Up-front payment under RD rule

Transcription

1 Rev. Econ. Design 9, 1 10 (2004) DOI: /s c Springer-Verlag 2004 Up-front payment under RD rule Ho-Chyuan Chen Department of Financial Operations, National Kaohsiung First University of Science & Technology, Nantz, Kaohsiung 811, Taiwan ( hcchen@ccms.nkfust.edu.tw) Received: 1 May 2002 / Accepted: 15 May 2004 Abstract. This paper explores the effect of an up-front payment to contracts under the reliance damage measure. We find that the efficiency in most cases fails, but can be obtained by a high enough total payment to assume away the seller s breach, a high enough up-front payment to ensure that the seller does not sue, and a high enough trading price to ensure the buyer s breach when the undesirable state occurs. Edlin s device (1996), which has a very low trading price to assume away the buyer s breach and a proper up-front payment to entice the seller to sign, fails to achieve the efficiency under the reliance damage measure. JEL classification: K12, L00, D21 Key words: Up-front, efficient contract, reliance damage, salvage value, contract breach, relationship-specific investment 1 Introduction Shavell (1980) and Rogerson (1984), among others, show that remedies to the Williamsonian holdup problem will much likely lead to reliance overinvestment. Henceforward, many other devices are provided in the contract literature to solve for this inefficiency. 1 An up-front payment in Edilin (1996) paves the way to induce efficiency when the expectation damage measure is applied and if a low enough I wish to thank an anonymous referee of this journal for valuable comments. 1 Examples include fill-in-the-price mechanisms in Hermalin and Katz (1993), hostages in Williamson (1983), money-back provisions in Mann and Wissink (1988), the buy-out clause in Demski and Sappington (1991), and renegotiations in Huberman and Kahn (1988), Chung (1991, 1992), Nosal (1992), Aghion et al. (1994), and Edlin and Reichilstein (1996).

2 2 H.-C. Chen price is also included. 2,3 On the contrary, an up-front payment only redistributes wealth between parties to a contract in Lee and Png (1990). To explore the role of an up-front payment in contrast to Edlin (1996), this paper instead focuses on the reliance damage measure (i.e., RD rule), which requires the defaulting party to compensate the breach victim for his reliance expenditures and also return to the victim payments he made. The paper actually finds that the efficient reliance level in most cases is not achieved. To obtain efficiency, three requirements need to be satisfied: a large enough total payment to assume away the seller s breach, a high enough up-front payment to ensure that the seller does not sue, and a high enough trading price to assure that the buyer breaches when an undesirable value state occurs. This is in sharp contrast to Edlin s device (1996), which requires a very low trading price to assume away the buyer s breach, and a proper up-front payment to provide the seller an incentive to sign the contract. The article is organized as follows. A two-state-two-period model with relationship-specific investment is set up in Sect. 2. Section 3 then analyzes the equilibrium reliance investment and presents this paper s findings. Section 4 examines whether Edlin s device works under the reliance damages measure, and Sect. 5 concludes. 2 The model I consider a two-state-two-period model, where a buyer (b) and a seller (s) trade for one unit of good. At the beginning of the first period, without knowledge of the buyer s value state (v) of the good, both of them negotiate over the contract, specifying an up-front payment (t) and the good s price (p). Once the contract is signed, the buyer has to immediately pay the pre-specified up-front payment to the seller, and then the seller makes a specific reliance investment (r), which can reduce production cost (c(r)) in the following period. In the second period the random value state of the buyer (v) is realized for both parties. After observing v, both the buyer and the seller decide whether or not to trade. If neither party breaches, then the good is produced and delivered. The seller s production cost is convexly decreasing with the reliance investment. If any party breaches, however, the good is not produced. The seller s reliance investment can then be sold for an alternative use and earn a salvage value (a(r)). If the breach victim sues, then he can receive damage compensation from the breacher from a court of law. At the end of the second period, the profits to both risk-neutral parties are realized. To exhibit the property of specificity, we assume that salvage value a(r) is concavely increasing, and is no greater than its corresponding reliance investment, and that production cost c(r) as well as trading opportunity cost a(r) +c(r) is 2 A low enough price will discourage the buyer s breach, while an up-front payment will induce the seller to sign. 3 The expectation damage measure will put the breach victim in the same position in which he would have been if there had not been any breach.

