to purchase the asset by matchng B s bd. Moreoer, the contract specfes that S cannot set ex-post resere prces. For smplcty, ths secton assumes that and are drawn ndependently from the unform dstrbuton on [,] and that B has lmted wealth of 5/4 at date. Denote the expected utltes of S, B, B and socal welfare as U, V, V, and W when S and B agree on an ex-ante contract. As a benchmark, f there s no ex-ante contract, S can choose any mechansm at date 3. As shown n the lterature, S s optmal sellng mechansms are equalent to the frst-prce or second prce aucton wth a resere prce of / for each buyer. The expected utltes for S, B and B are (5/, /, /. The socal welfare, then, s 7/. There s socal loss when < / and < /. But there s no msallocaton loss between B and B. Noember 7, 3, Market News Publshng 3 Aprl 9, 999, Platt's Ol gram News 4 The fact that prces are not fnalzed s not unque to pre-sale agreements. In many long-term contracts, only short-perod prces are specfed. Re-opener clauses, for example, allow contracted partes to negotate future-perod prces. 5

7 Wth the ex-ante contract, B has the rght of frst refusal and S cannot mpose ex-post resere prces. Walker (999 dscusses some potental reasons for usng the rght of frst refusal. Cho (6 compares the rght of frst refusal to standard prate-alue auctons wthout resere prces. In these standard auctons, B would wn the asset so long as hs aluaton s hgher than B s aluaton. Howeer, Cho (6 ponts out that when B has the rght of frst refusal, B would wn the asset only when B s aluaton s less than B s bd. As a result, there s the possblty of msallocaton of the asset. The followng proposton llustrates Cho s fndngs. Proposton : Assume that and are ndependently drawn from the unform dstrbuton on[,]. B s offered the rght of frst refusal n the ex-ante contract, and the optmal upfront transfer to S s 5/4. At date 3, B bds b =. B would exercse the rght of frst refusal f and only f b. If B does not exercse the rght, B wns and pays b. The expected utltes for S, B and B are (/4, /, /. There s msallocaton when / < <. Cho (6 s analyss, howeer, does not consder the optmal mechansm that S would choose at date 3 n the absence of an ex-ante contract. As n the benchmark case, S seeks rent sà-s B and B by specfyng resere prces. In contrast, the ex-ante contract mtgates S s expost rent-seekng. In ths llustraton, S commts not to set resere prces. Thus, there always s trade. Ths addtonal trade alue domnates the msallocaton loss. 5 Corollary : Assume that and are ndependently drawn from the unform dstrbuton on[,]. The ex-ante contract wth the rght of frst refusal and no resere prce s socally more effcent than the absence of ex-ante contracts. The socal welfare s 5/4. In sum, ths ex-ante contract has two characterstcs. Frst, t ges B a strategc adantage aganst B. Ths adantage, the rght of frst refusal, guarantees that, f B wns, hs payment s hgher than the jont opportunty cost for S and B. Second, ths ex-ante contract mtgates S s ex-post rent-seekng. Accordngly, there are two effects on socal effcency: affectng the allocaton between the buyers and facltatng more trade. Howeer, ths specfc contract may not be the optmal strategc ex-ante contract for S. What are the optmal ex-ante contracts for S? Are these optmal contracts always more effcent than the absence of ex-ante contracts? These questons wll be answered n the next secton. 4. S s Optmal Ex-ante Contract, Socal Effcency, and Implementaton The reelaton prncple apples to ths model. Ths secton frst examnes S s optmal ex-ante contract wth a drect reelaton mechansm and ts effects on socal welfare. Then the secton prodes examples of how to mplement S s optmal contract usng ndrect clauses. S s optmal ex-ante contract wth a drect reelaton mechansm Frst, note that, f there s no fnancal constrant for B, S would requre an approprate upfront transfer and make B the resdual clamant of any reenue generated at date 3. At date 3, B offers a monopoly prce to B based upon hs own aluaton. If B accepts the prce, then B recees the full payment from B. Otherwse, B owns the asset. In ths case, there may be msallocaton due to B s ex-post monopoly power. Moreoer, trade always happens. 5 Polcy makers or courts may not be able to ban the use of resere prces or strategc clauses, snce they may not hae enough nformaton on such ssues as sellers costs. More dscusson s n Secton 5. 6

8 Next, when B faces an ex-ante fnancal constrant, S s optmal ex-ante contract would nclude two parts: ( an upfront transfer, t, to be made from B to S at date ; and ( a drect reelaton mechansm to be used at date 3. Each buyer, B, s asked to report hs aluaton. Gen the reports (,, the mechansm specfes B s wnnng probablty, q (,, and B s expost payment to S, t (,. The followng notatons are used: Q ( s B s expected wnnng probablty, gen hs report ; T ( s B s expected ex-post payment to S, gen hs report ; V ( s B s nterm expected utlty; and V s B s e ex-ante expected utlty f there were no ex-ante contracts. Note that Q ( E q (, ] Q T. S would choose a contract ( The problem could be wrtten as follows usng ( Max { t, Q, T } t + T ( df ( + T ( df ( Subject to: Q ( T ( Q ( ~ T ( ~ Q ( T ( = [ j j and V ( = ( ( t, q (,, t (, t, Q (, T (. 