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{\large {\bf    Why Use Requirement Contracts? \\
 The Tradeoff between Price Premium and Breach 
}}

April 12, 2016

%\bigskip

 


   Eric   Rasmusen  

{\it Abstract}

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\begin{footnotesize}

  A requirements contract is a form of exclusive dealing in which  the buyer promises to buy  a particular product only from one seller, who agrees to fulfill all of that buyer's needs.  A  common-sense motivation for such contracts is that the buyer wants to ensure a reliable supply at a pre-arranged price. In the absence of transaction costs, however, a fixed-quantity contract is better for that purpose. This paper shows that the common-sense motivation makes sense, however, if  the buyer is unsure of his future demand, he wishes the seller to make a buyer-specific investment, and   the transaction costs of revising or enforcing  contracts are high.       If transaction costs make efficient breach too costly,  option and requirements  contracts have the advantage of not inducing inefficient performance. A requirements contract has the  further  advantage that it balances the profits of the seller across states of the world and thus allows for a   price closer to marginal cost.   
 

\noindent
Eric Rasmusen:   Dan R. and Catherine M.
Dalton
Professor, Department of Business Economics and Public Policy, Kelley
School
of Business, Indiana University, Bloomington Indiana.   
\href{mailto:erasmuse@indiana.edu}{ Erasmuse@indiana.edu}.  
Phone: (812) 345-8573.  Messaging: 8123458573@vtext.com. This paper:
\url{http://www.rasmusen.org/papers/holdup-rasmusen.pdf}.  

{ 
 \noindent
  Keywords: Hold-up, long-term contracts, requirements contracts, relational contracts, exclusive dealing, expectation damages, option contracts, procurement.}

\noindent
{  I would like to thank Harvard Law School's Olin Center  and the Harvard Economics Department for their hospitality while I wrote this paper, and  Scott Masten,   Jafar Olimov,   and participants in the Harvard Industrial Organization Workshop,  the 2015 INSIE conference and the 2015 IIOC conference for their comments.   }

 


\end{footnotesize}



\newpage

\noindent
{\sc  I.1. Introduction}

   In a requirements contract, the buyer agrees to purchase all of his requirements for a particular product from a given supplier for a  specified length of time.  Exclusive dealing,  of which this is one form,   has been much studied because of the variety of its 
 motivations, some efficiency-enhancing and some strategic, as summarized  in  Ramseyer \& Rasmusen (2015).   The common-sense explanation for a requirements contract is that the buyer wishes to lock in a price and his demand is uncertain.   As we will see, however, this explanation falls apart if transaction costs are low, and it does not explain why an exclusive contract, instead of just the option to buy at a fixed price, is used. The  common-sense explanation does make sense, however, if demand is uncertain, the   cost  of renegotiation and litigation is  high, and the buyer wishes the seller to make a specific investment. 
 

  This explanation presents a  contrast with the 
well-known efficiency-enhancing motivation  of inducing    relationship-specific investments by eliminating  the ``hold-up problem,"  a line of thought going back to    Klein, Crawford \& Alchian (1978).
 The hold-up problem   arises from the difficulty of determining whether a contract was breached.  Exclusivity helps if courts cannot tell whether the correct product has been delivered but can tell which supplier delivers it. The seller  will be reluctant to make a relationship-specific investment  if the buyer can speciously claim  quality is low and  refuse delivery unless the price is dropped.  The seller  exclusive right to supply the buyer helps because it closes off the buyer's outside option  and he cannot bargain  the seller down to as low a price.  
     This is the theme of  the   literature based on   Hart  \& Moore (1990).     Segal \& Whinston (2000) model it  with one seller and two buyers, one of whom can make a relationship-specific investment. In the  three-person bargaining specification employed,  a contract binding the   seller and that buyer does not change the level of investment. De Meza  \&   Selvaggi (2007) revisit the situation with a different bargaining specification and find that exclusivity does  promote investment. Other papers in this literature  include Bolton \& Whinston (1993) on vertical integration for supply assurance and  Noldeke \& Schmidt (1995) on the use of option contracts. 
 

   In the present paper,  neither  hold-up because of unenforceability   nor incentives for promoting a product will play a role. 
The motivation will be hold-up, but on the opposite side: the  buyer will fear being held up because of the seller's relationship-specific investment.  If the buyer needs a product with a specific investment and the  seller is the only firm that makes that investment,  buyer and seller will be in a bilateral monopoly. Once one supplier incurs the fixed cost to design a particular component that fits the particular needs of manufacturing firm, no other supplier will wish to   enter for fear of   head-to-head   competition. Thus, the buyer will want a long-term contract,  one that 
will provide  at lowest cost the right incentives to the seller to invest and  the right incentives to himself to buy once the investment is completed. 
Various long-term contracts are possible, however,  and we will address the question of how the  parties choose  between  an option contract (the buyer has the option to buy a specified amount at a specified price), a requirements contract (which adds exclusivity to the option contract) and a fixed-quantity contract (in which  the  exact   quantity is specified as well as the price).   

   We will compare the buyer's choice of contract in two situations, the first with zero transaction costs and the second with high organizational  costs of breach. With zero transactions costs, a fixed-quantity contract will create more surplus than an option or requirements contract because it   compensates the seller even if the buyer's demand turns out to be low. Under an option contract, the buyer would be free to buy a cheaper unspecialized product if it turned out he did not need the specialized feature, so   the contract price would have to be higher   to compensate   for the   specialized investment. Under a requirements contract,  the seller is compensated more often, but not as often as with the fixed-quantity contract because the buyer can still choose to buy nothing.   

    The advantage of the fixed-quantity contract relies on efficient breach. We will next  assume that the parties have personal reasons for not wishing to breach the formal terms of the contract, an assumption discussed in Section IV with references to the literatures on relational contracting.
 If the parties do not breach, then the fixed-quantity contract has the disadvantage of inflexibility. The buyer will feel compelled to buy even when the product is worth less than the contract price to him, and even when it is worth less than marginal cost. The fixed-quantity contract retains its benefit of paying the seller under the greatest variety of circumstances, but this may well be outweighed by the  cost  of wasteful production. Thus, we return to the   common-sense idea that a requirements contract is superior because it is more flexible when demand is uncertain. 

  


\bigskip

 \noindent
{\sc I.2. An Illustrative Example}

Let us start with an example. The conflict between  Tampa Electric Company and the Potter Towing Company  in 1955 led to a well-known antitrust case. Tampa Electric was building a coal-fuelled power plant and wanted to use a requirements contract for its coal supply. The Supreme Court describes the contract thus:\footnote{Unless noted otherwise, all the facts of the case come from the Supreme Court opinion, {\it Tampa Electric Co. v. Nashville Co.}, 365 US 320 (1961).}
 \vspace{-12pt}
\begin{quotation} \begin{small}
 \hspace{3pt}  
   The agreement, dated May 23, 1955, embraced Tampa Electric's ``total requirements of fuel . . . for the operation of its first two units to be installed at the Gannon Station . . . not less than 225,000 tons of coal per unit per year," for a period of 20 years. The contract further provided that ``if during the first 10 years of the term . . . the Buyer constructs additional units [at Gannon] in which coal is used as the fuel, it shall give the Seller notice thereof two years prior to the completion of such unit or units and upon completion of same the fuel requirements thereof shall be added to this contract." It was understood and agreed, however, that ``the Buyer has the option to be exercised two years prior  to completion of said unit or units of determining whether coal or some other fuel shall be used in same." Tampa Electric had the further option of reducing, up to 15\%, the amount of its coal purchases covered by the contract after giving six months' notice of an intention to use as fuel a by-product of any of its local customers. The minimum price was set at \$6.40 per ton delivered, subject to an escalation clause based on labor cost and other factors.
\end{small}  \end{quotation}
 \vspace{-12pt}
 \hspace{3pt}  
  Potter Towing transferred its contract and eventually the Nashville Coal Company succeeded to its contractual position as seller.\footnote{{\it Tampa Electric Co. v. Nashville Coal Co.}, 168 F.Supp. 456, 456 (1958).} Tampa Electric built its power plant, at a cost of \$3,000,000 more than the cost of an oil-burning plant, and the sellers spent \$7,500,000  readying themselves to perform the contract. Just before the first coal was to be delivered, the sellers  said  they would not deliver the coal. They also said that    the contract violated the antitrust laws and hence was not enforceable, because it foreclosed a substantial amount of the market for coal in Florida. Tampa Electric sued. It lost in the trial and appellate courts, but won in the Supreme Court, which ruled that the contract did not violate the antitrust laws.  In the meantime, Tampa Electric and the Love and Amos Coal Company had agreed to a similar requirements contract: 
\begin{quotation} \begin{small}
 \hspace{6pt} 
[O]n December 23, 1957, a purchase order contract for the total coal requirements of the Gannon Station was made with Love and Amos Coal Company. It was for an indefinite period cancelable on 12 months' notice by either party, or immediately upon tender of performance by respondents under the contract sued upon here. The maximum price was \$8.80 per ton, depending upon the freight rate. In its purchase order to the Love and Amos Company, Tampa estimated that its requirements at the Gannon Station would be 350,000 tons in 1958; 700,000 tons in 1959 and 1960; 1,000,000 tons in 1961; and would increase thereafter, as required, to ``about 2,250,000 tons per year."
\end{small}  \end{quotation}


