Financial Constraints and Product Market Competition: Ex-ante vs. Ex-post Incentives

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1 University of Rocester From te SelectedWorks of Micael Rait 2004 Financial Constraints and Product Market Competition: Ex-ante vs. Ex-post Incentives Micael Rait, University of Rocester Paul Povel, University of Houston Available at: ttps://works.bepress.com/micael_rait/5/

2 International Journal of Industrial Organization 22 (2004) Financial constraints and product market competition: ex ante vs. ex post incentives Paul Povel a, *, Micael Rait b a Department of Finance, Carlson Scool of Management, University of Minnesota, Minneapolis, MN 55455, USA b Simon Graduate Scool of Business Administration, University of Rocester, Rocester, NY , USA Received 23 April 2003; received in revised form 7 October 2003; accepted 21 April 2004 Available online 20 July 2004 Abstract Tis paper analyzes te interaction of financing and output market decisions in a duopoly in wic one firm is financially constrained and can borrow funds to finance production costs. Two ideas ave been separately analyzed in previous work: Some autors argue tat debt strategically affects a firm s output market decisions, typically making it more aggressive; oters argue tat te treat of bankruptcy makes debt financing costly, typically making a firm less aggressive. Our model integrates bot ideas; moreover, unlike most previous work, we derive debt as an optimal contract. Compared wit a situation in wic bot firms are unconstrained, te constrained firm produces less, wile its unconstrained rival produces more; prices are iger for bot firms. Bot firms outputs depend on te constrained firm s internal funds; te relationsip is U-saped for te constrained firm and inversely U-saped for its unconstrained rival. Te unconstrained rival as a iger market sare, not because of predation but because of te cost disadvantage of te financially constrained firm. D 2004 Elsevier B.V. All rigts reserved. JEL classification: G32; G33; L13 Keywords: Financial constraints; Debt; Product market competition * Corresponding autor. Tel.: ; fax: addresses: povel@umn.edu (P. Povel), rait@simon.rocester.edu (M. Rait) /$ - see front matter D 2004 Elsevier B.V. All rigts reserved. doi: /j.ijindorg

3 918 P. Povel, M. Rait / Int. J. Ind. Organ. 22 (2004) Introduction In te study of ow financial constraints affect a firm s output market decisions, two ideas play a central role. One is tat ex ante, a firm incurring debt as an incentive to mitigate te risk of bankruptcy by limiting its borrowing, and ence beaves more cautiously in its output market. 1 Te second idea is tat ex post, debt alters a firm s incentives to invest. For example, risk sifting can arise because te firm is te residual claimant to ig earnings but is protected from losses by limited liability. Similarly, bankruptcy costs provide an incentive to adopt strategies tat generate cas and tus reduce te risk of bankruptcy. Some of tese ex post effects lead to more aggressive output market beavior in te form of ig output or low prices; oters ave te opposite effect. 2 How ex ante and ex post effects work in isolation is well understood. However, in any realistic setting, we sould expect bot effects to be present, and little is known about ow tey interact. We study teir interaction in a model in wic a financially constrained firm competes in a Cournot market wit a firm tat is ric in cas. Te constrained firm can raise funds from an investor to finance its production costs. We follow te approac of Brander and Lewis (1986) and te subsequent industrial organization literature 3 in assuming tat te financially constrained firm (ereafter te firm ) cooses ow muc money to raise from an investor before deciding ow to spend its funds; tis decision cannot be specified in a contract. We go beyond tis literature in two ways. First, wile debt is a key element of oter models, its use is typically exogenously imposed. In reality, owever, financial contracting and product market decisions are not separately made. We terefore derive debt as an optimal contract, and sow tat te resulting implications about firms product market beavior are quite different from te predictions of models in wic debt is exogenous. 4 Second, we explicitly account for variable production costs, wic are typically ignored in te literature. We find tat tey play a central role. Our main results are te following: (1) Debt finance necessarily entails a risk of bankruptcy and te loss of future profits. Ex ante, te firm as an incentive to limit tis risk by reducing its borrowing. (2) Te ex post distortions typically associated wit debt vanis if debt is derived as an optimal contract; neverteless, te firm s incentives after signing a debt contract differ from its incentives ex ante. (3) Because te firm must finance production out of its available funds, its ex ante incentive to produce less overrides its ex post incentive to produce more: A financially constrained firm underinvests. (4) Te firm s output is U-saped, i.e., nonmonotonic, in its level of internal funds. (5) Variable costs are te critical link between a firm s financing and product market decisions; if costs are assumed to be zero, as is common in te literature, product market beavior does not 1 See, e.g., Gale and Hellwig (1985), Bolton and Scarfstein (1990), orstenbacka and Tombak (2002). 2 Firms become more aggressive in, e.g., Brander and Lewis (1986), Maksimovic (1988), and Hendel (1996); tey become less aggressive in, e.g., Glazer (1994) and Cevalier and Scarfstein (1996); eiter effect can occur in Sowalter (1995). For a survey of te literature, see Maksimovic (1995). 3 Cf. te references in te previous footnote. 4 Maurer (1999) and Faure-Grimaud (2000) also derive debt as an optimal contract in models of product market competition wit financial constraints. See Section 6.2 for a discussion of tese papers.