6 to maxmze hs expected reenue. for all,, ~ (IC for all [ Q ( T ( ] df ( t V, (IR (Ex-ante IR for B t k (Ex-ante fnancal constrant for B The frst nddual ratonalty constrant assumes that, at date 3, S cannot force each buyer to pay a transfer hgher than the buyer s aluaton. The ncente compatblty constrant guarantees truth tellng from each buyer. Moreoer, the ex-ante nddual ratonalty constrant makes ths contract accepted by B, and the fnancal constrant restrcts the upfront transfer. It can be shown that the ex-ante nddual ratonalty constrant s bndng, otherwse S always could ncrease the upfront transfer and/or change B s wnnng probablty Q (. Let λ = λ( k be the multpler correspondng to the ex-ante nddual ratonalty constrant. Wth the standard mechansm desgn approach, ntegratng the seller s problem by parts and substtutng Q ( = E q (, ] n: Max {,λ} q [ j j F λ ( ( (, F ( ( q + q, f f Subject to: λ { Q ( x dxdf ( k V } = Q ( s non-decreasng. q (, + q (, ( df ( df ( 6 If there are solutons to the problem wth nterm nddual ratonalty constrants usng expected payment functons ( constrants.., T, then there exst ( t, whch sole the ex-post nddual ratonalty 7

9 r Defne g ( ;λ = λ ( F ( f ( as the λ -adjusted rtual utlty and r ( k ( λ( k, as the alue that satsfes g r ( λ ( k ; λ( k =. In fact, λ( k (, or λ = s the shadow prce of B s expected utlty at date 3. Gen k, B could make an upfront transfer. In exchange, he should share more ex-post surplus than he would f there were no ex-ante contracts. Accordngly, hs rtual utlty s adjusted by ths shadow prce. The followng proposton presents S s optmal strategc ex-ante contract. Proposton : S s optmal strategc ex-ante contract specfes an upfront transfer, drect reelaton mechansm { q (,, (, t t, and a }, such that the expected ex-post payment from B s ( ( T = Q Q ( xdx. The shadow prce λ = λ( k [,] ( There exsts one unque ( k k such that λ ( k = f k k, and λ ( k > f. Also: k < k. ( λ =. λ s non-ncreasng n k. The upfront transfer s mn k, k. ( If B s adjusted rtual utlty s poste and greater than B s rtual utlty,.e., g ( ;λ max(, ( ; g, B wns the asset,.e., (, q = ; otherwse, q (, =. ( If B s rtual utlty s poste and greater than B s adjusted rtual utlty,.e., g ( ; max(, ( ; g λ, B wns,.e., (, q = ; otherwse, q (, =. t = ( Corollary : Rewrte the wnnng probabltes as q ( ; k and Q ( k,. In S s optmal ex-ante contract wth a drect reelaton mechansm: ( B s expected wnnng probablty Q ( ; k s non-decreasng n k and hgher than that f there were no ex-ante contracts; B s expected wnnng probablty Q ( ; k s non-ncreasng n k and lower than that f there were no ex-ante contracts. ( The probablty of hang trade s non-decreasng n k and hgher than the probablty of trade f there were no ex-ante contracts. ( S s expected utlty s non-decreasng n k. If B has no ex-ante wealth, the optmal ex-ante contract specfes the same mechansm as f there were no ex-ante contracts. ; Accordng to Corollary, f B has more ex-ante wealth to make a hgher upfront transfer, the shadow prce would be lower. Accordngly, B s adjusted rtual utlty s hgher. Ths s sgnfcant n two ways: frst, B s adjusted rtual utlty s more lkely to be poste, thereby ncreasng the probablty of tradng wth B; and second, B s adjusted rtual utlty s more lkely to be hgher than B s rtual utlty. Note that S and B hae a jont opportunty cost,, when sellng the asset to B. If the shadow prce s lower, B s adjusted rtual utlty s closer to. Ths strategc characterstc s smlar to the rght of frst refusal, snce both mechansms more, for S and B. accurately reflect the jont opportunty cost, Fgure shows the equlbrum outcome wth S s optmal strategc ex-ante contracts, when B faces dfferent ex-ante fnancal constrants. If k =, effectely there s no ex-ante contract. Ex-post, S seeks rent from prately nformed B and B. Accordngly, there s no trade n regon L+M+N. In regon O+P+Q, B wns, and S and B hae a jont opportunty cost equal to. Howeer, n some areas of regon O+P+Q, B 8

10 may pay less than or no larger than. 7 Therefore, n those areas, the jont reenue s lower than the jont opportunty cost for S and B. Ths s because B prately knows the jont opportunty cost, whle S and B look for ther nddual benefts non-cooperately. If k = k L >, B makes an upfront transfer and S commts to mtgate hs ex-post rentseekng s-à-s B. In regon N, trade occurs and ncreases the jont surplus for S and B. Moreoer, B has a compette adantage, so that the mechansm more accurately reflects the jont opportunty cost. Thus, S and B aod jontly unproftable trade wth B n regon Q, that mght happen when k =, or makes B s expected payment hgher n regon O+P. 8 Oerall, S s optmal ex-ante contract s more proftable for the jont surplus of S and B. As n Fgure, both effects are enhanced when B has more wealth. Socal effcency As shown aboe, S optmal strategc ex-ante contract, frst of all, reduces the deadweght loss of hang no trade by mtgatng hs ex-post rent seekng s-à-s B. Second, ths contract ges B compette adantage and therefore may cause msallocaton between B and B. For example, n Fgure, B wns n regon Q een f hs aluaton s less than B s aluaton. The next proposton summarzes these socal welfare effects and presents a comparate statc analyss when B s ex-ante fnancal constrant changes. Proposton 3: S s optmal ex-ante contract nduces a hgher probablty of trade than the absence of an ex-ante contract does, and may