Econ 522 – Lecture 13 (Oct 212008)
Some Logistics
- Homework 2 due Thursday, 1 p.m. sharp
- (if you’re coming late to lecture, email the homework to me ahead of time)
- Midterm a week from today
- In class (sorry if it’s crowded)
- Best guide for what types of questions I ask are homework questions (two on HW2 are from last year’s exams), also numerical examples like we’ve done in lecture
- I was asked to encourage everyone who’s eligible to register to vote. The following is from an email from Provost Patrick Farrell:
With the Tuesday, Nov. 4 presidential election drawing near, we would like to ask your help in promoting civic engagement by encouraging UW-Madison students to register and vote…
Most students who are U.S. citizens, will be 18 years of age on or before Election Day, and have been a resident of Wisconsin for at least 10 days prior to registering are eligible to vote.
Students may register to vote in person with the Madison city clerk from now until Nov. 4 or at their polling place on Election Day. Students who have moved since they originally registered need to re-register.
If students plan to register in person at the clerk's office or at the polls, proof of residence is required to register and is important to bring to the polls. For students in University Housing, a UW-Madison ID is acceptable.
Also, despite persistent rumors, registering to vote has no impact on a student's insurance, financial aid or student status. These rumors are totally false.
So, to sum up… do your homework, study for the midterm, and vote.
Last Thursday, we looked at the different types of remedies a court could impose for breach of contract. In particular, we considered:
- Expectation damages, designed to replace the value of performance
- Opportunity cost damages, designed to replace the value of the next-best alternative forgone by the promisee
- Reliance damages, designed to only replace the value lost by the promisee due to reliance
- Specific performance – requiring the promisor to honor the promise rather than imposing damages
Today, we’ll look more carefully at the different incentives created by each, and in particular how they influence the following three decisions:
- the promisor’s decision to perform or breach
- the promisor’s investment in performing, and
- the promisee’s investment in reliance
Put aside the question of reliance for the moment, and suppose that performance of the promise will have a fixed benefit for the promisee. The fact that the two parties agreed to the contract in the first place implies they believed this benefit was likely to greater than the cost to the promisor of performing. However, as we’ve already discussed, circumstances may change after the promise is made, in a way that makes the promisor less keen to keep his promise. (The price of building the airplane may go up, or my rich cousin may appear and value my painting more highly than you do.)
There are two ways for me to get out of my promise: I can renegotiate with you, getting you to “let me off the hook,” presumably in exchange for some money. Or I can breach our contract and live with the consequences, most likely the damages that a court imposes.
Think back to nuisance law. Recall that when an entitlement (say, the right to breathe clean air) was protected by injunction, the parties could still bargain for it – the polluter could offer the neighbor enough money to be willing to live with the pollution. When an entitlement was protected by damages, the polluter could instead simply pollute and pay whatever damages were ordered. We found that when transaction costs were low, either remedy would lead to efficiency; but since the two remedies changed the noncooperative outcome (the threat point) for each side, they led to different allocations of surplus. On the other hand, when transaction costs were high, the two remedies could lead to different results.
Here, the story is exactly the same. Consider a promise that is enforced by specific performance – the promisor is not allowed to breach unless the promisee agrees – versus a promise enforced by, say, expectation damages. When transaction costs are low, either one will lead to efficient breach; but the allocation of surplus to the two parties will be different. And when transaction costs are high, they may lead to different outcomes.
Let’s continue beating to death the example of the airplane I agreed to build for you. The plane will give you a value of $500,000, and we agree on a price of $350,000; I expect the plane to cost me $250,000 to build, but there is some chance it will instead cost me $1,000,000.
First, let’s consider what happens if our contract is protected by expectation damages.
Costs Low (Perform) / Costs High (Perform) / Costs High (Breach, pay exp damages)I Get / 100,000 / -650,000 / -150,000
You Get / 150,000 / 150,000 / 150,000
Total / 250,000 / -500,000 / 0
Now let’s see what happens if our contract is protected by specific performance, that is, you have the right to demand the airplane, and I can only breach with your permission.