   These  coal contracts are the kind of requirements contract  to be explained. Why was there a contract at all, rather than buying coal on the spot market? Why wasn't the quantity pinned down precisely in the contract? Why was the contract exclusive rather than giving  Tampa Electric the option to buy elsewhere if it could find a better price?    Note  that there was no attempt to use nonlinear pricing-- the  per-ton price was the same for all quantities.  And there were no lump-sum transfers. Tampa Electric could have used a contract in which it paid Potter Towing  a lump sum to obtain the contract and then received a   low  price per ton that just covered marginal cost, but instead it compensated them with a higher price.      

   I suggest that  a requirements contract was used  because   Tampa Electric wanted a long-term  contract to assure its supply at a low price rather than be faced later with a possible tight market with no seller or  just a few sellers who had    prepared for that eventuality and   could charge high prices.  Potter Brothers might have prepared to be the only seller in a tight market anyway by making customer-specific investments without a contract,   but Tampa Electric preferred a contract with a predetermined price.    A fixed-quantity contract would have required renegotiation later, since Tampa Electric did not know its own  future demand precisely.  Renegotiation would take up management time in the haggling  and require replanning of anything in the business that depended on the original contract.  An option contract would not  need  renegotiation  but it would need high prices to compensate for  Potter Towing's risk that Tampa Electric would  buy  from someone else. A requirements contract does not have these disadvantages.  It   does not require renegotiation, and the price that yielded the market rate of return to the supplier   could be lower because with outside supply ruled out, the Potter Brothers could expect  to  sell a bigger quantity. That is the story we will now proceed to model. 
 
   

 
\noindent
 {\sc   II.  The Model} 



The buyer's value for the single unit he might buy  of  a  good  is   $v$, unknown at the time of contracting and  distributed    with density $  f(v)$ on the support $[0, \overline{v}]$, where  $f>0$.  We will make the conventional  assumption   that $-2f(v) -  vf'(v) <0$    so that expected revenue will be concave in price and   profits will be rising in price up to the monopoly price.   The good's marginal cost is $c$. With probability $\theta$,  the market is ``thin'' and no supply is available unless some seller has invested fixed amount $I$ to provide it in this special circumstance.    With probability $(1-\theta)$,  the market is ``thick'' and the buyer can buy it from any of  $N$ suppliers who compete in simultaneous contract offers. 
Both players are risk neutral.  Each side captures half the surplus if bargaining takes place. We will assume that contracts use linear pricing and  do not use  lump-sum payments.

     Note that we exclude the   solution of vertical integration,  which can solve  any contracting problem. Also,  we   assume  the relationalship-specific investment is not contractible and is not always useful ex post. This investment could consist in capacity excess of normal or in the seller's refusal to accept orders from other buyers that might overwhelm his capacity, as in the model above. Or, it could consist in the usual example in economic models, that the buyer needs a special product, except that in the present model we would add that with some probability the buyer turns out not to need the special feature. 

  
 \noindent
 {\sc  II.1. Outcomes without Contracts:   First-Best, Decentralized Optimum, and Spot Sale   }
 

\noindent
{\it The first best.}
   The first best   maximizes  the sum of   the social    surplus    in the thin market when the specialized product is needed and successfully produced  plus the   surplus when the market is thick, minus the investment cost.  This is the surplus that would be achieved by vertical integration  if the buyer could make the investment and produce the product himself. Alternatively, it is the outcome if the price were set at $c$ and the buyer paid the seller $I$ conditional on his making the investment.    The first two terms are the surplus in a thin and a thick market (probabilities $\theta$ and  $1-\theta$) for purchase when $v\geq c$ and the third is the necessary investment. 
\begin{equation} \label{e1}
Surplus =    \theta    \int_c^{\overline{v}} (v-c   ) f(v)dv + (1-\theta)\int_c^{\overline{v}}   (v-c  ) f(v)dv  - I
\end{equation}

     
\noindent
{\it The decentralized optimum.}
 If the price equals marginal cost, the seller who invests will earn negative profit.  Consider  a social planner who can set prices $p_{thick}$ and $p_{thin}$ but  cannot force firms to buy, sell, or make investments. In this ``decentralized optimum,''  the social planner wishes to induce a seller to invest but  he cannot control which firm serves the buyer or force the buyer to purchase.  The buyer's surplus will be
\begin{equation} \label{e1}
Surplus (buyer) =    \theta    \int_{p_{thin}}^{\overline{v}} (v-{p_{thin}}   ) f(v)dv + (1-\theta)\int_{p_{thick}}^{\overline{v}}   (v-p_{thick}  ) f(v)dv  
\end{equation}

 
   
  
This is  subject to the constraint that the seller earn non-negative profit. Assume that if the buyer is indifferent among sellers they each have an equal chance of being selected. If $N_{thin}$ sellers invest $I$, then each  will have to satisfy a participation constraint of non-negative profits:  
 \begin{equation} \label{e1a}
\pi^s (invest) =    \frac{1}{N_{thin}}  \theta    \int_{p_{thin}}^{\overline{v}} ( p_{thin}-c    ) f(v)dv    +  \frac{1}{N}  (1- \theta   ) \int_{p_{thick}}^{\overline{v}} ( p_{thick}-c   ) f(v)dv    - I \geq 0 
\end{equation}


The sellers will also have to satisfy an incentive compatibility constraint that the profit from investing  is at least as great as from selling only in the thick market: 
 \begin{equation} \label{e1b}
 \pi^s (invest)  - \pi^s(not\; invest)  =     \frac{1}{N_{thin}}  \theta    \int_{p_{thin}}^{\overline{v}} (  p_{thin}-c   ) f(v)dv   - I     \geq 0 
\end{equation}

If the incentive compatibility constraint is satisfied then so is the participation constraint, since expression (\ref{e1b}) is less than expression (\ref{e1a}) if $p_{thick}> c$.  The buyer surplus is declining in the two prices, so since $p_{thick}$ is absent from the more stringent incentive compatibility constraint  the social planner will pick $p_{thick}=c$, the lowest level that will content sellers in the thick market.  Since it is sufficient for one seller to make the investment, the social planner should set $p_{thin}$ low enough that the incentive compatibility constraint is satisfied exactly for  $N_{thin}=1$, so 
 \begin{equation} \label{e1c}
  \pi^s (invest) = \theta    \int_{p_{thin}}^{\overline{v}} ( p_{thin} -c  ) f(v)dv   - I   = 0 
\end{equation}

 We will denote the value of $p_{thin}$ that satisifies equation (\ref{e1c}) as $p^*$. This is  
the ``price equals average cost''   of rate-of-return regulation. 
 The social planner  sets price equal to marginal cost in the thick market and   enough higher in the thin market that the seller's expected profit net of his investment is zero. Surplus will not be as high as in the first-best  since the buyer will buy inefficiently little at any  price  above marginal cost.

   It could happen  that     $p^*$ is greater than the monopoly price and equation (\ref{e1c}) cannot be satisfied, in which case it is impossible to induce investment  in the decentralized optimum, but we will  ignore that possibility for the rest of the paper. 