cause msallocaton between the two buyers. ( The socal welfare created from the addtonal trade s non-decreasng n B s ex-ante wealth, k. ( If B s and B s aluatons are dentcally dstrbuted, the msallocaton loss s larger when B has more ex-ante wealth. ( Ether of the two effects may domnate. In partcular, suppose that and are drawn from a unform dstrbuton, then there exsts a unque k ˆ, such that S s optmal exante contract s more effcent than the absence of ex-ante contracts, f and only f k kˆ. As exhbted n Fgure, the addtonal trade created by the contract happens n the range of smaller aluatons, whle msallocaton may happen n the range of hgher aluatons. When B s ex-ante wealth k s small, for the unform dstrbuton, the alue created from more trade s hgher than the msallocaton loss, because the msallocaton s less lkely to happen. When B s ex-ante wealth k s great enough, the margnal alue created from more trade s ery small. But there s a hgher probablty of msallocaton, snce B has a larger compette adantage. Accordngly, the msallocaton loss domnates the addtonal trade alue created. Accordng to the aboe result, polcy makers or courts may allow strategc ex-ante contracts, especally when the contractng partes are fnancally-constraned. They also may restrct the leel of upfront transfers that are specfed n contracts. One may argue that t would be more effcent not to allow strategc contracts or resere prces. Howeer, n practce, polcy makers mght not be able to do so. For example, they may not hae nformaton about the seller s costs. More dscusson wll be n Secton 5. The socal welfare effects of S s optmal ex-ante contract also depend upon the dstrbutons of trade surplus, as shown n the followng proposton: 7 For example, n the frst prce aucton, B s payments may be less than. In the second prce aucton, B s payment always s equal to. 8 Ths comparson depends upon whch specfc mechansm s used n the absence of ex-ante contracts. 9

11 Proposton 4: Suppose that the dstrbutons of the buyers aluatons shft from [, ] to [ +, + ], and that B s ex-ante wealth, k, s ncreased such that S s optmal ex-ante contract keeps the same shadow prce, λ. There exsts ˆ such that S s optmal ex-ante contract s less effcent than the absence of ex-ante contracts, f ˆ. If and are drawn from a unform dstrbuton, n partcular, there exsts a unque ˆ such that S s optmal exante contract s less effcent than the absence of ex-ante contracts, f and only f ˆ. When the trade surplus s dstrbuted throughout ranges of hgher alues, S wll ncrease the probablty of trade, een when there s no ex-ante contract. Therefore, polcy makers should not allow strategc ex-ante contracts n such cases. They mght be wllng to allow strategc ex-ante contracts when the trade surplus s dstrbuted throughout ranges of lower alues. Ths s llustrated by the followng two examples: f each buyer s aluaton s drawn from the unform dstrbuton on [,], S s optmal strategc ex-ante contract always s more effcent than the absence of ex-ante contracts; f each buyer s aluaton s drawn from the unform dstrbuton on,, S s optmal strategc ex-ante contract s less effcent than the absence of ex-ante contracts. [ ] Implementaton by ndrect contract clauses the case of unform dstrbuton Thus far, S s optmal ex-ante contract wth a drect reelaton mechansm has been examned. It also s nterestng to show how to mplement the optmal ex-ante contract by ndrect contract clauses. It s easy to show that the rght of frst refusal alone does not mplement S s optmal exante contract. In practce, many strategc ex-ante contracts use combnatons of seeral clauses. The followng proposton shows one example of S s optmal ndrect contracts. Proposton 5: Assume that and are drawn ndependently from the unform dstrbuton on λ = λ k satsfes [,]. The shadow prce n S s optmal ex-ante contract ( ( + λ ] = mn ( k,/ 4 + / /[3. The followng contract wth ndrect clauses s equalent to S s optmal ex-ante contract wth a drect reelaton mechansm: ( B pays an upfront transfer mn k,/ 4 to S at date ; ( B has an opton to purchase the asset at the strke prce, of ( λ ( + λ /, f B does not enter; and ( f B enters, B pays an entry fee λ [4( + λ ] to S, and B has the adjusted rght of frst refusal to match B s bd, b, and to pay a premum (or rebate f negate [(3 λ ( + λ] b ( λ ( + λ. In the optmal ndrect contract aboe, f B does not enter, the strke prce n the opton seres as a resere prce for B. Besdes, ths adjusted rght of frst refusal ges B a compette adantage and, accordngly, the jont opportunty cost for S and B s reflected more accurately. The entry fee for B s selected merely to create the optmal resere prce for B. There are many other commonly used ndrect contract clauses. When buyers learn prate nformaton ex-post, t could be shown that break-up fees, stock lockups or toeholds, and the rght of frst offer may not hae strategc characterstcs smlar to S s optmal strategc ex-ante contract, whle optons, non-compete clauses, and the rght of frst refusal do. 9 Take breakup fees as an example. Aghon and Bolton (987 analyze the use of a break-up fee to extract rent from an entrant. In ther model, B s aluaton s commonly known. Therefore, B must make a hgher bd than he would f there were no break-up fee, n order to nduce S to 9 Detaled dscusson of each of these clauses s aalable upon request.