3 Up-front payment under RD rule 3 convexly decreasing. That is, r a(r),a (r) > 0,a (r) < 0,c (r) < 0,c (r) > 0,a (r)+c (r) < 0, and a (r)+c (r) > 0. 4 Different from the expectation damages measure, which guarantees a breach victim (if he goes to court) the payoff as under trading, the reliance damages measure guarantees that the breach victim will be returned his net loss if he goes to court. Thus, if the breach victim brings a lawsuit to court, he will be secured with a zero profit. The up-front payment to the seller and the seller s reliance investment may or may not be sunk, depending on whether a lawsuit is brought about. If the seller goes to court, then all inputs in the first period are not sunk, because under the reliance damages measure the seller needs to return the up-front payment to the buyer and will receive damage compensation r a(r). On the contrary, if the buyer goes to court, then only the reliance investment is sunk, because the buyer could get back his up-front payment under the reliance damages measure. 5 Assume the random value state of the buyer (v) is in either a high value state (H) or a low value state (L), where H>L 0, with probability λ and 1 λ, respectively. The distribution of buyer s value for the good is common knowledge to buyer and seller. To make the problem interesting, for the society as a whole we let the buyer s high value state H indicate a desirable state, while the low value state L be an undesirable state, i.e., L a(r)+c(r) H. Therefore, trade benefits the society if H occurs, while no-trade benefits the society if L occurs. Defining the ex ante expected joint profit (denoted as J) by the expected profits sum of trading (when v = H) and no-trading (when v = L), we can obtain J as the following: J = λ[h r c(r)]+(1 λ)[ r + a(r)]. (1) By solving the first-order condition of Eq. (1), we obtain: λc (r )+(1 λ)a (r )=1, (2) where the reliance investment r indicates the efficient level. 6 We examine in the next section how an up-front payment influences a seller s reliance investment. 3 Equilibrium behaviors Denoting d i the damage compensation from breacher i to the breach victim, for i {b, s}. In the second period, after observing the reliance investment level and 4 The assumption a (r)+c (r) < 0 implies that the larger the investment is, the higher its derived value will be inside rather than outside the contract. However, we assume that the absolute value of the difference between the inside-contract and the outside-contract becomes smaller (i.e., a (r)+c (r) > 0), implying a decreasing rate of c(r) outweighing the increasing rate of a(r). 5 Without loss of generality, we simplify the model by assuming that resource to legal action by either party is costless as in Edlin (1996). In fact, the legal costs (which refers to the cost and uncertainty of legal processes) play the role as a threshold if it is taken into account, implying that either party will take legal action only when its expected profit outweighs its legal costs. This issue can be further exploited as an area for future research. 6 According to assumptions a (r) < 0 and a (r)+c (r) > 0, we obtain 2 J/ r 2 = λ[a (r)+ c (r)] + a (r) < 0, satisfying the second-order condition.