4 P. Povel, M. Rait / Int. J. Ind. Organ. 22 (2004) depend on te firm s internal funds or debt. (6) Oligopoly interaction does not fundamentally cange te effects of financial constraints on a firm s output market beavior; it merely amplifies tem. We conclude tat te empasis on te ex post effects of debt tat prevails in te industrial organization literature is a result of ignoring production costs and of treating debt contracts as exogenously given securities. Under metodologically more appealing assumptions, te effects of financial constraints on product market beavior strongly differ from most predictions of te industrial organization literature (see te references in footnote 2), and instead resemble wat simple models of debt-financed investment (wic ignore ex post effects) would predict. 5 Te setup of te model is follows. Like in Diamond (1984), Bolton and Scarfstein (1990), and Hart and Moore (1998), te firm s earnings are not contractible. We assume tat tey are unobservable to te investor, wic captures te idea tat te firm can easily divert or ide its cas flow. Te investor can treaten to liquidate te firm if it fails to repay, in wic case its owners forfeit future profits. In tis setting, a debt-like contract is optimal: It minimizes te probability of liquidation wile inducing te firm to repay and allowing te investor to break even on average. We extend te analysis in te papers mentioned by letting te output coice itself be unobservable, wic introduces an additional moral azard problem. Suc moral azard problems are key to industrial organization models tat analyze ex post incentives. Te contract affects te firm s output coice and ence its distribution of earnings, and an optimal contract must make sure tat te firm bot cooses te correct output level and as an incentive to repay. Tese goals may conflict, and terefore te design of te optimal contract cannot be separated from te output market incentives te contract induces. We sow tat in spite of tese complications a simple debt contract is optimal. As it turns out, once te contract is signed, te firm as first-best incentives; tat is, te distortions empasized in oter models do not arise. By design of te optimal contract, te usual distortion caused by a debt-like repayment pattern is exactly offset by a probability of liquidation tat increases wit te extent of te firm s default. Ex ante, at te borrowing stage, te firm internalizes te cost of liquidation because te investor must break even in expected terms. At tis stage, it prefers a smaller output level to limit its borrowing. Hence, te firm s incentives to produce are different ex ante and ex post. Wit positive variable costs, te firm cannot produce more tan it can finance using its own and borrowed funds. Tis implies tat it can effectively commit itself to produce little by restricting its borrowing ex ante, altoug ex post te firm would want to produce more. Positive variable costs imply a close link between borrowing and investing tat does not exist if marginal costs are zero or subsumed in a firm s earnings, as is often assumed in te industrial organization literature. 6 Wit zero variable costs and an optimal debt 5 For an extension of suc models, see, e.g., Stenbacka and Tombak (2002), wo assume tat financing and investment decisions are simultaneous, and study ow an oligopolistic firm s coice between debt and equity finance depends on its internal funds. 6 See, e.g., Brander and Lewis (1986), Glazer (1994), Sowalter (1995), orfaure-grimaud (2000).

5 920 P. Povel, M. Rait / Int. J. Ind. Organ. 22 (2004) contract, te firm would ex post always produce te Cournot quantity, and tere would be no link at all between financing and output decisions. Next, we study ow te firm s output varies wit te internal funds tat te firm can contribute to finance production. We find tat output is a U-saped function of te level of internal funds, wic is driven by two effects. First, tere is a cost effect : A decrease in internal funds increases te probability of liquidation for any given level of production because te firm must borrow more. Tis increases te marginal cost of output expansion, wic induces te firm to produce less. Te second effect is a revenue effect : Producing a ig output allows te firm to generate revenue tat it needs to repay te loan. Tis provides an incentive to increase output. For strongly negative levels of internal funds (wic can occur if te firm must also incur fixed costs), te revenue effect dominates te cost effect, and output increases as te firm s internal funds decrease. Tis nonmonotonicity implies tat wen looking at te output market effects of financial constraints, one as to distinguis between te existence of financial constraints and canges in te severity of tose constraints. For example, it is often suggested tat an increase in leverage leads a firm to produce more. In our model, te leveraged firm never produces more tan a financially unconstrained firm does. On te oter and, if more means, compared to te previous output level, tis effect can occur in our model if te level of internal funds is sufficiently negative. Our analysis of duopoly competition wit financial constraints yields several insigts. First, financial constraints weaken a firm s competitive position: It produces less tan te Cournot output, and in response its rival produces more, wile total industry output decreases. Under Cournot competition wit differentiated goods, te constrained firm s resulting market price is iger tan te rival s, but bot firms prices are iger tan wit two unconstrained firms. Second, competition amplifies te effects of financial constraints: Our results old for a monopoly, but are more pronounced in duopoly, because te rival s increase in output induces te constrained firm to reduce output even furter. Tus, te output market effects of financial constraints are likely to be iger in industries in wic competition is most intense. Tird, we discuss to wat extent financial predation can occur in our (static) model. We observe tat te notion of financial predation itself is not necessarily well defined because a financially strong rival may produce more and ave a lower price tan a constrained rival simply because te firms effective marginal costs are different, witout any explicit predatory sceme used. Our results are consistent wit most empirical studies: Opler and Titman (1994), Cevalier (1995a), Pillips (1995), Kovenock and Pillips (1995, 1997), Kanna and Tice (2000), and Grullon et al. (2002) find tat igly leveraged firms invest less and lose market sare, in line wit our underinvestment result. In addition, Cevalier (1995a) and Kovenock and Pillips (1995, 1997) find tat for te less leveraged rivals of firms undergoing an LBO, bot investments and sare prices increase. Cevalier (1995b) finds tat following an LBO, supermarkets carge iger prices if teir rivals are also leveraged, but lower prices if te rivals are less leveraged and concentrated. Te first effect is as predicted by our teory, te second possibly a result of predation. Pillips (1995) also finds tat after LBOs, prices generally increase. Zingales (1997), in contrast, finds evidence of lower prices on part of overleveraged firms in te trucking industry.