12 breach the contract. Howeer, ths may not be true when the buyers learn prate alues ex-post. Suppose that S and B sgn a contract specfyng that. S would hold the Englsh aucton at date 3, and would pay a breakup fee, d, to B when B fals to obtan the asset or when S breaches the contract. Assume that B s and B s aluatons are drawn from the unform dstrbuton on [,]. In the Englsh aucton, B s and B s optmal bddng strateges are b = d and b =. The break-up fee makes B less aggresse n auctons. Therefore, the break-up fee tself does not hae strategc characterstcs smlar to S s optmal ex-ante contract. In sum, S s optmal ex-ante contract mtgates hs ex-post rent-seekng s-à-s B and has strategc characterstcs by more accurately reflectng ther jont opportunty costs. Ths contract may cause msallocaton between the buyers, but also can facltate more trade. Allowng the use of strategc ex-ante contracts may be more effcent than strctly prohbtng ther use. Fnally, ths contract could be mplemented through a combnaton of commonly used clauses. 5. Robustness and polcy dscussons Ex-ante and ex-post fnancal constrants Preous sectons hae followed the framework n whch the contracted buyer does not hae ex-post, but ex-ante fnancal constrant. It also assumes that the fnancal constrant s common knowledge. As dscussed n secton, ths framework represents many scenaros. Interestngly, ex-post fnancal constrants wll not change the results qualtately. Laffont and Robert (996 sole the ex-post reenue-maxmzng mechansm when buyers hae prate aluatons and the same commonly-known budget. Maskn ( consders ex-ante effcency n the same framework. Malakho and Vohra (5 characterze the ex-post reenuemaxmzng mechansm when two buyers hae dscrete aluatons, and only one buyer s budget constraned. 3 All these mechansms use resere prces, though the resere prces are lower and less effecte n extractng rent from prately-nformed buyers than they are n the absence of fnancal constrants. Moreoer, these ex-post mechansms may cause msallocaton between the buyers because the seller cannot extract more than the buyer s budget and the seller may dstort allocaton to extract more rent from the buyer who has deeper pockets. Intutely, ex-ante contracts stll can mtgate S s ex-post rent-seekng such as usng resere prces s-à-s B. Ths effect facltates more trade. In addton, these contracts may not cause too much msallocaton, snce fnancal constrants restrct ex-post rent-seekng s-à-s B. The followng example shows that S s optmal ex-ante contracts may be more effcent than the absence of ex-ante contracts, een when the buyers hae ex-post fnancal constrants. Suppose that B s and B s prate aluatons, and, are drawn ndependently from the unform dstrbuton on [,] and that both buyers hae lmted wealth, /, both ex-ante and expost. 3 The tmng s the same as n Secton. If there s no ex-ante contract, usng the approach n Laffont and Robert (996, t can be shown that the seller s optmal ex-post drect reelaton mechansm s: when both buyers reported aluatons are larger than. 7747, the asset s allocated wth equal probablty to the buyers; otherwse, the buyer wth a hgher aluaton wns the asset f and only f hs aluaton s greater than a resere prce, r Note that there may be msallocaton between the two buyers when they both hae hgh aluatons. S s expected utlty s U. 37 and B s expected utlty s V. 3. The socal welfare s W Characterzng the reenue-maxmzng mechansm contnues to be a complex problem when budgetconstraned buyers hae contnuous and negate rtual alues, and when there are more than two buyers. 3 The ntuton n ths example stll holds f the buyers hae dfferent budgets.

13 If S and B sgn an ex-ante contract, S s optmal contract s: ex-ante B pays.4494 to S and becomes the resdual clamant; ex-post B can post a take-t-or-leae-t prce to B. Note that expost B cannot post the monopoly prce ( +. Instead, t s optmal to set the prce at B s budget / f and only f < /. There s no resere prce for B, so trade always happens. And there s more msallocaton loss than n the absence of ex-ante contracts. Moreoer, The expected utlty for S and B s U + V =. 565, and the socal welfare s W =. 65, hgher than n the absence of ex-ante contracts. Another queston on fnancal constrants s whether they are prately known by the buyers or commonly obsered. In many stuatons, frms fnancal postons and abltes to fnance n the captal market are publcly dsclosed or can be ealuated. For example, n mergers and acqustons, acqurers payment or fnancng abltes often are endorsed by banks or ealuated by sellers when pre-acquston agreements are sgned. Howeer, the potental trade alues for buyers are dffcult for sellers to assess. For example, acqurers prate estmaton of ther expected market performance and organzaton synerges s not aalable to sellers. Che and Gale (996 compare a seller s reenue n arous auctons when buyers hae prate nformaton about ther budgets. Che and Gale ( construct the ex-post reenue-maxmzng mechansm when there s one sngle buyer wth prate aluaton and a prate budget. Ths mechansm may nclude resere prces. Therefore, f the buyer does not know hs prate aluaton and prate budget at the ex-ante stage, ex-ante contracts stll may ncrease socal welfare. Ths may not be true when, ex-ante, the buyer learns hs prate budget. Ex-ante nosy nformaton The assumpton that S and B hae symmetrc nformaton at the ex-ante stage represents many scenaros. For example, n long-term energy supply contractng, ppelne companes and shppers often do not know market stuatons n future perods, but they may learn prate nformaton n ther current transactons. In negotatng botech strategc allance contracts, clents and R&D partners are uncertan about future benefts, but R&D partners may learn prate nformaton later on (for example, see Robnson and Stuart, 7. In mergers and acqustons, sellers and acqurers often share ther data and nformaton before enterng nto pre-acquston agreements. After then, acqurers may learn prate aluatons by conductng ndependent ealuatons and by seekng approal from shareholders. In some scenaros, the buyer B may hae prate but nosy sgnals about hs aluaton exante. Then, at the contractng stage, S uses ex-ante contracts to screen B s types and extract rent from B. Therefore, S and B may not reach an ex-ante contract. Howeer, ex-ante contracts stll can mtgate S s ex-post rent-seekng s-à-s B, snce expost they hae more asymmetrc nformaton. One related paper s by Courty and L (. In ther paper, a seller wll set lower resere prces n ex-ante contracts, when buyers ex-ante prate sgnals are less nformate. Howeer, n ther paper, there are no entrants and the seller can make long-term commtments. In contrast, ths paper consders the scenaro whereby the seller cannot make such long-term commtments wthout ex-ante contracts, and there are entrants. The followng example shows that, as long as B s ex-ante nosy sgnals are not too nformate, strategc ex-ante contracts stll may ncrease socal welfare. Suppose that and follows the unform dstrbuton on [,] and ex-ante B prately knows whether s n the low range [, 9/ or n the hgh range [9/, ]. The tmng s the same as n Secton. Wthout loss of generalty, assume that B s not fnancally-constraned. Wthout ex-ante contracts, S s optmal ex-post mechansm s equalent to the second prce aucton wth a resere prce ½. S s expected utlty s 5/. B s expected utlty s 38/ f [, 9/] and s 49/ otherwse. The socal welfare s 7/.