\noindent
 {\it Spot markets}. 
  A third way the market could be organized is using a spot market. 
   With  no contract  and thus no pre-set price, only one seller will invest, since if two did they would compete the price of the specialized good down to marginal cost, $c$.\footnote{We will ignore the  mixed-strategy equilibrium where two or  more sellers invest with  positive probability, with resulting waste and with the price either $c$ or $ \frac{v+c}{2}$. This too  is  an equilibrium the buyer would wish to prevent by contracting in advance.  } With one seller and no contract, the price will be the result of bargaining. Under our assumption on bargaining, the  price splits the current gains from trade equally (ignoring the sunk cost $I$), so $p =\frac{v+c}{2}$. 
The seller will have profit 
\begin{equation} \label{e7}
 {\displaystyle \pi^s_{spot} =  \theta   \int_{\frac{v+c}{2}}^{\overline{v}} \Bigl( \frac{v+c}{2} - c \Bigr)f(v) dv  - I}
\end{equation}
 
   Recall  that we denoted the decentralized optimum's zero profit price by $p^*$.  If $   (v+c)/2 < p^*$, the seller will not invest at all, because the price is less than his average cost.  Here we have  an example of the common hold-up explanation for long-term contracts: if investment costs are sunk at the time of bargaining over price,   investment will be inefficiently low.   
 If  $ (v+c)/2>p^*$, on the other hand,   the seller would make a profit.   This too is a problem from the point of view of the buyer, who would prefer to keep all the surplus,  To be sure, total surplus would  equal  the first-best, since monopoly with bargaining amounts to price discrimination in which the seller sells for all values of $v$ down to $c$, steadily reducing the price as the buyer's  value falls. This achieving of the first best must be treated with caution, however. If we go outside the model and ask why $v>c$ for a business purchase, it will usually be that the buyer has gone to some effort to find or invest in a profit opportunity. If that is the case, the more surplus the buyer loses to seller monopoly rents, the less incentive he has to create the opportunity. Thus, buyer surplus is a more appropriate target than total surplus in this context.  


The hold-up of the buyer   illustrates a   point Goldberg (1976) makes verbally:  a relationship-specific investment creates a natural monopoly, which creates the potential for the buyer to be held up. 
  The ordinary hold-up problem is that  the party making the investment will receive too low a price from  bargaining once his cost is sunk. The hold-up problem here is that the party {\it not} making the investment will pay too high a price from  bargaining,  because the investment opportunity is a natural monopoly, a tiny, firm-specific industry with room for only one firm. From the seller's point of view,    sunk costs are bad for bargaining, but  good for deterring competition. As Demsetz (1968) points out, one solution to the problem of natural monopoly is to auction off the right to be the monopolist, awarding the contract to the seller who will commit to the lowest price. We thus  observe long-term contracts not because the spot market is so disadvantageous to the seller     but because it is so costly for  the buyer. The observable implications are  much the same as with   hold-up of the seller---  we will see long-term contracts when one or both parties need to make relationship-specific investments--- but the motivation is different. Since Goldberg's point is underappreciated, I will flag it here:  

 


\noindent
{\bf Observation.} {\it  If a business relationship requires  a relationship-specific sunk investment by one party and  the gains from trade are large relative to the investment, the {\rm other party}  may wish to use a long-term contract to protect himself from bilateral monopoly. }

 
 \newpage
 
\noindent
 {\sc II.2. The Model with Zero Transaction Costs } 

  We  will now  look at the contracts the buyer might use to protect himself from hold-up.  We  will start by assuming zero  transaction costs. Zero transaction costs does not mean a player can breach without consequence; he must  meet his legal obligations. Those legal obligations can be met, however,  at zero real economic cost to either party. Managers do not need to hire lawyers,    discuss  breach with each other or subordinates,  estimate their own and the other party's costs from breach (either at the time of making the contract or after breach) or  haggle over out-of-court settlement.  
 

 \noindent
 {\it The fixed-quantity contract.} Consider a fixed-quantity contract for one unit.   We will let the price be conditioned on whether the market is thin ($p_{thin}$) or thick ($p_{thick}$).   
   If the buyer breaches, he will be liable to the seller for damages of $(p_{thin}-c)$ or  $(p_{thick}-c)$. As a result, he will breach if $v<c$. In a thin market, if   $v$ is between $c$ and $p_{thin}$  he will wish to buy   because his consumer surplus would be $v-p_{thin}$, which though negative would still be higher than $ -(p_{thin}-c)$.  In a thick market, if   $v$ is between $c$ and $p_{thick}$  he will be indifferent  between buying and paying damages. Buying from the contractual seller   would yield  a payoff of  $v-p_{thin}$, whereas if he bought in the marketplace and paid damages his payoff would be  $(v-c) - (p_{thin}-c)$. For concreteness, we will assume he buys, since it will not matter to either party's incentives whether he buys or pays damages. 
  

 The  seller will  thus  have expected  profit consisting of four  terms: (1) the profit from selling in a thin market, (2) the damages from buyer breach in a thin market, (3) the gain from selling in a thick market,   (4) the damages from buyer breach in a thick market, minus   (5) the   investment cost. Putting  these together we have: 
\begin{equation} \label{e9}
\begin{array}{lll}
 \pi^s_{fq}(I)  
   & =&  {\displaystyle    \theta     \int_{c}^{\overline{v}}  (p_{thin} - c)f(v) dv  +  \theta     \int_{0}^{c}  (p_{thin} - c)f(v) dv
   }\\
   & &  {\displaystyle   + 
  (1-\theta)     \int_{c}^{\overline{v}}  (p_{thick} - c)f(v) dv  +  (1-\theta)     \int_{0}^{c}  (p_{thick}  - c)f(v) dv - I  }\\

 &&\\
   & =&  {\displaystyle    \theta  \int_{c}^{\overline{v}}   (p_{thin} - c) f(v) dv +  
  (1-\theta)   \int_{c}^{\overline{v}}   (p_{thick} - c)f(v) dv      - I  }\\  
\end{array}
\end{equation}

   The buyer's maximization problem in writing a contract is  to maximize by choice of $  p_{thin} $ and $p_{thick}$
\begin{equation} \label{e3}
\begin{array}{l}
{\displaystyle Surplus ( p_{thin}, p_{thick} )   =  \theta     \int_{p_{thin}}^{\overline{v}}   (v- p_{thin}  ) f(v)dv +  (1-\theta) \int_{p_{thick} }^{\overline{v}}  ( v-p_{thick}  ) f(v)dv   
   }
\end{array}
\end{equation}
such that   seller profit is 
\begin{equation} \label{e3a}
{\displaystyle \pi^s =    \theta  \int_{c}^{\overline{v}}   (p_{thin} - c) f(v) dv +  
  (1-\theta)   \int_{c}^{\overline{v}}   (p_{thick} - c)f(v) dv      - I   \geq 0.}
\end{equation}

    

      
The  first order conditions    are, denoting the Lagrange multiplier by $\mu$, 
\begin{equation} \label{e4}
\begin{array}{lll}
Surplus'_{p_{thin}}  & =      &{\displaystyle  \theta \Bigl(- (p_{thin} - p_{thin})f(p_{thin}) - \int_{p_{thin}}^{\overline{v}}  f(v) dv \Bigr) -\theta \mu   = 0}\\
&&\\
Surplus'_{p_{thick}}  & =      &{\displaystyle  (1-\theta) \Bigl(- (p_{thick} - p_{thick})f(p_{thick}) - \int_{p_{thick}}^{\overline{v}}  f(v) dv \Bigr) - (1-\theta) \mu   = 0}\\
\end{array}
\end{equation}
  
Except for the  multipliers $\theta$ and $1-\theta$, the first order conditions for $p_{thin} $  and $p_{thick} $ in equation (\ref{e4}) are the same, so  $p_{thin}^*=p_{thick}^*$.  Let us call this optimal price $p^*$. The result that the  price should be equal whether the market is thick or thin  is an application of the  same idea as   Ramsey pricing in utilities: two medium price distortions are preferable to one big and one small  distortion because  surplus loss rises   with the square of the distortion.   This principle will apply  to all the contracts we will see later in the paper, but  we will  from now on  omit the proofs and only consider uniform prices. 

 

The seller now has two incentives to make investment high. First,  if the buyer  has a high enough valuation for  the specialized product, the seller  sells it at a profit. Second, if the buyer has a lower valuation, he breaches and pays the seller damages. 


The price  is  lower than in the decentralized optimum.    In  the decentralized optimum, the seller makes a profit only by selling in the thin market, so the zero-profit condition is
\begin{equation} \label{e3a}
{\displaystyle \pi_{do}^s =    \theta   \int_{p^*}^{\overline{v}}   (p^*-c  ) f(v)dv   -I =0. }
\end{equation}

This has the same first  term (with $p^*$ in  place  of $p_{fq}$) as the fixed-quantity profit in the first line of equation (\ref{e9}), but it omits the  thick-market profits and the two  damage  terms.  The seller earns revenue more often under the fixed-quantity contract, and this permits the break-even price to be lower. At the same time, the buyer only actually purchases the item if his value exceeds marginal cost, so there is no overproduction. 
 