Costs Low (Perform) / Costs High (Perform) / Costs High (renegotiate)I Get / 100,000 / -650,000
You Get / 150,000 / 150,000
Total / 250,000 / -500,000 / 0
Since performance is very costly, my outside option is very bad, so renegotiation may force me to accept fairly bad terms. Notice that by renegotiating the contract, we create a total surplus of $500,000 (beyond our outside options if you forced me to build the plane). Suppose that our negotiations lead us to divide this additional surplus evenly. This would lead you to get $250,000 beyond your outside option, which was $150,000, so your payoff would be $400,000; I would get $250,000 beyond my outside option, which was -650,000, which would be -400,000.
So as long as transaction costs are low, either remedy will lead to the same outcome. When it is efficient to breach, expectation damages lead me to breach without permission; and renegotiation will lead us to some sort of agreement to let me off the hook.
Of course, when the transaction costs of renegotiating our contract are too high, specific performance would lead to inefficient performance – I would have to build you the plane, even though it costs me more than your benefit – while expectation damages would still allow me to breach.
Other types of damages – opportunity cost damages, or reliance damages – would lead to inefficient breach, that is, I would choose to breach even when my cost of performing is lower than your benefit. However, when transaction costs are low, this could also be fixed through renegotiation.
To see an example of this, consider the same situation, but now suppose that the next-best contract would have sold you a similar plane for $400,000, but that now at this late date, no other planes are available. We agreed on a price of $350,000, but now costs go up somewhat, to $460,000.
Perform / Breach and pay Opp Cost Damages / Renegotiate and PerformI Get / -110,000 / -100,000 / P – 460,000
You Get / 150,000 / 100,000 / 500,000 – P
Total / 40,000 / 0 / 40,000
Renegotiating generates additional surplus of $40,000; if we split this evenly, we would each get a payoff $20,000 higher than our outside option, which would require the renegotiated price to be $380,000.
Again, however, if transaction costs were high, we would be unable to renegotiate the contract, and I would choose to breach and pay you $100,000 in opportunity cost damages.
(Cooter and Ulen point out that, just like efficiency demands enforcing contracts whenever the parties wanted them to be enforceable, efficiency demands enforcing renegotiated contracts whenever the parties wanted them to be enforceable at the time of renegotiation.)
So just like with nuisance law, we find the following:
- if it is cheap/easy to renegotiate terms, any of the remedies will lead to efficient breach, although they will lead to different allocations of surplus
- if it is expensive/hard to renegotiate terms, only expectation damages are guaranteed to lead to efficient breach – specific performance may lead to inefficient performance, and lower damages may lead to inefficient breach
An increase in the cost of performance is referred to as an unfortunate contingency. On the other hand, I may be less keen to keep my promise because I discover another buyer who values my product more than you do. This is referred to as a fortunate contingency. Earlier, we saw the example where you contracted to buy my painting, but my rich cousin appeared and valued it much more highly than you did. We can do the same exercise as before with the different remedies, and see the same thing – with low transaction costs, any remedy will lead to efficient breach, but with different allocations of surplus. This is done in the book (p. 267). Once again, specific performance is the most advantageous to the buyer, and higher damages are better for the buyer than lower damages.
One further point that we mentioned earlier but didn’t talk much about: efficient signing.
We saw that with expectation damages, when my costs remain low and I perform, I get a profit of $100,000 (the price you pay, $350, minus the costs I incur, $250). And when my costs jump up and I breach, I owe $150,000.
If the probability my costs rise is small enough, that’s no big deal – I take the risk of owing you expectation damages, because my profits in the cases where I don’t breach are large enough that it’s worth the risk.
But if the probability my costs rise is high, then my expected profit from this contract is negative. For example, suppose the probability of a dramatic rise in costs is ½. Then my expected payoffs from agreeing to build you the airplane are
½ (100,000) + ½ (-150,000) = -25,000
So now there’s no way I’d agree to the contract in the first place.
This is the point we mentioned before – expectation damages lead to efficient breach, but they may lead to inefficient signing. (If I’m the only airplane manufacturer available, it’s still efficient for us to sign this contract – it generates positive expected surplus – but under expectation damages, I would not sign this contract.)