14 If S offers a menu of ex-ante contracts and B always accepts one, S could hae dfferent offequlbrum belefs about the dstrbuton of B s aluaton. For smplcty, suppose S belees that s unformly dstrbuted on [,] n any off-equlbrum path. 3 Consder the followng offer: ex-ante, B purchases at a prce t H. 487, and ex-post he can post a monopoly prce and resell t to B; or ex-ante B pays t L. 36 and the ex-post drect reelaton mechansm uses ths allocaton rule -- B wns the asset when / ; otherwse B wns. B s expected ex-post payment s Q ( Q ( xdx 9, where Q ( s B s expected wnnng probablty. The aboe contract offer maxmze the jont surplus for S and B, snce there always s trade and B wns only f hs rtual utlty s greater than the jont opportunty cost,, for S and B. In equlbrum, when [, 9/], B wll pay t L. B s expected utlty s.563, the same as n the absence of ex-ante contracts. When [9/, ], B wll pay t H and ex-post offer the prce ( + / to B. B s expected utlty s.4638, the same as f he deates to choose t L. S s expected utlty s.4863, larger than hs expected utlty n the absence of ex-ante contracts. B s expected utlty s also hgher than that n the absence of ex-ante contracts. Moreoer, the socal welfare s 5/8, larger than that obsered n the absence of ex-ante contracts. In sum, f B s ex-ante prate sgnal s not ery nformate, S and B can sgn strategc exante contracts and these contracts may ncrease socal welfare. Ths may not be true f B s exante prate nformaton s too nformate. In the aboe example, f B knows, ex-ante, whether hs aluaton s n [, /] or [/, ], then S has no ncentes to offer ex-ante contracts whch can nduce a separatng equlbrum. Correlated aluatons Ths paper consders buyers ndependent aluatons. In many scenaros, the common alue of an asset s more easly learned by all players and therefore the buyers dosyncratc alues are crucal. Some emprcal research fnds that, n certan auctons, an ndependent-prate-alue paradgm s a more probable scenaro (for example, see Sareen, 3. Moreoer, when the buyers hae correlated aluatons, the strategc effects of ex-ante contracts stll hold. The lterature on strategc contracts has addressed specfc contract clauses n models wth correlated aluatons (for examples, Cho, 6; Che and Lews, 7. The queston s whether strategc ex-ante contracts stll mtgate ex-post rent-seekng, such as resere prces, f buyers aluatons are correlated. The lterature shows that, ex-post, a seller can extract the entre surplus from buyers whose aluatons are statstcally correlated, and that effcent trade always happens (Cremer and Mclean, 988; McAfee and Reny, 99. Howeer, these results of full surplus extracton depend upon the seller beng able to mpose hgh punshment upon the buyers. In fact, these results may not occur when buyers hae lmted lablty or rsk aerson (Robert, 99. In many stuatons, as noted n ths paper, buyers hae fnancal constrants. Moreoer, een ex-post they cannot be forced to pay hgher than ther aluatons. Therefore, wthout ex-ante contracts, the seller has ncentes to do ex-post rentseekng by usng resere prces. Accordngly, ex-ante contracts stll can facltate more trade. Polces on strategc ex-ante contracts Polcy debates and lawsuts on strategc contracts argue that these contracts reduce socal welfare, because the strategc effects often deter competton and cause asset msallocaton. 3 The results would not be affected qualtately as long as S belees that, n the off-equlbrum path, there s some probablty for B s aluaton to be n the hgh range. 3

15 Howeer, as shown n ths paper, strategc ex-ante contracts may facltate more trade and ncrease socal welfare by mtgatng ex-post rent-seekng between contractng partes. In partcular, f the buyers aluatons follow the unform dstrbuton, S s optmal ex-ante contracts ncrease socal welfare when the dstrbuton of trade surplus s not n ranges of hgh alues and/or when B s ex-ante fnancal constrant s tght. Therefore, polcy makers should consder such effcency n facltatng more trade, and may support ex-ante contracts. One natural queston s why polcy makers could not smply ban the use of ex-post resere prces or other ex-post rent-seekng. Frst of all, f a seller can make nestments to ncrease trade surplus, then bannng resere prces would reduce hs ncentes for nestments. Second, polcy makers or judges may not hae nformaton on the seller s costs and cannot dentfy dfferent ways of ex-post rent-seekng. In ths case, f only the seller and buyers obsere the seller s costs, t may be effcent for polcy makers to allow resere prces. If only the seller prately obseres hs costs ex-post, then comparsons of ex-ante contracts, ex-post rent-seekng mechansms, and mechansms wthout resere prces would be