 We are used to seeing how long-term contracts increase surplus by averting hold-up,  but the mechanism here is quite different. Contracts alleviate hold-up by preventing the buyer from bargaining down the seller to a low price, but in the decentralized optimum there is no bargaining. Rather, the advantage here is  that the contract gives the seller a flow of profits with higher probability  so the level of the flow can be smaller. Under the decentralized optimum, the seller only receives revenue when the buyer's value is high enough for him to make a purchase. Under the fixed-quantity contract, the seller also receives revenue from damage payments, so the product price can be reduced and the seller can still break even. 
 


 
\noindent
 {\it The option contract.}
Under an option contract at price $p_{oc}$,  the buyer has the option to buy or not buy from the contractual seller  so there is no possibility of breach. 
The  seller will   have expected  profit composed of the profit in the thin market  minus the investment cost: 
\begin{equation} \label{e12}
\pi^s_{oc} =        \theta    \int_{p_{oc}}^{\overline{v}}  (p_{oc} - c)f(v) dv  -I 
\end{equation}
 
 This is exactly the same as in  the decentralized optimum, so $p_{oc}= p^*$. 
  The only difference is that the seller has made himself liable for damages if he breaches in the out-of-equilibrium case in which he has failed to invest and the  buyer wishes to buy in a thin market.  Since the buyer  must set  $p_{oc}$ high enough to satisfy incentive compatibility anyway, the only effect of the potential damages is to make the seller's profit strictly negative instead of zero if he fails to make the investment. 
 

 
 
\noindent
 {\it   The requirements contract.}
Under  a requirements contract at price $p_{rc}$, the buyer is free to buy or not, but if he buys it must be from the contractual  seller, not the marketplace.   
The  seller will     have expected  profit  composed of (1) profit when  the market is thin,   (2) profit when the market is thick,   minus (3)     the investment cost.
\begin{align} \label{e14}
\pi^s_{rc}    &  =&   {\displaystyle     \theta    \int_{p_{rc}}^{\overline{v}}   (p_{rc}  - c  )   f(v)dv 
+  (1-\theta)  \int_{p_{rc}}^{\overline{v}} \Bigl(p_{rc}  - c  )   f(v) dv - I. 
   } 
  \end{align}

       This profit expression adds sales in the thick market to the thin-market revenue stream in the decentralized optimum. Thus,  the requirements contract price  can be lower and still yield zero profit. 


 
 
 
We can now prove  Proposition 1. 
 
\noindent
 {\bf Proposition 1:}  {\it With zero transaction  costs, the fixed-quantity contract generates higher surplus than   the requirements or option  contracts.}

\noindent
 {\it Proof.}   In equilibrium, competition among sellers will result in zero profits at the lowest price for a given type of contract that satisfies the seller's participation constraint.  Total surplus will equal the gains from trade, $v-c$,  minus the investment cost. The gains from trade will be realized under different values of $v$ for the three contracts. For the fixed-quantity contract, total surplus will be 
\begin{equation} \label{e110}
 Total \;Surplus\; (fq) =    \theta    \int_c^{\overline{v}} (v-c   ) f(v)dv + (1-\theta)\int_c^{\overline{v}}   (v-c  ) f(v)dv  - I 
\end{equation}
    
     The contract requires the buyer to always buy, regardless of $v$, or breach and pay damages. He will breach if $v<c$ but will always buy otherwise. The limits of integration in (\ref{e110}) are thus  $c$ and $\overline{v}$, with  $v-c$ representing the social surplus  for a given value of  $v$. 

Under the option contract, total surplus is 
\begin{equation} \label{e111}
 Total \;Surplus\; (oc) =    \theta    \int_{p_{oc}}^{\overline{v}} (v-c   ) f(v)dv + (1-\theta)\int_c^{\overline{v}}   (v-c  ) f(v)dv  - I 
\end{equation}
 
 The buyer will purchase from the seller in a thin market whenever his value exceeds $p_{oc}$, obtaining $v-c$ when he purchases. In a thick market, the buyer will buy from the marketplace at $c$.   The first term is less than the first term under the fixed-quantity contract and the second terms are identical, so surplus is higher under the fixed-quantity contract. 

     Under the requirements contract, surplus is 
\begin{equation} \label{e112}
 Total \;Surplus\; (rc) =    \theta    \int_{p_{rc}}^{\overline{v}} (v-c   ) f(v)dv + (1-\theta)\int_{p_{rc}}^{\overline{v}}   (v-c  ) f(v)dv  - I 
\end{equation}

    Under the requirements contract, each of the first two terms is less than under the fixed-quantity contract, because the buyer only buys if $v \geq p_{rc}$ instead of  $v \geq c$. Thus, the requirements contract also has lower surplus than the fixed-quantity contract. 
   \qed

 

 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

 \newpage
\noindent
 {\sc III.   The Model with High   Breach  Costs   }

We will now assume that both parties  make every effort to avoid breach because the transaction costs we assumed away in Section II are high enough to make undesired performance preferable to breaching.  We will discuss the realism of this  assumption in Section IV but proceed  directly to   the analysis here.  
  
 
 
\noindent
 {\it  The  fixed-quantity contract.}
The fixed-quantity contract requires   one unit to be traded at price $p$. 
  The value of   $p$ is chosen so that  the   seller's   expected  profit  is
\begin{equation} \label{16}
\begin{array}{ll}
 \pi^s_{fq}  &    =     (p_{fq}-c )  -I = 0.  \\
\end{array}
\end{equation} 

   The $p$ that solves  this is 
\begin{equation} \label{16a}
\begin{array}{ll}
 p_{fq} &    =    c  + I.    \\
\end{array}
\end{equation} 

 
 




  The    total surplus is  as usual equal to the buyer's surplus, the seller's surplus having been reduced to zero by choice of $p$. 
\begin{equation} \label{e17}
\begin{array}{ll}
{\rm Total \; surplus_{fq}   } &      {\displaystyle =    \int_{0}^{\overline{v}}  (v - p_{fq} )f(v) dv}   \\
 & \\
   &     {\displaystyle = \int_{p_{fq}}^{\overline{v}} \Bigl(v - p_{fq} \Bigr)f(v) dv  -  \int_{0}^{p_{fq}} \Bigl(  p_{fq} - v \Bigr)f(v) dv}   \\
  \end{array}
\end{equation}
 
 The first part of the surplus is positive, the consumer surplus when the buyer's value is above the contract price. The second  is negative, because the buyer continues to buy even if the price is above his value. An equivalent expression is 
\begin{equation} \label{e17a}
\begin{array}{l}
     {\displaystyle {\rm Total \; surplus_{fq}   }      
   = \int_{c}^{\overline{v}} (v-c) f(v) dv  -  \int_{0}^{c} (c-v)f(v) dv   - I.  }  \\
  \end{array}
\end{equation}

This second formulation shows how, as before,  the   advantage of the fixed-quantity contract is that  trade occurs whenever it would be efficient, but now  inefficient trade also occurs and drags down the surplus.  
 
 \bigskip
\noindent
 {\it  The  option contract.  }
 Our second possibility is  an option contract giving the buyer the right to choose the quantity traded at price $p_{oc}$.     The  seller will    have expected  profit 
\begin{equation} \label{e18}
\begin{array}{ll}
 \pi^s_{oc}  &=     {\displaystyle  \theta     \int_{p_{oc}}^{\overline{v}}     (p_{oc} - c) f(v) dv  -I }\\
\end{array}
\end{equation} 
 and the buyer will choose $ p$ to make seller profit equal to zero.

 If we substitute the equilibrium value of the fixed-quantity price $p_{fq}$ into profit expression (\ref{e18}) we get 
\begin{equation} \label{e18a}
\begin{array}{ll}
 \pi^s_{oc}   &=       {\displaystyle  \theta     \int_{  c  + I }^{\overline{v}}     ( c  + I  - c) f(v) dv  -I},\\
\end{array}
\end{equation} 
  which is negative  because $\theta <1$ and the lower bound of the integral is not 0, but   $c  + I$. The option  price must be higher than   the fixed-quantity price because   the seller only earns it with probability $\theta$ and  only   if the buyer's value exceeds  the contract price. 