(This does suggest that, even if expectation damages make a sensible default rule, it’s efficient for parties to be able to specify a different damages rule in the contract – that is, even if expectation damages are often efficient, they are not always efficient, so there’s no reason for them to be mandatory…)
So that’s breach. What’s left is investment in reliance, which we’ve already talked a bit about; and investment in performance, which we haven’t.
The book makes a big deal out of “the paradox of compensation,” which is basically what we already talked about earlier: the remedy for breach sets an incentive for both the promisor and the promisee, and it’s generally impossible to set both of these incentives efficiently at the same time. (The particular conflict they look at here is the way that reliance figures into expectation damages.)
Let’s go back to the airplane example once again, and again assume that, once you contract to buy my plane, you consider building yourself a hangar. But this time, rather than just a decision to build or not build, there is a whole range of different-quality hangars you could elect to build.
Suppose that, for any investment of x dollars, you can build a hangar that will enhance the value of having a plane by 600 sqrt(x), but is worthless without a plane.
Investment / Value of Hangarx / 600 sqrt(x)
100 / 6,000 / Large tarp held up by some rope connected to a telephone pole – still keeps some rain off the airplane
10,000 / 60,000 / Basic plywood frame, canvas roof
40,000 / 120,000 / Metal poles, rigid roof
160,000 / 240,000 / Functional heating
640,000 / 480,000 / Designer hangar with working Starbucks
Recall that whatever investment is made in reliance pays off when the promise is kept, but is lost when the promise is broken.
Suppose that expectations damages include the benefits anticipated based on reliance investments. Then the buyer would maximize
500,000 + 600 sqrt(x) – 350,000 – x
since he gets the same benefit whether or not the seller breaches; solving this gives the first-order condition
600/2sqrt(x) – 1 = 0 x = 300^2 = 90,000
so the buyer, when insulated from the risk of breach, invests $90,000 in a reasonably nice hangar, giving anticipated benefit of 600 sqrt(90,000) = 180,000.
What is the efficient level of reliance? The total social gain from the contract is
500,000 + 600 sqrt(x) – 250,000 – x
without breach, and –x with breach (the reliance investment is lost, and other than that, all that happens is transfers). Suppose the probability of breach is p; then the expected social benefit is
(1-p) (500,000 + 600 sqrt(x) – 250,000 – x) + (1 – p)(–x)
which leads to an efficient level of reliance equal to 90,000 (1-p)^2.
So for any p > 0, damages which include benefits from reliance lead to overreliance, that is, investment in reliance that is higher than what would be efficient.
On the other hand, suppose expectation damages did not include the benefits of reliance. Then the buyer maximizes
(1-p) (payoff without breach) + p (payoff with breach) =
(1-p) (500,000 + 600 sqrt(x) – 350,000 – x) + p (150,000 – x) =
150,000 + (1-p) 600 sqrt(x) – x
which leads to the same (efficient) level of reliance.
So if the level of damages includes the gains from reliance, this leads to overreliance; if the level of damages excludes the gains from reliance, this leads to efficient reliance.
(Recall that Cooter and Ulen hoped for damages which included the gains only from “efficient” reliance, which is a nice idea but incredibly hard to measure after the fact…)
But we also know that if the level of damages exclude the gains from reliance, and the buyer relies anyway, that this will lead to inefficient breach. That is, since the seller’s liability from breach is lower than the buyer’s gain from performance, there will be some instances where the seller breaches even though efficiency requires performance.
We said before that with no transaction costs, this problem can be solved: when breach would be inefficient, the parties can contract around it. Since it’s generally very clear whether a party has breached a contract or not, this shouldn’t be a particular problem.
However, there are situations in which a promisor can take actions to make performance less costly, or, to put it another way, to lessen the probability that breach is efficient. A contractor could buy raw materials ahead of time, to avoid the risk of changing prices; a manufacturer could start a project earlier and frontload the labor to avoid the risk of a strike. If a project were to require a building permit or zoning easement, he could lobby the local government (or bribe someone) to decrease the chances of hitting a snag.