ambguous. Further research should be done wth such double-sded prate nformaton. The followng example shows that bannng resere prces may not be socally effcent. Suppose that the seller, S, sells an asset to one sngle buyer, B. 33 B s aluaton follows the unform dstrbuton on [,], whle S s cost s wth a probablty of /3 and / wth a probablty of /3. Ex-post, S prately learns hs cost and B prately learns hs aluaton. If there s no ex-ante contract, ex-post S specfes a mechansm of sellng the asset to B. If no resere prces are allowed, there would be neffcent trade when S s cost s / whle B s aluaton s less than /. The expected socal loss s /. If there s no ex-ante contract and S can use resere prces ex-post, accordng to hs cost, S would offer a monopoly prce at ether / or 3/4. Therefore, trade may not happen and the expected socal loss s 3/48, lower than /. In contrast, consder ths ex-ante contract: ex-ante B pays /; ex-post, S ether delers the asset, or refunds the upfront payment and asks for a take-t-or-leae-t prce of 3 4. It can be shown that, n equlbrum, S would adjust the prce only f hs cost s ½. Compared to the absence of ex-ante contracts, ths contract ges B the same expected utlty, offers S a hgher expected net utlty ( + 3 4, and reduces the socal loss to ( Another queston s whether polcy makers could allow only ex-ante contracts wthout strategc or dscrmnate clauses. By defnton, strategc or dscrmnatory contracts create dfferent compette adantages for buyers from those wthout these contracts. Howeer, polcy makers may lack nformaton to dentfy whether contract clauses are strategc. Een f they can, t may not be effcent to suppress such contracts. For example, the lterature shows that strategc contracts may protect relatonshp-specfc nestments. Besdes, f there are contractng costs for S and B, strategc contracts mght ncrease ther ncentes for ex-ante contractng. Moreoer, buyers may be heterogeneous wth dfferent dstrbutons of aluatons. The followng example shows that non-dscrmnatory contracts may be less effcent than dscrmnatory contracts. Assume that the buyers aluatons are not dentcally dstrbuted: F (, F ( satsfy λ [ F ( ]/ f( = [ F ( ]/ f (. When only non-dscrmnatory contracts are allowed, B would wn the asset only f [ F ( ]/ f( [ F ( ]/ f (. Clearly there may be msallocaton between the buyers. Conersely, S s strategc ex-ante contract wth a shadow prce, λ, would not lead to msallocaton, snce s equalent to λ F ( ]/ f ( [ F ( ]/ f (. [ 33 The ntuton can be generalzed to the case wth multple buyers and entrants. 4

16 6. Conclusons Ths paper has examned strategc ex-ante contracts between a seller and an ex-ante fnancally-constraned buyer, and ther effects on socal welfare. After the tme of contractng, a second buyer enters and the buyers can learn prate nformaton. Compared to the absence of exante contracts, the seller s optmal strategc ex-ante contract mtgates hs ex-post rent seekng, s-à-s the contracted buyer, and facltates more trade. Moreoer, ths contract extracts more rent from the entrant by more accurately reflectng the contractng partes jont opportunty costs. Ths strategc effect may cause msallocaton between the buyers. Both the addtonal trade alue and the msallocaton loss ncrease when the contracted buyer s less fnancally constraned. In general, the seller s optmal strategc ex-ante contracts may ncrease socal welfare, dependng upon the dstrbuton of trade surplus and the contracted buyer s fnancal constrants. Polcy makers or courts should consder the effcency of strategc ex-ante contracts n facltatng trade, and may allow ex-ante contracts n certan crcumstances. These welfare effects are robust when the buyers hae ex-post fnancal constrants and when, ex-ante, the contracted buyer learns prate but not ery nformate sgnals about hs aluaton. The seller s optmal strategc ex-ante contract wth a drect mechansm can be mplemented by ndrect clauses. Ths paper has seeral emprcal mplcatons. Frst of all, upfront transfers n ex-ante contracts would be larger when these contracts prode more commtment to future trade and contracted buyers hae more faored strategc clauses. Robnson and Stuart (7 show that, n botech strategc allance contracts, upfront transfers from clents tend to be larger and szes of clents equty stake are less when they are protected by more seere ex-post contngent clauses. Secondly, the strength of commtment and strategc clauses tends to be postely related to contracted buyers fnancal condtons. Fnally, the use of strategc ex-ante contracts depends upon ex-post nformaton asymmetry between contractng partes and the possblty of entry. Seeral extensons would be meanngful for future research. Frst, strategc ex-ante contracts can protect relatonshp-specfc nestments or nformaton acquston efforts. Facltatng more trade, ex-ante contracts may prode more nestment ncentes. Secondly, f a seller has multple unts for sale, such as n the energy-supply ndustry, strategc ex-ante contracts also may cause quantty dstortons. Thrdly, t s nterestng to examne ex-ante contracts when contracted buyers hae ex-ante prate nformaton about ther fnancal constrants, and when there are other contractng constrants. Fnally, t s meanngful to explore the optmal scope of commtment n ex-ante contracts when contractng partes can learn ex-post prate nformaton. 