   The   total surplus equals the buyer surplus, which is  made up of consumer surplus in the thin market with probability $\theta$  at a price of $p_{oc}$ and in the thick market with probability $1-\theta$ at  a price of $c$ in the marketplace. 
\begin{equation} \label{e19}
\begin{array}{ll}
  {\rm Total \; surplus_{oc}} &{\displaystyle   = \theta \int_{p_{oc}}^{\overline{v}} ( v-p_{oc}) f(v)dv +  (1-\theta) \int_{c}^{\overline{v}} ( v-c) f(v)dv  }   \\
  \end{array}
\end{equation}
 

 \bigskip
\noindent
 {\it The  requirements contract.}
The requirements contract   allows the buyer to choose the quantity traded at price $p_{rc}$ but   forbids him from buying in the marketplace. 
The  seller will    have expected  profit 
\begin{equation} \label{e20}
 \pi^s_{rc} =     \int_{p_{rc}}^{\overline{v}}    (p_{rc} - c)f(v) dv   -I 
\end{equation}
and the buyer will set this equal to zero in the contract.
 

The surplus is the buyer surplus from  purchasing at a price of $p_{rc}$ if $v \geq p_{rc}$:
\begin{equation} \label{e21}
\begin{array}{ll}
 {\rm Total \; surplus_{rc} }  & {\displaystyle=     \int_{p_{rc}}^{\overline{v}} ( v-p_{rc}) f(v)dv  }       \\
  \end{array}
\end{equation}
 

How does this compare with the option contract?  Under the requirements contract, the buyer always faces price $p_{rc}$, but under the option contract, the buyer faces the higher  thin-market price $p_{oc}$ with probability $\theta$ and the lower thick-market price $c$ with probability $1-\theta$.  It turns out that the single moderate price creates higher surplus. 

\noindent
 {\bf Lemma 1:} {\it   When breach costs are high, the requirements contract has higher surplus than the option contract. }

\noindent
 {\bf Proof:}  Jensen's inequality  tells us that if  function  $h(\cdot)$ is strictly concave then
\begin{equation} \label{e21a}
\begin{array}{ll}
 \theta h(x) + (1-\theta) h(y)  <  h(\theta x + (1-\theta)  y )     \\
  \end{array}
\end{equation}

  We know that   profits are zero under both contracts. We have assumed that expected revenue is concave in price, so the function $h_1(p) =  \int_{p}^{\overline{v}} (p-c) f(v)dv$ is also concave.  Writing the profits using  that function, 
\begin{equation} \label{e21a1}
\begin{array}{ll}
  \pi^s_{oc} = \theta h_1(p_{oc}) + (1-\theta) h_1(0) - I  =   \pi^s_{rc}=    h_1(p_{rc}) - I  < h_1(\theta p_{oc} + (1-\theta)  (0))     \\
  \end{array}
\end{equation}
 where the last step applies Jensen's inequality. But that means   $p_{rc} < \theta p_{oc} + (1-\theta)  (0)$: the expected price is lower under the requirements contract. 

     It remains to connect the expected price to surplus. Define  $h_2(p) =  \int_{p}^{\overline{v}} ( v- p) f(v)dv$.  Its derivatives are  $h_2'(p) =  (p-p)f(p) +  \int_{p}^{\overline{v}}   f(v)dv$  and  $h''(p) = -f(p) <0$,    so $h(x)$ is concave. Using this function in the surplus functions (\ref{e19}) and (\ref{e21}), Jensen's inequality, and  our finding that   $p_{rc} < \theta p_{oc} + (1-\theta)  (0)$, 
\begin{equation} \label{e21b}
\begin{array}{l}
  {\rm Total \; surplus_{oc}}    = \theta h_2(p_{oc}) +  (1-\theta)   h_2(c) 
  <    h_2(\theta  p_{oc} +  [1-\theta]c)   
   < {\rm Total \; surplus_{rc} }  =    h_2(p_{rc})      \\
  \end{array}
\end{equation}
  Thus,   surplus is higher under the requirements contract than under the option contract. \qed

 
 
\bigskip
 
Comparison of the  requirements and fixed-quantity surpluses is less unambiguous.     An alternative way to represent total surplus under the requirements contract is in terms of the gains from trade. 
\begin{equation} \label{e21c}
 {\rm Total \; surplus_{rc} }    {\displaystyle=     \int_{p_{rc}}^{\overline{v}} ( v-c) f(v)dv   - I}  
\end{equation}

The difference between this requirements surplus and  the fixed-quantity surplus  in equation (\ref{e17a}) is 
\begin{equation} \label{e21d}
  {\rm Total \; surplus_{rc} -Total \; surplus_{fc} }    {\displaystyle=   \int_0^c ( c-v) f(v)dv    -   \int_c^{p_{rc}}  ( v-c) f(v)dv     }
\end{equation}



 Combining  equation (\ref{e21d}) with Lemma 1, we obtain Proposition 2. 

\noindent
 {\bf Proposition 2:} {\it  When breach costs are high,  the  requirements contract is superior to the option contract. It is superior to the fixed-quantity contract if  the surplus loss from overproduction is large enough relative to the loss from underproduction, that is, if }
\begin{equation} \label{e21e}
     \int_0^c ( c-v) f(v)dv  >  \int_c^{p_{rc}}  ( v-c) f(v)dv      
\end{equation}

    It is somewhat surprising that  when breach costs are high the requirements contract is not always superior to the fixed-quantity contract  but now that we have gone through the analysis the reason will be  apparent. The  advantage of the requirements contract over the option contract is that it  gives the seller profits even when circumstances are such that the special investment was unnecessary  ex post. These extra profits substitute  for paying   a lump sum as compensation for  investment; instead, the buyer commits to pay above   the market price even  if the market is thick.  The fixed-quantity contract adds   even greater probability of making a sale because the buyer purchases even when his value is below the market price.   Those extra sales do create negative surplus as a direct effect, but if it is not very negative it is outweighed by the requirement contract's distortion of a price higher than marginal cost.  

   The left term in inequality (\ref{e21e}) is the surplus loss from  producing too often under the fixed-quantity contract. The right term is the surplus loss from producing too seldom under the requirements contract.   The two terms are analogous to  the triangle losses  in a  supply-and-demand diagram from producing more than the equilibrium quantity  or less.  Note that which contract is better does not depend on  fixed-quantity contract price, because that price does not affect when the product is bought; its only importance is to induce the seller to participate.   A high requirements contract price does matter because it increases the requirement contract's curtailment of sales.   A high investment cost $I$ hurts    the requirements contract, as one would expect,   because  $p_{rc}$ must be higher.    

 The   connection between the surplus and the shape of the value distribution $f(v)$ distribution  is  complex.    Even in an example with uniform distribution for $f(v)$, the results depend on the parameters. When $f(v) = 1/\overline{v}$, it can be derived  that the requirements contract generates higher surplus if the following expression (the  seller's profit when the two contracts generate equal surpluses) is positive: 
\begin{equation} \label{e21d1}
  \frac{ 2c^3 - 3 c^2 - I \overline{v} + c(I  + \overline{v}) }{\overline{v} -c}
\end{equation}

    The denominator  of  (\ref{e21d1}) is positive since $\overline{v} >c$. The numerator becomes larger, to the advantage of the   requirements contract,  if $I$ is smaller.  An increase in $c$  favors the requirements contract if $c$ is sufficiently large but disfavors it if $c$ is sufficiently small.   Increasing  $\overline{v}$ favors the requirements contract if  $c>I$ because for  the uniform distribution that is equivalent to increasing $v$'s support. If $c$ is relatively high the increase in the waste of overproduction dominates, but if $I$ is high the decrease in the probability of a sale dominates.  


Inequality (\ref{e21e}) shows  more intuitively  what features of $f(v)$'s shape  favor each contract.
     The key is how $f(v)$  behaves near $f(c)$.   For all buyer values   below marginal cost  the seller gets no sales under the requirements contract, which drives up $p_{rc}$, but there is overproduction loss under the fixed-quantity contract. Thus, a high probability of $v<c$  increases the welfare loss from both contracts.  If the probability of values just below $c$ is low but  of values far below is high, however,   that  drives up   overproduction loss relative to  underproduction  because   only the total probability of $v<c$ matters to the value of $p_{rc}$,   not how it is distributed. In contrast, the shape of $f(v)$ for  values just above $c$ does not matter to  overproduction, but high probability there does increase the  loss from    $ p_{rc}>c$  because   a small price increase above marginal cost causes   a big reduction in sales. The buyer will decide on a contract based on which concern predominates. 