4 4 H.-C. Chen value state, both parties choose whether or not to produce the good to trade. If trade occurs, then the trading gain to the seller and the buyer is π s = t + p r c(r) and π b = v p t, respectively. If the buyer breaches, then he loses to the seller his up-front payment t, or a damage compensation d b, depending upon whether the seller goes to court. If t>r a(r) (i.e., if the up-front payment to the seller is big enough to compensate his net investment cost), then the seller will just walk away quietly without suing. Each party then obtains no-trading payoff π s = t r + a(r) and π b = t, respectively. In this case, all the first-period inputs are sunk, damage compensation d b = 0, and thus the buyer will breach only when his second-period trading gain is less than the trading price, i.e., only when v<p. 7 On the contrary, if the up-front payment is not big enough to cover the seller s net investment cost, i.e., if t<r a(r), then the seller will sue to get damage compensation r a(r) t. The resulting payoffs turn out to be π s = 0 and π b = r + a(r). For this case, all the first-period inputs are not sunk, and thus the buyer will breach only when second-period trading benefit v p is less than breaching loss t r + a(r), i.e., when v<p+ t r + a(r). 8 If the seller now breaches, then the buyer will definitely sue to get back his already-paid up-front payment. The resulting payoffs for both parties are π s = r + a(r) and π b =0. Since the up-front payment is not sunk in this case, the seller will breach in the second period if his second-period trading gain p + t is less than trading opportunity cost a(r)+c(r), i.e., if p + t<a(r)+c(r). 9 Utilizing the above results, we know that the case when both parties breach also does exist. If t<r a(r) and v<p+ t r + a(r) and if t + p<a(r)+c(r), then both will breach and both will bring a lawsuit to the court, as depicted above. We assume that the first defaulting party is presumed by the court to be the defaulting party, and the other party is thus the victim. For simplicity, we assume that the probability for any party to be presumed as the first defaulting party is exactly 1/2. Therefore, we obtain payoff π s = π b = (1/2)[r a(r)]. Alternatively, if t>r a(r) and v<p, and if t + p<a(r)+c(r), then both parties breach again, and no doubt the buyer will sue to get the up-front payment back. As for the seller, if he does not sue, then he will obtain π s = r + a(r), while receiving π s = 1/2 [r a(r)] if he goes to court. Obviously, he will definitely bring a lawsuit to court if this case happens. All the possible cases and resulting payoffs are summarized as the following: If trade occurs, then π s = t + p r c(r) and π b = v p t. If p + t<a(r) +c(r), then the seller breaches, and the buyer will sue. The resulting payoffs are π s = r + a(r) and π b = 0. The damage compensation to the buyer is d s = t. 7 In this case, the damage compensation d b =0. It can then be also derived by the comparison between the buyer s trading payoff v p t and breaching payoff t. 8 By comparing the total trading payoff v p t and the breaching payoff r + a(r), we can also derive the same result. 9 By π b = p + t r c(r) >π b = r + a(r), we can derive the same result.

5 Up-front payment under RD rule 5 If t<r a(r), then the seller will sue when the buyer breaches, which occurs if v < p + t r a(r). The resulting payoffs are π s = 0 and π b = r+a(r). The damage compensation to the seller is d b = r a(r) t. If t>r a(r), then the seller will not sue when the buyer breaches, which occurs when v < p. The resulting payoffs are π s = t r + a(r) and π b = t. The damage compensation to the seller is d b =0. If t<r a(r),v < p + t r a(r), and t + p<a(r) +c(r), orif t>r a(r),v <p, and t + p<a(r)+c(r), then both parties will breach and sue. The resulting payoffs are π s = π b = (1/2)[r a(r)]. We now can analyze the optimal behaviors of both parties by separating them into two categories as in the following sub-sections, based on the magnitude of the total payment p + t. 3.1 A high total payment: p + t>a(r)+c(r) In this case the seller s reliance investment is small enough such that the secondperiod trading opportunity cost is less than the trading gain, p + t > a(r)+c(r). The seller will never breach in the second period. To consider the buyer s behavior, we have to separate it into two subcases: t<r a(r) and t>r a(r). In the first subcase, t<r a(r), since the up-front payment is less than the seller s net investment cost, the seller will sue if the buyer breaches, which occurs when v<p+ t r + a(r). If high state H occurs, then trade does occur due to H>p+ t r + a(r). 10 If low state L occurs, then the buyer will breach and the seller will sue as long as L<p+ t r + a(r), which means the ex ante payoff of the seller in the first period will be: Eπ s = λ[t + p r c(r)]+(1 λ)[0] = λ[t + p r c(r)]. Deriving its first-order equation, we have c (r) = 1. The first-order equation s solution is denoted by r, and we can then observe that r >r in comparison to Eq. (2). The security of returning what the seller has invested through the reliance damages rule when an L state occurs will result in a larger incentive for him to invest. The seller thus over-invests in this case. If L>p+ t r + a(r), then the buyer will not breach, and the seller s ex ante payoff in the first period becomes: 11 Eπ s = λ[t + p r c(r)]+(1 λ)[t + p r c(r)] = t + p r c(r). The solution to its first-order equation is again r, indicating an overinvestment. The reason for overinvestment in this case is that no breach occurs 10 The total payment p + t will always be less than H, because the buyer s highest amount that he is willing to pay is H when a high state occurs. Moreover, p + t r + a(r) <p<p+ t because t r + a(r) < In this case, p + t>a(r)+c(r) >L>p+ t r + a(r). This implies that the total payment is large, but not large enough.