6 P. Povel, M. Rait / Int. J. Ind. Organ. 22 (2004) Te model Two risk-neutral firms, 1 and 2, compete in quantities and produce q 1 and q 2, respectively, at marginal cost c. Firm i s revenue is R i ( q 1, q 2, ), were is a random variable distributed wit density f() over some interval [, ]. We assume te following about R i : (1) R 1 (0, q 2, ) = 0 for all q 2 and. (2) R 1 and R 2 are twice differentiable in all arguments. (3) R and R 12 are bot negative. (4) R 1 is strictly concave and as a unique maximum in q 1 for eac q 2 and. (5) R 1 11 R 2 22 >R 1 21R 2 12 for all q 1, q 2,. (6) R 1 and R 2 are symmetric, i.e., R 1 ( q, qv, )=R 2 ( qv, q, ) for all q, qv,. Tus, all assumptions above about R 1 old mutatis mutandis for R 2. Because bot firms ave te same constant marginal cost, tese six assumptions also old for te firms net profits R i ( q 1, q 2, ) cq i. Te first five assumptions are standard in Cournot models. For convenience, tey are stated more restrictive tan necessary. Togeter wit te symmetry of te R i, tey guarantee te existence and uniqueness of a symmetric Nas equilibrium in q 1 and q 2 (wic will serve as a reference point for te asymmetric equilibrium we derive below). Tat is, tere exists q* suc tat q* ¼ arg max q 1 Z R 1 ðq 1 ; q*; Þf ðþd cq 1 ¼ arg max q 2 Z R 2 ðq*; q 2 ; Þf ðþd cq 2 : ð1þ We sall refer to q* as te Cournot quantity. Finally, if q i * ( q j ) denotes firm i s best response to q j as specified in Eq. (1), we assume tat (7) Te derivatives R i i and R qi are bot positive for any q i V q i * ( q j ). (8) R i ( q 1, q 2, ) = 0 for any q 1 and q 2. Assumption 7 states tat iger values of are good states of te world: Tey correspond to iger revenue and also a iger marginal return on output. A natural interpretation is to tink of as te state of demand. Te last assumption ensures tat a firm tat borrows will default wit positive probability. Togeter wit R i >0, it implies tat te probability of default converges to zero as te amount borrowed goes to zero. 7 7 Assumptions 7 and 8 imply R i i ( q 1, q 2, )>0 for all q 1 < q 1 *( q 2 ) and >, wic in turn is equivalent to te assumption tat increases in output lead to a first-order stocastic dominant sift in te distribution of realized revenues. Tat is, if G(R i ( q 1, q 2, )) is te c.d.f. of R i induced by q 1, q 2, and, ten R i i ( q 1, q 2, )>0 is equivalent to BG(R i ())/Bq i < 0. Assumption 8 is not necessary for wat follows; it merely serves to avoid tedious case distinctions tat add little insigt, see footnote 20.

7 922 P. Povel, M. Rait / Int. J. Ind. Organ. 22 (2004) Our model embodies te assumption tat production and sales are separated in time. In many industries, firms coose capacities and inputs (e.g., employees wo must be paid) before tey learn te actual level of demand, and set or adjust prices afterward. In contrast, it seems muc less common tat firms commit to prices witout knowledge of te level of demand and are unable to cange tem as information arrives. 8 We terefore believe tat in a model wit stocastic demand, it is not an arbitrary modeling coice weter firms compete in quantities or prices. To abstract from inventory building, we assume tat products (or inputs) can be stored temporarily, but not beyond te current period. Tis assumption seems most appropriate for industries selling perisable goods, services, or durable goods wit ig market depreciation (e.g., cars). 9 We assume tat firm 1 is financially constrained, wile firm 2 is not. More precisely, suppose tat firm 1 as retained earnings r 0 available and must finance bot fixed costs F and variable costs cq. Te fixed costs comprise bot production startup costs and any outstanding liabilities tat te firm may need to pay down before output is produced. We denote by internal funds te firm s own funds tat it can use to pay for variable production costs, w 0 = r 0 F. Let w*w cq* denote te cost of producing te Cournot output q*. Ten we say tat firm 1 is financially constrained if its internal funds are too small to finance te Cournot quantity, i.e., if w 0 < w*. If te fixed costs exceed te firm s retained earnings, te internal funds are negative. Because financing may still be feasible in tis case, we allow for negative values of w 0. Negative internal funds are also empirically relevant: Cleary et al. (2003) study 20 years of annual Compustat data and find tat different measures of internal funds are negative for approximately a quarter of all firm-year observations. In addition to its internal funds, firm 1 can raise funds from an investor I in a competitive capital market. In a first-best world, firm 1 would promise to produce q*, and it would agree wit I on some form of profit saring. However, we assume tat neiter q nor can be observed by I, and tat firm 1 cannot be forced to repay more tan it earned because of limited liability. Feasible contracts ten are ones in wic firm 1 makes some (verifiable) payment to I and te contract specifies a probability wit wic te firm will be liquidated. 10,11 If firm 1 is allowed to continue, its owners earn an additional payoff >0. Tis payoff may represent future profits generated by te firm, and/or control rents tat te firm s owners enjoy. Only part of can be transferred to I, wo upon liquidation obtains an 8 Instances of commitment to prices before demand is known include prices quoted in annual catalogs, on books, or at restaurants. Sowalter (1995) analyzes a model similar to tat of Brander and Lewis (1986), but in wic firms set prices instead of quantities. He sows tat firms will use strategic debt to commit to iger prices if demand is uncertain, but tat firms will not use strategic debt if costs are uncertain. Sowalter (1999) presents evidence in line wit tese predictions. 9 In Section 7.1, we argue tat our main results are likely to old in a setting (similar to tat of Kreps and Sceinkman, 1983) in wic, upon observing te state of demand, te firms compete in prices, taking teir previously determined production levels as given. 10 Alternatively, if te firm s assets are divisible, te contract could stipulate partial liquidation of te assets. Tis would be formally equivalent to probabilistic liquidation of all assets if liquidation of a fraction a of te assets yields a liquidation value al and a continuation value (1 a). 11 We abstract from any agency problems tat migt exist witin firm 1, e.g., among sareolders or between sareolders and managers. Suc problems literally do not exist if te firm is run by a single entrepreneur; owever, for reasons of symmetry, we prefer to speak of firm 1 rater tan an entrepreneur as competing wit firm 2.

8 P. Povel, M. Rait / Int. J. Ind. Organ. 22 (2004) amount L <. Tat is, transfer of ownersip to I and subsequent liquidation of te firm leads to a loss of L>0. As we will see, te assumption tat >L z 0 is essential for deriving debt as an optimal contract and for te relevance of financial constraints: If were zero, te firm would not ave any incentive to repay, in wic case debt-financed investment would not be feasible at all. And if L =, tere would not be any loss from transferring ownersip of te firm to I (upon default), in wic case external finance would be costless, and limits on te availability of internal funds irrelevant. 12 In a dynamic model, te firm s future profits are likely to depend on its revenue in te current period, and tus also on te firms output coices as well as te state of realized nature. We abstract from tis complication ere by assuming tat is constant. Te more general case in wic is a weakly increasing function of current revenue is discussed in Povel and Rait (in press); we comment in Section 5 to wat extent our results carry over to tis case. Te timing of te game is as follows: (1) Firm 1 can offer a financial contract to I to borrow w 1, wic I accepts or rejects. Firm 2 knows w 0 but cannot observe te contract between firm 1 and I. (2) Te firms produce q 1 and q 2, respectively, at constant marginal cost c. Firm 1 s output is constrained by cq 1 V w 0 + w 1. I cannot observe eiter firm s quantity. 13 (3) Te state of te world is realized, and te firms earn revenue R i ( q 1, q 2, ) (i = 1, 2). Wile te distribution of is common knowledge, only firm 1, but not I, can observe and its revenue. (4) Firm 1 makes some payment to I. Depending on tis payment and te provisions of te contract, te firm is eiter liquidated or allowed to continue. To abstract from adverse selection issues, we assume tat at te beginning of te game, bot firms and te investor ave te same information, wic also means tat I and firm 2 know firm 1 s financial position w 0. Firm 2, owever, cannot observe te contract between firm 1 and I. Tis assumption implies tat firm 1 cannot gain a first-mover advantage by committing itself to some output before firm 2 cooses its own. More precisely, firm 1 migt want to publicly commit itself, troug a contract wit I (or some oter tird party), to produce a iger output. Firm 2 would ten respond by producing less, and firm 1 would obtain an advantage in its output market (see, e.g., Vickers, 1985; Ferstman and Judd, 1987). Te problem wit tis idea, owever, is tat in te outcome of suc a game, firm 1 is not using a best response against firm 12 Our assumptions are tecnically equivalent to tose of Bolton and Scarfstein (1990), were te firm requires additional funds from te investor in te future to continue its operation. As a referee pointed out, it is not necessary to assume tat L represents a liquidation value; L could simply be te value of te firm in te ands of I. All tat is necessary is tat a transfer of ownersip of te firm to I leads to a loss of L>0 (oterwise, external finance would be costless in our model). However, we will neverteless speak of liquidation wenever suc a transfer of ownersip occurs, to distinguis tis case clearly from mere bankruptcy following default, were wit some probability te firm remains in te ands of te current owners. 13 We could allow for transfers or liquidation decisions at te end of stage 2; but as will become clear in Section 3, suc provisions would not be included in an optimal contract.

9 924 P. Povel, M. Rait / Int. J. Ind. Organ. 22 (2004) Any provisions of a publicly announced contract can be undone by a second, secret contract wereby firm 1 produces less tan announced, rendering te announcement noncredible. If firm 2 cannot observe te contract, as we assume ere, te parties play a simultaneous-moves game, altoug borrowing precedes and constrains te coice of output. Tis assumption does not per se rule out tat firm 1 produces above te Cournot level and induces its rival to produce less. However, firm 1 s contract and output must be a best response to firm 2 s output. Any commitment effect vis-à-vis firm 2 generated by a contract between firm 1 and I must follow from te agency problem tat creates te need for tis contract, and not from attempts to influence firm 2 s actions. For a discussion of tese issues, see Katz (1991), Bolton, (1990), and Caillaud and Rey (1994). Wile we do not allow firm 1 to commit itself by contract to a strategy tat is not an optimal response to firm 2 s strategy, we do assume tat firm 1 and I can commit to any contract tat is optimal at stage 2 of te game, taking firm 2 s strategy as given. Tat is, we do not allow renegotiation of te contract (say, between stages 3 and 4) even if its fulfillment may call for liquidation of te firm, wic by assumption is inefficient. We discuss te role of tis assumption more fully in Section A simple debt contract Our informational assumptions and te basic idea of te contract are similar to tose in Diamond (1984) and Bolton and Scarfstein (1990): Because revenue is not observable, te treat of liquidation is necessary to induce te firm to repay any money. If te firm ad no strategic decision to make (as te papers mentioned assume) or if te firm s output were contractible, it would ten follow from te analyses of tese papers tat te optimal contract must ave a debt-like structure. Here, owever, tere is an additional agency problem: Firm 1 makes an unobservable quantity coice tat affects te distribution of its revenue. Tis raises two questions, namely, wat does an optimal financial contract look like in tis setting, and ow does te optimal contract affect firm 1 s quantity coice? It turns out tat tese questions cannot be answered separately, wic complicates te presentation of our analysis. First, we derive te optimal contract for a given output coice (say, as if output were contractible); we call tis a simple debt contract. Suc a contract remains feasible in our setting, but may no longer be optimal because te details of te contract affect ow muc firm 1 decides to borrow and ten to produce. Specifically, wile a simple debt contract is optimal if firm 1 can commit itself to produce some q 1, firm 1 migt prefer to coose some oter q 1 V after signing a simple contract if commitment to q 1 is not possible. In tis case, a different contract migt be more efficient overall. To answer tis question, we analyze in Section 4 ow te simple debt contract affects firm 1 s incentives to produce bot ex post and ex ante. Based on tat analysis, we return to te question of contract design in Section 5 to sow tat a simple debt contract remains optimal in our setting wit an additional moral azard problem.