 

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 


\bigskip


 \noindent
 {\sc IV.   Discussion of the   Use of Contracts in the Absence of Courts }

     Section III  assumes  that managers have a high cost of breach     yet they care about the terms of the contract. This may be explained  by the costs that  negotiation over any changes in plans create:   managerial time and attention for  discussion,   bargaining breakdown,   changes of plans in coordination with other divisions of the business, and   new analysis of the other party's cost or demand functions. These costs are all hard to forecast, adding still another layer of trouble for the manager planning to breach or to cope with breach.  
 

  It  has long been observed that although many  businesses  devote great care to writing legally enforceable contracts with each other, they rarely go to court to enforce them except in endgames--- bankruptcy, or the collection of  bad debts after a relationship is severed. 
 Macaulay (1963) is the standard cite. In a later article, Macaulay (1977) says (citing Llewellyn [1931] and  Kurczewski \& 
  Frieske [1977]), 
\begin{small}
\begin{quotation}
The contract litigation process may also maintain a vague
sense of threat that keeps everyone reasonably reliable (see
Llewellyn, 1931:725 n.47). For this process to operate, it is not
necessary that business managers understand contract norms and
the realities of the litigation process. Perhaps all that is needed is a
sense that breach may entail disagreeable legal problems. The
Polish managers described by Kurczewski and Frieske reflect this
when they tell us that ``one needs to threaten [to use contract
 penalties] intelligently." The authors go on to remark, somewhat
paradoxically, that the ``system works well so long as the penalties
[for breach of contract] are not actually applied. They work well as
a threat, but their application will injure the relationship with the
cooperating enterprise so that in the future it will seek contacts
with other directors who have a more conciliatory approach"
(1977:497). 
\end{quotation}
\end{small}

The contract operates to establish the duties of each party, setting out the moral obligations of each side.  
 One way to understand this is as setting the  equilibrium trigger strategies of a prisoner's dilemma.  As explained in 
 Bull
(1987),  MacLeod \& Malcomson (1988, 1989), and  Baker, Gibbons  \& Murphy
1994), the two parties both wish the relationship to continue, and fear of falling into mutual distrust can prevent either from taking the small windfall profit from breaching or from not having prepared well enough to be able to  perform.  Later articles  show  how writing a legally enforceable contract  can be useful even if it is the threat of dissolving the relationship rather than the threat of court that is fundamental to maintaining cooperation. See 
 Bernheim
 \&  Whinston (1998a),   Baker, Gibbons \& Murphy (1999, 2002, 2011),  Levin(2003), 
  Gilson,  Sabel \&    Scott  (2010),  Baker  \&  Choi (2014), and 
 Gil \&  Zanarone  (2014).   A distinct though complementary motivation for good behavior is fear of losing not just the particular relationship but one's reputation with outsiders, the  argument from the literature starting with Klein \& Leffler (1981) which  is surveyed in MacLeod (2007) and  Malcomson (2012).  


 
  The  idea of the  informal  ``relational contract'' is that its most important features  concern  governance and  termination, not  specific transactions.  In the extreme, options would  not  be enforced, nor requirements, nor quantities--- in fact, none of those things would  be specified.  The agreement would be like a partial merger of the two parties, a  way to convert Coase's 1938 external transaction contracts   outside the boundary of the firm into his internal command-and-control governance--- though not, here, within the boundary. The threat of the legal consequences of  breach of transaction-specific terms would not even be  a  starting point for renegotiation.    Many contracts that are apparently fixed-quantity, option, or requirements contracts are really  like this. Such a fixed-quantity contract would {\it  not}  necessarily result in the buyer accepting delivery out of a desire to avoid breach, or the seller building wasteful capacity  to avoid being unable to deliver the quantity the buyer needs. In the ideal relational contract this would all be worked out efficiently. See, e.g.,  Goldberg (1985) and   Bernstein (2015).  Such contracts do allow for efficient breach; it is just that the threat is not   going to court.  The parties have little reluctance to breach, and pay each other damages, but   the ``breach'' must be mutually beneficial. The Uniform Commercial Code may not determine the damages, but surplus maximization does.  Thus, we  can interpret  the present model's case of zero transaction costs as either   zero costs of going to court or   zero costs of renegotiation within a  perfect relational; contract. The model's case of high breach costs rules out  breach or renegotiation either in the shadow of the court or within a relational contract, and is independent of whether the terms  would be enforceable in court. 

   Why, then, would a party not  engage in efficient breach?  I suggest it is because relational contracts  do not work so smoothly in practice.    The Coase Theorem says that in the absence of transaction costs  the parties will renegotiate  the promised performance does not maximize surplus. It also says that transaction costs can block efficient renegotiation. The transaction costs of going to court  can  prevent  efficient breach in non-relational contracts, but so too   can  the  costs of going to the other party to request mutually beneficial modifications in relational contracts.  Requesting {\it any} change in a relationship is disruptive. It requires the parties to rethink their actions and to re-open negotiations over how to split a surplus. These renegotiations are about ``taking surplus'' rather than ``making surplus'' and though businesses have no qualms about taking surplus, they know that it is a zero-sum game.   The        function of  the contract is to minimize  taking   and maximize   making, putting everything possible of the taking effort   into the initial negotiation rather than   performance. 

      When we consider the repeated games models that are often used to model relational contracts we can see a reason why renegotiation creates difficulty. How would a trigger strategy build in efficient breach?  ``Break the relationship if one party breaches the contract" is a simple trigger.  ``Break the relationship if one party breaches the contract without adequately compensating the other party"  is not. The key is ``adequately''.  It is not enough  to require that  the  injured party  agree to overlook the breach and not invoke the punishment. Punishment  of even uncompensated breach by breaking a relationship is costly, and if there were wiggle room to preserve the relationship   the injured party would,   ex post, wish to overlook the breach rather than invoke the punishment. If that is allowed,  the trigger strategy becomes useless to enforce cooperative behavior. Thus, a trigger strategy allowing efficient breach would have to   specify exactly what damages would be appropriate. Pre-specified liquidated damages would do this, but      the exact size of damages--- including not only the direct loss from the missed transaction but all the organizational costs of adapting to it--- is  costly to determine ex ante.  Thus,   the trigger must be pulled whenever there is breach, since to allow renegotiation would result in  uncompensated forgiveness that would   undermine the  trigger.  Without renegotiation, though, the parties will  review their contractual obligations very carefully to avoid pulling the trigger of relationship breakdown. 


  Bozovic \& Hadfield (2015) and Bernstein (2015) have studied business to business contracts by means of interviews and  the examination of  particular contracts.  
Managers  pay close attention to contracts even when they do not intend to go to court   and they expect each other to perform according to the terms.   It is routine for businesses to negotiate detailed contracts that they never intend to enforce in court.     Whether businesses use detailed contracts, spot purchases, or simple purchase orders, and how closely the actual transactions follow the written records depends on the type of business.  A common practice   is  to write down all relevant details for the planned relationship so that both sides are clear about what is expected,  but not because they intend to use the document in court (with the important exception of what happens if the  relationship terminates). Rather, once the expectations are set, both parties try  hard to meet them, and while many details must be left incomplete because they depend on as-yet-unavailable information, they depend heavily on each other doing what is promised. The biggest risk to reputation is conceivably that of being unable--- as opposed to unwilling--- to meet expectations. As a result, businesses are reluctant not only  to break   agreements but to suggest that performance is so difficult for them  that they wish to drop   a  requirement in exchange for voluntary damages. They want to know their exact obligations, so they can avoid conveying negative information by failing to meet them.  Bozovic \& Hadfield (2013)  for example, say 
\begin{small}
\begin{quotation}
The formal contracts that the businesses involved in innovation-oriented relationships spend significant resources to create and amend are not documents
that lie dormant in a drawer once they have been drafted. Instead, we heard,
they are frequently consulted by these businesses to understand their own
obligations and those of their partners. They are expressly brought out to
help settle disputes that arise during the course of the relationship.
\end{quotation}
\end{small}

Managers for online collaboration platforms told them   that:
\begin{small}
\begin{quotation}
I would use [the contract] as a reference document. It wouldn't be 
I never go back to these things,   they are in a file drawer. I dig them
out when I have to, when there is some reason: what did we do? I can't
remember, what did we agree to? Oh, that's what we agreed to. All right,
well that's the deal. Get on it with it. 
(appendix item 26) 
\end{quotation}
\end{small}
 and 
\begin{small}
\begin{quotation}
  [You find yourself] calling these lawyers [for advice in the context of a
dispute] who say these are non-enforceable contracts\ldots I always hear lawyers
say: don't do MOUs---memoranda of understanding---they are worthless;
they are not legally enforceable by law. Well they're right. They are not. But
that's not why we're doing it. This memorandum of understanding---it's a
memo that says what we've been talking about, what we agreed to, and we
want to be clear with each other. So it's all about clarity\ldots  and so those
types of things become useful instruments for communication clarity. [Even
if they] become a contract; well, I'd argue they are still for communication
clarity. (appendix item 43)
\end{quotation}
\end{small}
  