34 Appendx Proof of Proposton and Corollary : If there s no ex-ante contract, as shown n the lterature, the seller s optmal ex-post mechansm s equalent to the frst prce or second prce auctons wth a resere prce of /. And t s easy to dere that the expected utltes for S, B and B are (5/, /, /. The socal welfare s 7/. If the specfc ex-ante contract s offered, B would exercse the rght of frst refusal wheneer hs aluaton s hgher than B s bd,.e., b, so that B s wnnng probablty s F ( b = b. B would choose b to maxmze hs expected utlty, ( b b. The optmal bd s b = /. Thus, B would wn f / and pay the bd made by B. He would wn wth a probablty f < /. The players expected utltes and the socal welfare are: 34 Hart and Moore (4 address ex-ante contracts n whch frms do not specfy ther actons een f these actons are erfable. For example, professonal serce contracts between large nsttutons and small contactors often do not specfy the scope of serces. 5

17 U { d + ( / d } d + d V / =/4 / = = / ( d d + d / d V ( / ( / 5/ 4 = / / V { ( / } = d d =/ W = U + V + V =5/4. Q.E.D. Proof of Proposton and Corollary : The wnnng condtons for the buyers n Proposton follow drectly from maxmzng S s s ndeed non- reduced-form problem pont-wse. It remans to be erfed that Q ( decreasng. The hazard rate s monotone, such that H ( = ( F ( f ( n s decreasng, so that the λ -adjusted rtual utlty g ( ;λ = ( F ( f ( λ s nondecreasng n. Therefore, gen a partcular > j, f ', then q (, q ( ', Accordngly, Q ( Q ( '. Note that q (, s non-ncreasng n λ, and (, any two feasble shadow prces where λ < λ '. Accordngly, g ( ;λ g ( ; ' λ partcular, f g ( ;λ max(, g ( ;, (, f g ( ; λ' max(, g ( ;, then g ( ;λ max(, ( ; g, so that q (, reerse mght not be true, though. The same holds for q (,. Furthermore, suppose that there were k > k ', such that λ ( k > λ ( k' q (, ; k (, ; k' ( ; k Q ( ; ' k q s non-decreasng n λ. Take j j.. Gen a q =. Therefore, =. The >. Then q (the sgn may be strctly less for some aluatons. Thus, Q <. Howeer, accordng to the ex-ante nddual ratonalty constrant, { V } = Q ( x; k dxdf ( k < contradcton, λ( k unque ( x; k' dxdf ( k' V } { Q =. As a result of ths λ = s non-ncreasng n k, and t s easy to show that there exsts a k, such that λ ( k k =. Therefore, t = mn ( k, k Also, the shadow prce must be between and,.e., λ = λ( k [,] ; otherwse B s expected utlty would be lower than hs expected utlty f there were no ex-ante contracts. When λ =, clearly the mechansm s the same as when there are no ex-ante contracts. k =, ( correspondngly, s non- From the aboe analyss, q (, ; k, or Q ( ; k k and ( ; ( ; Q k Q k = ; q (, ; k, or Q ( ; k ncreasng n k and Q ( ; k Q ( ; k = correspondngly, s non-decreasng n. Moreoer, t s easy to show that the probablty of trade s non-decreasng n k. Fnally, S s expected utlty s non-ncreasng n λ or, equalently, non-decreasng n k. Q.E.D. Proof of Proposton 3: 6

18 Part (: Under S s optmal ex-ante contract, there s trade, as opposed to when there s no ex- f F r k λ k such that ante contract, f > ( ( ( λ. Defne ( r ( λ ( k f r ( λ( k F r ( λ k = λ k ( ( ( ( ( r ( k F ( r df ( r ( k alue ( = ( W + d W+ dk = ( (. Thus, the optmal ex-ante contract creates trade. When dfferentated wth respect to k, ( k = ( ( ( ( ( ( ( ( ( [ F( r ( k ] r ( k F r r ' k r k f r k = λ ' k F r λ( k H '( r ( k The last nequalty follows from the monotone hazard rate and '( k Clearly, ( ( k = ( df( W r λ by Proposton. Part (: The optmal ex-ante contract creates a msallocaton when λ ( F( f ( > ( F( f ( > ( F( f (. Defne δ = δ ( ;k, such that δ λ ( F( δ f ( δ = ( F( f (. δ ; k. The absolute alue of msallocaton loss s ( { } df( r. δ ( ; k d W dk ( k = λ ( k [ F( δ ( ; k ]( δ ( ; k λ( k H '( δ ( ; k ' ( df r (. λ. The last nequalty follows from the monotone hazard rate and the result '( k Part (: For the unform dstrbuton, t s suffcent to proe the case for whch =. 35 Under the optmal ex-ante contract, the absolute alue of the total socal loss from hang no trade and the msallocaton between B and B s: λ (+ + + λ λ (+ + + If λ, ( ( + λ L λ = d d d ( ( d + + λ + ( + λ + λ ( λ (+ + + If λ <, ( L λ = ( d d = ( λ / 4 Note that λ [,]. If λ <, then L '( λ = ( λ /. Second, f λ, dl( λ 3 ( / ( ( + (7 /( + λ = + ( +, whch s poste for a smaller 4 dλdλ λ λ and becomes negate when λ s larger than a threshold. Ths s because /( + / dl( λ gen λ. Furthermore, when λ =, t s easy to show that ( dλ. d 35 All results hold for a more general unform dstrbuton on [, + a] ( a > wth smlar proof. 7