6 6 H.-C. Chen under a low state L, which should have prompted both parties to not trade at all in terms of efficiency. Lemma 1. A high total payment whereby p + t>a(r)+c(r), together with a low up-front payment such that t<r a(r), leads to an over-investment for the seller. In the second subcase, t>r a(r), the seller will not sue in the case where the buyer is breaching since the up-front payment that is retained over-compensates the seller s net investment cost. In this case the buyer will breach only when v<p. Since H > p, trading occurs when high state H occurs. When low state L transpires and L<p, the buyer breaches and the seller will not sue. This is exactly the same as what happens under efficiency. 12 However, when L>p, trading arises even if it is not efficient. Thus, for the overall effect, trading takes place in fact too much, leading to the seller s over-investment. With the help of mathematics, the seller s ex ante payoff in the first period becomes: Eπ s = t + p r c(r). Obviously, its first-order equation also derives an over-investment level r. Lemma 2. A high total payment whereby p+t >a(r)+c(r), together with a high up-front payment such that t>r a(r), in general leads to an over-investment by the seller. Only p L will induce an efficient investment. A sufficiently high total payment to the seller guarantees that he will not breach. Since the seller is ready to trade no matter what case occurs, he would like to increase his investment so as to reduce production cost even more in the second period. Moreover, a sufficiently high up-front payment guarantees the seller full compensation of his reliance. In fact, he will never go to court even when there arises a low state L greater than the trading price, in which case the trade should have been cancelled in terms of efficiency. This is the reason for an over-investment problem. However, when p L, the buyer breaches and no lawsuit is brought about, which coincides with what efficiency requires. 3.2 A sufficiently low total payment: p + t<a(r)+c(r) In this case the seller always breaches even when high state H occurs, because his second-period trading gain p + t is less than trading opportunity cost a(r)+c(r). That is, the seller will breach even when the efficiency in fact requires trading under the occurrence of high state H. Under-investment for the seller thus results due to the certainty of the seller s breach. When only the seller breaches, i.e., when t < r a(r) and L > p+t r +a(r), or when t>r a(r) and L>p, the seller s ex ante expected profit becomes: 13 Eπ s = λ[ r + a(r)]+(1 λ)[ r + a(r)] = r + a(r). 12 Thus, the seller s ex ante profit is exactly the same as Eq. (2), and efficient level r is derived. 13 In this situation the buyer will never breach. Here, we assume that the breacher cannot bring about any lawsuit.