 These businesses write contracts carefully  and keep referring to them. The reason is   to establish clear expectations rather than to prepare for court battles, as managers from  two  high-tech consumer electronics firms told    Bozovic  and  Hadfield:
\begin{small}
\begin{quotation}
 I cite contracts all the time; you are in breach of this and that\ldots but I've
never actually said we are going to use the contract to extract something from
you and enforcing it in a court of law. I have never done that.    (appendix item 22)
\\
 
 
 Have I ever thought I would end up in court? No! We have spent a lot
of time on [the contract] and neither party has any intent to use this contract
because by the time you get to the point where you are [going to court], now
you have a public relations issue. We are a consumer electronics company.
You view those kinds of things\ldots'it has impact far beyond the contract: other
people don't want to do business with you, you could stifle
 innovation, you
could have a public relations or consumer products problem\ldots (appendix item 34) 
\end{quotation}
\end{small}

Ideally, the     transactions turn out automatic and smooth, without  non-performance, haggling, and delay.   The biggest concern is  predictability and speed. An online collaboration platform said: 
\begin{small}
\begin{quotation}
 The fundamental problem [with litigation], and again, this is very much
a Silicon Valley perspective, is: the things that delay you are as bad as the
things that don't happen. They're kind of equivalent. So, the minute you
open litigation, you've put in this time delay. [Moreover] if [your customers
see you involved in all kinds of legal problems, they start to wonder] 'what's
going on?'\ldots then they [decide]  I'm not going to do business with them." If
somebody views you as high-risk  it's absolutely deadly for small companies
to start up in anything to do with litigation\ldots      (appendix item 31)
\end{quotation}
\end{small}


Bernstein  pays particular attention to the extraordinary documentation that procurement managers provide their suppliers for education, not as constraint. The manufacturer   wants the  components it needs to arrive on time to enter into a complex production process.  Even if the supplier is trying its best, it is still useful for  the buyer  to  teach  the seller what to do.     Scorecard reports are a common means of informing suppliers  of how well they are doing. As in school, a major purpose of grades is to let the subject of the grade know   whether he needs to work harder.   The  grades   are helpful to the supplier by showing him how to increase the gains from trade,  and they even  help him do better in selling to other customers: 
\begin{small}
\begin{quotation}
 The incentives created by the scorecard are reinforced by buyers’
practice of granting status designations, like ``partner-level” 
supplier or ``certified” supplier to suppliers who continue to meet
or exceed specified performance criteria. Some of these designations
come with a valuable benefits, such as better or more extensive
information sharing, more frequent contact, dock-to-stock
status, and the award of business even when they are not the
low bidder so long as they are within a specified range of the low
bidder. In addition, some buyer questionnaires for new suppliers
ask if the supplier is a ``certified” supplier to any of its customers,
 thereby making such certification a valuable business
asset. 
\end{quotation}
\end{small}

     The  concern is as much with  information and ability to perform as with incentives  in these contracts. The supplier who fails to meet expectations cannot simply offer monetary compensation.   Monetary compensation for slack performance  may be in some scorecards, but it is not really a ``performance criterion''.     A supplier who fails can expect to eventually be terminated. 
\begin{small}
\begin{quotation}
 Under the scorecard system, the highest rated suppliers are eligible
for new business. Those with adequate ratings can keep their
existing levels of business, but are expected to improve. And suppliers
with lower ratings are warned that their business will decrease
if improvements are not quickly made. It is only after a few
rounds of low ratings (accompanied, in transactions with the largest
buyers, by consulting services designed to improve their operation)
that suppliers are terminated. 
\end{quotation}
\end{small}

   When contracts do specify damages, it is  sometimes   for information, not  compensation or incentivization. Damages provide    a dollar  summary of poor performance. 
 Stuart, 
Deckert,  Mcutcheon \&  Kunst (1998, p. 85) say that
 a manufacturer of factory automation parts would notify suppliers of the dollar cost of remedying the defect, but would not make them actually pay.  The idea was  ``to use the figures to foster
awareness rather than to assess penalties," like a boss who tells a blundering employee how much the mistake cost the company.  Bernstein (2015) also found this: 
 ``As one procurement manager explained, her
firm tended to impose these fines only when the relationship with the
supplier was deteriorating and/or she wanted to get the attention
of managers higher up in the organization in the hope that they
would correct the underlying problem.''
 

Finally,  Bozovic  and Hadfield   tell us that though trust is key, that doesn't mean renegotiation is easy. Parties   do not want to reveal adverse information to each other even if they trust each other to keep  promises. The business relationship is not so much like marriage as like trying to get asked out on another date.  The parties  conceal their weak points as far as they can. Admitting failure is often worse than muddling through and taking a short-term loss. 
  \begin{small}
\begin{quotation}
 What is revealing about our interviews
is the emphasis respondents placed on the barriers they perceived to ex post
negotiation and recontracting. It was very clear that at the time of initial
contracting, the parties who described innovative relationships to us often felt
they knew little about what it would be best to do in the future. They anticipated that each of the contracting parties would learn more privately as the
future unfolded. But, they reported, sharing information with a contracting
partner ex post is potentially very costly; there are lots of reasons, they indicated, for continuing to withhold information even if it would improve ex post
decision-making. One source of such costs is somewhat mundane: engaging
in ongoing negotiations and recontracting burns time and money and generates delay; with complex interactions and many dimensions of uncertainty,
it is simply not worth discussing everything. More fundamentally, however,
ongoing uncertainty about the durability of the relationship makes it costly
to reveal one's thinking as private information about the costs and benefits
of the collaboration accumulates, particularly relative to alternative oppor-
tunities such as taking a piece of the currently-contracted work in-house or
adding it to the scope of the collaboration with another contractual partner. 
\end{quotation}
\end{small}
 
  If, as these considerations suggest, there are many contracts in which managers wish to avoid renegotiation, it is worthwhile to analyze what happens in that case.  The theoretical model above shows   one  result:  requirements contracts   become attractive relative to fixed-quantity contracts. 
 

 

 %%%%%%%%%%%%%%%%%%%%%%%%%


 


\bigskip

\noindent
 {\sc V.   Concluding Remarks}
 
       A simple explanation for requirements contracts  is that the buyer does not know his future demand but wants to have an assured supply, and the seller does not want to be locked into a requirement to sell at a certain price unless he has assurance that the buyer will not buy elsewhere if the market price turns out to be lower.  That is one way to state the explanation of this paper, but there are important caveats  and the one-sentence explanation does not  do justice to the mechanisms at work. First, the explanation needs to engage with the possibility of efficient breach. In the absence of transaction costs,  a fixed-quantity contract would   works  just as well in giving flexibility.  It, too,  allows for flexible quantities, by letting the parties renegotiate the quantity using the initial contract as a starting point.

Second,  we must think about why the seller does not want to be locked into selling to this buyer.  If the contract price were high enough, the seller would be compensated enough for providing the buyer with an option to buy, even if the option were seldom to be exercised. The difficulty arises because if the contract price is high, the buyer will buy inefficiently little.  Thus, an attractive feature of a contract is that it pay    the seller with high probability, allowing the price to be lower and closer to marginal cost. A fixed-quantity contract is ideal in that respect  because the seller's revenue does not depend on the buyer's demand. Either the buyer purchases, or the buyer pays damages. 

  Even before distinguishing between contracts, we need to ask why the buyer wants a contract at all, rather than using the spot market.  A contract becomes attractive  when not only is demand uncertain  but  the buyer needs the seller to make a relationship-specific investment.  He  fears that if he does not contract in advance, only one seller will make the investment, who will be able to hold him up for a high bargained-over price as in a natural monopoly, or, if information is poor, that no seller will make the investment. Instead, the buyer wishes to choose which seller occupies the natural monopoly by auctioning off a contract in advance. 

If, in addition, the parties have a  high cost of breaching and renegotiating contracts, whether for reputational or internal transaction costs reasons, a fixed-demand contract has the  disadvantage of the buyer purchasing the fixed quantity even when his benefit is less than its marginal cost.  If the contract simply gave the buyer to option to buy,  granting him entire authority over the quantity to be traded, that would avoid inefficient purchases, but it would also allow the buyer to purchase from other suppliers if they turned out to be available. The requirements contract has the option contract's advantage of flexible demand plus the fixed-quantity contract's advantage of paying the seller his price with high probability. If the buyer's value for the product is below marginal cost, he need not buy at all. Otherwise, even  if cheaper suppliers turn out to be available,  if the buyer wishes to purchase any quantity at all, the seller will receive revenue. This high probability of making a sale allows his price to be lower and encourages him to invest more in the relationship. 