This sort of investment in performance, however, may be unobservable, or unverifiable; and therefore, even when this sort of investment is efficient, it may be very hard to build it into the contract. (It’s very hard to enforce a contract specifying “how hard I have to try” to convince the zoning board to approve your project.) Thus, investment in performance may only occur when it is in the promisor’s best interest.
Go back to the airplane example, and suppose there is some investment I can take that reduces the chance that my costs go up. (I can buy some of my supplies ahead of time, but I can’t completely insulate myself from risk.) Suppose that for each $27,726 I invest, I can reduce the probability I will need to breach by ½. That is, if I invest $27,726, the probability of breach goes from ½ to ¼. If I invest another $27,726, it goes down to 1/8. And so on.
For any investment z, then, we can write the probability that breach is still required as
½ * ½ ^(z / 27,726)
The reason I chose the number 27,726 is that we can rewrite this probability as
½ e^{- z/40,000)
Which makes it much easier to work with.
So, how much would a self-interested promisor invest in performance? Go back to the airplane example, and let D be the amount of damages that the promisor is liable for if he breaches. (D could be nothing; or the investment in reliance; or the opportunity cost; or the gain the buyer expected to achieve, with or without reliance.) Suppose only that D is low enough that breach is still preferable when costs go up. (Since we’ve been talking about costs rising to 1,000,000, this just requires D < 650,000, the loss I would take from performing.)
When costs remain low, the seller expects $100,000 in profits. So when deciding how much to invest in performance, the seller maximizes
(1 – Pr(breach)) 100,000 + Pr(breach) (-D) – investment in performance
= 100,000 – Pr(breach)(D + 100,000) – z
= 100,000 – ½ e^(-z/40,000) (D+100,000) – z
Taking the derivative gives ½ 1/40,000 e^(-z/40,000) (D+100,000) – 1 = 0
or ½ e^(-z/40,000) = 40,000/(D+100,000)
so the seller invests enough to reduce the probability of breach to 40,000/(D+100,000)
So if the seller can breach for free, he’ll invest enough to reduce the probability of breach from ½ to 40,000/100,000 = 2/5. Hestill prefers profits (100,000) over nothing, but he only invests a little, since he can still get out of the contract for free. (The investment here is about $9,000.)
Suppose D were expectation damages, without reliance. If he would owe expectation damages (without reliance) of $150,000, then he invests enough to reduce the chance of breach from ½ to 40,000/(150,000+100,000) = 4/25. (The investment this time is about $45,000.)
Suppose D were expectations damages, with reliance. We said that if expectation damages include reliance, the buyer spends $90,000 on a hangar giving $180,000 in benefits, so his benefit from performance is now 500,000 – 350,000 + 180,000 = 330,000. With damages at that level, the seller invests enough to reduce the probability of breach to 40,000/(330,000 + 100,000) = 40/430. (The investment to do this is about $67,000.)
But what would be efficient? Suppose that the buyer has already decided to build himself that nice $90,000 hangar. So the benefit of performance is 330,000. The cost of the hangar is sunk, so we can forget about it for now.
The total social surplus is
(1 – Pr(breach)) (330,000 + 100,000) + Pr(breach) (0) – z
= 430,000 – 430,000 ½ e^(-z/40000) – z
To maximize this, we take the derivative:
430,000 ½ 1/40,000 e^(-z/40000) – 1 = 0
Pr(breach) = 40,000/430,000
So given that level of reliance, the efficient level of investment in performance is enough to reduce the chance of breach to 40,000/430,000.
Which we just saw is exactly what the seller would do when he’s liable for expectation damages which include the benefit from reliance!
To sum up, the efficient level of investment leads to a 40,000/430,000 chance of breach. Damages which are set equal to D lead to a self-interested promisor to allow a probability of breach of 40,000/(D + 100,000). So when damages are set to 330,000 – damages include the benefit from reliance – the investment in performance is efficient. When damages are lower, the seller will underinvest in performance, leaving the risk of breach inefficiently high. (When damages are higher than this, the seller will overinvest in performance.)