7 Up-front payment under RD rule 7 Both parties, otherwise, will breach and both parties will sue when the low state occurs, while the buyer does not want to breach and instead goes to court when the high state occurs. The seller then obtains an ex ante expected payoff as: Eπ s = λ[ r + a(r)]+(1 λ)(1/2)[ r + a(r)] = 1+λ [ r + a(r)]. 2 The above two equations have the same first-order equation, in which we denote its solution by r. We can then observe that r <r, indicating under-investment by the seller. Lemma 3. A sufficiently low total payment, such that p + t < a(r) + c(r), in general induces an under-investment for the seller. With a low payment, the seller always stands to breach. Since the production stage never happens, the seller does not need to worry about matters of reducing his production cost through the first-period reliance increase There is thus little incentive for the seller to conduct a reliance investment. Through Lemmas 1, 2, and 3, we observe that, except for some specific case as shown in Proposition 1, the efficiency in general is not achived under the reliance damage measure: Proposition 1. Under the reliance damage measure, the efficiency is achieved only when p>l,t r a(r), and p + t a(r)+c(r). Proof. Direct implication of Lemmas 1 to 3. The conditions in Proposition 1 say that the seller never breaches because his trading gain is no less than the opportunity cost and he will never sue, if the buyer breaches, because the up-front payment over-compensates his net investment cost. Thus, trading will occur when H appears, while no trade will be conducted and a lawsuit will come about when L appears, which is exactly the same situation as what efficiency needs. This shows that the up-front payment plays an important role in inducing efficiency. Without a relatively high up-front payment that assumes away the seller s lawsuit, the seller will go to court when the buyer breaches at a low state so as to secure a zero payoff, which encourages the seller to over-invest. As Lemmas 1 to 3 show, without this deliberate device the seller will over-invest when p+t a(r)+c(r), while under-invest when p+t <a(r)+c(r). In general, the efficiency is not achievable under the reliance damage measure. This deliberate device is very different from what Edlin (1996) offers. His device requires a very low trading price to assume away the buyer s breach, and then requires a high enough up-front payment to entice the seller to sign. Our device here requires a high enough total payment to assume away the seller s breach under an efficient reliance, a high enough up-front payment to assume away the seller s lawsuit when the buyer breaches, and a high enough trading price to urge the buyer to breach when a low state occurs.

8 8 H.-C. Chen 4 On Edlin s device In this section Edlin s device, which helps achieve efficiency under an expectation damage measure, is examined under a reliance damage measure. Edlin (1996) employs a very low trading price and a high enough up-front payment to induce an efficient contract under the expectation damage measure. The very low trading price intends to remove the possibility of a buyer s breach, while the high up-front payment is to entice the seller s signing. To assume away the buyer s breach, Edlin picks trading price p to be less than the buyer s worst value of the good, which is low state L for this paper s setting. Thus, following Edlin (1996), we set p L. Because the buyer will breach when v < p d b, where d b = max{0,r a(r) t}, this setting could also effectively assume away the buyer s breach under a reliance damage measure. When p + t>a(r)+c(r) as set in Sect. 3.1, both parties will never breach even when L occurs, resulting in the seller s ex ante expected payoff as follows: Eπ s = λ[t + p r c(r)]+(1 λ)[t + p r c(r)] = t + p r c(r). No doubt, the seller will over-invest. On the contrary, when p + t < a(r)+ c(r) as in Sect. 3.2, the seller always breaches even though high state H occurs, and he will obtain the ex ante expected payoff as: Eπ s = λ[ r + a(r)]+(1 λ)[ r + a(r)] = r + a(r). Clearly, the seller under-invests in this case. Edlin s device, a sufficiently low trading price to assume away the buyer s breach, no longer works to induce an efficient investment under the reliance damage measure. Proposition 2. The contract with p L and an up-front payment, as adopted in Edlin s paper, in general fails to achieve efficiency under the reliance damage measure. When a very low trading price is specified, and the buyer is thus kept away from breaching, the chance to achieve efficiency happens at where the seller breaches under a low state L, but trades under a high state H. Unfortunately, under the reliance damage measure, the seller s breach depends on the comparison of the seller s second-period total payment and total trading opportunity cost, independent of the value state. Thus, it is difficult to obtain an efficient breach and an efficient trade. The figure changes under Edlin (1996) in which an expectation damage measure applies and efficiency is obtained. Two key points are needed for Edlin s device to achieve efficiency: first, the seller s breach does in fact depend on the value state; second, damage compensation d s to the buyer is constant and independent of the reliance investment. Under the expectation damage measure, if the seller breaches and if the buyer sues, then the buyer is guaranteed a payoff of v p t. Thus, the buyer will sue if v>psince the payoff to him when not suing is t. The damage compensation to the buyer is hence d s = max{0,v p}. The seller s payoff, if the buyer sues, becomes t r + a(r) (v p), indicating that the seller will breach only when