10 P. Povel, M. Rait / Int. J. Ind. Organ. 22 (2004) A preliminary and very general result is tat wen revenue is not observable, any optimal contract must resemble debt: Proposition 1. Any optimal contract between firm 1 and I as a debt-like structure: Firm 1 borrows w 1 from I and promises to repay D V. If firm 1 repays D, it is allowed to continue. If it repays r < D, it is liquidated wit a probability tat is decreasing in r. All proofs are in Appendix A. Te basic idea of te proof is standard 14 : Because revenue is unobservable, I can induce te firm to repay only by treatening wit liquidation upon default, in wic case te firm would lose. Moreover, wenever te firm is allowed to survive, I can obtain only some constant amount D (te face value of debt ). More precisely, denote by b(r) te probability tat te firm is allowed to continue, as a function of te repayment. Te firm can be induced to repay D only if b(r) satisfies te incentive constraint R D þ z R r þ bðrþ ð2þ for any r < D. To minimize te expected loss from liquidation, te optimal contract induces te firm to pay out all of its revenue if it defaults. Tis requires tat bðrþ z R r þ bðrþ ; ð3þ wic in turn implies tat b must be increasing in r. Tat is, a defaulting firm is not liquidated wit certainty, but wit a probability tat depends on te amount repaid: Failing to repay 99% of a debt obligation is worse tan failing to repay 1%. For Eq. (2) to old requires tat D V, as stated in Proposition 1. We assume in wat follows tat is sufficiently large, suc tat tis constraint is not binding. As will become clear, tis assumption for is convenience only: Te constraint D V may limit te amount w 1 te firm can borrow, and terefore its output, but does not affect te structure of te optimal contract, and does not qualitatively affect any of our oter results. Similarly, weter te firm or instead te investor as all bargaining power wen offering a contract does not qualitatively matter for any of our results. Proposition 1 is more general tan previous results in tat it also olds if te borrower s investment is not contractible. As te proof sows, it is always possible to switc from an arbitrary contract to a debt-like contract tat leads to a iger payoff for I wile leaving firm 1 s net payoff in eac state of te world, and ence its ex ante and ex post incentives, uncanged. Tis additional payoff can ten be redistributed to te firm in an incentiveneutral way. Te optimal contract for any given q 1 is te following: Proposition 2. If q 1 is contractible, a contract wit te structure described in Proposition 1 is optimal if for any repayment r < D, firm 1 is liquidated wit probability 1 b (r), were b (r) = 1 (D r)/. 14 See, e.g., Diamond (1984) or Faure-Grimaud (2000) for te case of continuous revenue considered ere, or Bolton and Scarfstein (1990) for te discrete case. For extensions to a multiperiod context, see Gromb (1994) and DeMarzo and Fisman (2000).

11 926 P. Povel, M. Rait / Int. J. Ind. Organ. 22 (2004) Firm 1 s repayment and survival probability as functions of its revenue are depicted in Fig. 1. Te debt-like repayment structure follows from Proposition 1: Firm 1 owes I a fixed amount D and faces te possibility of liquidation if it repays less. D, q 1, and q 2 implicitly define a bankruptcy state ĥ: D ¼ R 1 ðq 1 ; q 2 ; ĥþ: Fig. 1. Repayment and continuation probability as a function of revenue. If te realized state is < ĥ, te firm is in default; if z ĥ, it can repay D in full. 15 For a given q 1, te optimal contract minimizes te expected net cost of liquidation subject to Eqs. (2) and (3). Tis is acieved by setting b(r)=b (r) as defined in Proposition 2, suc tat Eqs. (2) and (3) old wit equality for any r < min{d,r}. Firm 1 is ten indifferent between paying D and paying less but suffering a loss of future profits wit some probability, and weakly prefers to repay D or else all it as (notice tat even if te repayment is zero, b may neverteless be positive). By contrast, a contract tat calls for certain liquidation wenever te firm defaults is feasible but not optimal. If te decision to liquidate does not depend on te amount of repayment, a firm tat is forced to default partially will always coose to default completely. Wen borrowing, it must promise a larger repayment, and ence is liquidated wit iger probability tan necessary. One implication of te optimal contract is tat after a default, te expected continuation value for te borrower is positive. In oter words, te optimal contract specifies tat absolute priority rules sould be violated in bankruptcy. Suc violations seem to be common in te United States. In practice, tey may be better described by eiter partial losses of control, or partial liquidations. We could easily ave adapted our ð4þ 15 Proposition 2 caracterizes te structure of repayment and liquidation as functions of D, but leaves open ow D is determined. In te next section, we close te model by assuming tat I must break even on average, wic allows us to determine D as a function of te anticipated duopoly equilibrium.

12 P. Povel, M. Rait / Int. J. Ind. Organ. 22 (2004) model to allow for certain but partial liquidation, instead of stocastic complete liquidation (cf. footnote 10). Te bankruptcy practice in many countries, particularly in te United States, may be regarded as a roug mecanism tat makes te liquidation decision depend on te firm s financial situation. In our model, larger defaults make liquidation more likely. In practice, small defaults may be forgiven by lenders, or tey may initiate one of several procedures tat deal wit insolvency. In te United States, firms can negotiate in private wit teir main lenders, to arrive at a so-called workout. If a workout is not feasible because some lenders disagree, te majority can agree on a plan and file it wit te bankruptcy court as part of a prepackaged Capter 11 (wic can ten be confirmed quickly). If negotiations prove even arder, it may be necessary to file for bankruptcy protection first, and ten to negotiate wit lenders under a bankruptcy judge s supervision (wile in Capter 11 ). If negotiations seem fruitless, te firm will ave to agree to its least preferred procedure, a liquidation (under Capters 7 or 11 of te Bankruptcy Code). Clearly, te legal process does not yield deterministic outcomes, and te extent of a default as an effect on wic of tese procedures will be used. If tis effect is sufficiently strong, it may induce a defaulting borrower to fully cooperate in bankruptcy, ensuring a iger expected recovery rate, and terefore ex ante a lower promised repayment. In Proposition 2, we ave ignored te problem tat firm 1 may prefer different levels of output before and after signing a contract. To address tis issue, we now turn to te output market incentives implied by a simple debt contract. 4. Output coice and duopoly equilibrium In tis section, we analyze firm 1 s output incentives and te resulting product market equilibrium wen firm 1 uses te contract described in Proposition 2 to obtain funds w 1 from I. In Section 5, we sow tat tis contract is indeed optimal in our setting Ex post output coice Our first result is tat at stage 2 of te game, after signing te contract wit I, firm 1 as first-best incentives at tis stage, but is constrained by te funds borrowed: Proposition 3. Suppose tat firm 1 as borrowed w 1 from I, signing a debt contract according to Proposition 2. Ten firm 1 as te same incentives as a financially unconstrained firm, but its output may be constrained by its available funds. Specifically, if w 0 +w 1 z w*, firm 1 produces q*, wile if w 0 +w 1 < w*, it produces q 1 = (w 0 +w 1 ) /c < q*. Te two cases of Proposition 3 are depicted in Fig. 2, wic sows te firms reaction curves at te output coice stage. Firm 1 s reaction curve is truncated at te igest output tat it can pay for. In panel (a), firm 1 as borrowed more tan it needs to produce te Cournot output: w 1 >cq* w 0. Here, firm 1 s financing constraint is not binding, and in te equilibrium of tis subgame, bot firms coose te Cournot output q*. In panel (b), firm 1 s own and borrowed funds are insufficient to produce q*. Its reaction curve is truncated

13 928 P. Povel, M. Rait / Int. J. Ind. Organ. 22 (2004) Fig. 2. Reaction curves at te output coice stage. at a level below q*, and te equilibrium is determined by te intersection of te two reaction curves, were firm 1 produces less tan q*, firm 2 more. Proposition 3 establises tat wit our simple debt contract, debt as no strategic effect on te borrower s incentives wen coosing an output level (altoug as panel (b) of Fig. 2 illustrates, tere is a strategic effect on te rival s output). Tis result stands in contrast to oter models in wic te repayment and liquidation provisions of debt are exogenous. In our model, unobservable revenue requires punising default wit possible liquidation, wic mitigates te distortion of te firm s output decision tat migt result from risk sifting or a fear of bankruptcy. If te contract is not only incentive compatible but also optimal (cf. te discussion of Proposition 2 above), te distortion is exactly eliminated: Wat te firm does not pay in money, it pays in expected loss of future profits. As a consequence, watever te outcome, te firm loses a constant amount and is tus te residual claimant to its revenue. Proposition 3 also demonstrates te significance of variable production costs. If c = 0, te firm may neverteless ave to borrow, e.g., to pay for fixed costs. In tis case, we ave w* = 0, and according to Proposition 3, firm 1 just produces its Cournot output; tat is, te firm s financing and output decisions are unrelated. 16 In contrast, if production costs are positive and are incurred before te firm sells its goods, te firm s financing and production decisions are linked directly: Te firm cannot spend more tan its available funds. Because te firm ex post as undistorted incentives, it produces q* if cq*v w 0 + w 1, or else as muc as possible, i.e., q 1 =(w 0 + w 1 )/c. In particular, wit te simple contract, a financially constrained firm never produces more tan an unconstrained firm. 16 See te results in Maurer (1999) and Faure-Grimaud (2000), discussed in Section 6.2.

14 4.2. Duopoly equilibrium and underinvestment We now derive te equilibrium of te full game between firm 1, firm 2 and I. If w 0 + w 1 >w*, Proposition 3 implies tat firm 1 spends only w* on production and olds d = w 0 + w 1 w* as cas. Tis part of te loan constitutes riskless debt; and firm 1 neiter gains nor loses anyting from borrowing in excess of w*. Terefore, we can witout loss of generality assume tat firm 1 borrows exactly te amount needed to finance a desired level of q 1, after contributing its entire own funds; tat is, w 1 = max{0, cq 1 w 0 }. Tis establises a one-to-one relationsip between q 1 and w 1. Firm 1 ten determines its output level wen it decides ow muc to borrow. On te oter and, because firm 2 cannot observe te contract between firm 1 and L, itisasif firms 1 and 2 and I play a simultaneous-moves game. Formally, an equilibrium of te overall game is given by te q 1, q 2, D, and ĥ suc tat q 1 and q 2 maximize te profits of firms 1 and 2: q 1 ¼ arg max q 1 V P. Povel, M. Rait / Int. J. Ind. Organ. 22 (2004) Z R 1 ðq 1 V; q 2 ; Þf ðþd D and ð5þ q 2 ¼ arg max q 2 V Z R 2 ðq 1 ; q 2 V; Þf ðþd cq 2 ; ð6þ subject to te investor s break-even constraint Z ĥ fr 1 ðq 1 ; q 2 ; Þþ½1 bðr 1 ðq 1 ; q 2 ; ÞÞŠLgf ðþd þ ProbðzĥÞD ¼ cq 1 w 0 ð7þ and Eq. (4), wic defines ĥ. Te rigt-and side of Eq. (7) is te amount I lends to firm 1; te left-and side is I s expected payoff, wic consists of firm 1 s repayment D if firm 1 is solvent and R 1 if it defaults and te expected returns from liquidating firm 1 s assets in te case of default. In Appendix A, we sow tat te program above as a unique solution. Because I must break even, firm 1 fully internalizes te costs of possible liquidation and trades off te benefits (iger current earnings) and costs of debt finance wen coosing ow muc to borrow. Define w :¼ E ½R 1 ðq*; q*þš L þ R 1 ðq;*q*; p Þ L cq* < 0: ð8þ 2 Te first two terms in te brackets in Eq. (8) are a weigted average of te expected revenue and te revenue for te igest level of demand wen bot firms set te Cournot quantity. Proposition 4. If firm 1 is financially constrained suc tat w 0 a (w,w*), ten financing is feasible using a simple debt contract as described in Proposition 2; if c>0, firm 1 produces strictly less tan q*.