19 In sum, the socal loss frst decreases, then s conex, and fnally ncreases and s concae n λ wthn the releant range. Also, note that the socal loss, f there s no ex-ante contract, s L ( λ =. Therefore, there exsts a unque λˆ such that L ( λ L (, f and only f λ ˆ λ. Let kˆ satsfy λ( k ˆ = ˆ λ. Snce λ = λ( k s non-ncreasng, S s optmal contract s more effcent than the absence of ex-ante contracts, f and only f k kˆ. Q.E.D. Proof of Proposton 4: r λ k Note that ( ( satsfes r ( ( k f r ( λ( k sde s ncreasng n r ( λ( k ( ( F ( r ( λ( k λ( k λ =. The left hand gen the dstrbuton functon. Now the dstrbuton s shfted from [, ] to [ +, + ]. There must be some ˆ, such that, for ˆ, + f + F +. Accordngly, when ˆ, een f there s no ex-ante ( ( ( ( contract, r ( λ ( k = λ equals the lower bound of the dstrbuton. Thus, the ex-ante contract creates no addtonal trade, but may lead to msallocaton between B and B. For a unform dstrbuton, t s suffcent to proe the case when =. Start at =. Let L ( λ; represent the expected socal loss, compared to the frst best outcome. Gen a certan λ <, f =, L ( λ; = < L ( ; =. If > λ, then L ( λ; = ( λ / 4, whch does not depend on. Accordngly, L ( λ ; > λ > L ( ; > λ exsts λ such that L ( λ; = L ( ;. If λ, L ( λ; equals: 3 /8 + / 3 / + λ /. By contnuty, there ( + {( λ} /[4( + λ ] + λ /[6( + λ ] + λ /[8( + λ] λ /[( + ( + λ ( + Note that λ (. Dfferentatng the aboe L ( λ; and substtutng L ( λ; = L ( ; n ges L ( λ; / L ( ; / = ( + [ /8 (/ ( λ /( + λ ]. Thus, for any partcular λ such that L ( λ; = L ( ;, L ( λ; / L ( ; /. Let ˆ be the lowest such that L ( λ; = L ( ;. Then for > ˆ, t must be true that L ( λ; ( ; Otherwse, by contnuty, there exsts a satsfyng L ( λ; = L ( ; and L ( λ; / < L ( ; /. Ths contradcts the aboe result. Therefore, there exsts a unque ˆ, such that L ( λ; L ( ;, f and only f ˆ. Q.E.D. Proof of Proposton 5: From Proposton, n S s optmal ex-ante contract, the shadow prce λ( k /[3( + λ ] = mn ( k,/ 4 + /. If λ ( + λ Q ( = [( + λ ] + ( λ ; otherwse, t s. If Q ( = [ ( + λ ] ( λ ( + λ T ( = ( + λ 4 + (λ λ (4 + 4 and ( ( + λ + (λ (4 + λ ]} L. λ = satsfes, B s expected wnnng probablty s, B s wnnng probablty s ; otherwse, t s. Ther expected ex-post payments are T = 4. Frst, the ndrect contract nduces the same expected wnnng probabltes as aboe. Suppose that B enters and bds b. B would exercse the adjusted rght of frst refusal f and only f b [(3 λ ( + λ] b ( λ ( + λ. Antcpatng ths, B knows that hs wnnng probablty s 4b ( + λ ( λ ( + λ. Accordngly, he chooses b to maxmze λ 8

20 4b ( + λ ( λ ( + λ( b. The optmal bd s b ( = + ( λ 4 B s expected wnnng probablty s [ ( + λ ] ( λ ( + λ = Q ( wnnng probablty s [( + λ ] + ( λ = Q (. Next, B s and B s expected ex-post payments are: + λ λ + λ ( + λ + ( 4b( ( + λ ( λ ( + λ d = ( / λ 4 + 4λ + [4b( ( + λ ( λ ( + λ]( b( == T (. ( T.. Therefore, ; B s expected Fnally, t s easy to determne that B s expected utlty s poste, f and only f λ /( + λ ; B s expected utlty s poste f and only f /. In sum, ths ndrect contract mplements S s optmal strategc ex-ante contract. Q.E.D. References Aghon, P. and Bolton, P. Contracts as a Barrer to Entry. Amercan Economc Reew, Vol. 77 (987, pp Bulow, J.I., Huang, M. and Klemperer, P.D. Toeholds and Takeoers. Journal of Poltcal Economy, Vol. 7 (999, pp Burch, T.R. Lockng Out Ral Bdders: the Use of Lockup Optons n Corporate Merger. Journal of Fnancal Economcs, Vol. 6 (, pp Che, Y-K. and Chung, T-Y. Contract Damages and Cooperate Inestments. Rand Journal of Economcs, Vol. 3 (999, pp and Gale, I. Expected Reenue of All-Pay Auctons and Frst-Prce Sealed-Bd Auctons wth Budget Constrants. Economcs Letters, Vol. 5 (996, pp and. The Optmal Mechansm for Sellng to a Budget-Constrant Buyer. Journal of Economc Theory, Vol. 9 (, pp and Hausch, D.B. Cooperate Inestments and the Value of Contractng. Amercan Economc Reew, Vol. 89 (999, pp and Lews, T.R. The Role of Lockups n Takeoer Contests. Rand Journal of Economcs, forthcomng. Cho, A. A Rent Extracton Theory of the Rght of Frst Refusal. Workng Paper, Unersty of Vrgna, 6. Chung, T-Y. Incomplete Contracts, Specfc Inestments, and Rsk Sharng. Reew of Economc Studes, Vol. 58 (99, pp Courty, P. Tcket Prcng Under Demand Uncertanty. Journal of Law and Economcs, Vol. 46 (3, pp