 
 






 
 

\newpage

\noindent
{\bf References}




Baker, George, Robert  Gibbon \& Kevin  J. Murphy (1994) ``Subjective Performance
Measures in Optimal Incentive Contracts,'' {\it The Quarterly Journal of Economics,} 109 (4): 1125--1156.

Baker,  George, Robert  Gibbons  \& Kevin  J. Murphy (1999) ``Informal   Authority in
Organizations,'' {\it Journal of Law, Economics \& Organization,}  15 (1):  56--
73.

Baker,  George, Robert  Gibbons  \& Kevin  J. Murphy (2002) ``Relational Contracts
and the Theory of the Firm,'' {\it  The Quarterly Journal of Economics,}  117: 
39--83.

Baker,  George, Robert  Gibbons  \& Kevin J. Murphy (2011) ``Relational
Adaptation,''  working paper.

  Baker, Scott   \& Albert Choi (2015) ``Contract's Role in Relational Contract,"  {\it Virginia Law Review} 101:559-607 (May 2015). 
 
 Bernheim, B. Douglas   \& Michael D. Whinston (1998a)  ``Exclusive Dealing," {\it The Journal of Political Economy,}  106: 64–103.



 Bernheim, B. Douglas   \& Michael D. Whinston (1998b) ``Incomplete Contracts and
Strategic Ambiguity,'' {\it The American Economic Review,}  88 (4):  902--932.

 
 Bernstein, Lisa (2015) ``Private Ordering, Social Capital, and Network Governance in Procurement Contracts: A Preliminary Exploration," U. of Chicago Law School working paper. 


Bolton,  Patrick   \& Michael D. Whinston (1993) ``Incomplete Contracts, Vertical Integration, and Supply Assurance," {\it   The Review of Economic Studies,}    60: 121-148.
 

Bozovic, Iva  \& 
 Gillian K. Hadfield (2015) ``Scaffolding: Using Formal Contracts
To Build Informal Relations in
Support of Innovation,''
University of Southern California Law School working paper  
(February 25, 2015).

Bull, C. (1987) ``The Existence of Self-Enforcing Implicit Contracts,'' {\it  The
Quarterly Journal of Economics,}  102 (1):  147--160.
 
    

De Mez, David  \& Mariano Selvaggi (2007) ``Exclusive Contracts Foster Relationship-Specific Investment," {\it  The RAND Journal of Economics},   38: 85-97.
  

Demsetz, Harold (1968) ``Why Regulate Utilities?" {\it Journal of Law and Economics},   11: 55-66  (April
1968).
 
   


  Gil, R. \& G. Zanarone  (2014) ``Testing for the Interaction of Formal and Informal Con-
tracts,"  working paper. 

  

  Gilson, Ronald J., Charles F. Sabel \&  Robert E. Scott. (2010) ``Braiding: The Interaction of Formal
and Informal Contracting in Theory, Practice and Doctrine," {\it  Columbia Law Review}, 110 (6):
1377-1447 (October 2010). 

Goldberg, Victor P. (1976) ``Regulation and Administered Contracts,''
{\it The Bell Journal of Economics,}   7(2): 426-448  (Autumn  1976).

Goldberg, Victor P. \&  John R. Erickson (1987) ``Quantity and Price Adjustment in Long-Term Contracts: A Case Study of Petroleum Coke,''
{\it  Journal of Law and Economics,}   30(2): 369-398  (Oct. 1987).

Goldberg, Victor P.  (2002) ``Discretion in Long-Term Open Quantity Contracts: Reining in Good Faith," 
{\it 
 U.C. Davis Law Review,} 35: 319-385 (2001-2002). 

Goldberg, Victor P.  (2007)   ``Desperately Seeking Consideration: The
Unfortunate Impact of U.C.C. Section 2-306 on
Contract Interpretation,''  {\it Ohio State Law Journal},  68:103--113. (2007). 

Goldberg, Victor P.  (2014)  ``The Future of Many Contracts,''
{\it Duquesne Law Review},  52: 323-334 (Summer 2014).


Halonen-Akatwijuka,  Maija   \& Oliver Hart (2015)  ``Short-Term, Long-Term, and Continuing Contracts,''
 \url{http://isites.harvard.edu/fs/docs/icb.topic1435734.files/Paper02_Hart_02-02.pdf.}
( January 2015)

  Hart, Oliver \& John Moore (1990) ``Property Rights and the Nature of the Firm,''
{\it The Journal of Political Economy},  98:   1119-1158.


Hart, Oliver \& John Moore (2008) ``Contracts as Reference Points,'' {\it The Quarterly Journal of Economics,} 123: 1-48. 

 


Martini, Joseph \& Matthew Brown (2013)  ``A Supplier's Guide to Requirements Contracts,''
{\it 
American Bar Association, Commercial Law Newsletter,} Joint Newsletter of the
Commercial Finance and Uniform Commercial Code Committee (Spring 2013). 
 
  
Klein, Benjamin, R. Crawford \& Armen Alchian (1978)  ``Vertical Integration, Appropriable Rents, and the Competitive Contracting
Process," {\it  The Journal of Law and Economics,}   21: 297-326.

  


 Klein, Benjamin \&    Keith B. Leffler (1981)  ``The Role of Market Forces in Assuring Contractual Performance,''
{\it The Journal of Political Economy}, 
  89(4):  615-641 (Aug. 1981).
 
   
Kurczewski, 
 Jacek \& Kazimierz Frieske (1977) ``Some Problems in
the Legal Regulation of the Activities of Economic Institutions,"   {\it  Law
\& Society Review}, 11: 489-505 (Winter 1977).



Levin, J. (2003) ``Relational Incentive Contracts,'' {\it  The American Economic
Review,}  93(3):  835--857.



Llewellyn,  Karl N. (1931) ``What Price Contract? An Essay in Perspective,"
   {\it Yale Law Journal}, 40: 704-751 (March 1931). 


 MacLeod, W. B.  (2007) ``Reputations, Relationships and Contract Enforcement," {\it  Journal of
Economic Literature,}  45:  595-628.
 
MacLeod, W. B.  \&   J. M. Malcomson (1988) ``Reputation and Hierarchy
in Dynamic Models of Employment,'' {\it  Journal of Political Economy,}  96 (4):  
832--854.

MacLeod, W. B. \& J. M. Malcomson (1989) ``Implicit Contracts, Incentive
Compatibility, and Involuntary Unemployment,'' {\it  Econometrica,}  57 (2): 
447--480.

 Macaulay, Stewart  
(1963) ``Non-Contractual Relations in Business: A Preliminary Study,"
{\it  American Sociological Review}, 28(1): 55-67 (Feb. 1963).

  Macaulay, Stewart   (1977)  
``Elegant Models, Empirical Pictures, and the Complexities of Contract,'' {\it 
  Law \& Society Review},   11:  507-528 (Winter  1977).




 Malcomson, James M. (2012)  ``Relational Incentive Contracts,"  in Gibbons, Robert \& John  Roberts, {\it 
The Handbook of Organizational Economics}, Princeton University Press, 1014-1065.


Marvel, Howard (1982) ``Exclusive Dealing," {\it The Journal of Law and Economics,} 25: 1-25.  
 
    
Noldeke, Georg   \& Klaus M. Schmidt (1995) ``Option Contracts and Renegotiation: A Solution to the Hold-up Problem," 
{\it  The RAND Journal of Economics,}   26: 163-179.


     Ramseyer, J. Mark  \& Eric Rasmusen  (2015) ``Exclusive Dealing: Before, Bork, and Beyond,'' {\it  The  Journal of Law and Economics},  
 57(S3): S145-S160 (Aug. 2014).
 

Rasmusen, Eric \& Jeffrey Stake (2001) 
``Lifting the Veil of Ignorance: Personalizing the Marriage Contract,"  {\it  Indiana Law Journal},  73: 454-502  (Spring 1998).

 Stuart, Ian,  Paul
Deckert, David Mcutcheon \& Richard Kunst (1998)   ``A Case Study: A Leveraged Learning
Network,''  {\it Sloan Management Review}, 39(4): 111,   (Summer 1998). 
 

 



 
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