15 930 P. Povel, M. Rait / Int. J. Ind. Organ. 22 (2004) Te first-order condition (A.12) derived in te proof can be equivalently expressed as Z R 1 1 ðq 1; q 2 ; Þf ðþd c þ k Z ĥ ½R 1 1 ðq 1; q 2 ; Þ cš f ðþd ¼ 0; ð9þ wit k>1. Compared to an unconstrained firm, firm 1 places additional weigt on te lower (default) states of demand, wic are also states of lower marginal profit. It terefore produces less tan te Cournot output. Put differently, because firm 1 may lose future profits, it as an incentive to reduce output below q* to decrease te probability of default. Ex post, te firm as first-best incentives, and if feasible, it would produce more (i.e., te Cournot level) tan it would ave wanted to commit to ex ante. Wit positive production costs, owever, te firm faces a financing constraint, and by borrowing little, it can effectively commit to a lower output level. Our result stands in contrast to te influential paper of Brander and Lewis (1986), wo obtain te result tat if a quantity-setting firm takes on debt, ten it increases its output because of risk sifting. In a Cournot duopoly, te rival s best response is to cut output, leading to te conclusion tat a firm may benefit from taking on debt purely for strategic reasons. Te contrast results from tree major differences between teir paper and ours. First, Brander and Lewis assume (as do some oter autors) tat a firm commits itself to some output before it learns about te level of demand, but can finance its production costs out of its later revenue. We argue tat tis is typically not feasible for a financially constrained firm. Woever extends credit to pay for te production costs (banks, trade creditors, etc.) as to trust tat te firm will repay te loan if its revenue is sufficient. In equilibrium, te parties will find it optimal to sign te debt-like contract derived ere. Second, in Brander and Lewis, bankruptcy is costless, wereas in our paper (part of) te firm s continuation value is lost if te firm is liquidated. 17 If one introduced a continuation value in te Brander Lewis model, worry about survival could outweig te limitedliability effect and ence lead to softer output market beavior, as in our paper. Neverteless, plays a very different role in tis extended Brander Lewis model tan in ours: In te Brander Lewis model, a firm s output would be decreasing in because a iger implies a iger cost of debt finance. In our model, output is independent of as long as te firm is not credit-constrained, i.e., as long as is large enoug. For smaller values of, firm 1 is credit-constrained, and its output is increasing in because a greater relaxes firm 1 s credit constraint. Tus, wile we assume for convenience tat is large, smaller values would lead to credit rationing and would only reinforce our underinvestment result. More fundamentally, te continuation value is necessary for debt finance to be feasible in te first place, because wit unverifiable revenue, te firm as an incentive to repay its debt only if it as someting to lose. In contrast, if (as in Brander and Lewis) te firm s revenue is verifiable, te firm and its investor would ave no reason to write a debt contract (oter tan because of its expected effects on a tird party, see te tird point below). More generally, witout some agency problem between investor and firm, tere 17 Brander and Lewis study te role of bankruptcy costs in teir 1988 paper, cf. our discussion in Section 6.2.

16 P. Povel, M. Rait / Int. J. Ind. Organ. 22 (2004) would be no need to use debt. Any agency problem, owever, entails some efficiency loss, wic must be borne by te firm for an investor to break even. Tird, Brander and Lewis assume tat a firm and its investor can publicly commit to a debt contract. Te problem wit tis assumption is tat in te resulting (Stackelberg-type) equilibrium, te cosen level of debt is not jointly optimal (for I and firm 1) if firm 2 cuts back its production in response. In our model, firm 1 s contract wit I is required to be a best response to firm 2 s strategy, cf. our discussion in Section Optimality of te simple debt contract Knowing ow te simple debt contract of Proposition 2 affects output market incentives, we can now prove its optimality. It was designed to minimize te probability of liquidation subject to incentive compatibility. Because any optimal contract must ave a debt-like repayment structure (cf. Proposition 1), an optimal contract tat is not simple must specify a function b tat lies below b (as defined in Proposition 2), and an equal or smaller D (because I benefits from a iger probability of liquidation). Wit a nonsimple contract, te firm s incentives wen coosing an output level may not be first-best any more. If te firm is induced to coose an output no larger tan q*, ten a nonsimple contract is strictly dominated because a simple contract can induce te same output coice at a lower expected liquidation loss. Te firm also cannot gain from a nonsimple contract tat induces it to coose an output larger tan q*. Notice tat Proposition 4 olds witout any constraints on te level of output. Tat is, wile Proposition 3 establises tat a q 1 >q* cannot be implemented, te proof of Proposition 4 does not make use of tis restriction. From Proposition 2 we know tat if q 1 were contractible, a simple debt contract would be optimal. But wit a simple contract, te firm prefers to produce less tan q*. Tus, if a nonsimple contract makes financing even more expensive (due to te increased liquidation treat), te firm sould limit its borrowing even more and tereby commit to producing less tan q*. Tus, deviating from a simple contract would induce eiter an output smaller tan Cournot tat can be implemented more efficiently by a simple contract, or an output level larger tan Cournot tat te firm would ex ante not want to coose. Hence, we ave: Proposition 5. A contract of te form given in Proposition 2 remains optimal if firm 1 s output is not contractible. Notice tat te simple contract is optimal even for small values of, i.e., our assumption tat is large does not affect tis result (see te discussion in Section 3). In Povel and Rait (in press), we consider (witin a single-firm model) an extension of te current setup were te firm s continuation payoff is a weakly increasing function of its first-period investment (or equivalently, its expected first-period payoff). We sow tat in tis more general setting, debt is still te optimal financial contract. Te continuation function b, owever, may take a more complicated form tan tat of b sown to be optimal ere. In particular, it may be necessary to punis default wit a iger probability of liquidation (lower b) to ensure tat te firm will not simply run away wit its borrowed funds. Also, te firm still underinvests, i.e., te equivalent of Proposition 4 above still

17 932 P. Povel, M. Rait / Int. J. Ind. Organ. 22 (2004) olds. However, because te exact form of te optimal debt contract can no longer be determined, it is also not possible to investigate ow te firm s investment (or output) coice varies wit its level of internal funds. Neverteless it is still possible tat a simple debt contract is optimal, in wic case te results derived below sould also generalize. We ave assumed tat firm 1 and I can commit to any contract tat is optimal ex ante, taking firm 2 s strategy as given. Tat is, if te randomizing device employed in te optimal debt contract calls for liquidation of firm 1, ten tis decision is binding and is not renegotiated, altoug liquidation is ex post inefficient (because >L). If, on te oter and, firm 1 expected to be able to renegotiate wit I, it migt want to witold cas to buy its assets back from I and tus avoid liquidation, at least wit some probability. In tis case, tere would be scope for renegotiation. Following a standard approac, we assume tat contracting parties can commit not to renegotiate in te future if tis commitment is ex ante in teir interest. Here, as in many oter contexts (see, e.g., Bolton and Scarfstein, 1990; Hart and Moore, 1998), it is: wile renegotiation leads to a iger surplus ex post, it also reduces te ex ante expected surplus. Because it is te treat of liquidation tat induces te firm to repay te investor, it becomes more difficult for te investor to get er money back if provisions to liquidate te firm are renegotiated. Se must ten demand a iger repayment to break even, wic reinforces te underinvestment result of Proposition 4, and leads to an overall less efficient outcome. Reasons to rule out renegotiation include its costliness, e.g., because of asymmetric information or a multiplicity of lenders. Lenders may also refuse to renegotiate, to defend a reputation for nonforgiveness tat is in teir long-run interest. More fundamentally, Maskin and Tirole (1999) ave argued tat if te parties anticipate an incentive to renegotiate in te future, one would expect tem to include rules tat govern suc situations in te original contract. Tat is, wile contracts may be incomplete because of unforeseen contingencies, it is less plausible to assume tat contracts are incomplete wit respect to predictable events (suc as, in our case, a decision to liquidate te firm) Internal funds and output coice We now look at ow firm 1 s output depends on te internal funds w 0 tat te firm can contribute to cover variable production costs. Te firm s internal funds may be negative if its fixed costs (including any outstanding bank loans te firm as to pay upfront) are ig. We include tis case in our analysis since up to some limit te firm can still obtain financing from I Nonmonotonicity of output Denote by q 1 (w 0 ) firm 1 s equilibrium output wen its internal funds are w For a similar criticism, see DeMarzo and Fisman (2000). Harris and Raviv (1995) analyze a model of financial contracting were te parties, anticipating teir incentive to renegotiate in te future, include rules tat govern renegotiation in te original contract. Te counterposition to te Maskin Tirole argument is presented in Hart and Moore (1999).

18 P. Povel, M. Rait / Int. J. Ind. Organ. 22 (2004) Fig. 3. Output as a function of firm 1 s internal funds. Proposition 6. Over te interval [w, w*], firm 1 s equilibrium quantity q 1 is a U-saped function of w 0. More precisely, q 1 (w*) = q 1 (w) = q*, and q 1 (w 0 ) as a unique minimum at some w <0. Proposition 6 is illustrated in Fig For w 0 z w*, bot firms produce te Cournot quantity q*. If firm 1 is financially constrained, its output is smaller tan q*, and firm 2 s is larger. Firm 1 s output reaces its minimum at a negative level of internal funds, wic we denote by w.atw 0 = w, te probability of a default reaces 1. Here, bot firms produce te Cournot output again. 20 For te example of footnote 19, q 1 (w 0 ) is sligtly concave over some range of w 0 >w. Tus, q 1 (w 0 ) is U-saped or more precisely quasi-convex, but not necessarily convex trougout. To understand tis result, observe tat te debt level D is implicitly determined by te investor s break-even constraint (7). Its derivative BD/Bq 1 in turn is te marginal cost of debt-financed output at te financial contracting stage, wic can be verified by inspection of te firm s objective function at tat stage (Eq. (5)). A cange in w 0 affects firm 1 s output by canging te marginal cost BD=Bq 1. Because q 1 enters in Eq. (7) in two ways, we can distinguis two direct effects of canging q 1. For given w 0 and ĥ, an increase in q 1 requires a larger loan cq 1 w 0 and ence larger debt D; we call tis te cost effect. On te oter and, given tat q 1 < q*, an increase in q 1 leads to iger revenue and terefore to a iger expected repayment for I; we call tis te revenue effect. 19 Te curves are derived for a omogeneous-goods Cournot duopoly wit inverse demand p = (1 q 1 q 2 ), were is uniformly distributed on [0, 2], and L =0. 20 Witout assumption 8, two cases can arise tat lead to a sligtly different picture. First, if debt is risk-free up to some level, ten te U-saped and te q 1 = q* segments of q 1 (w 0 ) meet to te left of w*. Second, te probability of bankruptcy may be strictly positive even wit infinitesimal borrowing. For levels of internal funds sligtly smaller tan w* te firm would ten not borrow at all and just spend its internal funds, i.e., coose q 1 = w 0 / c. InFig. 3, q 1 (w 0 ) would ave a tird, middle segment along te dased line, linking a lowered U-curve segment wit te q 1 = q* segment.