9 Up-front payment under RD rule 9 t r + a(r) (v p) >t+ p r c(r), i.e., only when v>a(r) +c(r). Therefore, if high state H occurs, then both parties do not breach. If low state L occurs, then the seller breaches and the buyer will sue. The resulting ex ante payoff to the seller turns out to be: Eπ s = λ[t + p r c(r)]+(1 λ)[t r + a(r) d s ] = λ[t + p r c(r)]+(1 λ)[t r + a(r)] (1 λ)d s. The efficiency is obtained, because the solution to the first-order equation is r. The constant damage compensation d s serves as a wealth transfer from the seller to the buyer if the seller breaches. Therefore, the seller, when considering his ex ante reliance level, undergoes the same situation as that under efficiency: total production cost r + c(r) under state H and net investment cost r a(r) under state L. 5 Conclusion This paper with a two-state-two-period model shows the role of an up-front payment to a contract under the reliance damage measure. We find that in most cases efficiency is not achievable even when an up-front payment is employed. To achieve efficiency, we need a deliberate device: First, a high enough total payment to make the seller unwilling to breach under the efficient reliance level; second, a high enough up-front payment to make the seller unwilling to sue under the efficient reliance level when the buyer breaches; third, a high enough trading price to make the buyer breach when the low state appears. Lacking any one of these situations, the efficiency fails. The up-front payment therefore plays an indispensable role for efficiency. In Lee and Png (1990), under efficiency failure, an up-front payment only serves as a sort of wealth redistribution. Edlin (1996), however, hinges on a very low trading price to assume away the buyer s breach, and efficiency is achieved as long as the up-front payment is high enough for the seller to sign the contract. The effect of an up-front payment in his paper is to entice the seller to sign the contract, and not to make a reliance investment. His device thus no longer works under the reliance damage measure. Under the reliance damage measure in my paper, an upfront payment has a real effect on the magnitude of reliance investment. It works more than just a wealth transfer, by influencing the choice of reliance level and hence leading to efficiency. References Aghion, P., Dewatripont, M., Rey, P. (1994) Renegotiation design with unverifiable information. Econometrica 64: Chung, T-Y. (1991) Incomplete contracts, specific investments, and risk sharing. Review of Economic Studies 58: Chung, T-Y. (1992) On the social optimality of liquidated damage clauses: an economic analysis. The Journal of Law, Economics, and Organization 8: Demski, J.S., Sappington, D.E.M. (1991) Resolving double moral hazard problems with buyout agreement. Rand Journal of Economics 22:

10 10 H.-C. Chen Edlin, A. (1996) Cadillac contracts and up-front payments: efficient investment under expectation damages. The Journal of Law, Economics, and Organization 12: Edlin, A., Reichelestein, S. (1996) Holdups, standard breach remedies, and optimal investment. The American Economic Review 86: Hermalin, B.E., Katz, M.L. (1993) Judicial modification of contracts between sophisticated parties: a more complete view of incomplete contracts and their breach. The Journal of Law, Economics, and Organization 9: Huberman, G., Kahn, C. (1988) Limited contract enforcement and strategic renegotiation. TheAmerican Economic Review 78: Lee, T.K., Png, I.P.L. (1990) The role of installment payments in contracts for services. Rand Journal of Economics 21: Mann, D.P., Wissink, J.P. (1988) Money-back contracts with double moral hazard. Rand Journal of Economics 19: Nosal, Ed. (1992) Renegotiating incomplete contracts. Rand Journal of Economics 23: Rogerson, W.P. (1984) Efficient reliance and damage measures for breach of contract. Rand Journal of Economics 15: Shavell, S. (1980) Damage measures for breach of contract. Rand Journal of Economics 11: Williamson, O.E. (1983) Credible commitments: using hostages to support exchange. The American Economic Review 73: